1COLLEGE OF ARTS AND SCIENCES

DEPARTMENT OF MATHEMATICS AND COMPUTER SCIENCE GRAMBLING STATE UNIVERSITY

MATH 099: Basic Math

Semester__________ Year___________

Instructor __________________________________________ Office Location __________________________________________ Phone # __________________________________________ Email __________________________________________ Time and Place __________________________________________ Conference Hours _____________________________________________________ _____________________________________________________ I. COURSE DESCRIPTION

Basic Math (Math 099) is a one-semester course designed to reinforce and enhance algebra skills or teach these skills for the first time. The course includes the following with respect to algebraic expressions; identifying, simplification, and factoring, solving equations and inequalities, graphing, and solving word problems. Computer Assisted Instruction (CAI), in the form of MODUMATH and MODUMATH ALGEBRA is an integral part of the course’s overall instructional plan designed to strengthen the students’ algebra skills, encourage self-monitoring activities and increase reasoning abilities.

II. RATIONALE

Mastery of the essential rules of Algebra, problem solving techniques, math study skills, and familiarity with appropriate technology (such as ModuMath Algebra) are necessary for success in college level mathematics courses and university courses, in general. Basic Math (Math 099) is designed to enable students to acquire such mastery as well as increase their reasoning abilities. The ModuMath Algebra technology provides our students with the opportunity to review and test themselves on basic algebra skills needed in Math 131 and Math 147.

This course is divided into ten segments: (1)REAL NUMBERS, (2) SOLVING LINEAR EQUATIONS AND INEQUALITIES, (3) FORUMULAS AND APPLICATIONS, (4) EXPONENTS AND POLYNOMIALS, (5) FACTORING, (6) RATIONAL EXPRESSIONS AND EQUATIONS, (7) GRAPHING LINEAR EQUATIONS, (8) SYSTEMS OF LINEAR EQUATIONS, (9) ROOTS AND RADICALS and (10) QUADRATIC EQUATIONS. Having mastered these elements, the student is prepared for the college level mathematics courses specific to his/her major.

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III. COMPETENCIES Students are expected to perform the following competencies at the 70% level of proficiency as measured by unit tests, quizzes, ModuMath Algebra assignments, web-based assignments, and the final examination (Departmental Mathematics Proficiency Test):

A. Use appropriate signs to represent inequalities when comparing numbers. B. Add, subtract, multiply, and divide real numbers. C. Solve linear equations and inequalities using the addition and multiplication principles. D. Graph integers, rational numbers, and inequalities on a number line. E. Translate English phrases into algebraic expressions and vice versa. F. Convert and solve problems using percents, decimals, and fractional notations. G. Convert between scientific notation and decimal notation; multiply and divide using scientific notation. H. Add, subtract, multiply, and divide polynomials. I. Solve word problems by translating them into equations. J. Factor different types of second and third degree polynomials. K. Solve quadratic equations by factoring. L. Compute least common multiples and denominators. M. Simplification and computation with rationale expressions. N. Simplify complex rational expressions and solve rational equations. O. Solve problems involving rational equations and proportions. P. Solve formulas for a specified variable. Q. Graph linear equations using slope and intercept information. R. Identify and graph functions. S. Write equations in slope-intercept form, point-slope form, and standard form. T. Solve systems of equations by graphing, substitution, or elimination. U. Simplify square roots and solve problems involving square roots. V. Add, subtract, multiply, divide and simplify square root expressions. W. Solve radical equations. X. Rewrite and/or simplify roots of degree 3 and higher. Y. Solve quadratic equations by using the principle of square roots, completing the square or the

quadratic formula. Z. Solve quadratic equations with complex solutions.

III. BEHAVIORAL OBJECTIVES Upon successful completion of this course, the student will be able to demonstrate the following skills with at least 70% proficiency:

A. Simplify arithmetic and algebraic expressions. B. Demonstrate proper use of the rules of operation for whole numbers, integers, percents,

decimals, exponents, and polynomials. C. Solve equations and inequalities. D. Translate given information into equation form. E. Solve equations involving iconic expressions, polynomial expressions, and rational

expressions. E. Solve word problems.

3F. Correctly simplify polynomial, rational, radical and complex expressions. G. Demonstrate proper use of rules of operation for polynomials, radical expressions, rational expressions and complex expressions . H. Factor 2nd and 3rd degree polynomials. I. Solve equations, inequalities, and/or systems involving graphing, polynomial expressions,

rational expressions and radical expressions. J. Construct graphs from given information and interpret the meaning.

IV. LEARNING ACTIVITIES Learning activities include the following: A. Attitudinal Motivation (POSITIVE THINKING). B. Textbook reading, notetaking, and assignments. C. Group learning activities. D. Computer assisted instruction, including ModuMath Algebra learning and testing

activities. E. Tutorial sessions. F. In-class drill and practice, including the proper use of calculators. VI. SPECIAL COURSE REQUIREMENTS

A. Consistent with University policy, all students are expected to attend (regularly and punctually) ALL classes in which they are enrolled. A student is allowed four (4) unexcused absences per semester. Absences, excused or unexcused, do NOT relieve a student of the responsibility for assignments or examinations missed. After a student exceeds four unexcused absences, s/he may not receive a passing grade. The course must be repeated the next semester the student enrolls in the university.

B. Students must be punctual! You are considered absent once the roll has been called. C. It is the student's responsibility to acquire the prescribed text and any other

materials required by the instructor and to bring them to class. (See section VIII). Materials: Notebook, graph paper and calculator with square root capability. D. All written work MUST be handed in on time.

E. Assigned Computer Assisted Instruction MUST be completed during the Academic Skill Center's extended hours or between the student's classes and handed in on time.

F. Students are required to use headphones with ModuMath computer work. G. A MINIMUM of six hours a week of homework should be expected. Two more

hours of computer laboratory work should also be expected. H. Students are expected to adhere to the University’s dress code. No head gear of any form

(male/female), proper shoes (no slippers or pajamas). Failure to do so may result in expulsion from class.

I. The use of cell phones as calculators is prohibited. Additionally, all phones are to be shut off when in class. The ringing of phones in class will result in expulsion from class.

VII. EVALUATION PROCEDURES A student will be evaluated based on the following performance: A. Class participation B. Written assignments C. Group cooperation and participation

4 D. Unit Quizzes/tests E. CAI (ModuMath Algebra) assignments The final grade is determined as follows: Unit tests, quizzes, assignments, and CAI 70% Midsemester Exam 10% Final Exam 20% Total 100% The grading system is the same as the university's with the exception of the NC (NO CREDIT) and the D grades. While the NC does not count against a student's grade point average (GPA), no credit is given for the course taken. The NC grade is given when the student attends class and does the prescribed work but does NOT meet the exit requirements. When a student fails to attend classes, a grade of F will be given. The D grade is not given for Developmental courses. Students enrolled in this course cannot withdraw from the course without special permission.

Grading Scale 100-90 A Superior 89-80 B Above Average 79-70 C Average 69-below NC/F Below Average

Diagnostic Placement Proper placement of entering Freshmen is determined by the results on the MAA test, which is administered at the beginning of each semester. Students scoring between 0-18 on the MAA test are placed in Basic Math (Math 099). Students scoring 19 or above on the MAA test are advanced to college algebra. VIII. REFERENCE MATERIALS Reference materials for Math 099 include the text to be used and computer assisted instruction. A. Textbook Angel, A. (2003). Elementary algebra for college students, 6th edition. Upper Saddle River, NJ: Prentice Hall. B. Computer Assisted Instruction

1. ModuMath Algebra 2. ModuMath

Note: Grambling State University complies with the Americans with Disabilities Act, which requires us to provide reasonable accommodations to students with disabilities. If you need accommodations in this class related to disability, please make an appointment as soon as possible. My office location and hours are listed in the material that you copied onto this syllabus.

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GRAMBLING STATE UNIVERSITY COLLEGE OF SCIENCE AND TECHNOLOGY

DEPARTMENT OF MATHEMATICS AND COMPUTER SCIENCE COURSE SYLLABUS

MATH 131: COLLEGE ALGEBRA Semester: Fall 2007

INSTRUCTORS

I. COURSE DESCRIPTION (Catalog Statement)

This course is designed for non-science majors. Fundamentals of algebra, linear and fractional equations and inequalities, quadratic equations, functions, relations, and graphs, coordinate geometry, systems of equations and inequalities, matrices, determinants, exponential and logarithmic functions, complex numbers, theory of polynomial equations, sequences, series. Mathematical induction, the Binomial theorem, elementary probability and statistics, sets and logic. Prerequisite: A grade of C or better in MATH 098 or satisfactory score on the math placement test or a score of 16 or higher on the math sub-score of the ACT.

II. RATIONALE

Mathematics 131 is the first course of a sequence (Math 131 and Math 132) designed for non-science majors with Basic Math background. Math 131 might be the only course in Math some students will take. Therefore, many learning aids are built into the course. These tools are meant to be a machine for learning, one that can help focus efforts and get the most from the time and energy invested. Emphasis is on general concepts that are around us as we go through our daily activities. Many of the concepts needed to be expressed mathematically, are already known intuitively.

Exploration of the media supplements will help students to view algebra as a valuable tool for understanding the world outside the classroom. It represents a useful integration of learning techniques. Competencies gained in Math 131 are essential to the skills and practice needed in problem solving, a requirement for a successful individual.

III. COMPETENCIES At the end of the semester, the student should be able to have the following competencies:

A. Perform arithmetic operations including exponents and use scientific notations,

B. Add, subtract, multiply, divide, and simplify rational expressions, polynomials, and matrices,

C. Solve linear, quadratic, and radical equations in one variable as well as polynomial and rational inequalities,

D. Graph lines, circles and inverse functions (f-1) and obtain equation of each,

E. Find the slope and intercepts of a line (vertical, horizontal, parallel, perpendicular, direct variation, inverse variation....),

F. Graph exponential and logarithmic functions, and identify characteristics of each,

G. Solve applied problems and problems involving simple and compound interest,

H. Solve a system of linear equations using the method of substitution, elimination and matrices,

I. Use mathematical induction to prove statements and find the general term of a sequence, and

J. Solve certain probability problems.

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IV. COURSE OBJECTIVES A. CHAPTER P - PREREQUISITE - FUNDAMENTAL CONCEPTS OF ALGEBRA (Six instructional hours)

This is a prerequisite chapter. The student should spend his/her own time and energy in understanding the concepts in this chapter in order to understand the following chapters.

P.1 The Real Number System (p. 2) a. Recognize subsets of the real numbers b. Use interval notations c. Evaluate absolute value P.2 Exponents and Scientific Notation (p. 13) a. Perform arithmetic operations including exponents b. Use scientific notations P. 3 Radicals and Rational Exponents (p. 24) a. Find the nth roots b. Simplify radical expressions using identified properties of nth roots (p.25) c. Rationalize denominators (p. 28) d. Combine radicals (p. 26) e. Simplify expressions with rational exponents (p. 31) f. Reduce the index of a radical (p.34) P.4 Polynomials (p. 36) a. Understand the vocabulary of polynomials (p.37) b. Add, subtract, and multiply polynomials (p. 38-45) P.5 Factoring Polynomials (pp. 48-56) a. Factoring the greatest common factor of a polynomial (p.49) b. Factoring by grouping (p. 50) P.6 Rational Expressions (p. 59) a. Simplify rational expressions (p. 59-66) b. Add, subtract, multiply, and divide rational expressions (p. 61-66) c. Simplify complex rational expressions (p. 66) B. CHAPTER ONE EQUATIONS, INEQUALITIES, AND MATHEMATICAL MODELS (Seven instructional hours) 1.1 Graphs and Graphing Utilities (p. 76) a. Plot points in rectangular coordinates (p. 77) b. Graph equations in rectangular coordinates (p. 77) c. Determine intercepts of a graph (p. 80) 1.2 Linear Equations (p. 84-92) a. Solve linear equations in one variable (p. 85) b. Solve equations involving fractions (p. 88-90) c. Solve equations involving rational expressions (p. 90)

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1.3 Formulas and Applications (p. 95-106) a. Solve word problems using formulas (p.95) b. Use linear equations to solve word problems (p. 97) c. Solve simple interest word problems related to investment in stocks and bonds (p. 100) d. Solve for a variable in a formula (p.102) 1.4 Complex Numbers (pp.108-112) a. Find powers of i (p.108) b. Add, subtract, multiply, and divide complex numbers (p.109-112) 1.5 Quadratic Equations (p.114-128) a. Solve a Quadratic Equation by Factoring (p.115) b. Solve a Quadratic Equation by Completing the Square (p.119) c. Solve a Quadratic Equation by Using the Quadratic Formula (p.121) 1.6 Other Types of Equations (p.131) a. Solve polynomial equations by factoring (p.132) b. Solve equations that are quadratic in form (p.138) c. Solve equations involving rational exponents (p.137) d. Solve radical equations (p.133) 1.7 Linear Inequalities a. Use properties of inequalities (p.144) b. Graph inequalities (p.145) c. Use interval notations (p.146) d. Solve linear inequalities (p.147) e. Solve compound inequalities (p.149) f. Solve inequalities involving absolute value (p.150-151) 1.8 Quadratic and Rational Inequalities (p.157-160) a. Solve rational inequalities (p.158-160) C. CHAPTER TWO - FUNCTIONS AND GRAPHS (Five instructional hours) 2.1 Lines and Slopes a. Compute the slope of a line (p.176) b. Write the point slope equation of a line (p.178) c. Write and graph the slope-intercept equation of a line (p.180) d. Graph equations of horizontal and vertical lines (p.181) e. Find the slopes and equation of parallel and perpendicular lines (p.184) 2.2 Distance and Midpoint Formulas and Circles a. Find the distance between two points on a line (p.193) b. Find the midpoint of a line (p.194) c. Write the standard form of a circle’s equation (p.196)

d. Give the center and radius of a circle whose equation is in a standard form (p. 196-197) e. Convert the general form of a circle’s equation to standard form (p.198) 2.3 Basics of Functions

a. Find the range and the domain of a relation (p.201) b. Determine whether a relation is a function (p.203) c. Determine whether an equation represents a function (p.204) d. Use f(x) notation (p.205) e. Find the domain of a function (p. 209)

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2.4 Graphs a. Graph functions and relations (p.215) b. Use the vertical line test to identify functions (p.217) c. Identify even and odd functions and recognize their symmetries (p.224-226) D. CHAPTER FOUR - EXPONENTIAL AND LOGARITHMIC FUNCTIONS (Four instructional hours) 4.1 Exponential Functions a. Differentiate between polynomial and exponential functions (p. 374) b. Evaluate exponential functions (p.375) c. Graph exponential functions (p.375) 4.2 Logarithmic Functions a. Identify characteristics of exponential and logarithmic functions (p.386-388) b. Change exponential expressions to logarithmic expressions (p.386-387) c. Change logarithmic expressions to exponential expressions (p.387-388) d. Graph logarithmic functions (p.389) 4.3 Properties of Logarithms a. Use the product quotient and power rules (p.398-400) b. Expand and condense logarithms expressions (p.401-403) 4.4 Exponential and Logarithmic Equations a. Solve exponential equations (p.408) b. Solve logarithmic equations (p.410) E. CHAPTER EIGHT-SYSTEM OF EQUATIONS AND INEQUALITIES 8.1 Systems of Linear Equations in Two Variables a. Decide whether an ordered pair is a solution of a linear equation (p.699) b. Solve linear systems in two variables by substitution (p.701) c. Solve linear systems in two variables by addition (p.703) F. CHAPTER NINE - MATRICES AND DETERMINANTS (Six instructional hours) 9.1 Matrix Solutions to Linear Systems a. Write the augmented matrix for a system (p. 769) b. Use matrices to solve a system (p.769-778) c. Perform matrix row operations (p.771) 9.3 Matrix Operations and their Application a. Use matrix notation (p.792) b. Determine whether matrices are equal (p.793) c. Perform operations with matrices (addition, subtraction, and multiplication) (p.793-803)

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G. CHAPTER ELEVEN - SEQUENCES, INDUCTION AND PROBABILITY (Six instructional hours) 11.1 Sequences, and Summation Notation a. Find particular terms of a sequence given the general term (p.926-928) b. Use factorial notation (p.929) c. Find the general term of a sequence (p.928) d. Expand, evaluate and write sums in summation notation (p.931) 11.4 Mathematical Induction a. Identify principles of mathematics induction (p.961) b. Use mathematical induction to prove a statement (p.962) 11.5 The Binomial Theorem

a. Identify patterns in binomial coefficients (p.971)

11.7 Probability a. Compute empirical probability (p.988) b. Compute theoretical probability (p.989) c. Find the probability that an event will not occur (p.993) d. Find the probability of one event or a second event occurring (p.993) e. Find the probability of one event and a second event occurring (p.996)

V. COURSE CONTENT CHAPTER P - PREREQUISITES: FUNDAMENTAL CONCEPTS OF ALGEBRA (Six instructional hours) P.1 Real Numbers and Algebraic Expressions a. Sets of real numbers (p. 2) b. Absolute value (p. 4) c. Use of absolute value to express distance (p. 5) d. Work Problem Nos. (p.11) 1,3,9,11,15,21,25,31,33,39-45 odd, 47,51,53,57 P. 2 Exponents and Scientific Notation a. Algebra’s basic rules (p. 15) b. Properties of exponents (p. 18) c. Scientific notation (p. 19) d. Work Problem Set P.2 (p. 22), Nos. 12,19,34,41,44,48,51,57,59,60,61,63,64,69,70,75,76 P. 3 Radicals and Rational Exponents a. The vocabulary of radicals (p. 24) b. Combination of radicals (p. 26) c. Rationalize denominators, rationalization (p. 28) d. nth roots (p. 31) e. Expressions with rational exponents (p. 32) f. Reduction of the index of a radical (p. 34) g. Work Problem Set P3 (p.34), Nos. 3,15,23,25,33,34,37,41,45,64,67,71,73,74,81,83,99,101 P. 4 Polynomials a. Vocabulary of polynomials (p. 37) b. Adding and subtracting polynomial (p. 38) c. Multiplying polynomials (p. 39) d. The square of a Binomial (p. 42) e. Work Problem Set p.4, (p. 46-47), Nos. 9,11,13,17,19,25,27,31,37

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P.5 Factoring Polynomials a. Factoring by grouping (p. 48) b. Factoring trinomials (p. 49) c. Factor out the greatest common factor of a polynomial (p. 49) d. Factoring the difference of two squares (p. 50) e. Factoring the sum and difference of two cubes (p. 52) f. Work Problem Set P3, (p.57) Nos. 6,14,15,16,20,22,23,24,25,39,40,47,53,55,63,64,75,81 P.6 Rational Expressions a. Simplifying of rational expressions (p. 59) b. Multiplication and Division of rational expressions (p. 60) c. Addition and subtraction of rational expressions (p. 63) d. Simplify complex rational expressions (p. 67) e. Work Problem Set P. 6, (p.68) Nos. 5,11,13,17,20,26,27,37,40,43,44,55,57,58 CHAPTER 1 - EQUATIONS, INEQUALITIES, AND MATHEMATICAL MODELS (P. 85) 1.1 GRAPHS AND GRAPHING UTILITIES a. Rectangular coordinates (p. 77) b. Graphs of equations (p. 78) c. Intercepts (p. 80) d. Interpretation of information given by graphs (p. 81) e. Work Problem Set 1.1 (pp. 81-82) pp. 1,3,5,9,11,13,14,20,21,23,25,26,33,34,35 1.2 LINEAR EQUATIONS (Seven instructional hours) a. Linear equations in one variable (p. 86) b. Linear equations with fractions (p. 88) c. Equations involving rational expressions (p. 89) d. Work Problem Set 1.2, (p.92)Nos. 9,11,14,18,29,30,35,37,39,41,47,51,57,59,61,63,69 1.3 FORMULAS AND APPLICATIONS a. Formulas and Modeling Data (p. 95) b. Problems solving with linear equations and wording problems (p. 97) c. Pet population, renting a car (p. 97-100) d. Solving wording problems relate to investment in stocks and bonds (p.100-103) e. Work Problem set 1.3 (p.103-106) Nos. 15-19,31,32,35,39,43,44,45,47,52,53,54,67,71,75,84,88 1. 4 COMPLEX NUMBERS a. The powers of i (p. 108) b. Addition, subtraction, multiplication, and division of complex numbers (p. 108) c. Conjugate of complex numbers (p. 111) d. Work Problem Set 1.4. , (p.112)Nos. 5,13,16,23,29,33,37 1.5 QUADRATIC EQUATIONS a. Quadratic equations and factoring (p. 115) b. Quadratic equations and the square root method (p. 117) c. Quadratic equations and completing the square (p. 119) d. Quadratic equations and the quadratic formula (p. 121) e. Work Problem Set 1.5, (p.128)Nos. 3,4,7,9,19,23,33,41,43,57,63,65,66,83,91

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1.6 OTHER TYPES OF EQUATIONS a. Polynomial equations and factoring (p. 131) b. Radical equations (one or two radicals)(p. 134) c. Equations with rational exponents (p. 137) d. Polynomial equations that are quadratic in form (p. 138) e. Equations involving absolute value (p. 140) f. Work Problem Set 1.6, (pp. 141-142), Nos. 1,3,13,15,61,63,76,83 1.7 LINEAR INEQUALITIES a. Linear inequalities (p. 141) b. Compound inequalities (p. 144) c. Inequalities involving absolute value (p. 150) d. Work Problem Set 1.7, (pp. 153-154), Nos. 9,29,31,37,43,51,53,59,61,71,75 1.8 QUADRATIC AND RATIONAL INEQUALITIES a. Quadratic inequalities (p. 157) b. Rational inequalities (p. 162) c. Work Problem Set 1.8, (pp. 165), Nos. 7,9,21,29,31,37,39 CHAPTER 2 - FUNCTIONS AND GRAPHS (p. 176) (Five instructional hours) 2.1 LINES AND SLOPES (p. 177) a. The slope of a line (p. 176) b. The point-slope form of a line (p. 178) c. The slope-intercept form of a line (p. 180) d. Equations for horizontal and vertical lines (p. 181) e. The general form of a line (p. 183) f. Equations for lines parallel and perpendicular to a given line (p. 184) g. Work Problem Set 2.1, (p.188), Nos. 7,8,9,17,31,35,43,47,49,53,57,59,61,63,66,67 2.2. DISTANCE AND MIDPOINT FORMULAS AND CIRCLES (p. 193) a. Distance formulas (p.194) b. Definition of a circle (p. 195) c. Standard form of a circle (p. 197) d. Converting general form of a circle to standard form (p. 198) e. Work Problem Set 2.2, (pp. 199), Nos. 3,6,9,19,21,31,33,35,43,45,47,49,51,53 2.3 BASICS OF FUNCTIONS (p. 201) a. The range and domain of a function (p. 202) b. Relations and functions (p. 203) c. Function f(x) notation, f(x), (p. 205) d. Evaluation of a function (p. 206) e. Work Problem Set 2.3, (pp. 211), Nos. 3,4,5,7,21,23,39,45,51,55,63

2.4 GRAPHS OF FUNCTIONS (p. 214)

a. Graphs of functions and relations (p. 215) b. The vertical line test to identify functions (p. 217) c. even and odd functions and symmetry (p. 224) d. Work Problem set 2.4, (pp. 228-229), Nos. 1,2,7,9,15,35,38,61,63,65,67

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CHAPTER 4 - EXPONENTIAL AND LOGARITHMIC FUNCTIONS (Four instructional hours) 4.1 EXPONENTIAL FUNCTIONS (p. 374) a. Exponential functions (p. 374) b. Graph of exponential functions (p. 375) c. Compound interest formulas (p. 380) d. Work Problem Set 4.1, (pp. 382-383), Nos. 11,12 4.2 LOGARITHMIC FUNCTIONS (p. 395) a. Logarithmic functions (p. 385) b. Graph of logarithmic functions (p. 389) c. Common and natural logarithms (p. 391) d. Work Problem Set 4.2,(pp. 395) Nos. 3,7,12,13,23,25,27,35 4.3 PROPERTIES OF LOGARITHMS a. Product Rule (p.398) b. Quotient Rule (p.399) c. Power Rule (p.400) d. Expanding and Condensing Logarithms (p.401) e. Work Problems set 4.3 (p.405) Nos. 7,11,13,19,22,25,28,35,49,55,59,69 4.4 EXPONENTIAL AND LOGARITHMIC EQUATIONS a. Exponential equations (p.408) b. Logarithmic equations (p.410) c. Work Problem set 4.4 (p.415) Nos. 1,5,9,13,27,29,31,33,37,39 CHAPTER 8 - SYSTEMS OF EQUATIONS AND INEQUALITIES (P. 701) 8.1 SYSTEMS OF LINEAR EQUATIONS IN TWO VARIABLES (p. 701) a. Solving linear systems in two variables by substitution (p. 702) b. Solving linear systems in two variables by addition (p. 704) c. Work Problem Set 8.1, (pp. 712), Nos. 3,4,7,13,17,23,26,27,35,39,43,44,45,46,47,48 CHAPTER 9 - MATRICES AND DETERMINANTS (Six instructional hours) 9.1 MATRIX SOLUTIONS TO LINEAR SYSTEMS (p. 769) a. The augmented matrix for a system (p. 769) b. Use of matrices to solve a system (p. 771) c. Matrix row operations (p. 771) d. Work Problem Set 9.1, (pp. 779), Nos. 1,4,7,9,10,13,16, 19-23 odd,27,28,29 9.3 MATRIX OPERATIONS AND THEIR APPLICATION (p. 792) a. Matrix notation (p. 792) b. Equality of matrices (p. 793)

c. Operations with matrices addition, subtraction, multiplication) (p. 793) d. Work Problem Set 9.3, (pp. 804), Nos. 4,7,8,12,19,27,29,31,35,37,39,41 9.4 MULTIPLICATIVE INVERSES OF MATRICES & MATIRX EQUATIONS (P.807) a. Find the multiplicative inverse of a square matrix (p.808) b. Use the inverses to solve matrix equations (p.816) c. Work Problem Set 9.4 (p.819) Nos. 5,9,13,14,19,21,29,30,31,32,33,34,35,37,38

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9.5 DETERMINANTS AND CRAMER’S RULE (P.822) a. Evaluate a second order determinant (p.823) b. Solve a system of linear equations in two variable using cramer’s rule (p.824) c. Evaluate a third order determinant (p.826) d. Solve a system of linear equations in three variable using cramer’s rule (p.829) e. Work Problem Set 9.5 (p.832), Nos. 6,14,15,17,27,28,33,34 CHAPTER 11 - SEQUENCES, INDUCTION AND PROBABILITY (Six instructional hours) 11.1 SEQUENCES, AND SUMMATION NOTATION (p. 926) a. Particular terms of a sequence given the general term (p. 926) b. The general term of a sequence (p. 927) c. Factorial notation (p. 929) d. Sums in summation notation (p. 931) e. Work Problem Set 11.1, (pp. 934), Nos. 1,5,7,10,19,23,29,33,34,43,47,51,52 11.4 MATHEMATICAL INDUCTION (p. 960) a. Principles of mathematical induction (p. 960) b. Use of mathematical induction to prove statements (p. 962) c. Work Problems Set 11.4, (pp 968), Nos. 1,3,7,6,11,15,17,18 11.5 THE BINOMIAL THEOREM (p. 969) a. Patterns in binomial coefficients (p. 971) b. Specified terms in a binomial’s expansion (p. 974) c. Work Problem set 11.5, (pp. 975) Nos. 1,3,8,9,11,13,15,31,39,43 11.7 PROBABILITY (p. 988) a. The probability of an event (p. 989) b. Work Problem Set 11.7, (pp. 998-1000), Nos. 9-24 (odd only), 33-39 (odd only), 45-50 VI. TEACHING METHOD

Learning activities include but are not limited to lectures, problem solving approach to homework assignments, tests, tutorial sessions, student’s solution manual, and the use of the Math Pack 5 Tutorial Software Package and video tapes.

The required software package is designed to generate practice exercises based on the exercises sets in the text. It provides the students with unlimited practice and generates graded and recorded practice problems with optional step-by-step tutorial. It includes a complete glossary including graphics and cross-references to related words. The instructional tapes are in a lecture format featuring worked out examples and exercises taken from each section of the text.

VII. COURSE REQUIREMENTS

1. Students must come to class with the required textbook. The required text is: Blitzer, R. (2001), Algebra &

Trigonometry, 2nd Edition, Upper Saddle River, NJ: Prentice Hall. 2. Punctual class attendance (entire class period) is required. It is the student’s responsibility to meet course

requirements, due dates, and catch up on all missing sessions and assignments. 3. No late work will be accepted without appropriate documentation for an excuse for the missed date(s). In order for

the excuse to be considered, it must be submitted to the instructor at the next class period following the day of absence.

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4. Read the assigned sections. Be prepared to participate in class discussion of required sections. 5. Take the exams and quizzes on designated dates. Only documented excused absences will be honored. All make-up

unit exams will be scheduled on specified dates during the semester to only eligible students. 6. Meeting the prerequisite requirements is the responsibility of the student.

VIII. EVALUATION AND GRADE ASSIGNMENT Unit Exams, Quizzes, Projects, Assignments, Home Work, Attendance....... 40 - 50% Quizzes are announced and/or unannounced. Mid-term Examination................................................................................ 20% Final Examination *....................................................................................... 30 - 40 %

TOTAL 100 * The final exam for all sections of Math 131 will be given at 9:00 a.m., Saturday, December 11, 2004.

IX. GRADING SCALE A = 90-100% D = 60 - 69% B = 80 - 89% F = Below 60% C = 70 - 79% NOTES A grade of C or better in Math 131 is a prerequisite for enrollment in Math 132.

• SUPPLEMENTARY MATERIALS 1. Videotapes 2. Computer software (included in the required textbook package) 3. Student Solution Manuel Math Pak 5

• ADA SPECIAL SERVICE STATEMENT If you need accommodations in this class/setting/facility related to a disability, please make an appointment to see the instructor as soon as possible.

• EXAM SECURITY

During exam periods all students will be required to show a valid University ID.

• CONTACT INFORMATION AND RESOLUTION OF CONCERN(S) / PROBLEMS(S)

Instructor _____________ Tel:# ___________ Location ________________. Office hrs. ___________________________ If you have any concern(s)/problems(s) regarding any aspect of the course or the instructor, please discuss it FIRST with the instructor AND THEN with the Dept. Head, Dr. B. Sims, Tel. 274-6177 if necessary. The departmental form designed for this purpose should be used.

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GRAMBLING STATE UNIVERSITY COLLEGE OF ARTS AND SCIENCES

DEPARTMENT OF MATHEMATICS AND COMPUTER SCIENCE

COURSE SYLLABUS MATH 132: TRIGONOMETRY

Semester: 2008

INSTRUCTORS:

I. COURSE DESCRIPTION (Catalog Statement)

Plane trigonometry, functions and their graphs, rectangular and polar coordinates, graphing techniques, transformations, trigonometric functions and their graphs and inverses, applications of trigonometry, trigonometric functions, complex numbers, symmetry and vectors. Prerequisite: a grade of C or better in MATH 131.

II. RATIONALE

Mathematics 132 is the second course of a sequence designed for non-science majors with a base math background. Math 132 might be the last course in math some of students will take. Therefore, many learning aids are built into the format of the required course. These tools are meant to be a machine for learning, one that can help focus efforts and get the most from the time and energy invested. Emphasis is on general concepts that are around us as we go through our daily activities. Many of the concepts that need to be expressed mathematically, are already known intuitively. Exploration of the web site (www.prenhal.com/blitzer) will help students to view trigonometry as a valuable tool for understanding the world outside the classroom. It represents a useful integration of learning techniques. Competencies gained in MATH 132 are essential to the skills and practice needed in problem solving, a requirement for a successful individual. Graphing utilities allow students to explore concepts visually, promoting an understanding of key objectives.

III. COMPETENCIES

At the end of the semester, the student should be able to have the following competencies: A. Determine the characteristics, properties, and notations of functions including the six

trigonometric functions. Properties include: domain, range, period, amplitude, whether the function is odd or even, dependent or independent variables.

B. Use reference angles and complementary angles to determine the value of a trigonometric function.

C. Convert from rectangular/polar coordinates to polar/rectangular coordinates. D. Find the values of trigonometric functions and their inverse functions and graph these

functions. E. Graph functions by shifting, compressing, stretching, transforming and/or reflecting. F. Find the functions/equations whose sinusoidal graphs are given. G. Construct functions in application, including piecewise-defined functions. H. Solve applied problems involving circular motion. I. Find and graph the composite of two functions and its domain. J. Use tests for symmetry in graphing functions

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IV. COURSE OBJECTIVES

A. CHAPTER 5 - TRIGONOMETRIC FUNCTIONS

5.1 Angles and Radian Measure (pp. 468-480)

• Recognize and use the vocabulary of angles. • Use degree measure. • Draw angles in standard position. • Find coterminal angles. • Find complements and supplements. • Use radian measure • Convert between degrees and radians. • Find the length of a circular arc. • Use linear and angular speed to describe motion on a circular path. • Homework (p. 480) Work Odd Problems (1-39)

5.2 Right Triangle Trigonometry (pp. 483-497)

• Use right triangles to evaluate trigonometric functions. • Recognize and use fundamental identities. • Use equal cofunctions of complements. • Use right triangle trigonometry to solve applied problems. • Homework (p.495) Work Odd Problems (1-47)

5.3 Trigonometric Functions of Any Angle (pp. 498-510)

• Use the definitions of trigonometric functions of any angle. • Use the signs of the trigonometric functions. • Find reference angles. • Use reference angles to evaluate trigonometric functions. • Homework (p. 510) Work Odd Problems (1-85)

5.4 Trigonometric Functions of Real Numbers; Periodic Functions (pp. 511-519)

• Use a unit circle to define trigonometric functions of real numbers. • Recognize the domain and range of sine and cosine functions. • Use even and odd trigonometric functions. • Use periodic properties. • Homework (p. 517) Work Odd Problems (1-31)

5.5 Graphs of Sine and Cosine Functions (pp. 520-539)

• Understand the graph of y = sin x • Graph variations of y = sin x • Understand the graph of y = cos x • Graph variations of y = cos x • Use vertical shifts of sine and cosine curves. • Homework (p. 537) Work Odd Problems (1-63)

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5.7 Inverse Trigonometric Functions (pp. 553-567)

• Understand and use the inverse sine function. • Understand and use the inverse cosine function. • Homework (p. 566) Work Odd Problems (1-17)

5.8 Applications of Trigonometric Functions (pp.568-582)

• Solve a right triangle. • Solve problems involving bearings. • Model simple harmonic motion. • Homework (p. 576) Work Odd Problems (1-11)

B. CHAPTER 6 - ANALYTIC TRIGONOMETRY

6.1 Verifying Trigonometric Identities (pp. 588-597)

• Use the fundamental trigonometric identities to verify identities. • Homework (p. 596) Work Odd Problems (1-11)

6.2 Sum and Difference Formulas (pp. 598-607)

• Use the formula for the cosine of the difference of two angles. • Use sum and difference formulas for cosines and sines. • Use sum and difference formulas for tangents. • Homework (p. 605) Work Odd Problems (1-3), (13-19)

6.3 Double-Angle, Power-Reducing and Half-Angle Formulas (pp. 608-618)

• Use the double-angle formulas. • Use the power-reducing formulas. • Use the half-angle formulas. • Homework (p. 615) Work Odd Problems (1-5)

6.4 Product-to-Sum and Sum-to-Product Formulas (pp. 619-625)

• Use the product-to-sum formulas. • Use the sum-to-product formulas.

6.5 Trigonometric Equations (pp. 626-641)

• Find all solutions of a trigonometric equation. • Solve equations with multiple angles. • Solve trigonometric equations quadratic in form. • Use factoring to separate different functions in trigonometric equations. • Use identities to solve trigonometric equations. • Homework (p. 637) Work Odd Problems (1-9), (11-17)

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C. CHAPTER 7 - ADDITIONAL TOPICS IN TRIGONOMETRY

7.1 The Law of Sines (pp. 646-656)

• Use the Law of Sines to solve oblique triangles. • Use the Law of Sines to solve, if possible, the triangle or triangles in the ambiguous case. • Find the area of an oblique triangle using the sine functions. • Solve applied problems using the Law of Sines. • Homework (p. 653) Work Odd Problems (1-15)

7.2 The Law of Cosines (pp. 657-664) • Use the Law of cosines to solve oblique triangles. • Solve applied problems using the Law of cosines. • Use Heron=s formula to find the area of a triangle. • Homework (p. 661) Work Odd Problems (1-7)

7.3 Polar Coordinates (pp. 665-675)

• Plot points in the polar coordinate system;. • Find multiple sets of polar coordinates of a given point. • Convert a point from polar to rectangular coordinates. • Convert a point from rectangular to polar coordinates. • Convert an equation from rectangular to polar coordinates. • Convert an equation from polar to rectangular coordinates. • Homework (pp. 673-674) Work Odd Problems (1-73)

7.4 Graphs of Polar Equations (pp. 675-686)

• Graph polar equations. • Use symmetry to graph polar equations. • Homework (p. 684) Work Odd Problems (1-33). Limit your work to testing for symmetry.

7.5 Complex Numbers in Polar Form; DeMoivre=s Theorem (pp. 687-697)

• Plot complex numbers in the complex plane. • Find the absolute value of a complex number. • Write complex numbers in polar form. • Convert a complex number from polar to rectangular form. • Find quotients of complex numbers in polar form. • Find powers of complex numbers in polar form. • Homework (p. 695) Work Odd Problems (1-49)

7.6 Vectors (pp. 698-710)

• Use magnitude and direction to show vectors are equal. • Visualize scalar multiplication, vector addition, and vector subtraction as geometric vectors. • Represent vectors in the rectangular coordinate system. • Perform operations with vectors in terms of i and j. • Find a unit vector in the direction of v. • Homework (p. 708) Work Odd Problems (1-63)

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7.7 The Dot Product (pp. 711-723)

• Find the dot product of two vectors. • Find the angle between two vectors. • Use the dot product to determine if two vectors are orthogonal. • Write a vector in terms of its magnitude and direction. • Homework (p. 724) Work Odd Problems (97-104)

V. COURSE CONTENT

A. TRIGONOMETRIC FUNCTIONS (Chapter 5, p. 467)

1. Angles and Radian Measure (p. 468) 2. Right Triangle Trigonometry (p. 483) 3. Trigonometric Functions of Any Angle (p. 498) 4. Trigonometric Functions of Real Numbers; Periodic Function (p. 511) 5. Graphs of Sine and Cosine Functions (p. 520) 6. Inverse Trigonometric Functions (p. 553) 7. Applications of Trigonometric Functions (p. 568)

B. ANALYTIC TRIGONOMETRY (Chapter 6, p. 587)

1. Verifying Trigonometric Identities (p. 588) 2. Sum and Difference Formulas (p. 598) 3. Double-Angle and Half-Angle Formulas (p. 608) 4. Product-to-Sum and Sum-to-Product Formulas (p. 619) 5. Trigonometric Equations (p. 626)

C. ADDITIONAL TOPICS IN TRIGONOMETRY (Chapter 7, p. 645)

1. The Law of Sines (p. 646) 2. The Law of Cosines (p. 657) 3. Polar Coordinates (p. 665) 4. Graphs of Polar Equations (p. 675) 5. Complex Numbers in Polar Form; DeMoivre=s Theorem (p. 687) 6. Vectors (p. 698) 7. The Dot Product (p. 711)

VI. TEACHING METHOD

Learning activities include, but are not limited to lectures, problem solving approach and sessions, homework assignments, tests, tutorial sessions, and the use of the Blitzer Website (www.prenhal.com/Blitzer). It is practically and virtually impossible to understand concepts, procedures of algebra and trigonometry by just reading the textbook or notes (own or classmates).

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VII. COURSE REQUIREMENTS

1. All relevant GSU policies and regulations shall apply.

2. Students must come to class with the required textbook. The required text is: Blitzer, R. (2007), Algebra & Trigonometry, 3rd Edition, Upper Saddle River, NJ: Prentice Hall.

3. Punctual class attendance (entire class period) is required. It is the student’s responsibility to meet course requirements, due dates, and catch up on all missing sessions and assignments.

4. Class participation includes but not limited to coming to class on time, being awake in the class, and not distracting other students from listening to the class lecture, and asking relevant questions. Class discussion will be highly encouraged. Please never hesitate to ask questions.

5. No late work will be accepted without appropriate documentation for an excuse for the missed date(s). In order for the excuse to be considered, it must be submitted to the instructor at the next class period following the day of absence.

6. Read the assigned sections. Be prepared to participate in class discussion of required sections.

7. Take the exams and quizzes on designated dates. Only documented excused absences will be honored. All make-up unit exams will be scheduled on specified dates during the semester to only eligible students.

8. Students who enter class more than 5 minutes late will be considered absent for computer attendance purposes.

9. Meeting the prerequisite requirements is the responsibility of the student.

10. Plagiarism will not be tolerated in any form. As a minimum, students will be given a grade of zero for any quiz or exam in which cheating, fraud, or misrepresentation is found. Two exactly similar pages will be treated as an act of plagiarism for both students.

11. The course requires a lot of hard work and additional practice. Student should carefully consider this in planning their other courses and activities. Attendance in all the classes is vitally important since class lectures have a close link with each other.

12. Always keep up with the class. There is a lot of material to be covered. It is important for us to reach to the last phase of this course because this information is very essential for your future courses.

13. It will be advisable to formulate study groups and meet at a designated place consistently

during evening hours or weekends to complete the related work on the same day.

14. Cell phones and other electronic pieces in the classroom are distractions. Therefore, please turn off your phone and other gadgets and do not respond to vibrating mode during the entire class period. Keep your phone and other electronic gadgets inside your bag.

15. An “I” grade will only be given when extremely adverse and well-documented circumstances

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arise at the end of the semester and the student is passing the course at the time the decision for the “I” grade was made. That definitely does not include making up for weak performance during the semester. In particular, the grade that the student had made until getting an “I” will still be included into computing the final grade after a student has completed the work necessary to alter the “I” grade.

VIII. EVALUATION AND GRADE ASSIGNMENT

Unit Examinations, Homework, Quizzes, Projects, Attendance…………………………. 40%-50%

Mid-term Examination……………………………………………………………………. 10%-20%

Final Examination…………………………………………………………………………. 30%-40%

TOTAL………………………………… 100%

IX. EXAM SECURITY

During exam periods all students will be required to show a valid University ID.

X. Grading Scale

A: 90 - 100% C: 70 - 79% F: Below 60% B: 80 - 89% D: 60 - 70%

XI. Supplementary Materials

1. Review Videos 2. Blitzer website - http://www.prenhall.com/blitzer/ 3. Student solutions manual

XII. ADA Special Service Statement

If you need accommodations in this class/setting/facility related to a disability, please make an appointment to see the instructor as soon as possible.

XIII. CONTACT INFORMATION AND RESOLUTION OF CONCERN(S)/PROBLEMS(S)

Instructor: _______________ Location:__________ Tel #: _________________ Email: __________________ Office hrs.: _________________________________________

XIV. CONCERNS/PROBLEMS If you have any concern(s)/problems(s) regarding any aspect of the course or the instructor, please discuss it FIRST with the instructor AND THEN with the Dept. Head, Dr. Sims, Tel. 274-6177 if necessary. Please use the departmental form designed for this purpose.

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Mathematics and Computer Science Department College of Arts and Sciences Grambling State University

Course Syllabus Academic Year 2008-2009

Math 147 (Section 7) – Precalculus I (CRN 11328)

Semester: FALL 2008 Time and Place: - LECTURE PROBLEM SESSION Instructor: Office: Telephone: Conference Hours: Others by Appointment Only Instructor E-mail: Text: Larson & Hostetler, Precalculus (Seventh Edition), Houghton Mifflin Company, 2007. Materials: Textbook, scientific calculator, notebook and Advance Organizer, graphing paper. Reference: Bennet & Briggs, Using and Understanding Mathematics: Quantitative Reasoning Approach, Pearson Addison Wesley Prerequisite: The student must have an ACT Math score of 18 or above. I. Course Description:

Elementary logic; Set operation; Properties of real and complex numbers; Algebraic expressions; Equations and inequalities; Functions and graphs; Polynomials; Inverse functions; Exponential functions; Logarithmic functions; Systems of equations and inequalities; Matrices and determinants, Sequences; Series; and Special Project.

II. Rationale

This Pre-calculus I is the first course of a sequence (MATH 147 and MATH148) designed for students with Basic Mathematics background. The course will also provide the students with the necessary foundation in order to pursue calculus concepts. MATH 147 might be the only Math course some students will take. Therefore, many learning aids are built into the course. These learning tools can help one focus efforts in order to get the most from the time and energy invested. Emphasis is on general concepts that are around us as we go through our daily activities. Many of the concepts needed to be expressed mathematically, are already known intuitively.

Exploration of the media supplements will help students to view Pre-calculus as a valuable tool for understanding the world outside the classroom. It represents a useful integration of learning techniques. Competencies gained in MATH 147 are essential to the skills and practice needed in problem solving, a requirement for a successful individual.

The course will provide the students with the necessary fundamentals of algebra in order to pursue the concepts in calculus.

III. Competencies

Upon successful completion of this course, students should be able to: A. Understand the properties of the real number system. B. Recognize Fallacies C. Analyze arguments D. Perform basic set operations.

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E. Learn to draw the graphs of functions. F. Understand the algebra of functions. G. Learn to find the inverse of a function. H. Determine the zeros of polynomial functions. I. Solve equations and inequalities J. Define complex numbers and some basic operations. K. Understand the Fundamental Theorem of Algebra. L. Understand the asymptotes and how to determine them. M. Define the exponential and logarithmic functions and learn their properties. N. Learn to solve equations involving exponential and logarithmic functions. O. Solve systems of equations P. Understand matrices and their operations in the Cartesian Plane Q. Understand Sequences. R. Understand the Binomial Theorem S. Understand Proofs by Induction T. Understand the concept of Probability

IV. Behavioral Objectives Upon successful completion of this course, students should be able to:

A. Give examples of some properties of the real number system. B. Use critical thinking in problem solving. C. Describe the domain and the range of basic functions. D. Use different methods to solve linear systems of equations. E. Discuss how to determine if a function is invertible. F. Define a function and draw its graph. G. Use shifting, reflecting, and stretching techniques to graphs of functions. H. Apply simple algebraic operations on functions. I. Determine the inverse of a function. J. Draw the graphs of some basic quadratic functions. K. Recognize a complex number and evaluate them using some basic algebraic operations. L. Use the fundamental theorem of algebra to determine the zeros of a polynomial function. M. Find the horizontal and vertical asymptotes. N. Use the properties of exponential and logarithmic functions to simplify expressions involving them. O. Solve exponential and logarithmic equations. P. Find the sums of arithmetic and geometric sequences, as well as apply series to problems Q. Solve proofs involving series R. Solve problems utilizing the principles of probability.

V. Course Content

A. Critical Thinking 1. Number Systems and their evolution 2. Recognizing Fallacies 3. Set and Venn Diagrams 4. Analyzing Arguments 5. Critical Thinking in Everyday Life B. Special Project

A project on prominent Mathematicians from a selected group, assigned by the Instructor.

C. Functions and their Graphs 1. Rectangular Coordinates 2. Graphs of Equations 3. Linear Equations in two variables 4. Functions 5. Analyzing Graphs of Functions 6. A library of Parent Functions 7. Transformations of Functions 8. Combinations of Functions: Composite Functions 9. Inverse Functions

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10. Mathematical Modeling D. Polynomial and Rational Functions 1. Quadratic Functions and Models 2. Polynomial Functions of Higher Degree 3. Polynomial and Synthetic Division 4. Complex Numbers 5. Zeros of Polynomial Functions 6. Rational Functions E. Exponential and Logarithmic Functions 1. Exponential Functions and their Graphs 2. Logarithmic Functions and their Graphs 3. Properties of Logarithms 4. Solving Logarithmic and Exponential Equations 5. Exponential and Logarithmic Models

F. Matrices and Determinants 1. Systems of Equations and Matrices 2. Operations with Matrices 3. The Inverse of a Square Matrix 4. The Determinant of a Square Matrix

G. Sequences and Series 1. Summation Notation 2. Sequences and Series 3. Arithmetic Sequences and Series 4. Geometric Sequences and Series

VI. TEACHING METHOD

Learning activities include but are not limited to lectures, problem solving approach to homework assignments, tests, and tutorial sessions, student’s solution manual and video tapes. Special handouts (ADVANCE ORGANIZERS) will be given before a concept is covered in the class. These handouts will be due at the beginning of the next class period. A late submission will not be accepted unless it is approved by the instructor with appropriate valid excuse. The problem solving session will be one hour every week, and the attendance is mandatory. The session will involve students solving assigned problems and presenting the solution to the class. A portion of the final grade will be assigned for the problem session.

Eduspace will be used for this course this semester as a learning aid. It is imperative that you have or obtain an email address so that you can be successful in this course.

VII. Special Course Requirements Students must come to class with the textbook and a scientific calculator. The required text is Larson & Hostetler, Precalculus (Seventh Edition), Houghton Mifflin 2007

The textbook is packaged with Math Space CD, DVD, Eduspace, and Student Solutions Manual. The ISBN for the package is 0-618-79883-8

The textbook is required for this course. General Course Requirements

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REMINDERS AND STUDY TECHNIQUES:

• Always keep up with the progress of the course. A problem that is ignored will not disappear. It will only mushroom. Advance Organizers: Use them to prepare for class sessions and also as note taking aids.

• Study before each lecture to know what to look for. Also browse through your notes immediately after the lecture. • Retention of knowledge is best achieved by revising good notes within 3 hours (but definitely within 12 hours) after

the lecture. • Maintain well-organized and comprehensive notes. Expand them when reading the book and when attending class.

I suggest using loose-leaf paper and putting the date on each page. • Textbook and notes should always be brought to class because they will be referred to during most lectures. • I will do my best to help you set and achieve your goals. Don't hesitate. Keep in touch. POLICIES:

• If you have a cellular telephone, then it must be turned off during the entire class period. If it should ring, you will be asked to leave for the remainder of class. Students are not allowed to use the calculator function on a cellular phone or laptop during exams/quizzes. If caught using these items, your test will be invalidated.

• A valid university identification (ID) will be required during the examination periods. No ID, No Exam !!!!

Obviously, every student in this class is assumed to be a mature, responsible, and capable individual who is preparing

himself/herself for a successful professional career. The following points are simply a statement of some of the behavioral traits expected from a responsible professional. • Class attendance is a privilege and a duty. Everyone is expected to arrive on time and remain for the entire class period unless he/she asks for, and is granted, permission to leave. The class attendance will be taken at the beginning of the class, if you are late more than 5 minutes, then you will be marked absent.

Tardiness is equivalent to an absence unless I excuse it at the end of the class period upon student's request. It will not be excused unless there is a valid proof /reason and it happens only once or twice in entire semester.

Attendance record will be maintained. • An absent student is responsible for finding out and covering the missed work. • No make up tests will be given, unless proper document is obtained and an appointment is made within two (2)

days after returning to the class. • There will be absolutely no opportunity to raise your grade by doing extra credit work. Each student will be graded solely on the basis of criteria mentioned below (exams, quizzes, and homework etc.).

Please do not ask for "Extra Credit Work". • An "I" grade will only be given when extremely adverse and well-documented circumstances arise at the end of the

semester. That definitely doesn't include making up for weak performance during the semester. In particular, the grade that the student had made until getting an "I" will still be factored into computing the final grade after the student has completed the work necessary to change the "I".

• Everyone is expected to study the reading assignments before the lectures and to participate in class discussions in a constructive manner.

• Group discussions/study outside the classroom is strongly encouraged. Cheating, of any kind, is a very serious matter and will result in an "F" grade in the course.

• Of course, all relevant GSU policies and regulations also apply.

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Evaluation Process A. Methods

Students will be evaluated based on their performance in examinations (including final examination), quizzes, homework, and class participation.

B. Grading Scale: Homework, Quizzes, Tests, etc. 50% Midsemester Exam 15% Special Project 10% Final Exam 25% Total 100% HOMEWORK: Homework assignments are extremely important. They can really make the subject material extremely clear and prepare you for tests and quizzes. I will assign the homework daily, however, I will not collect or grade all the assignments I give. I may pickup assignments randomly for grading. If you do your homework assignments regularly and conscientiously you will really benefit from the course a lot. I will able to cover more material in the class and this, in turn, will provide you rewarding experiences in your other courses. QUIZZES: There may be several unannounced quizzes throughout the semester. There will be no makeup

for the quizzes. The purpose of the unannounced quizzes is two fold -- to make students come to the class on time and to make students read and understand course material as the course progresses. Quizzes might be given at any time during the class period. If a quiz is given at the beginning of the class period and if ten minutes are allocated for a quiz and a student comes six minutes late to the class, s/he has only 4 minutes to complete the quiz.

Examinations: There will be at least three major tests, and a comprehensive mid-semester and final examinations. The schedule of Final Examination (FALL 2008) is as follows: Final Exam Will be given on the day and time specified for this class in the University final Exam Schedule.

GRADING: Each Test will be 100 Points; and each quiz and Advance Organizers will be 10 points. The mid-semester and final examination (comprehensive) will be 200 points each.

The Final grade will be determined on the basis of total average at the end of the semester using the following scale: 90 -100 A, 80 - 89 B, 70 - 79 C, 60 - 69 D, 0 - 59 F

The following clause is for students participating in any GSU extra curricula activity. Any student participating in extra curricular activities (example band, football, track,

etc. …) must bring signed verification from activity's sponsor/ director on or before the third week of school. Notification of scheduled events that conflict with test or assignment dates must be given in advance so that test may be rescheduled. Test or assignments may be rescheduled to an earlier date than the scheduled date, but must be completed prior to the next class period. If the student neglects to give early notification a score of Zero (0) will be given for that test or assignments. An official excuse for student participation is required to makeup an assignment.

SUPPLEMENTARY MATERIALS

1. Videotapes 2. Computer software 3. Student Solution Manuel

CONTACT INFORMATION AND RESOLUTION OF CONCERN(S) PROBLEMS(S)

Instructor Tel:# Office Location

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If you have any concern(s)/problems(s) regarding any aspect of the course, please discuss it FIRST with the instructor AND THEN with the Dept. Head, Dr. Brett Sims, Tel. No. 274-6177, if necessary.

Special Course Requirements

ADA SPECIAL SERVICE DISABILITY STATEMENT: Grambling State University complies with the American with Disabilities Act, which requires us to provide reasonable accommodations to students with disabilities. If you need accommodation in this class/setting/facility related to disability, please make an appointment to see me as soon as possible. My office location and conference hours are asset forth at the beginning of this document.

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Mathematics and Computer Science Department College of Science and Technology

Grambling State University

Course Syllabus Math 148 – Precalculus II

AY 2008 - 2009

Semester: Time and Place: Instructor: Office: Contact Information: Conference Hours:

Text: Larson & Hostetler, Precalculus (Seventh Edition), Houghton Mifflin Company, 2007. Materials: Textbook, notebook I. Course Description: Partial fractions; analytic geometry; right triangle trigonometry; trigonometry; trigonometric functions; trigonometric identities and equations; applications of trigonometry; polar coordinates; complex numbers and vectors Prerequisite: A grade of “C” or better in Math 147. Note: This 3 hour course includes an additional 1 hour Problem Solving Session and therefore will meet 4 times per week. II. Rationale: The purpose of this course is to provide the necessary skills (in trigonometry) to enable the student to solve equations and problems involving angles and triangles. Trigonometry involves the study of triangles and the relationships of angles and sides of triangles. Trigonometry has applications to calculus, physics, engineering, and most other scientific and technological fields III. Competencies At the end of this course the student should be able to:

A. Find the partial fraction decomposition of a rational expression. B. Convert from radians to degrees and vice versa. C. Solve right triangles for missing parts. D. Determine the trigonometric functions of any angle. E. Construct the graphs of the trigonometric functions and analyze them. F. Evaluate the inverse trigonometric functions of a number. G. Learn and use the basic fundamental identities to prove that other equations are identities. H. Solve trigonometric equations. I. Learn and apply sum and difference identities. J. Learn and apply multiple-angle and product-sum formulas. K. Learn and apply the Law of Sines formula. L. Learn and apply the Law of Cosines formula. M. Learn and apply DeMoivre’s Theorem N. Add, subtract, and find the magnitude and direction of a vector. O. Find the dot product of two vectors and vector components.

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P. Perform operations on matrices and solve systems of equations. Q. Determine the inverse of a square matrix and find the determinant of a square matrix. R. Learn and apply hyperbolic trigonometric functions.

IV. Behavioral Objectives At the completion of this course the student will be able to do:

A. Write the partial fraction decomposition of a rational expression. B. Change an angle in radians to degrees and vice versa. C. Solve a right triangle for its missing parts. D. Find the value of a trigonometric function of an angle. E. Graph the sine and cosine functions and determine their amplitude, period and phase shift. F. Graph the other trigonometric functions. G. Evaluate the inverse trigonometric function of a number. H. Prove trigonometric identities. I. Expand expressions using multiple-angle formulas and product-sum formulas J. Use the Law of sines and cosines to solve oblique triangles. K. Use DeMoivre’s Theorem to find powers of complex numbers. L. Find the sum and difference of vectors; find the magnitude and direction of a vector. M. Find the components of a vector and the dot product. N. Add, subtract, and multiply matrices. O. Find the determinant and the inverse of a square matrix. P. Solve a system of linear equations by substitution and by elimination. Q. Evaluate the hyperbolic functions of an angle.

V. Course Content

A. Trigonometric Functions 1. Radian and Degree Measure 2. Trigonometric Functions: The Unit Circle 3. Right Triangle Trigonometry 4. Trigonometric Functions of any Angle 5. Graphs of Sine and Cosine Functions 6. Graphs of other Trigonometric Functions 7. Inverse Trigonometric Functions

B. Analytic Trigonometry 1. Using Fundamental Identities 2. Verifying Trigonometric Identities 3. Solving Trigonometric Equations 4. Sum and Difference Formulas 5. Multiple-Angle and Product-Sum Formulas

C. Additional Topics in Trigonometry 1. Law of Sines 2. Law of Cosines 3. DeMoivre’s Theorem

D. Augmented Topics 1. Vectors in the plane 2. Vectors and Dot Products 3. Matrices and Systems of Equations 4. Operations with Matrices 5. The Inverse of a Square Matrix 6. The Determinant of a Square Matrix 7. Introduction of Hyperbolic Functions

E. Topics in Analytic Geometry 1. Introduction to Conics: Parabolas 2. Ellipses 3. Hyperbolas 4. Rotation and System of Quadratic Equations

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5. Parametric Equations 6. Polar Coordinates

VI. Course Format

This course will be taught through traditional, active learning, and/or electronic modes using lecture, discussion, problem solving sessions, problem solving using a calculator, and computer related applications.

Blackboard will be used for this course this semester as a learning aid. It is imperative that you have or obtain an email address so that you can be successful in this course.

VII. Course Requirement

1. Meeting the prerequisite requirements is the responsibility of the student. 2. Students must come to class with the required textbook. 3. Punctual class attendance is required. Attendance will be taken at the beginning of class.

It is the student’s responsibility to meet course requirements, due dates, and catch up on missing sessions and assignments. If you are absent from class you must obtain class notes from a classmate. Class participation includes but not limited to coming to class on time, being awake in class, not distracting other students from listening to the class lecture, and asking relevant questions. Class discussion will be highly encouraged.

4. Read the assigned sections and work the example problems before class. Be prepared to

participate in class discussion of required sections. 5. All cell phones MUST be in the silent or vibrate mode. If it should ring,

you will be asked to leave for the remainder of class. Students may not use the calculator function on a cellular phone or laptop during exams/quizzes. If caught using these items, your test may be invalidated. A student must not have headphones on during class or examinations.

6. No late work will be accepted without an official excuse (doctor, lawyer, funeral director,

etc.) for the missed date(s). The excuse must be submitted to the instructor at the next class period following the day of absence.

7. Missed information, assignments and/or exams due to registration delays is the

responsibility of the student. The student must obtain missed information and assignments from classmates.

8. Take the exams and quizzes on designated dates. Only documented excused absences

will be honored. All make-up unit exams will be scheduled on specified dates during the semester to only eligible students. The missed exam must be taken within two (2) class periods. There will be no make-ups for quizzes.

9. Notification of scheduled events (doctor appointments, club/organization trips, etc) that conflict with test dates must be given in advance so that tests may be rescheduled. Test or assignments may be rescheduled to an earlier date than the scheduled date, but must be complete prior to the next class period. If the student neglects to give early notification, a grade of F will be given for that test or assignment.

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10. Group discussions/study outside the classroom is strongly encouraged. Cheating, of any kind, is a very serious matter and will result in an “F” grade in the course.

11. No work for extra credit will be assigned on individual basis during, or after, the

semester. Every student will be given the same opportunity to achieve his/her potential.

12. An “I” grade will only be given when extremely adverse and well-documented circumstances arise at the end of the semester. That definitely doesn’t include making up for weak performance during the semester. In particular, the grade that the student had made until getting an “I” will still be factored into computing the final grade after the student has completed the work necessary to change the “I”.

13. Acceptable Excuses are participation in an activity appearing on the university

authorized activity list, death or major illness in a student’s immediate family, illness of a dependent family member, participation in legal proceedings or administrative procedures that require a student’s presence, religious holy days, illness that is too severe or contagious for the student to attend class (to be determined by Health Center or off-campus physician), required participation in military duties.

VIII. Evaluation Process

Students will be evaluated based on their performance on examinations (including final examination), quizzes, home work and class participation.

TESTING: There will be approximately four 50 minute class tests which include a

comprehensive mid-semester test and a comprehensive final examination. All students are required to take every exam when scheduled. No makeup examination will be given without an official excuse (See Acceptable Excuses above).

GRADING SCALE A 90 -100 pts B 80 - 89 pts C 70 - 79 pts D 60 - 69 pts F 0 - 59 pts IX. Changes to the Syllabus

I reserve the right to change the syllabus as necessary to ensure adequate student progress.

X. ADA Special Service Statement If you need accommodation in this class related to a disability, please make an appointment to see me as soon as possible.

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Mathematics and Computer Science Department College of Arts & Sciences

Grambling State University

Course Syllabus Academic Year 2008 - 2009

Math 153 Calculus I

Semester: Time and Place: Instructor: Office: Telephone: Conference Hours: Instructor Email: Text: Calculus, Larson, 8th ed. Materials: Textbook, calculator, notebook, graphing paper Prerequisite: C or better in Math 148 or 22 or above ACT (Math). I. Course Description:

Entry level Calculus is a first course in differential calculus which furnishes the essential algebra and precalculus content necessary for success in calculus simultaneously while providing formal calculus content. The course reviews techniques for solving equations and graphing functions involving linear, quadratic, higher order polynomials, rational, radical, exponential and logarithmic, and trigonometric expressions, and techniques for solving inequalities. Calculus content studies limits and continuity of functions, the derivative; definition, differentiation formulas, and applications, curve sketching, implicit differentiation and related rates, antiderivatives, and an introduction of the integral. II. Rationale

This is a course in differential calculus designed for Science, Technology, Engineering, and Mathematics (STEM) majors or minors. The course will provide the students with the necessary fundamentals of algebra and precalculus simultaneously while students pursue and learn the concepts and techniques in formal differential calculus. The course will be taught using a graphical, theoretical, and analytic approach to learning calculus. The aim of this course is to efficiently develop students in the use of the language of differential calculus in theory and in applications to the natural sciences engineering and technology. Fundamentally, this course will provide all relevant content, concepts, and techniques prerequisite for Calculus II. III. Competencies

Upon successful completion of this course, students should: A. Understand the concept of limits using a graphical, intuitive,

and analytic ( εδ − definition of a limit) approach. B. Know how to use the appropriate computational and theoretic techniques for evaluating limits. C. Understand the concept of continuity using a graphical, intuitive, and formal definition (limits) approach. D. Understand the concept of the derivative graphically, intuitively, and by formal definition (limits). E. Understand the relationship between local and global extrema, curve structure and the derivative. F. Know how to interpret results from the application of differential calculus to the natural sciences. G. Know how to solve for the derivative implicitly. H. Understand the concept of related rates and its use. I. Understand the concept of the antiderivative. J. Know the geometric significance of the Integral.

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IV. Behavioral Objectives Upon successful completion of this course, students should be able to:

A. Discuss the concept of limits using a graphical, intuitive, and analytic ( εδ − definition of a limit) approach.

B. Evaluate the limits of polynomial, rational, trigonometric, and transcendental functions using computational techniques and theorems. C. Discuss and determine the continuity of various types of functions. D. Use the definition of the derivative to evaluate the derivative of various functions and to verify certain derivative formulas. E. Apply appropriate derivative formulas to evaluate the derivative of various functions. F. Use the derivative to sketch the graph of various functions. G. Apply the derivative to solve various problems in the natural sciences. H. Apply the appropriate method for finding the derivative implicitly. I. Use related rates to solve various problems in applied calculus. J. Use simple antiderivatives and the power rule for evaluating integrals.

V. Course Content

Calculus Topics are numbered. Brackets [ ] indicate essential review material for the associated Calculus Topic. Calculus 1. Limits (*All Functions) verbal, graphical, and analytic definition and existence

[functions and graphing, absolute value inequalities, factoring, simplifying rational expressions, interval notation]

2. Continuity (*All Functions) graphical and analytic criteria [functions, domain and range, combinations, compositions, especially piecewise functions]

3. Derivatives (Definition and Differentiation Formulas for all Functions) [integral and rational exponents, definition of slope and equation of straight line, rational, exponential, hyperbolic, logarithmic, and trigonometric functions including their graphs; including inverse-trigonometric and hyperbolic functions with their graphs and identities]

4. Applications of Derivatives [linear functions, radical functions, rational functions, parallel and perpendicular lines] 5. Curve Sketching (Extrema and Inflection Points, Applications) [solving equations: linear, quadratic, rational, radical, exponential-logarithmic, trigonometric] 6. Implicit Differentiation (Definition and Applications) 7. Related Rates [basic geometry and physics formulas, solving equations] 8. Antiderivative (Definition and Application) 9. The Integral (Introduction: geometric significance, definite, indefinite)

*All Fuctions: Linear, Quadratic, Higher order Polynomial, Rational, Radical, Exponential and Logarithmic, Hyperbolic, Trigonometric, Inverse Trigonometric.

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VI. Course Format

VII. Course Requirements

VIII. Evaluation Process

TESTING: Three Exams and a Final QUIZZES:

HOMEWORK:

ATTENDANCE:

GRADING: IX. GRADING SCALE 90% & above A 80.0-89% B 70-79% C 60-69% D Below 60% F

X. Supplementary Materials Calculus texts in the Library, Historical books prescribed by the instructor XI. Changes to the Syllabus I reserve the right to change the syllabus as necessary to ensure adequate student progress.

XII. ADA Special Service Statement

If you need accommodation in this class related to a disability, please make an appointment to see me as soon as possible.

1

Mathematics and Computer Science Department College of Arts and Sciences Grambling State University

Course Syllabus

Math 154 – Calculus II

CRN # 21023 AY 2007-2008

Semester: Time and Place: Instructor: Office Location: E-mail: Conference Hours: Catalog Course Description: Review of the techniques of differentiation; The Indefinite integral; sigma notation; the definite integral and the fundamental theorem of calculus; Applications of definite integral: the area between two curves; Volumes by disks, washers and cylindrical shells; Length of plane curve; other applications; Integration by the method of substitution; integration of trigonometric, transcendental and inverse functions; Integration by parts; Reduction formula; Integration by partial fractions; Indeterminate forms; Improper integrals; Infinite sequence and series . Prerequisite: A grade of C or better in MATH 153. I. Rationale

This is the second course in Calculus after the students have achieved thorough background in differential calculus. The objective of this course is to teach students the contents of integral calculus and, therefore, prepare them for different situations where they might need to apply the subject material of Integral Calculus. The course demonstrates many applications of Integral Calculus in science, engineering, and business. This course is crucial for STEM majors and is a prerequisite for Calculus III and Differential Equations.

II. Competencies Upon successful completion of this course, students should be able to:

A. Completely review and consolidate different techniques of differentiation for a variety of functions. B. Understand clearly about the importance of the concept of Integration (Anti-derivatives). C. Understand the origins of integration, systematic development of the concepts, and its unique place in

areas of mathematics, science, and engineering. D. Able to differentiate between indefinite and definite integrals. E. Understand the fundamental concepts of summations, Riemann Sums, and definite integral. F. Understand method of substitution to evaluate indefinite and definite integrals. G. Able to evaluate definite integrals using two different methods. H. Understand the Fundamental Theorems of Calculus. I. Understand the Mean-Value Theorem for Integrals. J. Learn different applications of Definite Integrals: such as Area, Volume, and Length of a curve. K. Master techniques of integration: Integration by parts, Trigonometric substitution, and Partial Fractions. L. Understand characteristics and methods of evaluating various indeterminate forms in the studies of limits. M. Understand difference between proper and improper integrals and methods of evaluation of improper integrals. N. Comprehend the properties of infinite sequence and series. O. Understand and apply a variety of tests to find the convergence or divergence of infinite series. P. Understand the significance of Maclaurin and Taylor polynomials and series, their importance in the area

of numerical methods, and applications in scientific and engineering problems. III. Behavioral Objectives

Upon successful completion of this course, students should be able to:

A. Evaluate indefinite integrals by the method of substitution B. Evaluate definite integrals by the method of substitution C. Importance of the sigma notation in evaluating definite integrals

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D. Evaluate definite integrals by finding the area under the curve. E. Find the area between the two curves. F. Find the volume by slicing and cylindrical shell methods. G. Find the length of curves. H. Find the area of a surface of revolution. I. Evaluate integrals using the method of integration by parts. J. Evaluate integrals using the method of trigonometric substitution. K. Evaluate integrals of a rational function by using partial functions. L. Differentiate between various methods to evaluate limits with indeterminate forms. M. Establish correlation between different techniques of evaluating proper and improper integrals. N. Recognize different types of infinite series and choose relevant test that determines the convergence and

divergence of infinite series. O. Recognize the importance of Taylor and Maclaurin series in numerical analysis.

IV. Course Content A. Review of the techniques of differentiation (1 hour)

B. Integration (11 hours)

1. Importance of anti-differentiation or integration – A brief description of Differential Equations 2. Sigma Notation (Summation) 3. The Definite Integral, Area, and Riemann sums 4. Properties of Definite Integrals 5. The Fundamental Theorem of Calculus 6. The Mean-Value Theorem for Integrals and Average 7. Evaluating Definite and Indefinite Integrals by Substitution 8. Exponential and Logarithmic Functions: Integration 9. Inverse Trigonometric Functions: Integration 10. Hyperbolic and Inverse Hyperbolic Functions: Integration

C. Applications of the Definite Integral (4 hours)

1. Area under a Curve 2. Area between two Curves 3. Volumes by Slicing; Disks and Washers 4. Volumes by Cylindrical Shells 5. Length of a Plane Curve 6. Area of a Surface of Revolution 7. An Introduction of the First Order Differential Equations and their Applications

D. Techniques of Integration (10 hours)

1. An overview of Integration Methods 2. Integration by Parts 3. Inverse Trigonometric Functions 4. Trigonometric Integrals 5. Trigonometric Substitution 6. Integrating Rational Functions by Partial Fractions

E. Indeterminate Forms and Improper Integrals: (3 hours)

1. Indeterminate Forms of Type 0/0 and ∞ / ∞ 2. Other Indeterminate Forms ( ∞⋅∞−∞∞ ∞ 0,,1,,0 00 ) 3. Improper Integrals: Infinite Limits 4. Improper Integrals: Infinite Integrands

F. Infinite Series: (6 hours)

1. Properties of Sequences 2. Infinite Series - Convergence and Divergence 3. Convergence Tests

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4. Alternating Series; Conditional Convergence 5. Power Series 6. Maclaurin and Taylor Series

G. Review and Tests (5 hours)

V Learning Activities

Learning activities include regular class lectures, class room discussions, peer group problem solving sessions, regular homework problems, writing exercises, surprise quizzes, and regular tests. Periodic evaluations are provided to help promote mastery of concepts and skills. Students have opportunities to make use of Instructional DVDs available to learn subject material at their own pace. Students will also able to make use of “Eduspace”, powered by Blackboard. It provides comprehensive homework exercises, tutorials, and testing keyed to the textbook by section.

VI Special Course Requirements

A. Prerequisites by Topic:

1. Properties of trigonometric, exponential, logarithmic, hyperbolic, and inverse functions 2. Concepts of limits 3. Partial fractions 4. Elementary knowledge of plane and analytic geometry. 5. Techniques of differentiation 6. Students enrolled in this course must have a grade of “C” or better in Calculus I (Math 153). 7. The textbook is required for this course. Please bring your textbook to class everyday.

B. General Course Regulations/Suggestions:

• All relevant GSU policies and regulations shall apply. • An “I” grade will only be given when extremely adverse and well-documented circumstances arise at

the end of semester. That definitely does not include making up for weak performance during the semester. In particular, the grade that the student had made until getting an “I” will still be included into computing the final grade after a student has completed the work necessary to alter the “I” grade.

• Plagiarism will not be tolerated in any form. As a minimum, students will be given a grade of zero for any quiz or exam in which cheating, fraud, or mis-representation is found. Two exactly similar pages will be treated as an act of plagiarism for both the parties.

• Class participation includes but not limited to coming to class on time, being awake in the class, and not distracting other students from listening to the class lecture, and asking relevant questions. Class discussion will be highly encouraged. Please never hesitate to ask the questions.

• The course requires lot of hard work and additional reading. Students should carefully consider this in planning their other courses and activities. Attendance in all the classes is vitally important since class lectures have a close link with each other.

• Always keep up with the class. There is lot of material to be covered. It is important for us to reach to the last phase of this course because this information is very essential for your future courses.

• It will be advisable to formulate study groups and meet at a designated place consistently during evening hours or weekends to complete the related work on the same day.

• Cell phone in the class room is a big distraction. Therefore, please turn off your phone and do not respond to vibrating mode during the entire class period. Keep your phone inside your bag.

VII. Evaluation Process

A. Methods Students will be evaluated based on their performance in examinations (including comprehensive mid-term test and final examination), quizzes, homework, and class participation. The details are as follows:

Examinations: There will be four major tests (including comprehensive mid-term) and a cumulative final

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examination. None of the tests will be dropped for the lowest score or for any other reason. The schedule for Spring 2008 is as follows:

Test # Duration Date & Day Material Test #1 50 Minutes 2/08/08, Friday 1/14/08 to 2/01/08

Test #2 (Mid Term) 55 Minutes 3/05/08, Wednesday Comprehensive Test #3 50 Minutes 4/09/08, Wednesday 3/07/08 to 4/07/08 Test #4 50 Minutes 4/30/08, Wednesday 4/11/08 to 4/28/08 Final Exam 2 hours TBA Comprehensive (Grad Seniors) Time: TBA Final Exam 2 hours 5/07/08, Wednesday Comprehensive (All other students) Time: 10:30 a.m.-12:30 p.m.

All students are required to take every test as scheduled above. No makeup tests will be given unless arranged for in advance. The makeup test should be arranged within a week since the original date scheduled. The official excuse is required for all the students to take a makeup test. No more than one makeup test per student will be allowed during the semester. Since the examination schedule, for the entire semester, has been provided right on the first day of the beginning of classes, students are advised to schedule all their other activities keeping this schedule in mind. No early final exam will be given. Students will also be required to bring their University Identity Card when they take any test. If you will not able to present your Identity Card you will not be allowed to take the test. The following clause is for students participating in any GSU extra curricula activity. Any student participating in extra curricular activities (example band, football, track, etc. …) must bring the official activity schedule for the Spring 2008 semester on or before the January 31, 2008. Test or assignments may be rescheduled to a mutually convenient date than the above scheduled dates, but permission from the instructor must be sought in advance. If the student neglects to give a prior notification, a score of Zero (0) will be given for that test or assignment. An official excuse for student participation is required to makeup a test or an assignment. Quizzes: There will be many (about 10-15) unannounced quizzes throughout the semester. There will be no makeup for the quizzes. However, one quiz with the lowest score will be dropped. The purpose of the unannounced quizzes is two fold -- to make students come to the class on time and to make students read and understand course material as the course progresses. Quizzes might be given at any time during the class period. If a quiz is given at the beginning of the class period and if ten minutes are allocated for a quiz and a student comes six minutes late to the class, s/he has only 4 minutes to complete the quiz.

Assignments: Homework assignments are extremely important. They can really make the subject material extremely clear and prepare you for tests and quizzes. I will assign the homework daily, however, I will not collect or grade all the assignments I give. I will pickup assignments randomly for grading. If you do your homework assignments regularly and conscientiously you will really benefit from the course a lot. I will able to cover more material in the class and this, in turn, will provide you rewarding experiences.

Attendance: Attendance will be taken every day. The GSU attendance policy will be followed (refer to GSU Student Handbook). It is the responsibility of the student to make up the work he or she missed irrespective of excused or unexcused absentees. The student is always welcome to come and take help from me in my conference hour or any other time mutually convenient.

B. Grading Scale:

Each test will be worth 100 Points, each quiz will be worth 10 points, and each home work (collected) will be worth 20 points. The Mid-semester and Final examinations (both comprehensive) will be worth 200 points each. Rather than grading on a strict percentage basis, I use the following method for determining your grade. At the end of the course, I make a total of all points you received, calculate the percentage points, and make a distribution of this percentage for all the members of this class, from the highest to lowest. Next, I look for a "Natural Break" in the scores and award a letter grade. The philosophy I use is

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that similar scores will receive the same grade. Generally the distribution is as follows:

85.0% & above A 71.0-84.0% B 55.0-70.0% C 40.0-54.0% D Below 40% F VIII. References

A. Textbook

Larson, Hostetler, Edwards; Calculus, Houghton Mifflin; Eighth Edition, 2006

B. Additional References: Anton, Bivens, and Davis Calculus, John Wiley & Sons, Eighth Edition; 2005

Smith and Minton, Calculus: Concepts & Connections, McGraw Hill, 2006

Assurance Statement Grambling State University adheres to all applicable Federal, State, and Local laws, regulations, and guidelines with respect to providing reasonable accommodations for students with disabilities. Students with disabilities should register with the ADA Student Services Coordinator and contact their instructor(s) in a timely manner to arrange for appropriate accommodations. ADA Student Services Center is located in Foster-Johnson Health Center – West Wing (Tel. #: 318-274-3277/3338). If you need accommodations in this class related to a disability, please make an appointment with me as soon as possible. My office location and hours are: Carver Hall 113-C; 11:00 a.m.-12:00 noon R, 2:30-5:30 p.m. TR, and 4:00-5:30 p.m. MWF

WISHING YOU A VERY HAPPY, REWARDING, AND SUCCESSFUL SPRING 2008

PLEASE DO NOT HESITATE FOR ANY HELP YOU NEED FOR THE COURSE DURING ENTIRE SEMESTER AND EVEN AFTERWARDS WHEN YOU USE

CALCULUS IN YOUR OTHER COURSES. I HAVE A STRONG WILL TO TEACH AND MAKE YOU UNDERSTAND THE MATERIAL IN THIS COURSE.

TOGETHER, WE CAN MAKE THINGS EASY AND ENJOYABLE.

1

Mathematics and Computer Science Department College of Arts and Sciences Grambling State University

Course Syllabus

Math 201– Calculus III

AY

Semester: Time and Place: Instructor: E-Mail: Office: Conference Hours: Course Description: This course covers Functions of multi-variables; Limits and Continuity of multi-variables; Partial Derivatives; Differentiability and Chain Rules for Functions of Two Variables; Curves; directional derivatives; normal and tangent lines and planes to surfaces; differentials; Double and triple integrals; Multiple Integrals in Cartesian, cylindrical, and spherical Coordinates; Line and surface integrals; Greene’s, Divergence, and Stokes’s Theorems. Prerequisite: A grade of C or better in MATH 154. I. Rationale

The purpose of this course is to provide additional analytical tools to the students of natural sciences, mathematics, secondary mathematics education, and computer science. The topics learnt in this course are crucial to grasp the subject material of the core courses required by the majors in aforementioned disciplines. The course challenges the students to think critically and analytically. This course is also useful for students who plan to pursue their graduate study in any of these areas.

II. Competencies Upon successful completion of this course students should be able to:

A. Understand the significance of vectors in the study of three dimensional spaces. B. Get preliminary knowledge of the calculus of multi-variables. Students should able to understand the

fundamental concepts of the limit and continuity for functions of two or more variables. C. Understand the importance of partial derivatives in scientific and engineering problems. Students should

be able to evaluate the partial derivatives of functions involving two or more variables. D. Understand the importance of multiple integrals. Students should be able to evaluate double and triple

integrals in Cartesian, cylindrical, and spherical coordinates. E. Understand the definition of gradient, extrema, and differentials. F. Understand the definition of double and triple integrals. G. Understand the definition of line and surface integrals. H. Understand Greene’s, Divergence, and Stokes’s Theorems.

III. Behavior Objectives

Upon successful completion of this course students should be able to:

A. Find the Dot and Cross Product of vectors and also use vectors to find equations for lines and

planes. B. Graph basic multivariable functions in 3-dimensional space and determine the existence of the

limit and continuity of a multivariable function. C. Find Partial Derivatives of multivariable functions. D. Describe curves, their tangents and their normals, in terms of vectors.

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E. Find extrema for multivariable functions. F. Use calculus to describe projectile motion along a curve in 3-dimensional space. G. Use gradients to determine directional derivatives, and normal and tangent lines and

planes to surfaces, and differentials. H. Use double and triple integrals to determine area and volume. I. Use double and triple integrals in Cartesian, cylindrical, and spherical coordinates. J. Evaluate and interpret line and surface integrals K. Apply and discuss Greene’s, Divergence, and Stokes’s Theorems. L. Discuss the significance of multivariable-calculus in science and engineering fields and

compare it with single variable calculus. IV. Course Content

1. Vectors In 3-Dimensional Space • The Dot Product • The Cross Product • Lines • Planes

2. Functions of Two or More Variables

• Graphs • Limits and Continuity • Partial Derivatives • Differentiability and Chain Rules for Functions of Two Variables • Curves

3. Gradients and Extreme Values • Directional Derivatives • Normal and Tangent Lines and Planes • Maxima Minima and Saddle points • Differentials

4. Multiple Integrals: (6 hours) • Double Integrals (Cartesian and Polar Coordinates) • Area and Volume • Triple Integrals (Cartesian Coordinates) • Triple Integrals (Cylindrical and Spherical Coordinates)

5. Line and Surface integrals

• Line Integrals • Green’s Theorem • Surface Integrals • The Divergence Theorem • Stokes’s Theorem

V Learning Activities

Learning activities include regular class lectures, class room discussions, peer group problem solving sessions during class, regular homework problems, writing exercises, and regular tests.

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VI Special Course Requirements

A. Prerequisites by Topic:

1. Properties of trigonometric, exponential, logarithmic, hyperbolic, and inverse functions 2. Concepts of limits 3. Partial fractions 4. Sigma notation and summation of series containing n terms 5. Properties and equations of straight line and all conic sections 6. Techniques of differentiation and integration.

B. General Course Regulations/Suggestions:

• All relevant GSU policies and regulations shall apply. • An “I” grade will only be given when extremely adverse and well-documented circumstances arise at

the end of semester. That definitely does not include making up for weak performance during the semester. In particular, the grade that the student had made until getting an “I” will still be included in computing the final grade after the student has completed the work necessary to alter the “I” grade.

• Plagiarism will not be tolerated in any form. As a minimum, students will be given a grade of zero for any quiz or exam in which cheating, fraud, or mis-representation is found. Two exactly similar pages will be treated as an act of plagiarism for both the parties involved.

• There will be absolutely no opportunity to raise your grade by doing extra credit work. The students will be graded solely on the basis of criteria mentioned below (exams, quizzes, homework, and class participation). Please do not ask for "Extra Credit Work".

• Class participation includes but not limited to coming to class on time, being awake in the class, and not distracting other students from listening to the class lecture, and asking relevant questions. Class discussion will be highly encouraged. Please never hesitate to ask the questions.

• The course requires lot of hard work and additional reading. Students should carefully consider this in planning their other courses and activities. Attendance in all the classes is vitally important since class lectures have a close link with each other. Missing the classes and consistently coming late will hinder in understanding the material of the course.

• It will be advisable to formulate study groups and meet at a designated place consistently during evening hours to complete the related work on the same day.

VII. Evaluation Process

A. Methods Students will be evaluated based on their performance in examinations (including comprehensive mid-term test and final examination), quizzes, homework, and class participation. The details are as follows:

Examinations: There will be four major tests (including comprehensive mid-term) and a cumulative final examination. None of the exams will be dropped for the lowest score or for any other reason. The schedule

All students are required to take every test as scheduled above. No makeup tests will be given unless arranged for in advance. The makeup test should be arranged within a week since the original date scheduled. The official excuse is required for all the students to take a makeup test. No more than one makeup test per student will be allowed during the semester. Assignments: Homework assignments are extremely important. They can really make the subject material extremely clear and prepare you for tests and quizzes. I will assign the homework daily, however, I will not collect or grade all the assignments I give.

4

Attendance: Attendance will be taken every day. The GSU attendance policy will be followed (refer to GSU Student Handbook). It is the responsibility of the student to make up the work he or she missed irrespective of excused or unexcused absentees. The student is always welcome to come and take help from me in my conference hour or any other time mutually convenient. B. Grading Scale: 90% & above A 80-89% B 70-79% C 60-69% D Below 60% F VIII. References

A. Textbook

Larson, Hostetler, Edwards; Calculus, Houghton Mifflin; Eighth Edition, 2006 B. Additional References:

Salas, Hille, and Etgen, Calculus One and Several Variables, John Wiley & Sons, Tenth Edition; 2007 Smith and Minton, Calculus: Concepts & Connections, McGraw Hill, 2006 Anton, Bivens, and Davis Calculus, John Wiley & Sons, Eighth Edition; 2005

For effective study strategies and techniques please refer to http://www.cas.lsu.edu

Assurance Statement Grambling State University adheres to all applicable Federal, State, and Local laws, regulations, and guidelines with respect to providing reasonable accommodations for students with disabilities. Students with disabilities should register with the ADA Student Services Coordinator and contact their instructor(s) in a timely manner to arrange for appropriate accommodations. ADA Student Services Center is located in Foster-Johnson Health Center – West Wing (Tel. #: 318-274-3277/3338). If you need accommodations in this class related to a disability, please make an appointment with me as soon as possible. My office location and hours are: Carver Hall 113-C; 10:00-11:00 a.m. MWF, 11:00 a.m.-12:00 noon Daily, and 4:00-5:00 p.m. TR

WISHING YOU A VERY HAPPY, REWARDING, AND SUCCESSFUL SPRING 2008

PLEASE DO NOT HESITATE FOR ANY HELP YOU NEED FOR THE COURSE DURING ENTIRE SEMESTER AND EVEN AFTERWARDS WHEN YOU USE

CALCULUS IN YOUR OTHER COURSES. TOGETHER, WE CAN MAKE THINGS EASY AND ENJOYABLE.

GRAMBLING STATE UNIVERSITY DEPARTMENT OF MATHEMATICS AND COMPUTER SCIENCE

MATH 309 – 1

LINEAR ALGEBRA

Semester: Time and Place: Instructor: Office: Telephone: Conference Hours: Instructor Email: Textbook: Elementary Linear algebra by Howard Anton and Chris Rorres, 9th edition, Wiley Course Description: The analysis of linear equations and their solutions. To investigate the algebra and geometry of finite-dimensional vector spaces, linear transformations, their corresponding matrix relative to some basis, determinants, the algebra of matrices, some concepts of eigenvalues, eigenvectors and quadratic forms. Prerequisite: A grade of C or better in MATH 154. I. Rationale

This course provides the student with his (her) first experience in axiomatic mathematics, while staying in touch with the computational aspects of the subject. The mere ability to manipulate matrices is no longer adequate. This course affords an excellent opportunity to develop a capability for handling abstract concepts.

II. Competencies

Upon successful completion of this course students should be able to: A. Solve linear systems of equations. B. Use matrix methods in solving linear systems. C. Employ the definition of vector spaces. D. Illustrate the concepts of orthogonality as it relates to the Gram-Schmidt algorithm. E. Demonstrate the use of linear transformations. F. Use eigenvalues and eigenvectors in related applications.

III. Behavior Objectives Upon successful completion of this course students should be able to:

A. Perform determinant, B. Perform matrix operations C. Calculate inverses D. Diagonalized matrices E. Perform operations dealing with vector spaces F. Find orthonormal bases

IV Course Content A. Determinants

B. System of Linear Equations C. Matrices and Matrices Operations D. Intuitive Vector Spaces and subspaces (Vectors in 2-space and 3-space)

E. Vectors spaces in n-space (General) F. Inner products G. Linear Transformations H. Eigenvalues and Eigenvectors I. Diagonalization J. Quadratic Forms

V Learning Activities

Learning activities include: • Regular class lectures • Classroom Discussion • Conference hours • Homework problems • Quizzes • Labs and Projects • Seminar and Presentations • Exams

VI. General Requirements Obviously, every student in this class is assumed to be a mature, responsible, and capable individual who is preparing himself/herself for a successful professional career in science, mathematics, and engineering areas. The following points are simply a statement of some of the behavioral traits expected from a responsible professional.

• 1. Class attendance is a privilege and a duty. Everyone is expected to arrive on time and remain for the entire class period unless he/she requests for, and is granted, permission to leave. Failure to do so is considered an absence.

• 2. Attendance record will be maintained. • 3. An absent student is responsible for finding out and covering the missed work. • 4. No make up tests will be given, unless informed in advance and proper

document is obtained. • 5. An "I" grade will only be given when extremely adverse and well documented

circumstances arise at the end of the semester. That definitely doesn't include making up for weak performance during the semester. In particular, the grade that the student had made until getting an "I" will still be factored into computing the final grade after the student has completed the work necessary to change the "I".

• 6. Cheating [ Copying someone else’s assignment] and Plagiarism [ The practice of taking someone else’s work or ideas and passing them off as one’s own] are serious ethical matters. Any offense will result in a grade of zero for the assignment and additional actions may be taken.

VI. Evaluation Process Methods: Students will be evaluated based on their performance in exams, quizzes, homework, and projects and presentations:

• A. Quizzes: There will be several unannounced quizzes throughout the semester. There will be no makeup for the quizzes. However, a number of quizzes with the lowest scores will be dropped. The purpose of the unannounced quizzes is two fold -- to make students come to the class on time and to make students read and understand course material as the course progresses. Quizzes might be given at any time during the class period

• B. Homework: Homework assignments are extremely important. They can really make the subject material extremely clear and prepare you to understand the concepts and also for

tests and quizzes. I will assign homework daily, however, I will collect and grade randomly chosen problems every week. If you do your homework assignments regularly and conscientiously you will really benefit from the course a lot. I will able to cover more material in the class and this, in turn, will provide you rewarding experiences in your other courses.

• C. Attendance: Attendance will be taken every day. The GSU attendance policy will be followed (refer to GSU Student Handbook pp18-19). It is the responsibility of the student to make up the work he or she missed irrespective of excused or unexcused absentees. Each student is always welcome to come and seek help from me during my conference hour or any other time mutually convenient.

• D. Exams. There will be two (2) tests, one (1) comprehensive midterm and one (1) comprehensive final. [ the lowest test will be dropped]

• E. Projects, Labs and Presentations: There will be many (Individual and Group) research projects and Lab sessions throughout the semesters with power point presentations. There will be a main research project to be presented at the end the semester.

VIII. Grade distribution

• Quizzes and Homework 10% • Lab and Seminar 30% • Tests 10% • Midterm 10% • End of semester Projects 15 % • Attendance 5 % • Final 20 %

IX Grading scale

• A: 90 - 100 EXCELLENT • B: 80 - 89 GOOD • C: 70 - 79 FAIR • D: 60 - 69 MEDIOCRE • F: Below 60 UNACCEPTABLE

X. ADA Policy Gambling State University adheres to all applicable federal, state, and local laws with respect to providing reasonable accommodations for students with disabilities. Students with disabilities of any kind should register with the Student Intervention Resources Center (Special Services Facilitator) ASAP. The phone number is 318. 274- 3338. The student must inform his professor of any disabilities in a timely manner so that accommodations can be made.

XI. Important Dates

Last day to Register or Add Courses Aug. 24 Midterm: Oct. 8 -12 Last day to Drop courses: Oct 26 Homecoming week: Oct. 22 – 27 Last day of Classes: Nov. 28 Final exams: Dec. 3 - 7

GRAMBLING STATE UNIVESITY COLLEGE OF ARTS AND SCIENCES

Protecting the heritage: Cultivating knowledgeable, skilled and compassionate educators and community leaders in "The Place Where Everybody is Somebody." Math 313: Instructor: 3 Semester Hours Phone: Prerequisite(s) A grade of C or better in Math 131. Course Description Studies algebraic structure of the number system; algebra of sets and logic; systems numerations; systems of rational, real and complex numbers; relations and functions; modular systems; probability and statistics; introductory algebra; intuitive geometry. Conceptual Framework Theme and Selected Program Outcomes For This Course Through broad-based curricula, consisting of performance-based assessment, research- based instruction and strategic field experiences, the teacher education and educational leadership programs at Grambling State University, graduates teachers and educational community leaders. Content, professional and pedagogical knowledge, skills and dispositions enable professional educators to help all students reach their full potential. The department recognizes three strands; master of subject matter content, facilitators of learning, and enhancers and nurturers of affective behaviors. The following program outcomes represent what teacher candidates will know and be able to do at the completion of this course as it relates to the conceptual framework.

Discussion of Program Outcomes for Each Strand 1.0 Knowledge: Masters of Subject Matter Content: 1.1 Demonstrate knowledge of content that underlies professional competencies.

(Cognitive) 1.2 Apply knowledge of best pedagogical practices for use in the instructional

Process. 1.3 Describe diverse strategies for interrelating disciplines in the instructional

process. (Cognitive, Psychomotor) 1.4 Identify technology infusion strategies for diverse populations. (Cognitive, Psychomotor) 1.5 Plan effective lesson procedures and demonstrate effective delivery strategies. (Cognitive, Psychomotor) 1.6 Interpret and implement appropriate and multiple measures of assessment.

(Cognitive, Psychomotor)

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1.7 Reflect on the value of practices, knowledge inquiry, and critical thinking behaviors. (Cognitive, Affective) 1.8 Identify personal, professional, curricular values. (Cognitive, Affective)

2.0 Skills: Facilitators of Learning 2.1 Demonstrate the effective delivery of standards-based instruction. (Cognitive, Psychomotor) 2.2 Create and maintain effective management strategies (organization of time, space, resources, and activities.) (Cognitive, Psychomotor) 2.3 Devise activities that promote active involvement, critical/creative thinking arid problem solving skills foe all students. (Cognitive, Psychomotor) 2.4 Demonstrate the use of diverse experiences that incorporate the underlying

philosophy of education that is multicultural across the curriculum. (Cognitive, Psychomotor)

2.5 Perform strategies that accommodate diverse leaner needs by selecting and using appropriate resources. (Cognitive, Psychomotor)

2.6 Apply strategies that accommodate diverse learner needs by selecting and using appropriate resources. (Cognitive, Psychomotor)

2.7 Analyze research that relates to strategies for promoting effective teaching and learning in a global society. (Cognitive)

2.8 Commit to the continuing development of life-long learning in a global society. 2.9 Relate knowledge of educational theories to planning, lesson deliveries, and

classroom management. (Cognitive, Psychomotor) 2.10 Demonstrate an awareness of the social, cultural political, economic, and

comparative context of schools and learners. (Cognitive, Psychomotor, Affective)

2.11 Utilize technology in planning and presenting lessons, research, and professional development. (Cognitive, Psychomotor)

3.0 Dispositions: Enhancers and Nurturers of Affective Behavior

3.1 Display positive self-concept development and respect for others. (Affective) 3.2 Practice a positive attitude and mutual respect for others. (Affective) 3.3 Display sensitivity to divers learning styles and multiple intelligences.

(Affective, Psychomotor) 3.4 Demonstrate sensitivity to the many facets of diversity. (Cognitive, Affective) 3.5 Organize school, family, and community partnerships. (Cognitive,

Psychomotor) 3.6 Influence the development of the healthy mental, physical, and social lifestyles.

(Affective, Psychomotor) 3.7 Display a commitment to the improvement of student learning and school

improvement. (Affective, Psychomotor) 3.8 Display a classroom climate that is conducive to learning. (Affective,

Psychomotor)

Course Goals/Rationale

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The main focus of the course is toward developing reasoning, conjecturing, inventing, and problem solving skills and toward connecting mathematics with other experience. The NCTM curriculum and Evaluation Standards, p.253, states that "Prospective elementary teachers must be taught in a manner similar to how they are taught -- by exploring, conjecturing, reasoning, and so forth." Mathematics content for grades K-8 and pedagogy recommended by the NCTM Standards are emphasized.

Course Objectives and Corresponding Program Outcomes

At the end of the semester, the student should be able to have the following competencies:

A. Use problem solving strategies that include posing questions, organizing information,

drawing diagrams, analyzing situations, graphing and modeling. (LCET – IA1, IA2, IA4, IA5, IIA2, IIB1, IIB2, IIIA1, IIIA2, IIIA3, IIIA4, IIIA5,

IIIB1,IIIB2, IIIB3, IIIC2, IIIC3, IIIC4,) (NCTM - 1,2,6,10) B. Regularly apply inductive deductive reasoning techniques to build convincing

mathematical arguments. (LCET – IA1, IA2, IA4, IA5, IIAl, IIA2, IIB1, IIB2, IIIA1, IIIA2, IIIA3, IIIA4, IIIA5, IIIB1, IIIB2, IIIB3, IIIC2, IIIC4,) (NCTM -2, 6, 7)

C. Use appropriate technology to solve problems and check the reasonableness of their results. (LCET - IA1, IA2, IA4, IA5, IIAl, IIA2, IIB1, IIB2, IIIA1, IIIA2, IIIA3, IIIA4, IIIA5, IIIB1, IIIB2, IIIB3, IIIC2, IIIC3, IIIC4, IIID1-IIID4) (NCTM -2, 3, 10)

D. Apply mathematics to other subjects and to the real world. (LCET - IA1, IA2, IA4, IA5, IIAl, IIA2, IIB1, IIB2, IIIA1, IIIA2, IIIA3, IIIA4, IIIA5, IIIB1, IIIB2, IIIB3, IIIC2, IIIC4) (NCTM -2, 6, 9, 10)

E. Use a variety of methods to solve linear equations. (LCET - IA1, IA2, IA4, IA5, IIAl, IIA2, IIB1, IIB2, IIIA1, IIIA2, IIIA3, IIIA4, IIIA5, IIIB1, IIIB2, IIIB3, IIIC2, IIIC3, IIIC4) (NCTM - 1, 2, 6, 10)

F. Use statistical methods to describe, analyze, evaluate, and make decisions. (LCET - IA1, IA2, IA4, IA5, IIAl, IIA2, IIB1, IIB2, IIIA1, IIIA2, IIIA3, IIIA4, IIIA5, IIIB1, IIIB2, IIIB3, IIIC2, IIIC4, IIID1- IIID4) (NCTM -2, 6, 7)

G. Create experimental and theoretical models of situations involving probabilities. (LCET - IA1, IA2, IA4, IA5, IIAl, IIA2, IIB1, IIB2, IIIA1, IIIA2, IIIA3, IIIA4, IIIA5, IIIB1, IIIB2, IIIB3, IIIC2, IIIC4, IIID1- IIID4) (NCTM -2, 6, 7)

H. Use geometry in solving problems.

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(LCET - IA1, IA2, IA4, IA5, IIAl, IIA2, IIB1, IIB2, IIIA1, IIIA2, IIIA3, IIIA4, IIIA5, IIIB1, IIIB2, IIIB3, IIIC2, IIIC4, IIID1- IIID4) (NCTM -2, 6, 9, 10)

Proposed Resources and Materials Primary Textbook: Bilistein, R., Libeskind, S. and Lott, LW., A Problem Solving Approach to Mathematics for Elementary Teachers (2001), (7th ed.) Addison Wesley Longman.

Supplementary Textbooks: Billstein, It., Problem Solving Approach to Mathematics for Elementary School Teachers (6th ed.) Addison Wesley Longman.

Additional Resources: 1. Smarthinking. corn 2. Student Solution Manual 3. A Problem Solving Approach to Mathematics for Elementary School Teachers

Videotapes. 4. InterAct Math CD Tutorial software.

Course Requirements as Related to Course Objectives and their Corresponding Program Outcomes

• Consistent with university policy all students are expected to attend (regularly and punctually) ALL classes in which they are enrolled.

• It is the student's responsibility to acquire the prescribed text and any other

materials required by instructor.

Materials: Notebook: Graphing Paper and Calculator

• All written work must be handed in on time.

Technology Component

Technology to be used: Computer, scientific calculator, graphing calculator, SMARTHINKIITNCi.com (web tutorial), Internet.

Student Evaluation

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Unit Exams, Quizzes, Projects, Assignments, Homework, Attendance..........40 % Mid-term Examination.....................................................................................20% Final Examination............................................................................................40% TOTAL ..........................................................................................................100% Grading Scale: A = 90 -100% B = 80-89% C = 70-79% D = 60-69% F = 0-59% ***Grambling State University considers cheating of any form on a quiz, examination or assignment to be a very serious offense. Any student not adhering to the code of honor policy will be subject to likely consequences of censure, disciplinary probation, suspension, and/or dismissal form the university. Changes to the Syllabus: I reserve the right to change the syllabus as necessary to ensure adequate student progress. Contesting a Grade or other Concern: If you have nay concerns(s)/problem(s) regarding any aspect of the course or the instructor, please discuss it FIRST with the instructor AND THEN with the Dept. Head, Dr. Brett Sims, Tel. 274-6177 if necessary. The departmental form designed for this purpose should be used. Assurance Statement Grambling State University adheres to all applicable federal, state, and local laws, regulations, and guidelines with respect to providing reasonable accommodations for students with disabilities. Students with disabilities should register with the Student Intervention Resource center (Special Services Facilitator). Course Content

I. Geometry 1. Identify, describe, compare, and clarify geometric figures. 2. Predict the results of combining, subdividing and changing shapes. 3. Represent and solve problems using geometric models. 4. Apply geometric properties and relationships. II. Behavioral Objectives

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Students must show proficiency in the following skills before exiting Math 131

Modem Math for Elementary Teachers. A. Use problem solving strategies that included posing questions, organizing

information, drawing diagrams, analyzing situations, graphing, and model. B. Regularly apply inductive and deductive reasoning techniques to build convincing

mathematical arguments. C. Use appropriate technology to solve problems and check the reasonableness of their

results. D. Apply mathematics to other subjects and to the real world. E. Use a variety of methods to solve linear equations and inequalities. F. Use statistical methods to describe, analyze, evaluate and make decisions. G. Create experimental and theoretical models of situations involving probabilities. H. Use geometry in solving problems III. Course Content Chapter 1. Introduction to Problem Solving (3 instructional hours) 1.0 Preliminary Problem

1.1 Mathematical Patterns 1.1.1 Explorations with patterns 1.1.2 Inductive reasoning

1.1.3 Arithmetic and geometric sequences 1.1.4 Work ongoing assessment 1.1, #’s 8,2, 3, 10, 16, 18, 25. 1.2 Problem Solving 1.2.1 Four-step problem-solving process 1.2.2 Strategies for problem solving 1.2.3 Work ongoing assessment 1.2, #’s 1,2(b), 8, 10, 13, 17, 18, 14, 15 1.3 Using calculators as a problem solving tool 1.3.1 Special features 1.3.2 Work ongoing assessment #’s 1.3 1.3.3 Solution to Preliminary problem Test- Chapter I Chapter 2- Sets, Functions, and Logic (3 Instructional Hours) 2.0 Preliminary Problem 2.1 Describing Sets

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2.1.1 Set definitions and notation 2.1.2 Equal and equivalent sets; one-to-one correspondence 2.1.3 Work Ongoing assessment 2.1 #’s 1,2, 3,5,6, 14, 16 2.2 Relationships and operation sets 2.2.1 Set union and intersection 2.2.2 Set difference and complement 2.2.3 Properties of set operations 2.2.4 Work ongoing assessment 2.2 #’s 1,2,4,5,6,9,12,14,18,21, 26, 29, 30 2.3 Functions 2.3.1 Functions 2.3.2 Range and domain 2.3.3 Applications 2.3.4 Work ongoing assessment 2.3 #`s 1,2,4, 5(b, e), 9, 12, 13, 14, 24, 26, 27 2.4 Logic: An Introduction 2.4.1 Statement 2.4.2 Negation 2.4.3 Compound statement conjunction 2.4.4 Disjunction 2.4.5 Conditional statements 2.4.6 Valid reasoning 2.4.7 Work ongoing assessment 2.4 #’s 2, 4, 6, 7, 9, 11, 13, 15, 18, 19 2.5 Solution to preliminary problem p.101 Test Chapter 2 Chapter 3 - Numeration Systems and Whole Numbers (3 Instructional hours) 3. 0 Preliminary problem 3.1 Numeration Systems 3.1.1 Properties of numeration systems give basic structure to the system 3.1.1.1 Place Value property 3.1.1.2 Additive Property 3.1.1.3 Subtractive property 3.1.1.4 Multiplicative property 3.1.2 Work ongoing assessment 3.1 #’s 1,2, 4,5,7, 8, 10,21,23,25,26 3.2 Addition and subtraction of whole numbers 3.2.1 Work ongoing assessment 3.2#'s 6, 7, 8, 9, 10 3.3 Multiplication and division of whole numbers

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3.3.1 Work ongoing assessment 3.3#’s 2, 3, 5, 6, 8, 10, 12, 14, 16, 18, 23 3.4 Algorithms for whole number addition and subtraction 3.4.1 Work ongoing assessment 3.4 #’s 2,4,6 8, 10, 13 15, 18, 20, 21, 22, 3.5 Algorithms for whole number multiplication and division 3.5.1 Work ongoing assessment 3.5 #’s 1,3,5. 6, 8, 10, 12, 16, 34(a, c, e, g) 3.6 Solution to the preliminary problem, p. 169 Chapter 4- Integers and number theory (4 Instructional Hours) 4.0 Preliminary problems 4.1 Integers and the operations of addition and subtraction 4.1.1 Work ongoing assessment 4.1 #’3 3,4, 6, (d), 13, 18, 20, 21,23,26, 34. 4.2 Multiplication and Division of Integers 4.2.1 Work ongoing assessment 4.2 #’s 4, 6, 7, 16, 18,20,26 (a, e) 4.3 Divisibility 4.3.1 Divisibility/theorems 4.3.2 Divisibility tests 4.3.3 Work ongoing assessment 4.3 #’s 2(a, e), 3, 5, (a, c), 15, (a, c,), 18 4.4 Prime and composite numbers 4.4.1 Primes 4.4.2 Fundamental theorem of arithmetic 4.4.3 Work ongoing assessment 4.4, #’3 1,3, 12, 15,20,34 4.5 Greatest Common Divisor and lease common multiple 4.5.1 Greatest common divisor 4.5.2 Euclidean algorithm 4.5.3 Work ongoing assessment 4.5 #’s 1, 2, 3,4, 15 (a, c, e, g) 4.6 Clock and modular arithmetic 4.6.1 Work ongoing assessment 4.6 #’s 3 (a, c, e, g,), 4(a, c, e, g), 5, 6, 9, 10, 12, 13 (a, c) 4.7 Solution to preliminary problem Test Chapter 4 (Instructional Hours) Chapter 5- Rational Numbers and Fractions (3 Instructional Hours) 5.0 Preliminary problem 5.1 Set of Rational numbers

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5.1.1 Work ongoing assessment 5.1 #’s 5, 6,7, 10, 11, 12,20,23, 24, 15, 32 5.2 Addition and subtraction of rational numbers 5.1.2 Work ongoing assessment 5.2 #’s 1 (a, c, e, g), 2(a, c,), 3(a, c), 16, 18, 21, 33 5.3 Multiplication and division of rational numbers 5.3.1 Work ongoing assessment 5.3 #’3 2,4, (a, c), 3(a, c, e), 5(a, c), 6(a, c, e, g) 5.4 Solution to the preliminary problem pg. 288 Chapter 6- Exponents and Decimals (3 Instructional Hours) 6.0 Preliminary problem 6.1 Integer exponents and decimals 6.1.1 Work ongoing assessment 6.1 #’s 1, 2(c, d), 4, 6,20, 22(a, c) 6.2 Operations on decimals 6.2.1 Work ongoing assessment 6.2 #’s 8, 13, 15, 18 6.3 Real Numbers 6.3.1 Work ongoing assessment 6.3 #’s 7, 10, 16, 18(a, b), 19, 22, 25(a, b), 50, 48, 49 6.4 Solution to the preliminary problem pg. 333 Test - Chapter 6 Chapter 7 - Equations and Inequalities (4 Instructional Hours)

7.0 Preliminary problem 7.1 Algebraic thinking

7.1.1 a. Work ongoing assessment 7.1 #’s 1((b), c, d, a,), 2(2, 5, 7(a, b), 8, 6(a-K), 10(e), 11 (a-f)

7.2 Word Problems 7.2.1 Workongoingassessment7.2#’s 1,3, 5,8, 10, 12,16,18 7.3 Lines in a Cartesian coordinate system 7.4 Ratio and Proportion 7.4.1 Work, ongoing assessment 7.4 #’s 2, 4, 6, 8, 10, 12, 16, 19 7.4 Percents 7.4.1 Work ongoing assessment 7.5 #’s 1(b, c, g, L) 2, 5, 6, 10, 12, 16, 18, 20, 22, 29, 36 7.5 Solution to the preliminary problem pg. 405 Chapter 8 - Probability (3 Instructional Hours)

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8.1 How probabilities are determined 8.1.1 Determining probabilities 8.1.2 Mutually exclusive, complementary and non-mutually exclusive events 8.1.3 Properties of probabilities 8.1.4 Work ongoing assessment 8.1 #’s 2,3,4,5,7,8, 9(a, c, e, g), 11, 13(a, c, e, g), 15, 16,21,20 Chapter 9- Statistics: An introduction (3 Instructional Hours) 9.1 Descriptive Statistics 9.1.1 Pictographs 9.1.2 Line plots 9.1.3 Stem and leaf plots 9.1.4 Frequency tables 9.1.5 Histograms 9.1.6 Bar graphs 9.1.7 Circle graphs 9.1.8 Box plots 9.1.9 Work ongoing assessment 9.1 #’s 2, 4, 5 9.2 Measures of central tendency 9.2.1 The mean 9.2.2 The median 9.2.3 The mode 9.2.4 Measures of variation - variance and standard deviation 9.2.5 Work ongoing assessment 9.2#’s l(a, c. e), 3, 5, 8, 14, 20

Test -Chapter 9 Chapter 10 - Introductory Geometry (4 Instructional Hours) 10.1 Basic geometric notions 10.1.1 Points, lines, planes 10.1.2 Collineax and coplanar points 10.1.3 Concurrent and intersecting lines, skew lines 10.1.4 Parallel planes 10.1.5 Space 10.1.6 Angles 10.1.7 Work ongoing assessment l0.1#’s 2(a, b, e), 6 10.2 Plane figures 10.2.1 Polygonal curves 10.2.2 Polygons 10.2.3 Triangles, quadrilaterals, circles 10.2.4 Work ongoing assessment 10.2 #’s 1,4, 7 10.3 Linear measure

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10.3.1 The English system 10.3.2 The metric system 10.3.3 Distance 10.3.4 Work ongoing assessment 10.3 #’s 2, 12 10.4 Theorems involving angles 10.4.1 Supplements and complements of the same angle 10.4.2 Vertical angles 10.4.3 Corresponding and alternate interior angles 10.4.4 Sum of measures of angles of a triangle 10.4.5 Work ongoing assessment 10.4 #’s 3, 7, 6a, 8, l8a 10.5 Three -dimensional figures 10.5.1 Polyhedrons 10.5.2 Prisms, pyramids, regular polyhedral, cylinders, cones, and spheres 10.5.3 Work ongoing assessment 10.5 #’s 4 (a, b), 5 Test - Chapter 10 IV. Learning Activities

1. Classroom lectures/discussions/activities 2. In-class assignment 3. Daily assignment 4. Periodic testing 5. Peer and instructor tutoring

Course Format, Reflection Process and Teaching Strategies Used in this Course

This course will be taught using lecture, group discussion, the scientific and

Graphing calculator. Students are encouraged to view videotapes in the Curriculum Resource Center. The student can use the internet and access SMARTHINKING which is an online tutorial in math.

Technology Infused into this Course:

Technology to be used includes:

1.The scientific calculator 2.The graphing calculator 3.The Internet/computer 4.Geometer's sketchpad 5.InterAct Math CD Tutorial software

6. SMARTHINKING

REFERENCES:

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Troutman, A. and Lichtenburg, B. (1995). Mathematics: A Good Beginning. New York,

N.Y.: Brooks/Cole.

Lindquist, M. (1992). Geometry in the Middle Grades: addenda series K-6. Resting, VA.: National Council of Teachers of Mathematics.

Usiskin, F. (1991). Resolving the Continuing Dilemmas in School Geometry. Glenview Illinois: Scott-Foresman.

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MODERN MATHEMATICS FOR ELEMENTARY TEACHERS Mathematical Enrichment Activities Conference Instructor Reference # Hours Class Hour Days Class Location Mr. Eugene Taylor Instructor MWF: 11-12 pm; 6 – 8:50 pm Wednesdays CH 279 MWF 2 – 4 pm; FRI 9 – 10 am NOTE: All enrichment activities and content assignments must be turned in on the day of final exam in a portfolio form. DAY1 I. Introduction A. Name B. Family C. Educational Background D. Synopsis of Why you are in the teaching profession E. Hobbies and Interests II. Read Assignment/Activities Outline III. DiscussionlQuestions Pertinent to Assignment of Activities IV. Complete Survey Poll for Technology A. PowerPoint B. EXCEL (etal) REVIEW OF ASSIGNMENTS V. Long Term Assignments A. Presentation - PowerPoint 1. PowerPoint of Content presented by mid-term and semester as a review during mid-term and semester test week 2. Submit hardcopy and diskette B. Research 1. Find ten mathematical manipulatives a. Incorporate use of manipulatives into mid-term presentation b. Incorporate manipulatives into semester presentation 2. Find ten evaluation instruments in education a. Incorporate use of evaluation instruments into mid-term presentation b. Incorporate use of evaluation instrument into semester presentation 3. Find ten research-based teaching strategies in education a. Incorporate research-based teaching strategies into presentation for mid-term presentation

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b. Incorporate research-based strategies into presentation for semester VI. Use EXCEL in a presentation pertinent to probability statistics and basic trgonometry A. Submit hardcopy B. Submit Diskette - Ala-Mode *Complete simulation (Trig-Alamode) Compute central tendencies using EXCEL (Classroom-group activity) *Skittles or jellybeans will be needed to complete this activity mid-term and semester activity VII. Construct a simulation A. Submit hardcopy B. Submit Diskette VIII. Selection of groups for presentation (mid-term and semester) IX. Quiz X. Complete Leaps & Bounds - Understanding the X, Y, Z Generation Note: Presentation must be presented via Bloom's Taxonomy

MATH 320 –Selected topics in Mathematics

Semester: Time and Place: Instructor: Office: E-mail: Conference Hours: Course Description: Sets, Relations, mappings/functions, order, well-ordering; Peano Axioms, Integers, Fundamental Algebraic structures.Metric spaces; Continuity and separation axioms; topological spaces; Bases and neighborhoods; Continuous mapping and homomorphism; Product spaces; Compactness; and Connectedness . Homotopy, Covering spaces, Fundamental group. Plane and space curves, arc length, curvature, Elementary theory of surfaces. Prerequisite: A grade of C or better in Math 201. (Formerly Math 310)

I. Rationale: The course is intended to introduce students to some concepts and language of algebra, topology and geometry, with copious examples including those from the courses already taken by the students. It starts with fundamental concepts in Algebra which are necessary to understand other areas of mathematics.Then

comes some concepts of Topology, generally regarded as a study of continuity, which generalizes notions associated with the study of the real line as well as provides ways of classifying geometric objects into sets containing ‘topologically Equivalent’ objects. In analogy to the notions of similarity or congruence of triangles that students are familiar with from Euclidean geometry. Finally, the course interprets notions familiar to the students from calculus, e.g. curves, surfaces, tangent and normal curves in the language of differential geometry.

II. Competencies On completion of this course students should be able to

A Understand some interconnections between algebra, topology and geometry, B Upgrade their knowledge of mathematics, and have better preparation to Further their mathematics education at graduate level, C develops the ability to comprehend and use abstract concepts.

III. Behavior Objectives

A. To enable students to understand some interconnections between Algebra, Topology and geometry.

B. To provide a grounding for further study in several areas of mathematics and Applications.

D. To improve students' powers of abstraction, problem-solving and visualization

IV. Course Content:

1. ALGEBRA

* Sets, Operations on set

* Relations, Equivalence relations. * Mappings/functions, * Order, partial, total order.,well-ordering, Zorn’s lemma

* Peano axioms, integers. * Groups rings fields.

2. TOPOLOGY

* Metric spaces , and General toplogical space

* Open, closed sets, basis, relative topology, Types of topological spaces * Connectedness * Compactness and sequential compactness. One-point compactification. * Products of topological spaces.

* Introduction to basic ideas in algebraic topology---homotopy, covering spaces,

* Computation of fundamental group of various spaces,e.g the n-sphere. Torus,

* Introduction to sinplical complexes and homology.

3 DIFFERENTIAL GEOMETRY

• Plane and space curves.

• Arc length, curvature,

• Elementary theory of surfaces

• Analytic Representations,

• Normal, tangent planes

V. Learning Activities

Learning activities include class lectures, and homework assignments and discussions.

VI. Special Course Requirements

A. Regular and punctual class attendance is expected of each student. The student is responsible for understanding and adhering to course requirements and meeting schedule deadlines.

B. The students are expected to participate in the discussion of material from the textbook.

C. The students are expected to complete the assignments individually. A student may be called upon to present the solution on an assignment to the class.

VII. Evaluation Process:

A. Students will be evaluated based on their performance in examinations, homework assignments. There will be two midterm exams and final exam. Final grades will be based on weekly assigned homework (20%), two midterm exams (25% each) and a final exam (30%).

VIII. References

Textbooks

A. O. Kuku—Abstract algebra Ibadan University Press. 199 J. R. Munkers. Topology, Prentice Hall, 2000.

If you need accommodations in this class/setting/facility related to a disability, please make an appointment to see me as soon as possible.

GRAMBLING STATE UNIVERSITY DEPARTMENT OF MATHEMATICS AND COMPUTER SCIENCE

MATH 323

MODERN ALGEBRA II

Semester: Fall 2009 Time and Place: Instructor: Office: Telephone: Conference Hours:

Instructor Email: Textbook: Abstract algebra by A.O.Kuku Ibadan University Press; Galois theory by I Stewart; Chapman and Hall Course Description: Isomorphism theorems in group theory; Sylow theorems, Direct product of groups; , Ideals and quotient rings; polynomials over rings, prime and maximal ideals ;Principal idea domains and Euclidean domains; Modules, submodules, quotient modules, isomorphism theorems for modules; modules over principal ideal domains; extension fields- algebraic extensions, geometric constructions, finite fields, introduction to Galois theory. Prerequisite: A grade of C or better in MATH 321 or consent of the department.

I. Rationale This is the second part of a sequence of two courses that introduce students to various aspects of modern algebra. The course also provides the necessary background for advanced mathematics at the graduate level.

II. Competencies

Upon completion students should be able to: understand isomorphism and Sylow theorems and their applications,;underatand modules as a generalizations of the notions of vector spaces and abelian groups; understand how to handle and compute field extensions and Galois groups

III. Behavior Objectives

Upon completion students should be able to: classify low order groups. perform operation on rings and modules know how to construct fields extensions asd construct Galois groups

IV Course Content

• Isomorphism theorems in groups • Sylow theorems • Direct product of groups • Ideals and quotient rings, • Principal ideal and Euclidean domains • Modules, submodules, quotient modules • Modules over principal ideal domains

• Algebraic and transcendental Extensions of fields, • Introduction to Galois theory.

V Learning Activities Learning activities include:

• Regular class lectures • Classroom Discussion • Conference hours • Homework problems • Exams

VI. General Requirements Obviously, every student in this class is assumed to be a mature, responsible, and capable individual who is preparing himself/herself for a successful professional career in science, mathematics, and engineering areas. The following points are simply a statement of some of the behavioral traits expected from a responsible professional.

• 1. Class attendance is a privilege and a duty. Everyone is expected to arrive on time and remain for the entire class period unless he/she requests for, and is granted, permission to leave. Failure to do so is considered an absence.

• 2. Attendance record will be maintained. • 3. An absent student is responsible for finding out and covering the missed work. • 4. No make up tests will be given, unless informed in advance and proper document is

obtained. • 5. An "I" grade will only be given when extremely adverse and well documented

circumstances arise at the end of the semester. That definitely doesn't include making up for weak performance during the semester. In particular, the grade that the student had made until getting an "I" will still be factored into computing the final grade after the student has completed the work necessary to change the "I".

• 6. Cheating [ Copying someone else’s assignment] and Plagiarism [ The practice of taking someone else’s work or ideas and passing them off as one’s own] are serious

ethical matters. Any offense will result in a grade of zero for the assignment and additional actions may be taken.

VI. Examinations, Grading and Course evaluations. There will be two midterm examinations and a final examination. Final grades will be based on weekly assigned homework (20%0; two midterm examinations(each 25%) and a final exam (30%) Submission of homework assignments is mandatory.

VII ADA Policy Gambling State University adheres to all applicable federal, state, and local laws with respect to providing reasonable accommodations for students with disabilities. Students with disabilities of any kind should register with the Student Intervention Resources Center (Special Services Facilitator) ASAP. The phone number is 318. 274- 3338. The student must inform his professor of any disabilities in a timely manner so that accommodations ccan be made.

MATH 345 Introduction to Topology

Semester: Time and Place: Instructor: Office: Conference Hours: ; Others by Appointment Only Course Description: Introductory concepts; Metric spaces; Continuity and separation axioms; topological spaces; Bases and neighborhoods; Continuous mapping and homomorphism; Product spaces; Hausdorff Spaces; Compactness; and Connectedness with applications to analysis. Prerequisite: A grade of C or better in Math 201. (Formerly Math 310)

I. Rationale: Topology, an invention of this century, is the study of the geometric and analytic properties of sets of points. Take an interval on the line. It may be open, closed, half-open, bounded, or unbounded. All these properties (except half-open) extend to more general sets (on the line or in other spaces) which it is the business of topology to investigate. How can we distinguish between sets that fall naturally into several pieces and those which do not? This module will tell. Another idea is that of distance in space. This generalizes to distance between functions, which leads to efficient proofs of many, apparently unrelated results.

II. Competencies on completion of this module, students should be able to:

A. Recall and discuss the basic definitions and theorems of point-set topology accurately B. Write out proofs involving topological spaces, “open and closed-ness”, continuity,

connectedness, compact spaces, metric spaces and sequences. C. Write out proofs using definitions, simpler theorems, and propositions D. Apply their knowledge to examples of specific topological and metric spaces.

III. Behavior Objectives

A. Students will be able to discuss basic concepts of point set topology; B. To reinforce basic concepts of analysis;

C. To provide a grounding for functional analysis, topology and differential geometry; D. To improve students' powers of abstraction, problem-solving and visualization

IV. Course Content:

1. Abstract topological spaces -definition and examples, subspace topology.

2. Connectedness -connected components -characterization of open sets in the real line.

3. Neighborhoods, closed sets, closure, interior.

4. Continuous functions: definition and various criteria, homeomorphisms.

5. Continuity and connectedness. The real line not homeomorphic to higher-dimensional spaces.

6. The Cantor space; space-filling curves.

7. Metric spaces. Equivalence. Sequences. Continuity in metric spaces.

8. Completion of a metric space.

9. Contraction Mapping theorem. Picard's Theorem. Implicit function theorem.

10. Hausdorff spaces and normal spaces.

11. Compactness and sequential compactness. Characterization of compact sets in Rn. Ascoli's theorem on compact sets in C(X). One-point compactification.

12. Nets (or filters) in a topological space. Continuity properties in terms of nets. Weak

topologies. Examples to show sequences are not always adequate. 13. Characterization of compactness in terms of convergence

14. Products of topological spaces. Tychonoffs theorem for finite and arbitrary products.

15. Topological Groups

V. Learning Activities

Learning activities include class lectures, and hands-on experience assignments

VI. Special Course Requirements

A. Regular and punctual class attendance is expected of each student. The student is responsible for understanding and adhering to course requirements and meeting schedule deadlines.

B. The students are expected to participate in the discussion of material from the textbook.

C. The students are expected to complete the assignments individually. A student may be called upon to present the solution on an assignment to the class.

VII. Evaluation Process:

A. Students will be evaluated based on their performance on examinations, assignments, and pop quizzes. Four tests 60% Comprehensive Final 20% Computer Lab Assignments and Quizzes

Four tests 60% Comprehensive Final 20% Computer Lab Assignments and Quizzes

20%

B. Grading scale

~ Percentile Grade: 90 -100 A 80-89 B 70-79 C 60-69 D 0-59 F

VIII. References

A. Textbook

Carlos R. Borges,ElementaryTopologyand Applications,World ScientificPublicationCo., 2000.

Dennis Roseman, ElementaryTopology, Prentice Hall, 1999.

B. Additional References

Seymour Lipschutz, General Topology, Schaum's Outline Series, McGraw-Hili Book Company.

If you need accommodations in this class/setting/facility related to a disability, please make an appointment to see me as soon as possible.

GRAMBLING STATE UNIVERSITY DEPARTMENT OF MATHEMATICS AND COMPUTER SCIENCE

MATH 418 – 2

INTRODUCTION TO THEORY OF NUMBERS

I Course Information Semester: Time and Place: Instructor: Office: Telephone: Conference Hours:

Instructor Email:

II Textbook Required Textbook: Elementary Number Theory by Gareth A. Jones and J. Mary Jones, Springer. Suggested Textbook: A Friendly Introduction to Number Theory by Joseph Silverman. III Course (Catalog) Description: Examines divisibility of Integers; congruence; quadratic residues; distribution of prime numbers; continued fractions; and theory of ideals . Prerequisite: A grade of C or better in MATH 153 or consent of the department Head. IV Course Content

• Divisibility • Prime Numbers • Congruence • Distributions of Primes • Quadratic Residues • Arithmetic Functions • Continued Fractions • Sum of Squares • Applications in Cryptography and Computer Science

V Learning Activities Learning activities include:

• Regular class lectures • Classroom Discussion • Conference hours • Homework problems • Projects • Seminar and Presentations • Exams

VI. General Requirements Obviously, every student in this class is assumed to be a mature, responsible, and capable individual who is preparing himself/herself for a successful professional career in science, mathematics, and engineering areas. The following points are simply a statement of some of the behavioral traits expected from a responsible professional.

• 1. Class attendance is a privilege and a duty. Everyone is expected to arrive on time and

remain for the entire class period unless he/she requests for, and is granted, permission to leave. Failure to do so is considered an absence.

• 2. Attendance record will be maintained. • 3. An absent student is responsible for finding out and covering the missed work. • 4. No make up tests will be given, unless informed in advance and proper document is

obtained. • 5. An "I" grade will only be given when extremely adverse and well documented

circumstances arise at the end of the semester. That definitely doesn't include making up for weak performance during the semester. In particular, the grade that the student had made until getting an "I" will still be factored into computing the final grade after the student has completed the work necessary to change the "I".

• 6. Cheating [ Copying someone else’s assignment] and Plagiarism [ The practice of taking someone else’s work or ideas and passing them off as one’s own] are serious

ethical matters. Any offense will result in a grade of zero for the assignment and additional actions may be taken.

VI. Evaluation Process Methods: Students will be evaluated based on their performance in exams, homework, and projects and seminar presentations:

• B. Homework: Homework assignments are extremely important. They can really make the subject material extremely clear and prepare you to understand the concepts and also for tests and quizzes. I will assign homework daily, however, I will collect and grade problems every week. If you do your homework assignments regularly and conscientiously you will really benefit from the course a lot. I will able to cover more material in the class and this, in turn, will provide you rewarding experiences in your other courses.

• C. Attendance: Attendance will be taken every day. The GSU attendance policy will be followed (refer to GSU Student Handbook pp18-19). It is the responsibility of the student to make up the work he or she missed irrespective of excused or unexcused absentees. Each student is always welcome to come and seek help from me during my conference hour or any other time mutually convenient.

• D. Exams. There will be one (1) comprehensive midterm and one (1) comprehensive final. • E. Projects, and Presentations: There will be many (Individual and Group) research projects

throughout the semesters with power point presentations. There will be a main research project to be presented at the end the semester.

VIII. Grade distribution

• Weekly homework or Presentations 40% • Midterm 20% • End of semester Projects 20 % • Final 20 %

IX. Grading scale

• A: 90 - 100 EXCELLENT • B: 80 - 89 GOOD • C: 70 - 79 FAIR • D: 60 - 69 MEDIOCRE • F: Below 60 UNACCEPTABLE

X. ADA Policy

Gambling State University adheres to all applicable federal, state, and local laws with respect to providing reasonable accommodations for students with disabilities. Students with disabilities of any kind should register with the Student Intervention Resources Center (Special Services Facilitator) ASAP. The phone number is 318. 274- 3338. The student must inform his professor of any disabilities in a timely manner so that accommodations can be made.

XI. Important Dates

• Last day to Register or Add Courses Jan. 18 • Mardi Gras Holidays: Feb. 4 - 6 • Midterm: Mar. 3 - 7 • Last day to Drop courses: Mar. 14 • Spring Break : Mar. 15 - 24 • Last day of Classes: Apr. 30 • Final exams: May 5 - 9