LADOKE AKINTOLA UNIVERSITY OF TECHNOLOGY, OGBOMOSO.

DEPARTMENT OF PURE AND APPLIED MATHEMATICS

MATHEMATICSFACULTY OF PURE AND APPLIED SCIENCES

STUDENT HANDBOOK

LADOKE AKINTOLA UNIVERSITY OF TECHNOLOGY,

PMB 4000, OGBOMOSO

DEPARTMENT OF PURE AND APPLIED MATHEMATICS

FACULTY OF PURE AND APPLIED SCIENCES

STUDENTS’ INFORMATION HANDBOOK

SEPTEMBER, 2012

TABLE OF CONTENTS

Front Cover ……………………………………………………………………..iTable of Contents…………………………………………………………….....iiThe Viusitors…………………………………………………………………...iii

THE VISITORSExecutive Governor of Oyo State

SENATOR ISIAKA ABIOLA AJIMOBI

Executive Governor of Osun StateMr. RAUF ADESOJI AREGBESOLA

LIST OF PRINCIPAL OFFICERS OF THE UNIVERISTY

CHANCELLORHON. ASIWAJU AHMED TINUBU

Ag. VICE CHANCELLORProf. Adeniyi Sulaiman Gbadegesin

DEPUTY VICE-CHANCELLOR Prof. T. A. Adebayo

THE UNIVERSITY REGISTRARMR. J. A. AGBOOLA

Ag. UNIVERSITY BURSARMr. A. B. C. Olagunju

THE UNIVERSITY LIBERIAN Mr. I. O. AJALA

STAFF LIST

Academic Staff

Ag. HeadDr. S. O. AdewaleB. Tech, M. Tech, Ph.D, (Ogbomoso) Reader

Prof. (Mrs.) F. O. AkinpeluB.Sc. (Zaria), M. Sc., Ph.D. (Ilorin) Professor

Prof. A. T. OladipoB. Sc., M. Sc., Ph.D (Ilorin) Professor

Dr. A. W. Ogunsola MAN, NMSB. Tech. M. Tech. (Ogbomoso), Ph.D. (Ogbomoso) Reader

Dr. (Mrs.) T. O. OluyoB. Sc. (Ilorin), M. Tech., Ph.D. (Ogbomoso) Senior Lecturer

Dr. S. OluyemiB. Sc. (Lagos), M. Sc. (Ibadan), Ph.D. (Ogbomoso) Senior Lecturer

Dr. O. A. AjalaB. Tech. M. Tech. Ph.D. (Ogbomoso) Senior Lecturer

Mr. O. A. AdepojuB. Tech. M. Tech. (Ogbomoso) Lecturer II

Mr. S. OlaniyiB. Tech. (Ogbomoso), M. Sc., (Ibadan) Assistant Lecturer

Administrative Staff

Mrs. E. O. Olaleye - Senior Confidential SecretaryMrs. F. A. Asafa - Chief Data Management OfficerMrs. C. O. Olaniyi - Clerical OfficerMrs. R. T. Bhadmus - Senior Office Assistant

Other Departmental Officer

Examination Officers - Dr. T. O. Oluyo/Mr. R. A. OderinuUse of Computers Coordinator - Mr. R. A. Oderinu

LEVEL ADVISERS

100 Level - Dr. O. A. Ajala200 Level - Dr. S. O. Adewale300 Level - Dr. (Mrs.) T. O. Oluyo400 Level - Mr. S. Olaniyi500 Level - Mr. O. A. Adepoju

DEPARTMENTAL COMMITTEES

Board of Examiners

Dr. S. O. Adewale - ChairmanAll Academic Staff from rank of Assistant Lecturer and above - MemberMrs. E. O. Olaleye - Secretary

Board of Studies

Dr. S. O. Adewale - ChairmanAll Academic Staff from rank of Assistant Lecturer and above - MemberMrs. E. O. Olaleye - Secretary

BRIEF HISTORY OF THE DEPARTMENT

1. BRIEF HISTORY OF THE DEPARTMENT

The Department of Pure and applied Mathematics was established in 1990 with

Professor R. O. Ayeni as the foundation Head of Department. Three programmes were

approved to run in the department. These are B. Tech. Mathematics, B. Tech. Industrial

Mathematics and B. Tech. Statistics.

The Department has graduated at least thirteen (13) sets of students with B. Tech

Mathematics three (3) sets of students with B. Tech. Statistics. Moreover, Senate at one

of its meetings in May, 2012 gave approval for the separation of the B. Tech Statistics

programme from the department which led to the creation of a new Department of

Statistics.

2. PHILOSOPHY

The philosophy that guides the programme is to train the students in order to

produce Professional mathematicians who are able to apply mathematical techniques in

the study of scientific and technological problem and are competent enough to undertake

research activities in various branches of mathematics and Science in general. In line

with the University’s mission the training of the graduate will be geared towards

producing quality graduate with great entrepreneural skills suitable for national

development.

3. THE OBJECTIVES OF THE DEPARTMENT PROGRAMMES

The main objectives of the Department Programmes at the undergraduate level are:

(i) To provide adequate instructions and training of professional Mathematicians

who will be able to apply mathematical techniques in the study of scientific and

technological problems and who will be competent enough to undertake research

activities in various branches of mathematics ; and

(ii) To give instructions and expert advice in mathematics to those who require them

in some other disciplines in the various departments of the University.

4. DEGREES OFFERED

The department offers two programmes leading to the following degree

(i) B. Tech (Maths) with restricted electives in Physical Sciences and Engineering

(Industrial Mathematics).

(ii) B. Tech (Maths) with restricted electives in Biology (Biomathematics). Thirteen

(13) sets of students had been graduated from the B. Tech (Maths) with restricted

electives in Physical Sciences and Engineering. Many of these graduates are

working in several sectors of the Nigerian economy and other countries. Some of

them had obtained higher academic qualifications, including M. Sc and Ph.D

Degrees.

5. MODES OF ADMISSION INTO B. TECH PROGRAMMES OF THE

DEPARTMENT

Admissions can be sought

(i) into 100 Level

(ii) direct into 200 Level

(iii) into any approved level by transfer

(iv) change from other programmes of the university to any of the programmes in the

department

6. ADMISSION REQUIREMENTS

(i) To be eligible for admission by any mode, a candidate must possess at least five

credit passes in the WAEC/NECO SSCE or the O/L GCE or any equivalent

qualifications. The credit passes must include English Language, Biology,

Chemistry, Mathematics and Physics.

(ii) To be eligible for admission into 100 Level, a candidate in addition to 5 (i) above

must pass both the UTME and the University post UTME Examination or score a

minimum of 250 marks in the University Pre-Degree final Examinations.

(iii) To be eligible for admission direct into 200 Level, a candidate must in addition to

5 (i) above, possess at least one of

(a) A/L GCE or equivalent qualifications with passes in mathematics, Physics and

any one of Biology and Chemistry

(b) NCE (Maths/Stats) with minimum grade of B. and

(c) OND (Statistics) with a minimum of Upper Credit Pass

(iv) To be eligible for transfer from another programme within the University to any

of the programmes in the department, a candidate can do so through the

University approved process, provided he/she meets the initial requirements for

admission into the department’s programme of his/her choice.

(v) To be eligible for transfer from another university into any of the programmes in

the department, a candidate must satisfy the university regulations governing this

mode of admission into the university. Normally no such transfer is to be

entertained above 200 Level.

7. MATRICULATION

All students entering the University for the first time will be required to matriculate at a

formal ceremony to be presided over by the Vice-Chancellor which normally takes place

after registration and having been certified that such candidates are qualified for the

courses offered them on admission.

The Dean of each Faculty presents students from his/her Faculty for matriculation while

the registrar administers the matriculation Oath. Students are made to solemnly

undertake and swear to observe and respect the provisions of the Ladoke Akintola

University of Technology, Ogbomoso, laws and status ordinances and regulations which

are now in force or which may be brought into force in addition to not belonging to

secrete cult.

8. DURATION OF B. TECH DEGREE PROGRAMME

Normally, the B. Tech Programmes are five year programmes

(i) A student admitted through UTME or Pre-Degree is expected normally to spend a

minimum of five (5) years and a maximum of seven and half (7½) years

(ii) A student admitted through Direct entry is expected normally to spend a

minimum of four (4) years and a maximum of six (6) years.

(iii) A student admitted though transfer is expected normally to spend a minimum of

the number of years left for him/her to graduate and a maximum of one and half

(1½) of the number of years left. For example, a student transferred to 300 Level

has three years left to graduate. Therefore he/she normally has a minimum of

three (3) years and a maximum of four and half (4½) years to graduate.

9. REGISTRATION FOR courses

All students of the department must register at the beginning of each semester for courses

approved by the university authority. Normally a student is allowed to register for a

minimum of twelve (12) units and a maximum of twenty-four (24) units per semester,

unless otherwise stated in a situation where a final year student needs to exceed the

maximum of twenty-four (24) units for him/her to be able to graduate, a formal

application to that effect must be made in writing to the senate through the HOD and

through the Dean for approval.

A student is free to “borrow” courses from other departments if he/she wishes to do so.

10. UNIT LOAD

A unit is fifteen one-hour lecturer or tutorial or a series of fifteen three-hour practical

classes, or the combination of these types of instruction.

11. REGISTRATION PROCEDURE

11.1 New Students

The procedure for the registration of new students is as follows:

i. Obtaining the students pre-registration forms. Filling it and returning it to the

Admissions Officer with the require credentials.

ii. Collecting the registration kit (green file) from the Admission officer

iii. Presenting the originals of the required credential to the Admission Officer who

will sign the pre-registration forms and academic clearance after the credentials

have been checked and verified and entry qualifications confirmed.

iv. Proceeding to the Faculty Officer who will issue course registration forms and

direct students to the appropriate Heads of Departments for guidance in selecting

courses.

v. After selection of courses, filling course registration forms separately and

completely with biro and obtaining the signature of Course and Level Adviser.

vi. Submitting course registration forms to the Faculty officer for the signature of the

Dean; and

vii. Finally, asking the Faculty Officer for copy of the course registration form.

IMPORTANT: Note that registration is not complete until all payments are made and

registration forms are submitted to appropriate places.

11.2 Returning Students

i. After the payments have been made, proceeds to the Faculty Officer and obtain

course registration forms.

ii. Consult with the appropriate Head of Department for guidance in selecting

courses.

iii. After the selection of courses obtaining signature of Course and level Adviser

iv. Submitting course registration forms to the Faculty Officer for the signature of the

Dean.

v. Finally, asking the Faculty Officer for copy of the course registration form.

NB: The online registration is in full operation now.

12. SEMESTER AND SESSION

The University runs a semester system.

A semester is normally a period of sixteen (16) weeks of instruction. The period of

instruction is followed by a period of examinations.

A session consists of two consecutive semesters as determined by the University Senate

(Harmattan & Rain).

13. REGULATIONS IN RESPECT OF CONDUCT OF EXAMINATIONS

14.1 REGULATIONS GOVERNING THE CONDUCT OF UNIVERSITY

EXAMINATIONS

DEFINITION OF TERMS

(i) University Examinations

University Examinations include semester.

Professional and other Examinations involving the participations of both the

Department of Faculty and the examination office.

(ii) Continuous Assessment means course tests, tutorial and other graded assignments

done within the Department/Faculty where the course is being taught.

(iii) Semester

A semester is one-half of an academic year as determined by senate.

(iv) Session

A session consists of two semester otherwise referred to as an Academic year as

determined by senate.

(v) Course Unit/Credit

One credit/unit represents fifteen of lecture/tutorial or 45 hours practical work per

semester.

Two units/credits represent thirty hours of lecture/tutorial or 90 hours of practical

work per semester.

Three credits/units represent forty-five hours of lecturer/tutorial or 135 hours of

practical work per semester.

There are courses that purely theoretical or practical while some others are

combination of both.

15 EXAMINATION OFFENCES AND SANCTIONS

1. Code of Conduct: Candidates shall

a. Not use or consult, during an examination, such books, papers,

instruments or other materials or aids as are specifically permitted or

provided by the Department in which the examination is being held.

b. Not introduce nor attempt to introduce into examination venue hand-bags,

notes, instruments or other materials or aids that are not permitted.

c. Not enter any examination venue with any inscription on any part of the

body e.g. palm, arm, thigh, etc, if such inscriptions bear any relevance to

the examination.

d. Not pass or attempt to pass any information from one person to another

during an examination.

e. Neither act in collusion with any other candidate(s) or person(s) or copy

nor attempt to copy from another candidate, nor engaged in any similar

activity.

f. Not disturb or distract any other candidate(s) during the examination

g. Not be allowed to leave an examination venue until after 75% of the time

allocated for the particular paper has expired.

h. Not use other people to sit for any University Examination on their behalf.

Failure to observe any of the rules (a) to (h) above, shall prima constitute examination

misconduct. The table below contains the various examination offences and the respective sections

as approved by the senate.

S/N Examination Offence Sanction

1. Involvement in leakages of examination questions and/or marking scheme:Student(s) involvedStaff involved

ExpulsionDismissal

2. Illegal possession of answer script(s) by student

Blank answer script(s) Script(s) containing answers

Suspension for two (2) SemestersExpulsion

3. Possession of unauthorized text(s) filled with more than one handwriting:Student(s) involvedStaff complicity in multiple handwriting malpractices

ExpulsionDismissal

4. Possession of unauthorized text(s) and illustration(s) of any form that aid examinations malpractice

Suspension for 4 Semesters

5. Impersonation (machinery) in writing examinations:Student(s) involvedStaff complicity in impersonation malpractices Impersonation in any form

Expulsion

Dismissal6. Student(s) Involvement in assault on personnel involved in

InvigilationExpulsion/Dismissal of parties involved

7. Assaults on personnel involved in invigilation

Harassment and/or battery of personnel involved in Invigilation

Suspension for 4 SemestersExpulsion

8. Harassment of co-students for non-cooperation in examination malpracticesBattery of co-students for non-cooperation in examination malpractices

Suspension for 2 SemestersExpulsion

9. Falsification of identity, such as names, matriculation number, etc, by a student

Suspension for 4 Semesters

10. Grafting Suspension for 2 Semesters

11. Exchanging of scripts or information during examination failure to submit examination answer script

Suspension for 4 semesters

2. Procedure for Investigating Alleged Examination Misconduct:

(a) At the discretion of the Chief invigilator, a candidate may be required to

leave the examination venue when his/her conduct is judged to be

disturbing or likely to disturb the examination. The Chief Invigilator shall

report immediately any such action taken to the Dean through the Faculty

Examination Coordinator after the completion of the examination by the

candidates.

(b) Any candidates suspected of any examination irregularity shall be required

to sine and submit to the Chief Invigilator a written statement in the

Examination Hall Failure to make a written statement shall be regarded as

an admission of the charge against such a candidate.

(c) The dean shall, within 48 hours of receipt of a report, set up a panel of not

less than three (3) academic staff to investigate the report.

Recommendation shall be made available within two (2) weeks through

the Deputy Registrar (Academic) to the Registrar who shall on the basis of

the recommendations, determine whether or not the matter should receive

the attention of the Students Disciplinary Committee.

(d) The Student Disciplinary Committee shall within weeks of receiving such

a report, investigate and recommend penalty in cases of proven

misconduct to the Vice-Chancellor in accordance with section 17 of the

University Act.

16. THE COURSE GRADING SYSTEM

SCORE% LETTER GRADEPOINT

0–39 F 0

40-44 E 1

45-49 D 2

50-59 C 3

60-69 B 4

70-100 A 5

17. GRADING POINT, GRADE POINT AVERAGE AND CUMULATIVE

GRADEPOINT AVERAGE.

17.1 GRADE POINT (GP)

If a student has a score of 61% in a course that has 3 units, then the student’s

letter grade is B and the corresponding point is 4. Therefore the student’s grade

point (GP) for that course is 3 x 4 = 12.

GP = number of units X corresponding point.

17.2 The grade point average (GPA) is the average of grade points for the semester. If

a students for the Harmattan Semester are as follows:

(1) (2) (3) (4) (5) (6)

Course Units Score%Letter Grade Point GP

MTH 201 3 60 B 4 12

MTH 203 2 54 C 3 6

MTH 207 3 64 B 4 12

MTH 211 3 80 A 5 15

STA 207 4 60 B 4 16

BCH 201 3 50 C 3 9

CSE 201 3 65 B 4 12

GNS 209 2 71 A 5 10

23 92

The entries under (6) are the products of corresponding entries under (2) and (5)

For example the 15 for MTH 211 is obtained from 3 x 5

The sum of the units is 23

The sum of the GPs is 92

Therefore the average of the GPs is

92GPA = = 4

23

NOTE that GPA is computed per semester

17.3 Cumulative Grade Point Average (CGPA)

The cumulative grade point average (CGPA) is the grade point average of all the course

taken to date.

Example: Suppose a student in year 2 who is a direct admission student has the following

cumulative records:

HARMATTAN RAIN SEMESTERCourse Units Grade GP COURSE Units Grade GPMTH 201 3 B 12 MTH 202 3 C 9MTH 203 2 C 6 MTH 206 2 B 8MTH 207 3 B 12 MTH 208 3 C 9MTH 211 3 A 15 MTH 212 4 B 16STA 207 4 B 16 MTH 210 2 B 8BCH 201 3 C 9 STA 208 4 B 16CSE 201 3 B 12 CSE 202 2 B 8

CSE 204 2 C 8GNS 209 2 A 10 GNS 202 2 C 6

23 92 24 98

GPA = 92 = 4 GPA = 88 = 3.667 23 24

CGPA = GPA = 4 CGPA = 92 + 88 = 180 = 3.8923 + 24 47

18. GOODSTANDING, PROBATION AND WITHDRAWAL

(i) Good standing: At the end of semester a student is said to be in good standing if

his/her cumulative grade point average (CGPA) is at least 1.0

(ii) Probation: A student shall be on probation for the duration of the semester

following a semester at the end of which he/she is found not to be in good

standing

(iii) Withdrawal: A student shall be advised to withdraw from the programme if at the

end of the probational semester he/she still has a CGPA less than 1.0

19. GRADUATION REQUIREMENTS

To qualify for the award of the degree of the programme admitted into, a student

must be found worthy in learning if he/she satisfies the following conditions.

(i) Passed all the University required courses

(ii) Passed all the Department required courses

(iii) Satisfied residential requirements in terms of duration of studentship with respect

to mode entry.

20. CLASSIFICATION OF DEGREE

The degree awarded by the University are classified according to CGPA as follows:

CGPA RANGE CLASS OF DEGREE4.50 5.00

3.50 4.49

2.40 3.49

1.50 2.39

1.00 – 1.49

First Class Honours

Second Class Upper Honours

Second Class Lower Honours

Third Class Honours

Pass

21. LEVEL ADVISORS

The level advisors are to assist/advise students on choice of courses. They should also

provide academic guidance and counseling to the students, particularly the weak ones.

Students are encouraged to interact adequately with their level advisers, who also double

as their level academic record keepers.

22. PROGRAMMES OF INSTRUCTION

To be awarded a B.Tech Degree of the University a student must pass all of the following

courses or parts of the specified on the programme.

22.1 UNIVERSITY REQUIREMENTSThe University requires each student of the Department to offer and pass the

following courses in order to qualify for an award of a degree of the University

22.2 DEPARTMENTAL REQUIREMENTSDepartmental Requirement for B. Tech (Maths) Restricted electives in physical

Sciences and Engineering.

100 LEVELS

Course Code Course Title L T P Units

BIO 101 General Biology I 3 0 0 3

BIO 102 General Biology II 3 0 0 3

BIO 103 Experimental Biology I 0 0 3 1

BIO 104 Experimental Biology II 0 0 3 1

CHM 101 General Chemistry I 3 1 0 4

CHM 102 General Chemistry II 3 1 0 4

CHM 191 Experimental Chemistry I 0 0 3 1

CHM 192 Experimental Chemistry II 0 0 3 1

PHY 101 General Physics I 3 1 0 4

PHY 102 General Physics II 3 1 0 4

PHY 191 Experimental Physics I A 0 0 3 1

PHY 192 Experimental Physics I B 0 0 3 1

MTH 101 Elementary Mathematics I 4 1 0 5

MTH 102 Elementary Mathematics II 4 1 0 5

GNS 101 Use of English I 2 0 0 2

GNS 102 Use of English II 2 0 0 2

FAA 101 Fundamental Drawing 1 0 3 2

GNS 104 Science & Technology in Africa 2 0 0 2

CSE 100 Introduction to Computing 1 1 1 1

LIB 101 Use of Library 1 0 0 0

200 LEVELS

Course Code Course Title L T P Units

MTH 201 Mathematical Method I 2 1 0 2MTH 203 Linear Algebra I 1 1 0 2MTH 207 Real Analysis I 1 1 0 2MTH 211 Introductory Applied Mathematics 2 1 0 3STA 207 Statistics for Physical Science

and Engineering 3 1 0 4CHM 231 Basic Physical Chemistry 3 1 0 4GNS 209 Citizenship Education

MTH 202 Elementary Differential Equation I 2 1 0 3MTH 206 Linear Algebra II 1 1 0 2MTH 208 Introduction to Numerical Analysis 2 1 0 3MTH 212 Mathematical Method II 3 1 0 4MTH 210 History of Mathematics 1 1 0 2STA 208 Probability II 3 1 0 4

300 LEVEL Course Code Course Title L T P UnitsMTH 301 Abstract Algebra I 2 1 0 3MTH 303 Elementary Differential Equations 2 1 0 3MTH 305 Vector and Tensor Analysis 2 1 0 3MTH 307 Sets, Logic and Algebra 2 1 0 3MTH 309 Electromagnetism 2 1 0 3CSE 301 Computer Programming 2 1 0 3MTH 304 Metric space Topology 2 1 0 3MTH 306 Real Analysis II 2 1 0 3MTH 308 Computer Analysis I 2 1 0 3MTH 310 Dynamics of a Rigid Body 2 1 0 3STA 302 Probability III 3 1 0 4CSE 310 Numerical Computation II 2 1 0 3

400 LEVEL Course Code Course Title L T P UnitsMTH 401 Complex Analysis II 2 1 0 3MTH 403 Abstract Algebra II 2 1 0 3MTH 405 Introduction to Mathematical

Modeling 2 1 0 3MTH 407 Lebesque Measured and Integration 2 1 0 3MTH 409 Fluid Dynamics I 2 1 0 2MTH 411 Theory of Algorithms & Application 2 0 3 3CSE 311 Theory Computation 2 1 0 3

500 LEVEL Course Code Course Title L T P UnitsMTH 501 Intro, to Operation Research 2 1 0 3MTH 503 Partial Differential Equations 2 1 0 3MTH 507 Functional Analysis 2 1 0 3MTH 509 Fluid Dynamics II 2 1 0 3MTH 511 Mathematical Methods III 3 0 0 3MTH 512 Analytical Dynamics 2 1 0 3MTH 513 Elasticity 3 0 0 3MTH 514 System Theory 2 0 3 3MTH 517 Quantum Mechanics 3 0 0 3MTH 502 General Topology 2 1 0 3

MTH 504 Ordinary Differential Equations 2 1 0 3MTH 508 Measure Theory 3 1 0 4STA 504 Non-Parametric Method 3 1 0 4STA 506 Operation Research II 3 1 0 4STA 508 Laboratory for Operation Research 0 0 2 2MTH 509 Project 0 0 0 6

DESCRIPTION OF MATHEMATICS COURSESMTH 101 Elementary Mathematics I (4 – 1 -0) 5 UnitsSet Theory: Set, Union, Intersection, Empty set and universal set, complement of a set, subset,

finite and infinite set, Venn diagram, Mapping and Functions. Operations with Real Numbers.

The real number R and its extension to the set of complex number C Equation involving one

variable. The Reminder Theorem and the Factor Theorem. Equation is two variables,

inequalities, partial fractions, surds indices and logarithms.

Theory of Quadratic Functions and Equations. The quadratic function and the relation between

the roots of a quadratic equation and the co-efficients.

Sequences and Series: Finite sequences and series, the arithmetic sequences and series, the finite

and infinite geometric sequences and series.

The Binomial Theorem: Elementary examples in the use of induction, permutation and

combination and their applications. The Binomial Theorem for a positive integral index. The

use of the expansion (1 + x)”, where n is fractional or negative: simple approximations.

Matrices: Definition of m x n matrices: addition of matrices, matrix multiplication and inversion.

Determinant of a matrix, application simple linear equations, consistency and linear dependence.

MTH 102 ELEMENTARY MATHEMATICS 11 (4-1 0) 5 UNITS

Trigonometry: Circular measure, small angles, definition and properties of si ne, cosine, tangent,

etc Formulae for Sin(A + B), Cos(A + B) Sin A/2, Tan A/2. Etc Sine and Cosine formulae, factor

formulae, inverse trigonometric function, functions, General solution of trigonometric equations

such as a CosØ + bSinØ = C.

Calculus: Differentiation of algebraic of algebraic, exponential, trigonometric, product and

quotient functions, applications of differentiation to curve sketching, etc. Maxima and minima.

Definite and indefinite integrals with application to areas and volumes. Simple techniques of

integration such as Integration by parts etc. Simple first order ordinary differential equation.

Co-ordinate Geometry: Co-ordinates, Equations of lines, circles ellipse, hyperbola and parabola.

Statistics: Finite sample spaces, definition of probability of finite sample spaces and examples.

Probability as proportion of areas, conditional probability of events. Independence, tree

diagrams, variables and cumulative frequency distributions mean, median, variable and co-

variance conditional expectation and linear correlation, using scatter diagram.

MTH 201 MATHEMATICAL METHOD: 2-1- 0 (3 UNITS)

Prerequisite MTH 102

Sequence and series : Limits, continuity, Differentiability, Implicit functions, sequences, series,

test for convergence, sequences and series of function.

Numerical Methods: Introduction of iterative methods, Newton’s method applied to finding

roots. Trapezium and Simson 1 as rules of integration.

Differential Equations: Introduction equation of first order and first degree, separable equations,

homogeneous equation, exact equations linear equation, Bernoulli’s and Riccati equations.

Application to mechanics and electronic Orthogonal and oblique trajectories. Second order

equations with constant coefficients. General theory of nth order linear equations. Laplace

transform, solution of initial value problem by Laplace transform method. Simple treatment of

partial equations in two independent variables.

MTH 202 ELEMENTARY DIFFERENTIAL EQUATIONS I: 2-1-0 (3 UNITS)First order ordinary differential equations. Existence and uniqueness. Second order ordinary

differential equations with constant co-efficient. General theory of order linear equations. Lap

lace transforms, solution of partial differential equations in two independent variables.

Applications of O.D.E. and P.D.E to physical, life and social sciences.

MTH 203 LINEAR ALGEBRA 1;1 1(2 UNITS)Pre-requisite MTH101, 102

Vector space over the real field. Subspace, linear independence. Basis and dimension. Linear

transformation and their representation by matrices. Algebra matrices.

MTH 207 REAL ANALYSIS 1: 2 1 0 (3UNITS)Pre-requisite MTH101

Bound of real numbers, sequence and series convergence, converge of sequence numbers.

Monotone sequence, the theory of nested intervals. Cauchy sequences, test of convergence of

series.

Absolute and conditional convergence of series, and rearrangements.

Completeness of real and incompleteness of rationale.

Continuity and differentiability of functions. Rolle’s mean and value theorem for differentiable

functions. Taylor’s series.

STA 207 STATISTICS PHYSICAL SCIENCES AND ENGINEERING 3-1-0 (4 UNITS)

Measures of location and dispersion in simple and grouped data exponentials. Element of

probability and probability distribution. Estimation and tests of hypotheses concerning the

parameters of distributions. Regression, correlation and analyjsis of various contingency table.

Non-parametric inference.

MTH 208 INTRODUCTION TO NUMERICAL ANALYSIS: 2-1-0 (3 UNITS)Pre-requisite –MTH 101Solution of algebraic and transcendental equations. Curve fitting. Error analysis. Interpolation

and approximation. Zeros of non-linear equations is one variable. Systems of linear equations.

Numerical differentiation an integration. Initial value problems of ordinary differential equations.

MTH 210 HISTORY OF MATHEMATICS: 1-1-0 (2 UNITS)Topics in the History of Mathematics with emphasis on the development of modern

Mathematics.

MTH 211 INTRODUCTORY APPLIED MATHEMATICS : 2 1 0 (3UNITS)Vectors, geometry and dynamics

Geometric representation of vectors in 1 – 3 dimension, components, direction cosines.

Addition, Scalar, multiplication of vectors, linear independence. Scalar and vector products

MTH 212 MATHEMATICAL METHODS II 3 – 1- 0 ( 4 UNITS)Use of the Neyman – Pearson lemma Hypotheses testing, the power of a test. Point and internal

estimation. (Testing and estimation of large sample situations) binomial, Poisson, normal

contingency tables, Goodness of fit tests.

HARMATTAN SEMESTER

MTH 301 ABSTRACT ALGEBRA I: (3 UNITS) 2-1-0Pre-requisite –MTH 101, 203

Group: Definition, examples including permutation groups. Subgroups, coset. Lagrange’s

theorem and applications. Cyclic groups. Rings: definition examples including Z, Zn rings of

polynomials and matrices. Integral domains, fields. Polynomial rings, factorization. Euclidean

algorithm for polynomials H.C.F. an L.C.M of polynomials.

MTH 303 ELEMENTARY DIFFERENTIALEQUATIONS II: (3 UNITS)Series solution of second order linear equations. Bessel, Legendre and pypergeometric equations

and functions. Gamma Beta functions Sturnliouvelle problems.Orthogonal polynomials and

functions. Fourier, Bessel and Fourier –Legendre Series. Fourier transformation. Solution of

Laplace, wave and heat equations by Fourer method.

MTH 305 VECTOR AND TENSOR ANALYSIS: (3 UNITS)Pre-requistie – MTH 201,212Vector algebra. Vector, dot and crossProducts. Equation of curves and surfaces. Vector

differentaiation and applications. Gradient, divergence and curl. Vector integrate, line surface

and volume integrals.Greens Stoke’s and divergence theorems. Tensor products of vector space.

Tensor algebra. Symmetry. Gartesan tensors

MTH 307 SETS, LOGIC AND ALGERA: (3 UNITS)Pre-requisite – MTH 101Introduction to the language and concepts of modern Mathematics. Topic include; Basic set

theory mappings, relations, equi-valence and other relations, Cartesian products. Binary logic,

methods of proof. Binary operations. Algebraic structures, semigroups, rings, integral domains

fields. Homoeomaphics. Number systems; properties of integers, rationals, real and complex

numbers.

MTH 309 ELECTROMAGNETISM: (3 UNITS)Maxwell’s field equations. Electromagnetic waves and Electromagnetic theory of lights. plane

detromagnetic waves in non-conducting media, reflection and refraction at place boundry.

Waves guides and resonant cavities. Simple radiating systems. The Lorentz-Einstein

transformation. Energuides and momentum. Electromagnetic 4-vectors. Transformation of (E.H)

fields. The Lorentz force.

RAIN SEMESTERMTH 304 METRIC SPACE4 TOPOLOGY: (3 UNITS 2-1-0)Sets matrices, and examples open spheres (or balls). Open sets and neighborhoods. Closed sets.

Interior exterior, frontier, limits points and closure of set. Dense subsets and separable space.

Convergence in metric spare homomorphism. Continuity and compactness, Pre-requisite MTH

202

MTH 306 REAL ANALYSIS II: (3 UNITS: 2-1-0)Riemann integral of functions r…) R: continuous monopositive functions. Functions of bounded

variation. The Riemann still jets integral. Point wise and uniform convergence of sequences and

series of function R…) R. Effects on limits (sums) when the functions are continuous

differentiable or Riemann

Pre-requisite MTH 207

MTH 308 COMPLEX ANALYSIS 1 (3 UNITS: 2-1-0)Functions of a complex variable. Limits and continuity of functions of a complex variable.

Derivation of the Cauchy-Riemann equations. Cauchy’s theorems and its main consequences.

Convergence of sequences and series of functions of a complex variable. Power series. Taylor

series.

Pre-requisite MTH 203, 207

MTH 310 DYNAMICS OF A RIGID BODY: (3 UINTS: 2-1-0)General motions of a rigid body as a translation plus a rotation. Moment, and products of inertia

in three dimensions. Parallel and perpendicular axes theorems. Principal axes, Angular

momentum, kinetic energy of rigid body. Impulsive motion. Examples involving one and two-

dimensional motion of simple system. Moving rates of reference; rotating and translating frames

of reference. Coriolis force. Motion near the Earth’s surface. The Foucault’s pendulum. Euler’s

dynamical equations for motion of a rigid body with one point fixed. The symmetrical top.

Procession.

MTH 401 COMPLEX ANALYSIS II. (3 UNITS: 2-1-0)Co-requisite – MTH 307

Laurent expansions. Isolated singularities and residues. Residue theorem Calculus of residue, and

application to evaluation of integrals and to summation of series. Maximum Modulus principles.

Argument principal. Rouches therem. The fundamental theorem of algebra. Principle of analytic

continuation. Multiple valued functions and Riemann surfaces. Dirichlet and Newman problems.

Maximum principle.

Pre-requisite MTH 202.

MTH 403 ABSTRACT ALGEBRA II: (3 UNITS: 2-1-0)Normal subgroups and quotient groups. Monomorphic isomorphism theorem. Cayley’s

theorems. Direct products. Groups of small order. Group acting on sets. Sylow theorems. Ideal

and quotient rings. P.I.D. 8, U.F.D’S Euclid’s rings. Irreducibility, Field extensions, degree of an

extension, minimum polynomial. Algebraic and trans-cendental extensions. Straightedge and

compass constructions.

Pre-requisite – MTH 207, MTH 307

MTH 405 INTRODUCTION TO MATHEMATICAL MODELLING: (3UNITS: 2-1-0)Methodology of model building: Identification, formulation and solution of problems, cause-

effect diagrams. Equation types. Algebraic, ordinary differential equations. Application of

mathematical models to pluprical, biological, social and behavioral sciences.

MTH 407 LEBESGUE MEASURE AND INTEGRALS (3 UNITS: 2-1-0)

Lebesque measure, measureable and non measureable sets, Measurable function, Lebsque

integral: Integration of non-negative functions, the general integral converged theorems.

Pre-requisite MTH 207, MTH 307

MTH 409 FLUJID DYNAMICS: I (3 UNITS: 2-1-0)Real and Ideal fluids. Differentiation following the motion of fluid particles. Equations of motion

and continuity for incompressible invisoid fluids. Velocity potentials and Stoke’s Stream

functions. Bernoulli equation with application to flow along curved paths. Kinetic energy.

Sources, sinks, doubles in 2 – and 3- dimensions, limiting streamlines. Images and rigid planes.

Pre-requisite – MTH 202

MTH 501 INTRODUCTION TO OPERATION RESEARCH: (3 UNITS: 2-1-0)Phases of operation Research Study. Classification of operation Research models, linear;

Dynamic and integer programming. Decision Theory. Inventory Models, Critical Path Analysis

and project Controls.

MTH 502 GENERAL TOPOLOGY (3 UNITS: 2-1-0)Topological spaces, definition, open and closed sets neighborhoods. Coarser, and finer

topologies. Basis and sub-bases. Separates axioms,. Compactness, local compactness,

connectedness. Continuous functions, homeomorphones, topological invariants, spaces of

continuous functions: Point wise and uniform convergence.

Pre-requisite – MTH 301.

MTH 503 PARTIAL DIFFERENTIAL EQUATIONS (UNITS: 2-1-0)Initial value problems for hyperbolic and parabolic equation. Characteristic surfaces. Domain of

dependence. Wave phenomena. Elliptic equation, Harmonic function. Green’s function.

MTH 504 ORDINARY DIFFERENTIAL EQUATION1: (3 UNITS: 2-1-0)Existence of solutions. Uniqueness of solutions. Method of successive approximations.

Continuation of solutions. Systems of differential equations. The order equation. Extension of

the idea of a solution, maximum and minimum solutions. Elementary differential inequalities.

Dependence of solutions on initial. Conditions and parameters. Variation of solutions with

respect to initial conditions and parameters.

Pre-requisite MTH 201, 202 , 203, 305.

MTH 507 FUNCTIONAL ANALYSIS (3 UNITS: 2-1-0)Normed Linear Spaces: Definition and Examples. Convex sets. Norms. Holder’s Minkowski’s

inequalities. Riesz-Fisher theorem. Linear operations on finite dimensional spaces. Linear

functionalism, space. Banach spaces, examples. Quotient spaces: Inner product spaces

Topological linear spaces.

Hilbert spaces, examples. Linear operators in Hilbert spaces. Joint operators. Hermitian

operators. Orthogonality; orthogonal complement and projections in Hilbert’s spaces.

Pre-requisite MTH 314 and MTH 403

MTH 508 MEASURE THEORY (4 UNITS: 3-1-0)Abstract Integration. Set-theoretic notations and terminology. The concepts of measurability.

Simple functions. Elementary properties of measures. Integration of positive functions.

Integration of complex functions. The role played by sets measure zero. Convex functions and

inequalities. Lp-spaces Approximation by continuous functions.

MTH 509 FLUID DYNAMICS II 3 UNITS: (2-1-0)Navier-stokes equations, Equation of energy. Simple exact solutions. Dynamic similarity, slow

flows: stokes and OSeen flows. Laminar boundary layer theory. Thinkness, skin friction and heat

transfer. Blasius solution for flat plate and similar solutions. Laminar boundary layer separation,

small disturbance theory. Normal and oblique shock waves.

MTH 511 MATHEMATICAL METHODS (3 UNITS: 2-1-0)Calculus of variation: Lagrange’s functional and associated density. Necessary condition for a

weak relative extremum. Hamilton’s principles Lagrange’s equations and geodesic problems.

The Du Bois-Raymond equation and corner conditions. Variable end-points and related

theorems. Sufficient conditions for a minimum. Isoperimetric problems. Variation integral

transforms. Laplace, Fourier and Hankel transforms. Complex variable methods convolution.

Pre-requisite MTH 207, MTH 307

MTH 512 ANALYTICAL DYNAMICS II (3 UNITS 2-1-0)

Lagrange’s equation for non-holonomic systems. Langrangian multipliers. Variational

Principles. Calculus of variation. Hamilton’s principle, Lagrange’s equation from Hamiltton’s

principle. Canonicals transformations. Normal models of Variations. Hamilton Jacabi

equations.

MTH 513 ELASTICITY (3 UNITS 2-1-0)

Particle gravitational field: Curvilinear co-ordinates, integrals. Covariant differentiation.

Christofel symbol and matrix tensor. The constant gravitational field Rotation.

MTH 514 SYSTEMS THEORY (3 UNITS 2-1-0)

Lyapunov theorems. Solution of Lyapunov statibility equation ATP ? PA Q = Controllability

and observability. Theorem on existence of solution of linear systems of differential operations

with constant coefficients.

MTH 517 QUANTUM MECHANICS (3 UNITS 2-1-0)

Perticle-ware duality. Quantum poatulates. Schroedinger equation of motion. Potential steps

and wells in I dimensia. Heisenberg formulation. Classical limit of Quantum mechanics.

Computer brackets linear harmonic oscillator. Angular momentum 3-d square well potential.

The hydrogen atom collision in 3-d.

Approximation methods for stationery problems.