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Page 1: Handbook 2011-2012

Faculty of Science Handbook, Session 2011/2012

0

http://www.math.um.edu.my

Page 2: Handbook 2011-2012

Faculty of Science Handbook, Session 2011/2012

1

BACHELOR OF SCIENCE (MATHEMATICS) SESSION 2011/2012 (123 CREDITS)

1. UNIVERSITY COURSES (21 CREDITS) Please refer to programme structure Bachelor of Science

2. CORE COURSES PROGRAMME (92 CREDITS)

(I) COMPULSORY COURSES (61 CREDITS)

LEVEL 1 (23 CREDITS)

COURSE CODE

COURSE NAME PRE-REQUISITE CREDIT

SJEM1110 Basic Mathematics STPM Mathematics T/S or equivalent 4

SJEM1111 Calculus I STPM Mathematics T/S or equivalent 4

SJEM1130 Introduction to Computing STPM Mathematics T/S or equivalent 3

SJEM1211 Calculus II SJEM1111 (pass with a minimum of grade C) 4

SJEM1230 Mathematical Methods I SJEM1111 (pass with a minimum of grade C) 4

SJEM1250 Probability & Statistics I SJEM1111 (pass with a minimum of grade C) 4

LEVEL 2 (38 CREDITS)

SJEM2210 Advanced Calculus SJEM1211 (pass with a minimum of grade C) 4

SJEM2211 Linear Algebra SJEM1110 (pass with minimum of grade C) 4

SJEM2212 Introduction to Combinatorics SJEM1110 4

SJEM2213 Algebra I SJEM1110 4

SJEM2214 Introduction to Analysis SJEM1211 4

SJEM2215 Complex Variables SJEM1211(pass with a minimum of grade C) 4

SJEM2230 Mathematical Methods II SJEM1230 (pass with a minimum of grade C) 4

SJEM2231 Structured Programming SJEM1111 (pass with a minimum of grade C) 4

SJEM2250 Probability & Statistics II SJEM1250 (pass with a minimum of grade C) 4

SJEM2280 Appreciation of Mathematics SJEM1211 (pass with a minimum of grade C) 2

(II) ELECTIVE COURSES (at least 31 CREDITS)

COURSE CODE COURSE NAME PRE-REQUISITE CREDIT

SJEM2416 Theory of Differential Equations SJEM1230 and SJEM2211 4

SJEM2417 Geometry SJEM1110 4

SJEM3411 Graph Theory SJEM2212 4

SJEM3412 Combinatorial Mathematics SJEM2212 4

SJEM3413 Number Theory SJEM1110 4

SJEM3414 Advanced Linear Algebra SJEM2211 4

SJEM3415 Matrix Theory SJEM2211 4

SJEM3416 Algebra II SJEM2213 4

SJEM3417 Ring Theory SJEM2213 4

SJEM3418 Group Theory SJEM2213 4

SJEM3419 Differential Geometry SJEM2210 4

SJEM3420 Topology SJEM2210 4

SJEM3421 Complex Analysis SJEM2215 4

SJEM3422 Real Analysis SJEM2214 4

SJEM3380 Mathematical Science Project 4

SJEM3190 Industrial Training 4

(III) NON CORE COURSES (10 CREDITS) * Courses Offered by Other Institute/Department of Specialization (Please refer to the Non Core Courses from other Institute/Department within the Faculty of Science )

The exact number of elective core courses offered in each year may be different. The core courses, under the program of Bachelor of Science (Computational and Industrial Mathematics), Bachelor of Science (Statistics) or Bachelor of Science (Actuarial and Financial Mathematics) except those with codes SJER4***, can be taken as elective core courses. Please refer to respective program.

Attention: The students who wish to specialize in Bachelor of Science (Mathematics) must take at least 20 credits in the courses with codes SJEM3*** (not including SJEM3190) from the program of Bachelor of Science (Mathematics), Bachelor of Science (Computational and Industrial Mathematics), Bachelor of Science (Statistics) or Bachelor of Science (Actuarial and Financial Mathematics).

Page 3: Handbook 2011-2012

Faculty of Science Handbook, Session 2011/2012

2

PROGRAMME GOAL To produce graduates with sound knowledge of mathematics, capable of critical thinking and problem solving; who can adapt to diverse environment and contribute significantly in various professions. PROGRAMME LEARNING OUTCOMES At the end of the programme, graduates with B.Sc (Mathematics) are able to: 1. Explain mathematical theory (pure, applied and statistics) which includes mathematical arguments, proofs and abstract concepts. 2. Perform mathematical computation, apply mathematics software and formulate real world problems as mathematical

models. 3. Conduct professional activities with good social skills, and demonstrate sense of responsibility in society. 4. Practice characteristics associated with professionalism and ethical responsibility in the field of mathematics. 5. Communicate using critical thinking with effective, accurate and relevant concepts. 6. Analyse and assess problems, and develop strategies to obtain solutions. 7. Engage in life-long learning to advance knowledge and applications of mathematics. 8. Apply managerial and entrepreneurial skills to manage resources needed to complete a task.

Page 4: Handbook 2011-2012

Faculty of Science Handbook, Session 2011/2012

3

LIST OF COURSES ACCORDING TO SEMESTER

(PLANNING OF COURSES)

COMPONENT SEMESTER 1 SEMESTER 2 TOTAL

CREDIT COURSE CREDIT COURSE CREDIT

University Courses

GTEE1101/1102/ 1103/1104 English

3 GXEX1414 TITAS

2 12

GXEX1412 Basic Entrepreneurship Culture

2 GTEE1101/2/3/4 English 3

GXEX1411 Ethnic Relations 2

Programme

Core Courses

Compulsory Courses

SJEM1110 Basic Mathematics

4 SJEM1211 Calculus II

4 23

SJEM1111 Calculus I 4 SJEM1230 Mathematical Methods I

4

SJEM1130 Introduction to Computing

3 SJEM1250 Probability & Statistics I

4

Elective Courses

Non-Core Courses

Total Credit 16 19 35

COMPONENT SEMESTER 3 SEMESTER 4 TOTAL

CREDIT COURSE CREDIT COURSE CREDIT

University Courses

GXEX1401 Information Skills Course

1 GXEX Cocuriculum

2 3

SXEX1102 Statistics 3 3

Programme Core

Courses

Compulsory Courses

SJEM2210 Advanced Calculus 4 SJEM2230 Mathematical Methods I

4 30

SJEM2211 Linear Algebra 4 SJEM2231 Structured Programming

4

SJEM2250 Probability & Statistics II

4 SJEM2212 Introduction to Combinatorics

4

SJEM2215 Complex Variables 4 SJEM2214 Introduction to Analysis

4

Elective Courses

Non-Core Courses 3 3

Total Credit 18 21 39

Page 5: Handbook 2011-2012

Faculty of Science Handbook, Session 2011/2012

4

COMPONENT SEMESTER 5 SEMESTER 6 TOTAL

CREDIT COURSE CREDIT COURSE CREDIT

University Courses SXEX1411 Introduction to Science and Technology Studies

3

3

Programme Core

Courses

Compulsory Courses

SJEM2280 Appreciation of Mathematics

2

28 Elective Courses

SJEM2213 Algebra I 4 SJEM2*** / 3*** 4

SJEM2*** / 3*** 4 SJEM3*** 4

SJEM2*** / 3*** 4 SJEM3*** 4

Non-Core Courses 5 5

Total Credit 19 17 36

COMPONENT SPECIAL SEMESTER TOTAL

CREDIT COURSE CREDIT

University Compulsory Courses -

Programme Core

Courses

Compulsory Courses

Elective Courses SJEM3*** 4

12 SJEM3*** 4

SJEM3*** 4

Non-Core Courses 2 2

Total Credit 14 14

Page 6: Handbook 2011-2012

Faculty of Science Handbook, Session 2011/2012

5

BACHELOR OF SCIENCE (COMPUTATIONAL AND INDUSTRIAL MATHEMATICS) SESSION 2011/2012 (123 CREDITS)

1. UNIVERSITY COURSES (21 CREDITS) Please refer to programme structure Bachelor of Science

2. CORE COURSES PROGRAMME (102 CREDITS)

(I) COMPULSORY COURSES (61 CREDITS)

LEVEL 1 (23 credits)

COURSE CODE COURSE NAME PRE-REQUISITE CREDIT

SJEM1110 Basic Mathematics STPM Mathematics T/S or equivalent 4

SJEM1111 Calculus I STPM Mathematics T/S or equivalent 4

SJEM1130 Introduction to Computing STPM Mathematics T/S or equivalent 3

SJEM1211 Calculus II SJEM1111 pass with a minimum of grade C 4

SJEM1230 Mathematical Methods I SJEM1111 (Pass with a minimum of grade C) 4

SJEM1250 Probability & Statistics I SJEM1111 (pass with a minimum of grade C) 4

LEVEL 2 (38 credits)

SJEM2210 Advanced Calculus SJEM1211 (pass with a minimum of grade C) 4

SJEM2211 Linear Algebra SJEM1110 (pass with minimum of grade C) 4

SJEM2230 Mathematical Methods II SJEM1230 (pass with a minimum of grade C) 4

SJEM2231 Structured Programming SJEM1111 (Pass with a minimum of grade C) 4

SJEM2232 Vectors and Mechanics SJEM 1211 (pass with a minimum of Grade C) 4

SJEM2233 Basic Operational Research SJEM1110 4

SJEM2234 Transforms & Partial Differential Equations SJEM2230 4

SJEM2250 Probability & Statistics II SJEM1250 (pass with a minimum of grade C) 4

SJEM2280 Appreciation of Mathematics SJEM1211 (pass with a minimum of grade C) 2

SJEM3190 Industrial Training 4

(II) ELECTIVE COURSES (at least 31 credits)

SJEM2430 System of Differential Equations SJEM2230 4

SJEM2431 Management Mathematic SJEM1111 4

SJEM2432 Optimization Technique SJEM2210 4

SJEM2433 Computer Graphics SJEM1130 or SJEM2231 4

SJEM3430 Wavelets and Their Applications SJEM1130 and SJEM2211 4

SJEM3431 Introduction to Quantum Mechanics with Computers

SJEM2231 4

SJEM3432 Cryptography SJEM2231 and SJEM1250 4

SJEM3433 Computational Fluid Dynamics SJEM2232 4

SJEM3434 Analysis of Mathematical Models SJEM2430 4

SJEM3435 Numerical Methods and Analysis SJEM2230 4

SJEM3436 Production and Inventory System SJEM2233 atau SJEM2431 4

SJEM3437 Heuristic Methods SJEM2231 4

SJEM3438 Mathematical Programming SJEM2233 4

SJEM3439 Industrial Operational Research SJEM2233 4

SJEM3440 Computational Geometry SJEM2231 4

SJEM3441 Scientific Computing SJEM2231 4

SJEM3380 Mathematical Science Project

(III) NON CORE COURSES (10 CREDITS) * Courses Offered by Other Institute/Department of Specialization ( please refer to the Non Core Courses from other Institute/Department within the Faculty of Science )

Core courses under the B.Sc. (Mathematics), B.Sc. (Statistics) and B.Sc. (Actuarial and Financial Mathematics) program, except courses with codes SJER4***, can also be taken as electives for this program. Please refer to the respective programs.

Attention: Students who wish to specialize in B.Sc. (Computational and Industrial Mathematics) must take at least 20 credits from courses with codes SJEM3*** from those listed in this program structure.

Page 7: Handbook 2011-2012

Faculty of Science Handbook, Session 2011/2012

6

PROGRAMME GOAL To produce graduates with (sound) knowledge of computational and industrial mathematics, capable of critical thinking and problem solving; who can adapt to diverse environment and contribute significantly in various professions. PROGRAMME LEARNING OUTCOMES At the end of the programme, graduates with B.Sc (Computational And Industrial Mathematics) are able to: 1. Explain the principles and concepts of mathematics and it applications; 2. Apply the mathematical principles in solving real world problems; 3. Conduct professional activities with good social skill and demonstrate a sense of responsibility; 4. Practice characteristics associated with professionalism and ethical responsibility in the filled of mathematical applications. 5. Communicate using critical thinking with effective, accurate and relevant concepts. 6. Convert problems into mathematical models, and develop scientific strategies to obtain solutions. 7. Engage in life-long learning to advance knowledge and applications of mathematics. 8. Apply managerial and entrepreneurial skills to manage resources needed to complete a task.

Page 8: Handbook 2011-2012

Faculty of Science Handbook, Session 2011/2012

7

APPENDIX 1

LIST OF COURSES ACCORDING TO SEMESTER (PLANNING OF COURSES)

COMPONENT SEMESTER 1 SEMESTER 2 TOTAL

CREDIT COURSE CREDIT COUSE CREDIT

University Courses

GTEE1101/1102/ 1103/1104 English

3 GTEE1101/2/3/4 English 3 10

GXEX1412 Basic Entrepreneurship Culture

2 GXEX1411 Ethnic Realtions

2

Programme

Core Courses

Compulsory Courses

SJEM1110 Basic Mathematics

4 SJEM1211 Calculus II 4 23

SJEM1111 Calculus I 4 SJEM1230 Mathematical Methods I

4

SJEM1130 Introduction to Computing

3 SJEM1250 Probability & Statistics I

4

Elective Courses

Non-Core Courses

Total Credit 16 17 33

COMPONENT SEMESTER 3 SEMESTER 4 TOTAL

CREDIT COURSE CREDIT COURSE CREDIT

University Courses GXEX1401 Information Skills Course

1 GXEX Cocuriculum SXEX1102 Statistics

2 3

6

Programme Core

Courses

Compulsory Courses

SJEM2210 Advanced Calculus

4 SJEM2230 Mathematical Methods II

4 30

SJEM2211 Algebra Linear

4 SJEM2231 Structured Programming

4

SJEM2250 Probability & Statstics II

4 SJEM2233 Basic Operational Research

4

SJEM2232 Vectors and Mechanics

4 SJEM2280 Appreciation of Mathematics

2

Elective Courses

Non-Core Courses

Total Credit 17 19 36

Page 9: Handbook 2011-2012

Faculty of Science Handbook, Session 2011/2012

8

COMPONENT SEMESTER 7

TOTAL CREDIT COURSE CREDIT

University Compulsory Courses

Programme Core Courses

Compulsory Courses

0

Elective Courses

SJEM3*** 4

12 SJEM3*** 4

SJEM3*** 4

Non-Core Courses 3 3

Total Credit 15 15

COMPONENT SEMESTER 5 SEMESTER 6 SEMESTER KHAS TOTAL

CREDIT COURSE CREDIT COURSE CREDIT COURSE CREDIT

University Compulsory Courses

SXEX1411 Introductionto Science and Technology Studies

3 GXEX1414 TITAS

2 5

Programme Core

Courses

Compulsory Courses

SJEM2234 Transforms & Partial Differential Equations

4 SJEM3190 Industrial Training

4 8

Elective Courses

SJEM2*** 4 SJEM2*** 4

20 SJEM2*** 4

SJEM3*** 4

SJEM3*** 4

Non-Core Courses 4 3 7

Total Credit 19 17 4 40

Page 10: Handbook 2011-2012

Faculty of Science Handbook, Session 2011/2012

9

BACHELOR OF SCIENCE (STATISTICS) SESSION 2011/2012 (123 CREDITS)

1. UNIVERSITY COURSES (21 CREDITS) Please refer to programme structure Bachelor of Science

2. CORE COURSES PROGRAMME (102 CREDITS)

(I) COMPULSORY COURSES (65 CREDITS)

LEVEL 1 (23 credits)

COURSE CODE

COURSE NAME PRE-REQUISITE CREDIT

SJEM1110 Basic Mathematics STPM Mathematics T/S or equivalent 4

SJEM1111 Calculus I STPM Mathematics T/S or equivalent 4

SJEM1130 Introduction to Computing STPM Mathematics T/S or equivalent 3

SJEM1211 Calculus II SJEM1111 pass with a minimum of grade C 4

SJEM1230 Mathematical Methods I SJEM1111 (Pass with a minimum of grade C) 4

SJEM1250 Probability & Statistics I SJEM1111 (pass with a minimum of grade C) 4

LEVEL 2 (42 credits)

SJEM2210 Advanced Calculus SJEM1211 (pass with a minimum of grade C) 4

SJEM2211 Linear Algebra SJEM1110 (pass with a minimum of grade C) 4

SJEM2230 Mathematical Methods II SJEM1230 (pass with a minimum of grade C) 4

SJEM2231 Structured Programming SJEM1111 (pass with a minimum of grade C) 4

SJEM2250 Probability and Statistics II SJEM1250 (pass with a minimum of grade C) 4

SJEM2251 Further Mathematical Statistics SJEM2250 4

SJEM2252 Stochastic Processes SJEM2250 4

SJEM2253 Non-parametric Statistics SJEM1250 4

SJEM2254 Regression Analysis SJEM1250 4

SJEM2255 Data Analysis I SJEM1250 4

SJEM2280 Appreciation of Mathematics SJEM1211 (pass with a minimum of grade C) 2

(II) ELECTIVE COURSES (at least 27 CREDITS)

SJEM3190 Industrial Training 4

SJEM3380 Mathematical Science Project 4

SJEM3450 Introduction to Multivariate Analysis SJEM2250 4

SJEM3451 Computer Intensive Methods in Statistics SJEM2250 4

SJEM3452 Applied Stochastic Processes SJEM2252 4

SJEM3453 Time Series and Forecasting Methods SJEM2250 4

SJEM3454 Further Topics in Regression Analysis SJEM2250 and SJEM2254 4

SJEM3455 Data Analysis II SJEM2250 and SJEM2255 4

SJEM3456 Introduction to Survey Sampling SJEM2250 4

SJEM3457 Statistical Process Control SJEM2250 4

SJEM3458 Introduction to Data Mining SJEM2250 4

SJEM3459 Bioinformatics SJEM2250 4

SJEM3460 Design and Analysis of Experiments SJEM1250 and SJEM2254 4

SJEM3461 Java Methods for Statistics and Actuarial Science SJEM1250 and SJEM2231 4

SJEM3462 Analysis of Failure and Survival Data SJEM2250 4

(III) NON CORE COURSES (10 Credits) * Courses Offered by Other Institute/Department of Specialization ( Please refer to the Non Core Courses from other Institute/Department within the Faculty of Science )

Core courses in B.Sc. (Mathematics), B.Sc. (Industrial and Computational Mathematics) and B.Sc. (Actuarial and Financial Mathematics), except courses with codes SJER4*** can also be taken as electives for this program. Please refer to the respective programmes.

Attention: Students who wish to specialize in B.Sc. (Statistics) must take at least 20 credits from courses with codes SJEM3*** (excluding SJEM3190) from those listed in this program structure.

Page 11: Handbook 2011-2012

Faculty of Science Handbook, Session 2011/2012

10

PROGRAMME GOAL To produce graduates with (sound) knowledge of statistics, capable of critical thinking and problem solving; who can adapt to diverse environment and contribute significantly in various professions. PROGRAMME LEARNING OUTCOMES At the end of the programme, graduates with B.Sc. (Statistics) are able to: 1. Explain the principles and concepts of mathematics and statistics; 2. Apply the mathematical and statistical principles in solving real world problems; 3. Conduct professional activities with good social skill and demonstrate a sense of responsibility; 4. Practice characteristics associated with professionalism and ethical responsibility in analyzing real life phenomena; 5. Communicate using critical thinking with effective, accurate and relevant concepts, and exhibit team work and leadership skills; 6. Convert problems into mathematical and statistical models, and develop scientific strategies to obtain solutions; 7. Engage in life-long learning to advance knowledge and applications of mathematics and statistics; 8. Apply managerial and entrepreneurial skills to manage resources needed to complete a task.

Page 12: Handbook 2011-2012

Faculty of Science Handbook, Session 2011/2012

11

LIST OF COURSES ACCORDING TO SEMESTER

(PLANNING OF COURSES)

COMPONENT SEMESTER 1 SEMESTER 2 TOTAL

CREDIT COURSE CREDIT COURSE CREDIT

University Courses

GTEE1101/2/3/4 English

3 GXEX1411 Ethnic Relations

2

12 GXEX1412 Basic Entrepreneurship Culture

2 GXEX1414 TITAS

2

SXEX1102 Statistics

3

Programme Core

Courses

Compulsory Courses

SJEM1110 Basic Mathematics

4 SJEM1211 Calculus II

4

23 SJEM1111 Calculus I

4 SJEM1230 Mathematical Methods I

4

SJEM1130 Introduction to Computing

3 SJES1250 Probability & Statistics I

4

Elective Courses

Non-Core Courses

Total Credit 16 19 35

COMPONENT SEMESTER 3 SEMESTER 4 TOTAL

CREDIT COURSE CREDIT COURSE CREDIT

University Courses GXEX1401 Information Skills Course

1 GXEX Cocurriculum

2 3

Programme Core

Courses

Compulsory Courses

SJEM2210 Advanced Calculus

4 SJEM2230 Mathematical Methods II

4

34

SJEM2211 Linear Algebra

4 SJEM2251 Further Mathematical Statistics

4

SJEM2231 Structured Programming

4 SJEM2253 Non-Parametric Statistics

4

SJEM2250 Probability & Statistics II

4 SJEM2254 Regression Analysis

4

SJEM2280 Appreciation of Mathematics

2

Elective Courses

Non-Core Courses

Total Credit 19 18 37

Page 13: Handbook 2011-2012

Faculty of Science Handbook, Session 2011/2012

12

COMPONENT SEMESTER 5 SEMESTER 6 TOTAL

CREDIT COURSE CREDIT COURSE CREDIT

University Courses SXEX1411 Introduction to Science and Technology Studies

3 GTEE1101/2/3/4 English

3

6

Programme Core

Courses

Compulsory Courses

SJES2252 Stochastic Processes

4

8 SJEM2255 Data Analysis I

4

Elective Courses

SJEM3*** 4 SJEM3*** 4

16 SJEM3*** 4

SJEM3*** 4

Non-Core Courses Courses outside institute or

outside faculty 3 Courses outside

institute or outside faculty

3 6

Total Credit 18 18 36

COMPONENT SEMESTER 7

TOTAL CREDIT COURSE CREDIT

University Compulsory Courses

Programme Core Courses

Compulsory Courses

Elective Courses

SJEM3*** 4

12 SJEM3*** 4

SJEM3*** 4

Non-Core Courses Courses outside institute or outside faculty

4 4

Total Credit 16 16

Page 14: Handbook 2011-2012

Faculty of Science Handbook, Session 2011/2012

13

BACHELOR OF SCIENCE (ACTUARIAL AND FINANCIAL MATHEMATICS) SESSION 2011/2012 ( 143 CREDITS)

1. UNIVERSITY COURSES (21 CREDITS) Please refer to programme structure Bachelor of Science

2. CORE COURSES PROGRAMME (122 CREDITS)

(I) COMPULSORY COURSES (90 CREDITS)

LEVEL 1 (23 credits)

COURSE CODE COURSE NAME PRE-REQUISITE CREDIT

SJEM1110 Basic Mathematics STPM Mathematics T/S or equivalent 4

SJEM1111 Calculus I STPM Mathematics T/S or equivalent 4

SJEM1130 Introduction to Computing STPM Mathematics T/S or equivalent 3

SJEM1211 Calculus II SJEM1111 (pass with a minimum of grade C) 4

SJEM1230 Mathematical Methods I SJEM1111 (pass with a minimum of grade C) 4

SJEM1250 Probability & Statistics I SJEM1111 (pass with a minimum of grade C) 4

LEVEL 2 (36 credits)

SJEM2210 Advanced Calculus SJEM1211 (pass with a minimum of grade C) 4

SJEM2211 Linear Algebra SJEM1110 (pass with minimum of grade C) 4

SJEM2230 Mathematical Methods II SJEM1230 (pass with a minimum of grade C) 4

SJEM2231 Structured Programming SJEM1111 (pass with a minimum of grade C) 4

SJEM2250 Probability & Statistics II SJEM1250 (pass with a minimum of grade C) 4

SJER2211 Interest Theory and Derivatives SJEM1110 4

SJER2212 Microeconomics STPM Mathematics T/S or equivalent 3

SJER2213 Macroeconomics STPM Mathematics T/S or equivalent 3

SJER2214 Introduction to Accounting STPM Mathematics T/S or equivalent 3

SJER2215 Introductory Life Contingencies SJEM2250 3

LEVELS 3 and 4 (31 credits)

SJER3191 Industrial Training in Actuarial Science 8

SJER3216 Further Life Contingencies SJER2215 3

SJER3217 Investment and Financial Analysis I SJEM2250 and SJER2211 4

SJER3218 Introduction to General Insurance SJEM2250 and SJER2215 3

SJER4221 Life Insurance and Takaful SJEM2250 and SJER2215 3

SJER4222 Investment And Financial Analysis II SJER3217 4

SJER4223 Loss Reserving, Accounting and Reinsurance for Property and Casualty Insurance

SJEM2250 and SJER2215 3

SJER4271 Group Presentations on Selected Topics in Actuarial Science and Finance

SJEM2250 and SJER2215 3

(II) ELECTIVE COURSES (at least 22 CREDITS)

SJEM2233 Basic Operational Research SJEM1110 4

SJEM2251 Further Mathematical Statistics SJEM2250 4

SJEM2252 Stochastic Processes SJEM2250 4

SJEM2254 Regression Analysis SJEM1250 4

SJEM3380 Mathematical Science Project 4

SJEM3451 Computer Intensive Methods in Statistics SJEM2250 4

SJEM3452 Applied Stochastic Processes SJEM2252 4

SJEM3453 Time Series and Forecasting Methods SJEM2250 4

SJEM3454 Further Topics in Regression Analysis SJEM2250 and SJEM2254 4

SJEM3461 Java Methods for Statistics and Actuarial Science SJEM1250 and SJEM2231 4

SJEM3462 Analysis of Failure and Survival Data SJEM2250 4

SJER4323 Credibility and Ruin Theory SJEM1211 and SJEM2250 3

SJER4324 Introduction to Risk Theory SJEM1211 and SJEM2250 3

(III) NON CORE COURSES (10 Credits) * Courses Offered by Other Institute/Department of Specialization ( Please refer to the Non Core Courses from other Institute/Department within the Faculty of Science )

Core courses under B.Sc. (Mathematics), B.Sc. (Statistics) and B.Sc. (Computational and Industrial Mathematics) may also be taken by a student in B.Sc. (Actuarial and Financial Mathematics) programme as elective courses. Please refer to the relevant programmes.

Page 15: Handbook 2011-2012

Faculty of Science Handbook, Session 2011/2012

14

Attention: Courses with the codes SJER2212, SJER2213, SJER2214, SJER3191 and SJER 4*** are to be taken only by the student in the B.Sc. (Actuarial and Financial Mathematics) programme.

*These courses are only offered once per session.

Elective Courses (Non Core Courses) (10 credit hours)

Courses offered from other Institutes/Departments or outside the Faculty of Science

Course code Name of Courses Prerequisite Credit Hours

CBEB2102 Financial Management 3

CBEB3104 Corporate Finance CBEB2102 3

PROGRAMME GOAL To produce graduates with (sound) knowledge of actuarial and financial mathematics, capable of critical thinking and problem solving; who can adapt to diverse environment and contribute significantly in various professions. PROGRAMME LEARNING OUTCOMES At the end of the programme, graduates with B.Sc (Actuarial and Financial Mathematics) are able to: 1. Explain the principles and concepts of actuarial science, finance, statistics and mathematics. 2. Apply actuarial science, finance, statistics and mathematics concepts to solve real-world problems. 3. Conduct professional activities with good social skills and demonstrate a sense of responsibility. 4. Practise characteristics associated with professionalism and ethical responsibility in analyzing real life phenomena. 5. Communicate using critical thinking with effective, accurate and relevant concepts, and exhibit team work and leadership skills. 6. Convert problems into mathematical and statistical models, and develop scientific strategies to obtain solutions; 7. Engage in life-long learning to advance knowledge and applications of actuarial science, finance, statistics and mathematics; 8. Apply managerial and entrepreneurial skills to manage resources needed to complete a task.

Page 16: Handbook 2011-2012

Faculty of Science Handbook, Session 2011/2012

15

LIST OF COURSES ACCORDING TO SEMESTER (PLANNING OF COURSES)

COMPONENT SEMESTER 1 SEMESTER 2 TOTAL

CREDIT COURSE CREDIT COURSE CREDIT

University Courses

GTEE1101/2/3/4 English

3

GTEE1101/2/3/4 English

3

13 GXEX1412 Basic Entrepreneurship Culture

2 GXEX1411 Ethnic Relations

2

SXEX1102 Statistics

3

Programme Core

Courses

Compulsory Courses

SJEM1110 Basic Mathematics

4 SJEM1211 Calculus II

4

23

SJEM1111 Calculus I

4 SJEM1230 Mathematical Methods I

4

SJEM1130 Introduction to Computing

3

SJEM1250 Probability & Statistics I

4

Elective Courses

Non-Core Courses

Total Credit 16 20 36

COMPONENT SEMESTER 3 SEMESTER 4 TOTAL

CREDIT COURSE CREDIT COURSE CREDIT

University Compulsory Courses

GXEX1401 Information Skills Course

1 GXEX Cocurriculum

2 3

Programme Core

Courses

Compulsory Courses

SJEM2210 Advanced Calculus

4 SJEM2230 Mathematical Methods II

4

30

SJEM2211 Linear Algebra

4 SJER2231 Structured Programming

4

SJEM2250 Probability & Statistics II

4 SJER2215 Introductory Life Contingencies

3

SJER2211 Interest Theory and Derivatives

4

SJER2212 Microeconomics

3

Elective Courses

SJEM 2***

4

4

Non-Core Courses CBEB2102

Financial Management 3

3

Total Credit 20 20 40

Page 17: Handbook 2011-2012

Faculty of Science Handbook, Session 2011/2012

16

COMPONENT SEMESTER 5 SEMESTER 6 TOTAL

CREDIT COURSE CREDIT COURSE CREDIT

University Courses SXEX1411 Introduction to Science and Technology Studies

3

3

Programme Core

Courses

Compulsory Courses

SJER3216 Further Life Contingencies

3 *SJER2213 Macroeconomics (week 1 – 7)

3

24

SJER3217 Investment and Financial Analysis I

4 *SJER2214 Introduction to Accounting (week 1 – 7)

3

*SJER3218 Introduction to General Insurance (week 1 – 7)

3

SJER3191 Industrial Training in Actuarial Science (week 9 – 15 and Semester 3 consecutively)

8

Elective Courses

SJEM2/3***

4

4

Non-Core Courses

CBEB3104 Corporate Finance

3 5 Courses outside institute

or outside faculty 2

Total Credit 19 17 36

* Students have to double their number of credits for the first 7 weeks because they have to register for Industrial Training for 16 weeks.

COMPONENT SEMESTER 7 SEMESTER 8 TOTAL

CREDIT COURSE CREDIT COURSE CREDIT

University Courses GXEX1414 TITAS

2

2

Programme Core

Courses

Compulsory Courses

SJER4221 Life Insurance and Takaful

3 SJER4222 Investment and Financial Analysis II

4

13 SJER4223 Loss Reserving, Accounting and Reinsurance for Property and Casualty Insurance

3

SJER4271 Group Presentations on selected Topics In Actuarial Science and Finance

3

Elective Courses

SJEM 3*** /SJER 4*** 4 SJEM 3*** /SJER 4*** 4 16

SJEM 3*** /SJER 4*** 4 SJEM 3*** /SJER 4*** 4

Non-Core Courses Courses outside institute

or outside faculty 2

2

Total Credit 16 17 33

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NON-CORE COURSES (For students from other institute/departments in Faculty of Science. Students may choose any of the following course)

Course code

Course name Prerequisite Credit

SJEM1110 Basic Mathematics STPM Mathematics T/S or equivalent 4

SJEM1111 Calculus I STPM Mathematics T/S or equivalent 4

SJEM1211 Calculus II SJEM1111 (pass with a minimum of grade C) 4

SJEM1230 Mathematical Methods I SJEM1111 (pass with a minimum of grade C) 4

SJEM1250 Probability & Statistics I SJEM1111 (pass with a minimum of grade C) 4

SJEM2211 Linear Algebra SJEM1110 (pass with a minimum of grade C) 4

SJEM2212 Introduction to Combinatorics SJEM1110 4

SJEM2233 Basic Operational Research SJEM1110 4

SJEM2250 Probability & Statistics II SJEM1250 (pass with a minimum of grade C) 4

SJEM2431 Management Mathematics SJEM1111 4

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INSTITUTE OF MATHEMATICAL SCIENCES

The Institute of Mathematical Sciences was established as a department in the Faculty of Science when the University of Malaya was founded in Kuala Lumpur in 1959. It has grown into three branches, Pure Mathematics, Applied Mathematics and Statistics. The Institute offers 6 first degree programmes. The Institute also offers various service courses to other faculties including the Faculty of Engineering. For the 2011/2012 session, the Institute offers the following first degree programmes: Bachelor of Science (Mathematics) Bachelor of Science (Industrial and Computing

Mathematics) Bachelor of Science (Statistics) Bachelor of Science (Actuarial and Financial

Mathematics) Bachelor of Science with Education (Mathematics) Bachelor of Arts (Mathematics) The four Bachelor of Science programmes are set up to provide more opportunities for an undergraduate to major in the field of mathematics according to his or her interests. In addition, the Bachelor of Science in Education (Mathematics) is a programme that enables a student to expand and consolidate his or her mathematical knowledge in line to become a graduate educator. All these programmes will assist to fulfill the vacancies of skilled workforce in science and technology in the public and private sectors in line with Malaysia's aspiration to become an industrial nation.

STAFF The Institute has a group of experience lecturers in teaching. They are also active in doing research and have been publishing many writings in local and international journals. The research activities encompass a broad spectrum; from findings and knowledge which are abstract in nature, to those with direct applications in the industry. The Institute also strives to establish and forge a close relationship with industry and other research institutions. This will strengthen the quality of teaching and supervising of projects/theses for students in Bachelors, Masters and Doctoral levels. HEAD: Prof. Madya Dr. Mohd Omar, MSc(Hull), PhD(Exeter), BSc DEPUTY HEAD: Prof. Dr. Angelina Chin Yan Mui, BSc, MSc, PhD(Q'ld), Associate Prof. Abdul Hadi Yaakub, BSc(Nevada), MSc(Illinois)

PURE MATHEMATICS

COORDINATOR: Dr. Chia Gek Ling, BSc, MSc, PhD, FTICA PROFESSOR: Dr. Angelina Chin Yan Mui, BSc, MSc, PhD(Q'ld), Dr. Chia Gek Ling, BSc, MSc, PhD, FTICA Dr. Lim Ming Huat, BSc(Nan), PhD(BrCol) Dr. Suzeini Abd Halim, BSc(NSW), PhD(Wales)

Dr. Wong Peng Choon, BSc, MSc, PhD(NYU) ASSOCIATE PROFESSOR: Dr. Chooi Wai Leong, BSc, MSc, PhD Dr. Deng Chai Ling, BSc, MSc, PhD Dr. Kon Song How, BSc, MSc, PhD LECTURER: En. Mohamad Bakri Zubir, BSc, MSc(Exeter) Dr. Ong Siew Hui, BSc, MSc, PhD Dr. Loo Tee How, BSc, MSc, PhD Dr. Oon Shea Ming, BSc, MSc, PhD(UHP) Dr. Wong Kok Bin, BSc, MSc, PhD Dr. Siraj Uddin, MSc, PhD(Aligarh)

APPLIED MATHEMATICS COORDINATOR: Dr. Noor Hasnah Moin, BSc, MSc(Sussex), PhD(Sheff) PROFESSOR: Dr. Bernardine R. Wong Cheng Kiat, BSc, MSc,PhD, CPhys, MInstP Dr. Kurunathan Ratnavelu, BSc, MSc, PhD(Flinders), CPhys, MinstP, FASc ASSOCIATE PROFESSOR: Dr. Mohd Omar, MSc(Hull), PhD(Exeter), BSc Dr. Nordin Haji Mohamad, BSc, MSc(Lond), PhD(City) Dr. Noor Hasnah Moin, BSc, MSc(Sussex), PhD(Sheff) Dr. Wan Ainun Mior Othman, BSc(UNCC), MSc(N Carolina State), PhD(USM) LECTURER: Dr. Amran Hussin, BSc, MSc (Soton), PhD (Soton) Ms. Che Wan Mariam Saad, BA(Chico), MSc(Irvine) Mr. Mohd Abu Omar Awang, BSc(Lond), MPhil(East Anglia), ARCS Dr. Mohd. Khanafiah Ismail, BSc, MSc(Brun), PhD(Dundee) Dr. Yap Yee Jiun, PhD(Brunel) Ms. Siti Suzlin Supadi, BSc, MSc Mr. Zailan Siri, BSc, MSc Dr. Kumaresan Nallasamy, PhD(Gandhigram)

STATISTICS COORDINATOR (B.Sc STATISTICS): Dr. Nor Aishah Hamzah, BSc(Southampton), MSc(Leeds), PhD(Bristol), DipEd(UKM), MIS(UK) COORDINATOR (B.Sc ACTUARIAL AND FINANCIAL MATHEMATICS) Dr. Ng Kok Haur, BSc, MSc(UPM), PhD PROFESSOR: Dr. Nor Aishah Hamzah, BSc(Southampton), MSc(Leeds), PhD(Bristol), DipEd(UKM), MIS(UK) Dr. Ong Seng Huat, BSc, MSc, PhD

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ASSOCIATE PROFESSOR: Mr. Abdul Hadi Yaakub, BSc(Nevada), MSc(Illinois) Dr. Ibrahim Mohamed, BSc(Bristol), MSc(Reading), PhD (UITM). Dr. Omar Mohd. Rijal, BSc(Ulster), PhD(Glasgow) LECTURER: Ms. Wu Swee Leng, BSc, MSc Dr. Ng Kok Haur, BSc, MSc(UPM), PhD Dr. Adriana Irawati Nur Ibrahim, BSc, MSc, PhD(Bath) Dr. Rossita Mohamad Yunus, BSc, MSc, PhD(USQ) Dr. Ng Choung Min, BSc, MSc, PhD COORDINATOR ((B.Sc. Ed (Mathematics)) Dr. Amran Hussin, BSc, MSc (Soton), PhD (Soton)

COMPUTER FACILITIES To date the Insitute has a computer lab equipped with 6 tablet PCs, 10 laptops, 2 workstations, 90 Pentium IV computers, 3 laser printers, 1 colour printer, 4 heavy duty dot matrix printers, all interconnected in a network system. The lab is also equipped with 5 LCD projectors, 1 visualizer, and 2 scanners. The lab utilizes state of the art software such as Matlab (with various Toolboxes), Mathematica v6, MathType v5.2, Minitab R14, Visual C++, S-PLUS v8, Scientific Word 5.5, PcTeX 32 and MathCAd v13. In addition, three of the lecture halls are equipped with a LCD projector and a visualizer each. Level II and III students specialising in the programmes of the Institutes are provided with internet access.

BACHELOR OF SCIENCE PROGRAMMES Please refer to programme charts for courses.

FURTHER DEGREE Apart from teaching and supervising in the Bachelors level, the staff of the Institute also supervise research projects that lead to Masters and Doctorate degrees in the three branches of mathematics. The modes for further degree programmes at the Institute are by research with dissertation or theses.

JOB OPPORTUNITIES

The learning of mathematics will help increase one's skills in problem solving and analysis. It trains the mind to manipulate information, to form accurate, complicated and abstract ideas and to enable one to discern complicated arguments. The training to think quantitatively, logically and analytically in problem solving may prove valuable in one's chosen career. Since the use of mathematics is all encompassing in human endeavour, a graduate career opportunities are almost limitless and not only confined to teaching and research. Many graduates from this Institute have found employment in the financial sectors (banking, accountancy and insurance for instance), management, business, industry and computing sectors.

SYNOPSIS OF COURSES SXEX1102 STATISTICS (FACULTY OF SCIENCE) Introduction to Statistics. Presentation and organization of data. Descriptive statistics. Sample and population. Measures of location and dispersion. Probability, Axioms. Probability distributions: Binomial, Poisson and normal. Sampling distributions. Central limit theorem. Estimation confidence intervals and hypothesis testing for mean and proportion. Statistical inference involving two populations. Hypothesis testing using the chi-square distribution. Assessment: Final Examination: 70% Continuous Assessment: 30% Medium of Instruction: English Humanity Skill: CS3, CT3 References: 1. S-Plus 2000 Guide to Statistics Volume 1, Mathsoft

corporation. 2. Mann, Prem. S., (2003). Introductory Statistics, John

Wiley & Sons. 3. Siegel, A.W., and Morgan, C.J., (1998). Statistics and

Data Analysis, John Wiley & Sons. 4. Evans, J.R. and Olson, D.L. (2002) Statistics, Data

Analysis and Decision Modeling and Student CD-ROM (2nd Edition). Prentice Hall

SJEM1110 BASIC MATHEMATICS

Introductory logic. Mathematical statements. Quantifiers. Rules of inference. Mathematical induction, binomial theorem. Sets, Cartesian products, equivalence relations, functions, bijections, inverse functions. Integers, rational numbers, real numbers. Complex numbers. DeMoivre’s theorem and roots of unity. Polynomials and equations. Remainder theorem, fundamental theorem of algebra, conjugate roots.

Systems of linear equations, row reduction, echelon forms. Matrix operations, algebraic properties of matrices, inverses, elementary matrices, linear independence and homogeneous linear systems, matrices with special forms. Determinants, cofactor expansion, properties of determinants, Cramer’s rule, eigenvalues, eigenvectors and diagonalization. Assessment: Final Examination: 60% Continuous Assessment: 40% Medium of Instruction: English Humanity Skill: CT2, LL1

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References: 1. Gilbert, Will J., Vanstone, Scott A. (2005). Introduction

to Mathematical Thinking: Algebra and Number Systems, Pearson Prentice Hall Inc.

2. Douglas E. Ensly, J. Winston Crawley, (2006). Discrete Mathematics. John Wiley and Sons.

3. Devlin, K. (1992). Sets, Functions and Logic, Chapman & Hall (2nd edition).

4. Anton, H., Rorres, C. (2005). Elementary Linear Algebra with Applications, Wiley High Education Inc (9th edition).

5. Larson, R. and Falvo D.(2010 Elementary Linear Algebra. Brooks/Cole Cengage learning (6th edition).

SJEM1111 CALCULUS I Real numbers and real line. Inequality and absolute values. Functions and their graphs. Combining Functions. Limits: Intuitive, limit laws, one-sided limits, limits involving infinity, epsilon-delta definition for limits. Continuity. Derivatives: tangent lines and definition for derivatives. Differentiation Rules including the Chain Rule and implicit differentiation. Rolle's Theorem, The Mean Value Theorem, Maximum, minimum, concavity and points of inflection. Graph sketching. Indeterminate forms and L'Hospital's Rule. Definite and indefinite integrals. Fundamental theorem of Calculus and differentiation of integrals. Integration methods. Assessment Final Examination: 60% Continuous Assessment: 40% Medium of Instruction: English Humanity Skill: CT2, LL1 References: 1. Weir, Maurice D., Joel Hass & Giordano, Frank R.

(2005) Thomas' Calculus, Pearson Education, Inc (11th edition).

2. Stewart, J. (2003). Calculus, Brooks and Cole, (5th. Edition).

3. Adams, Robert A. (2006). Calculus: A complete course, Pearson Education.

4. Anton, H., Bivens, I. & Davis, S. (2002) Calculus, John Wiley & Sons, (7th edition).

5. Smith, R.T., Minton, R.B., (2002). Calculus, McGraw Hill, (2nd edition) .

SJEM1130 INTRODUCTION TO COMPUTING MATLAB – The Matlab environment, entering matrices, variables and constants, operations, built-in functions, formatted output, graph plotting, logical data type, branching and loops, scripts, user-defined functions. Excel – spreadsheet basics, entering labels, numbers and formulae. Absolute & relative addressing, Excel functions. Graph plotting, use of solvers. Solving nonlinear equations, system of linear equations. Assessment Final Examination: 50% Continuous Assessment: 50%

Medium of Instruction: Malay / English Humanity Skill: CT2, LL1 References: 1. Matlab Programming for Engineers by Stephen

J.Chapman, Thomson, 2004. 2. Introduction to Engineering Programming: In C, Matlab

and Java, by Mark Austin and David Chancogne, Wiley, 1999.

3. Mastering MATLAB 7 by Duane Hanselman and Bruce Littlefield, Pearson Education; 2005.

4. Excel for Engineers and Scientists by S. C. Bloch and Sylvan Charles Bloch, John Wiley & Sons 2003

5. Excel for Scientists and Engineers: Numerical Methods by E. Joseph

Billo, Wiley-Interscience; 2007 SJEM1211 CALCULUS II Transcendental functions, inverses of functions and their derivatives, exponential, logarithmic and hyperbolic functions, inverses of hyperbolic functions, partial fractions and trigonometric substitutions, improper integrals, series, Taylor and Maclaurin series, Power series. Vectors, lines and planes. Conic sections, polar coordinates. Cyclinder and quadric surfaces, functions of two variables and their graphs and level curves. Limits and continuity of functions of two variables. Cylindrical and spherical coordinates, vector-valued functions and space curves, trajectory. Differentiation and integration of vector valued functions. Applications. Assessment: Final Examination: 60% Continuous Assessment: 40% Medium of Instruction: English Humanity Skill: CT3, LL2 References: 1. Weir, M.D., Hass, J. & Giordano, F.R., (2005).

Thomas’s Calculus. Pearson Addison-Wesley (11th ed).

2. Smith, R.T. & Minton, R.B. (2005). Calculus, McGraw-Hill, (2nd ed).

3. Thomas, G. B. & Finney, R.L. (1996). Calculus and Analytic Geometry. Addison-Wesley Publ. Co. (9th ed)

4. Repka, J. (1994). Calculus with Analytic Geometry, Wm. C. Brown Publ. Co.

5. Ellis, R. & Gullick, D. (1994). Calculus with Analytic Geometry. Harcourt Brace & Co. (5th ed)

SJEM1230 MATHEMATICAL METHODS I Numerical methods: Computer arithmetic: floating-point numbers, round off error, machine precision, overflow/underflow, numerical cancellation, truncation error.

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Roots of Nonlinear equation: Taylor series, bisection method, fixed-point iteration, Newton – Raphson method, secant method. Interpolation: Lagrange interpolation, Divided differences, Hermite interpolation, cubic spline interpolation. Ordinary Differential Equations (ODE): 1st degree ODE: Definitions, solution concepts, valid solution intervals. Solutions to variable separable equations, linear equations, Bernoulli, exact and non-exact, homogeneous equations and equations with constant coefficients. Some examples of applications of 1st degree ODE. Linear ODE with order 2 and higher: Definitions, solution concepts, linear independence, Wronskian. Solution to homogeneous and non-homogeneous equations. Method of undetermined coefficients. Assessment: Final Examination: 60% Continuous Assessment: 40% Medium of Instruction: English Humanity Skill: CS2, CT2, LL1 References: 1. Friedman F. L. and Koffman, Elliot B. (1997) Problem

solving, Abstraction and Design Using C++ Addison-Wesley

2. Computer Science- A Structured Programming Approach using C- Third Edition Thomson

3. Landau (Princeton Press) Rubin H. (2008) A Survey of Computational Physics : Introductory Computational Science.

4. Press, W. H. (2007). Numerical Recipes 5. Kincaid David R. and Ward Cheney, E. (2002)

Numerical Analysis: Mathematics of Scientific Computing, (3rd Edition).

SJEM1250 PROBABILITY & STATISTICS I Properties of probability. Counting techniques. Conditional probability. Independent events. Bayes Theorem. Discrete random variables. Mathematical Expectation. Discrete distributions: uniform, hypergeometric, Bernoulli, binomial, geometric, negative binomial and Poisson. Moment generating function. Continuous random variables and its mathematical expectation. Continuous distributions: uniform, exponential, gamma, chi-squared and Normal. Bivariate distributions. Distributions of functions of random variables. Random functions related to the normal distribution. Central limit theorem. Approximation for discrete distributions. Limiting moment generating functions. Assessment: Final Examination: 60% Continuous Assessment: 40% Medium of Instruction: English

Humanity Skill: CS2, CT2, LL2, EM2 References: 1. Hogg, R.V. & Tani,s E.A. (2010).Probability & Statistics

Inference,Prentice Hall (8th ed). 2. Larson, H.J. (1982) Introduction to Probability Theory

& Statistical Inference, Wiley ( 3rd ed). SJEM2210 ADVANCED CALCULUS Partial derivatives. Differentiability and continuity. Linearization and differentials. The Chain Rule, Partial derivatives with constrained variables. Directional derivatives. Gradient, divergence and curl. Tangent planes. Taylor’s Theorem. Extremum problems of functions of two variables. Lagrange multipliers. Double integrals, iterated integrals and Fubini’s Theorem. Applications to areas and volumes. Double integrals in polar form. Triple integrals, iterated integrals. Volumes and masses. Triple integrals in cylindrical and spherical coordinates forms. Substitution in multiple integrals, Jacobians. Functions, bijective functions, inverse functions. Finite and infinite sets, countable and uncountable sets. The Real Number system. Bounds, supremum and infimum. Archimedean property. Rational and irrational numbers. Properties of real numbers. Sequences of real numbers, convergence. Limit Theorems. Monotone sequences, Cauchy sequences and subsequences. Open and closed sets, accumulation points. Limits of functions, Continuity of functions. Review of some important properties of continuous functions. Assessment: Final Examination: 60% Continuous Assessment: 40% Medium of Instruction: English Humanity Skill: CS1, CT2, LL1 References: 1. Thomas, G.B. & others, (2007). Thomas’ Calculus,

Pearson/Addison-Wesley (11th Edition). 2. Stewart, J. (2008). Brooks/Cole Publishing Co. (ITP),

Calculus (6th Edition). 3. Anton, H., Bevins, I. & Davis, S. (2005). John Wiley &

Sons, Calculus, (8th ed) . 4. Kosmala, W. (2004). A Friendly Introduction to

Analysis, Pearson (2nd Edition). SJEM2211 LINEAR ALGEBRA Vector spaces and subspaces, basis and dimension, row space and column space, rank and nullity. Linear transformations, kernel and range, matrix representation, similarity and diagonalizability, Cayley-Hamilton Theorem. Assessment: Final Examination: 60% Continuous Assessment: 40%

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Medium of Instruction: English Humanity Skill: CS1, CT2, LL1 References: 1. Anton, H. (2004). Elementary Linear Algebra, John

Wiley and Sons Inc (9th Edition) . 2. Johnson, L.W., Riess, R.D. & Arnold, J.T. (2002).

Introduction to Linear Algebra, Addison-Wesley Publication Co (5th Edition).

3. Lay, D.C. (2000). Linear Algebra and its application, Addison-Wesley Publication Co. (2nd Edition).

4. J.H Kwak & S.P Hong (2004) Linear Algebra, Brikhauser (2nd Edition).

5. Cheney, W. & Kincaid, D. (2008) Linear Algebra: Theory and Applications, Jones and Bartlett Publishers.

SJEM2212 INTRODUCTION TO COMBINATORICS Ordered and equivalence relations, binomial and multinomial theorems, recurrence relations, principle of inclusion and exclusion, Latin squares, magic squares, basic properties of graphs, circuits and cycles in graphs, trees and their applications. Assessment: Final Examination: 70% Continuous Assessment: 30% Medium of Instruction: English Humanity Skill: CS1, CT2, LL1 References: 1. Chen, C.C. & Koh, K.M. (1992). Principles and

Techniques in Combinatorics, World Scientific. 2. Lovasz, L., Pelikan, J. & Vesztergombi, K. (2003).

Discrete Mathematics : Elementary and Beyond, Springer.

3. Rouse, W.W. & Coxeter, H.S.M. (1974). Mathematical Recreations and Essays, Univ. of Toronto Press (12th ed).

SJEM2213 ALGEBRA I Groups and subgroups. Order of an element. Lagrange’s theorem. Normal subgroups and factor groups. Homomorphisms and isomorphisms, Rings, integral domains and fields. Subrings and subfields. Ideals and quotient rings. Rings of polynomials. Division algorithm and Euclidean algorithms in polynomial rings. Unique factorization theorem. Assessment: Final Examination: 60% Continuous Assessment: 40% Medium of Instruction: English Humanity Skill: CT3, LL2

References: 1. Durbin, J.R. (2004). Modern Algebra, An Introduction,

John Wiley 5th edition. 2. Fraleigh, J.B. (2002). A First Course in Abstract

Algebra, 7th edition Addison Wesley (7th edition). 3. Gilbert, W.J, (2002). “Modern Algebra with

Applications”, New edition. Wiley-Interscience. SJEM2214 INTRODUCTION TO ANALYSIS Infinite series, convergence. Tests of convergence. Absolute and conditional convergence. Rearrangement of series. Topology of the real line. Properties of continuous functions. Uniform continuity. Derivative of a function. Properties of differentiable functions. Mean Value Theorems. Higher order derivatives. L’Hospital’s Rules. Assessment : Final Examination: 60% Continuous Assessment: 40% Medium of Instruction: English Humanity Skill: CS2, CT2, LL1 References: 1. Kosmala, W. (2004). A Friendly Introduction to

Analysis, Pearson (2nd ed). 2. Gaughan, E. (1998). Intoduction to Analysis.

Brooks/Cole Publishing Co (5th ed). 3. Haggarty, R. (1993). Fundamentals of Mathematical

Analisis. Addison-Wesley Publ. Co. (2nd ed). 4. Rosihan Mohamed Ali & Ong Boon Hua( 1999).

Pengantar Analisis, Penerbit Universiti Sains Malaysia

5. Pownall M.W. (1994). Real Analysis: A First Course with Foundations, Wm. C. Brown Publ. Co.

6. Bartle R.G. & Sherbert,D.R. (1992). Introduction to Real Analysis John Wiley & Sons Inc (2nd ed).

SJEM2215 COMPLEX VARIABLES Complex number system. Complex function, limits, continuity, differentiability and analytic function. Cauchy-Riemann equations, Harmonic functions. Mapping and other properties of elementary functions. Complex Integration, Cauchy’s Theorem, Cauchy’s Integral Formula. Sequences and series of complex functions. Assessment: Final Examination: 60% Continuous Assessment: 40% Medium of Instruction: English Humanity Skill: CT2, LL1

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References: 1. Churchill, R.V. & Brown, J.W. (2003). Complex

Variables and Applications, McGraw-Hill Book Co (7th ed).

2. Mathews John H. and Howell, Russell W. (2006).Complex Analysis: for Mathematics and Engineering,.Jones & Bartlett Pub.Inc. (5th ed).

3. Nguyen Huu Bong, (1994). Analisis Kompleks dan Penerapan, Dewan Bahasa dan Pustaka.

4. Howie, John M.( 2007). Complex Analysis. Springer, (3rd ed).

SJEM2230 MATHEMATICAL METHODS II Numerical Method Numerical differentiation: Forward, backward and central finite difference. Numerical Integration: rectangular, trapezoidal, Simpson’s, Romberg’s. Composite method. Systems of linear and non-linear equations: Matrix factorization, LU factorization. Ordinary Differential Equations 2nd and higher order ordinary differential equations: Solutions of non-homogeneous equations, variation of parameters. Series solution of ordinary differential equations. Frobenius’s method, Legendre and Bessel’s equations. Assessment: Final Examination: 60% Continuous Assessment: 40% Medium of Instruction: Malay / English Humanity Skill: CS2, CT3, TS1, LL1 References: 1. Mathematical Elements for Computer Graphics, 2nd

Ed., D.F. Rogers & J.A. Adams, McGraw Hill International Editions, 1990

2. Computer Graphics, Donald Hearn, M. Pauline Baker, Prentice Hall, 1994

3. Computer Graphics Using Open GL, 2nd Ed., F. S. Hill, Jr, Prentice Hall, 2001

4. Computer Graphics, Schaum’s Outlines Series 5. OpenGL SUPER BIBLE (2nd Ed), Richard S. Wright,

Jr., Michael Sweet, Waite Group Press, 2000D.G. Zill & M.R. Cullen, Differential Equations with Boundary-Value Problems, 7th Edition, Brooks/Cole, 2005

SJEM2231 STRUCTURED PROGRAMMING Algorithms: Structured programming – sequence, decision and loops. Object-oriented design. C++ programming: fundamental data types – int, double, char. C++ operators, precedence. Pre-processor directives. In-Built functions. User-defined functions – pass by value, pass by reference. One-dimensional and two-dimensional arrays. Introduction to user-defined data types – structures and classes.

Applications to numerical methods: integer- and floating point arithmetic, root-finding, solution of ordinary differential equations. Use of random number generators. Assessment: Final Examination: 50% Continuous Assessment: 50% Medium of Instruction: English Humanity Skill: CS3, CT3, TS2, LL2 References: 1. Programming with C++(2nd Ed.), John R. Hubbard,

McGraw-Hill, (2000). 2. C++ program design: an introduction to programming

and object- oriented design (3rd Ed.), James P. Cohoon and Jack W. Davidson, McGraw-Hill, (2002).

3. Problem Solving, abstraction and design using C++ (3rd Ed.), Frank L. Friedman and Elliot B. Koffman, Addison-Wesley, (2000).

4. Numerical Recipes in C++: The art of scientific computing, William H. Press, Saul A. Teukolsky, William T. Vetterling and Brian P. Flannery, Cambridge U. P., (2002).

5. Numerical Analysis: Mathematics of Scientific Computing, 3rd Edition David R. Kincaid and E. Ward Cheney (2002).

SJEM2232 VECTORS AND MECHANICS Introduction to Vector. Dot and Cross product. Vector differentiation (normal and partial) – space, curves, tangent. Displacement, velocity and acceleration.Scalar fields – gradient. Vector fields – divergence and curl. Polar, cylindrical and spherical coordinate systems. Introduction to Mechanics. Inertial reference frame. Particle motion in 1-, 2- and 3-dimensions. Newton’s laws of motion. Central forces. Concept of work and energy. Conservation laws. Simple harmonic motion. Non-inertial reference frames. Assessment: Final Examination: 60% Continuous Assessment: 40% Medium of Instruction: Malay / English Humanity Skill: CS3, CT3, LL1 References: 1. Engineering Mathematics (5th ed), KA Stroud & D

Booth, Palgrave, (2001). 2. Advanced Engineering Mathematics (8th ed), Erwin

Kreszig, Wiley, (1998). 3. Modern Engineering Mathematics (2nd ed), Glyn

James, Addison-Wesley, (1996). 4. Analytical Mechanics (7th ed), Fowles G.R. &

Cassiday G.L (2005), Thomson Publishing. 5. Classical Mechanics, Chow T.L., John Wiley & Sons,

(1995).

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6. An Introduction to Mechanics, Daniel Kleppner and Robert J.Kolenkow, McGraw-Hill International Edition.

7. Theoretical Mechanics, Schaum's Series, M.R.Spiegel, (1983).

SJES2233 BASIC OPERATIONAL RESEARCH Introduction to the problems in operational research, modelling, formulation and examples. Linear programming, transportation and assignment problems. Integer programming, game theory, network and dynamic programming. Assessment: Final Examination: 60% Continuous Assessment: 40% Medium of Instruction: English Humanity Skill: CT3, LL2 References: 1. H.A. Taha, Introduction to Operational Research, John

Wiley. 2. W.L. Winston (1994), Operational Research:

Applications and Algorithm, Duxbury Press. 3. F.S. Hillier and G.J. Lieberman (2005), McGraw-Hill

International Edition,(Eight Edition) 4. B. van der Veen (1967), Introduction to the Theory of

Operational Research, Cleaver-Hume P. London. SJEM2234 TRANSFORMS & PARTIAL DIFFERENTIAL

EQUATIONS Laplace transforms and Fourier transforms. Fourier series. Partial Differential Equations. Assessment: Final Examination: 60% Continuous Assessment: 40% Medium of Instruction: Malay / English Humanity Skill: CS2, CT3, LL1 References:

1. Zill D.G. & Cullen M.R., Differential Equations with Boundary-Value Problems, 7th Edition, Brooks/Cole, 2005

2. Kreyzig E. (2006), Advanced Engineering Mathematics, 9th Edition, John Wiley & Sons.

3. Butkov E. (1966), Mathematical Physics, Addison-Wesley

4. Nagle R.K. & Saff E.B. (1996), Fundamentals of Differential Equations and Boundary Value Problems, 2nd Edition, Addison-Wesley.

5. Boyce W.E. & DiPrima R.C. (2005), Elementary Differential Equations and Boundary Value Problems, 8th Edition, John Wiley & Sons.

SJEM2250 – PROBABILITY & STATISTICS II Two and higher dimensional random variables. Trinomial and multinomial distributions. Correlation coefficient. Conditional distribution, mean and variance. Bivariate normal distribution. Transformation of random variables: t and F distributions, and distributions of order statistics. Biased and unbiased estimators. Method of moment. Method of maximum likelihood. Interval estimation of mean, variance, difference between two means of normal populations, proportion and difference between two proportions of binomial populations. Hypothesis testing for the mean, proportion and variance of a single population. Power of the tests and sample size. Testing the equality of the means and variances between two normal populations. Chi-square goodness-of-fit tests and contingency tables Asymptotic distribution for the maximum likelihood estimation. Rao-Cramer's Inequality. Chebyschev's inequality. Convergence in probability and distribution. Best critical region. Likelihood ratio tests. Assessment: Final Examination: 60% Continuous Assessment: 40% Medium of Instruction: English Humanity Skill: CS3, CT3, LL2 References: 1. R.V. Hogg & E.A. Tanis (2005), Probability and

Statistical Inference, 7th ed., Prentice Hall. 2. R.V. Hogg & T.C. Craig (1995), Introduction to

Mathematical Statistics, 5th ed., Prentice-Hall. 3. N. Mukhopadhyay (2002), Probability and Statistical

Inference, Marcel Dekker. SJEM2251 FURTHER MATHEMATICAL STATISTICS

Sufficient and complete statistics. Minimum variance unbiased estimators. Sufficient statistics and best estimators. Distributions of special quadratic forms. One and two factors analysis of variance. Simple regression theory and inference of parameters. Correlation analysis in bivariate normal distribution. Multiple regression and normal equations. Sequential probability ratio test. Assessment: Final Examination: 60% Continuous Assessment: 40% Medium of Instruction: English Humanity Skill: CS3, CT3, TS2, LL2

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References: 1. R. V. Hogg & A. T. Craig (1995) Introduction to

Mathematical Statistics, 5th ed., Wiley. 2. R. V. Hogg & E. A. Tanis (2005) Probability and

Statistical Inference, 7th ed, Prentice-Hall. 3. A. M. Mood, F. A. Graybill & D. C. Boes, Introduction to

the theory of Statistics, 3rd ed., Mcgraw-Hill. SJEM2252 STOCHASTIC PROCESSES

Definiton and examples of stochastic processes Introduction to simple random walk. Discrete time Markov Chains. Transition probability. Properties of class. Transience and recurrence properties Absorbing probability. Stationary distribution and limiting probability.

Assessment Final Examination: 60% Continuous Assessment: 40% Medium of Instruction: English Humanity Skill: CS3, CT3 References:

1. Lefebvre, M. (2007) Applied stochastic processes. Springer.

2. Ross, S. M. (2007) Introduction to probability models, 9th edition.

Academic Press. 3. Chung, K. L. and Farid Aitsahlia (2003) Elementary

probability theory with stochastic processes and an introduction to mathematical finance, 4th edition. Springer

4. Jones, P. W. (2001). Stochastic processes: An introduction. Arnold.

SJEM2253 NON-PARAMETRIC STATISTICS Statistical hypotheses, binomial test, runs test, sign test, contingency tables, median test, chi-square Goodness of Fit test. Some methods based on ranks. Assessment: Final Examination: 60% Continuous Examination: 40% Medium of Instruction: English Humanity Skill: CS2, CT2, TS1, LL2, EM2 References: 1. Daniel W.W. (1990), Applied Nonparametric Statistics,

2nd ed PWS-Kent. 2. Gibbons J.D. (1985), Nonparametric methods for

Quantitative Analysis American Science Press,Columbus.

3. Conover W.J. (1980), Practical NonParametric Statistics, Wiley.

SJEM2254 REGRESSION ANALYSIS Simple linear regression: Estimation, hypothesis testing, analysis of variance, confidence intervals, correlation, the residuals, prediction. Model inadequacies, diagnostic, heterogeneity of variance, nonlinearity, distributional assumption, outliers, transformation. Selected topics matrix theory and multivariate normal distribution: An introduction to multiple linear regression. Assessment: Final Examination: 60% Continuous Assessment: 40% Medium of Instruction: English Humanity Skill: CS2, CT3, LL2, EM1 References: 1. Weisberg S. (1985), Applied Linear Regerssion, 2nd

ed., Wiley. 2. Bowerman B. L. & O'Connel R.T. (1990), Linear

Statistical Models, 2nd ed., PWS-Kent. 3. Myers, R.H. & Miltors J.S. (1991), A First Couse in the

Theory of Linear Statistical Models, PWS-Kent. 4. Montgomery, D.C., Peck, E. A. (1992), Introduction to

linear regression analysis, Wiley. 5. J.S. Milton, J.C. Arnold (2004) Introduction to

Probability and Statistics, McGrawHill SJEM2255 DATA ANALYSIS I Statistical Analysis for mean, variance, count and proportion: Hypothesis testing, confidence interval and tests of independence. Statistical analysis for regression and Correlation: continuous response data, simple and multiple linear model. Statistical tests: Goodness of fit tests, ANOVA, Nonparametric test Assessment: Final Examnination: 50% Continuous Assessment: 50% Medium of Instruction: English Humanity Skill: CS3, CT3 References: 1. S-Plus 2000 Guide to Statistics Volume 1, Mathsoft

corporation. 2. Mann, Prem. S., (2003). Introductory Statistics, John

Wiley & Sons. 3. Siegel, A.W., and Morgan, C.J., (1998). Statistics and

Data Analysis, John Wiley & Sons. 4. Evans, J.R. and Olson, D.L. (2002) Statistics, Data

Analysis and Decision Modeling and Student CD-ROM (2nd Edition). Prentice Hall

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SJEM2280 - APPRECIATION OF MATHEMATICS Students will be put into groups. Each group will be given 2 mathematical tasks to work on. These tasks will come from a variety of topics selected from, but not limited to: algebra, geometry, combinatorics, applied and computational mathematics, probability and statistics, science & technology, mathematics and society, management science, finance mathematics, actuarial sciences, history and philosophy. Students collectively will use tools/elements of mathematics to undertake each task. In undertaking these tasks, students are required to carry out to a certain extend some literature survey, background reading and explore some elementary research problems. During guided learning sessions, students are also expected to critique, analyse, argue logically and deduce findings. Each group is required to produce and present reports for the tasks given. Assessment: Participation in discussion, Communication & Presentation: (25%) Peer Review : (10%) Teamwork & Ethics: (15%) Project Report: (50%) Medium of Instruction: English Humanity Skill: CS4, TS3, LL2, EM2, LS2 SJEM2416 THEORY OF DIFFERENTIAL EQUATIONS The existence and uniqueness theorem. Solutions to the system of linear differential equations with constant coefficients. Automatic linear system and linear approximation of dimension two, types of critical points, stability. Assessment: Final Examination: 60% Continuous Assessment: 40% Medium of Instruction: English Humanity Skill: CS1, CT5, LL1 References:

1. Zill D.G. & Cullen M.R. (2009), Differential Equations with Boundary-value Problems, 7th ed., Thomson

2. Simmons G.F. (1991), Differential Equations with Applications and Historical Notes, 2nd ed., McGraw-Hill

3. Edwards H. & Penney D. (2008), Differential Equations Computing and Modeling, 4th ed., Prentice Hall.

SJEM2417 GEOMETRY Euclidean Geometry, congruence, parallelism, similarity, isometry, Incidence geometry of the sphere, motions of the sphere.

Assessment: Final Examination: 60% Continuous Assessment: 40% Medium of Instruction: English Humanity Skill: CS1, CT3, LL1 References: 1. Ryan P.J. (1986), Euclidean and non-Euclidean

geometry, Cambridge Univ. Press. 2. Kumaresan S. (2005), An expedition to geometry,

Hindustan Book Agency. 3. Cederberg J.N. (2004), A course in modern

geometries, 2nd ed., Springer. SJEM2430 LINEAR & NON LINEAR SYSTEM OF

DIFFERENTIAL EQUATIONS System of homogeneous linear first order differential equations with constant coefficients. System of non homogeneous linear differential equations. Autonomous systems for linear and almost linear systems, and stability. Liapunov’s method. Applications. Assessment: Final Examination: 60% Continuous Assessement: 40% Medium of Instruction: Malay / English Humanity Skill: CS4, CT5, TS1, LL1 References: 1. Elementary Differential Equations and Boundary Value

Problems (8th ed.), William E. Boyce & Richard C. Prima, Wiley (2005)

2. Differential Equations with Boundary Value Problems (8th ed.), Dennis G. Zill & Michael R. Cullen, Brooks/Cole (2007)

3. Fundamentals of Differential Equations and Boundary value Problems ( 4 th ed.), Kent nagle R. & Edward B. Saff, Addison-Wesley (2004)

SJEM2431 MANAGEMENT MATHEMATICS Output function: Theory and some concepts. Break even model. Optimization profit for monopoly and oligopoly market. Inventory model. EOQ Model, reordering point, finite input rate, shortage and quantity discount. Probabilistic Model, safety stock and efficiency level. Assessment: Final Examination: 60% Continuous Assessment: 40% Medium of Instruction: Malay / English Humanity Skill: CS2, CT3, LL1

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References: 1. Baldani, J. (1996), Mathematical Economics, The

Dryden Press. 2. Davies, K.R., McKeown, P.G. & Rakas, T.R. (1986),

Management Science : An Introduction, Kent Publishing Company.

3. Winston, W.L. (1994), Operations Research: applications and algorithms, 3rd ed., Duxbury Press.

4. Hillier, Frederick S. (1995), Introductory to Operations Research, 6th edition, New York, McGraw-Hill.

5. Taha, Hamdy A(2007)., Operations Research: An Introduction, 8th,New York, Mcmillan.

6. Waters C.D.J. (2003), Inventory Control and Management, University of Calgary, Canada.

SJEM2432 OPTIMIZATION TECHNIQUE Unconstraint optimization, necessary and enough conditions for optimality. Constraint optimization. Type of constraint. Special technique for solving non-linear problem. Assessment: Final Examination: 60% Continuous Assessment: 40% Medium of Instruction: Malay / English Humanity Skill: CS2, CT3, LL1 References: http://www.geocities.com/riorhs SJEM2433 COMPUTER GRAPHICS Introduction to C++ Compiler and OpenGL. Plane geometric coordinate. Coordinate transformations. Polynomial interpolation. Continuity. Curve and surface design. Assessment: Final Examination: 60% Continuous Assessment: 40% Medium of Instruction: Malay / English Humanity Skill: CS2, CT3, TS1, LL1 References: 1. Mathematical Elements for Computer Graphics, 2nd

Ed., Rogers D.F. & Adams J.A. (1990), McGraw Hill International Editions.

2. Computer Graphics, Donald Hearn, Pauline Baker M. (1994), Prentice Hall.

3. Computer Graphics Using Open GL, 2nd Ed., F. S. Hill (2001), Prentice Hall.

4. Computer Graphics, Schaum’s Outlines Series. 5. OpenGL SUPER BIBLE (2nd Ed), Richard S. Wright,

Michael Sweet Jr., Waite Group Press, 2000D.G. Zill & Cullen M.R. (2005), Differential Equations with Boundary-Value Problems, 7th Edition, Brooks/Cole.

SJEM3190 INDUSTRIAL TRAINING Candidates are required to spend 8 weeks working with selected companies in selected areas of industry. Assessment: Continuous Assessment: 100% Medium of Instruction: Malay / English Humanity Skill: CS4, CT3, TS2, LL2, EM2, LS3 References: Universiti Malaya Guidebook for Industrial Training SJEM3380 MATHEMATICAL SCIENCE PROJECT Up to lecturer Assessment: Continuous Assessment: 100% Humanity Skill: CS4, CT4, TS1, LL2 SJEM3411 GRAPH THEORY Graph theory and its applications. Topics will be selected from the following : Eulerian graphs, trees, planar graphs, graph colourings and chromatic polynomials, Hamiltonian graphs, matching theory, directed graphs and the shortest path problem, network theory. Assessment: Final Examination: 70% Continuous Assessment: 30% Medium of Instruction: English Humanity Skill: CT2, LL1 References: 1. Chartrand, G & Zhang, P. (2005), Introduction to graph

theory, McGraw-Hill. 2. Chartrand, G & Lesniak, L. (1996), Graphs and

Digraphs,. Chapman and Hall, New York (3rd ed.). 3. Diestel, R. (2005). Graph Theory, Springer-Verlag. 4. Wilson, R. J. & Watkins, J.L. (1990), Graphs – An

Introductory Approach, John Wiley & Sons, SJEM3412 COMBINATORIAL MATHEMATICS Theory of Enumeration: Topics will be chosen from: Permutation and Combination, advanced counting numbers, generating functions, principle of inclusion and exclusion. Combinatorial Designs: Topics will be chosen from: Block designs, balanced incomplete block designs, Steiner triple system, Hadamard matrices, pigeonhole principle and Ramsey theory for graphs.

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Assessment: Final Examination: 70% Continuous Assessment: 30% Medium of Instruction: English Humanity Skill: CS1, CT3, LL1 References: 1. Brualdi, R. A. (1977), Introductory Combinatorics,

North Holland Publ. Co. 2. Matousek, J. & Nesetril, J. (2008). Invitation to Discrete

Mathematics, Oxford University Press (2nd Edition). 3. Tucker, A. (1980), Applied Combinatorics, John Wiley

and Sons, New York. 4. Wallis, W.D. (2007). Introduction to Combinatorial

Designs, Chapman & Hall/CRC (2nd Edition). SJEM3413 NUMBER THEORY Prime Numbers. The Division Algorithm and Unique Factorization Theorem for Integers. Linear Diophantine Equations. Theory of congruence and the Chinese Remainder Theorem. RSA encryption. Legendre symbol and Quadratic reciprocity law. Arithmetic functions. Primitive roots. Assessment: Final Examination: 60% Continuous Assessment: 40% Medium of Instruction: English Humanity Skill: CS1, CT5, LL1 References: 1. Burton, D. (2007), Elementary Number Theory,

McGraw Hill Publ. Co. (6th ed.). 2. Rosen, K. H. (2005), Elementary Number Theory and

Its Applications, Pearson Addison Wesley (5th ed.). SJEM3414 ADVANCED LINEAR ALGEBRA Inner product spaces, the Gram-Schmidt orthogonalization process and orthogonal complements. Orthogonal operators, unitary operators, self-adjoint operators and positive definite operators. Dual spaces, bilinear forms. Diagonalization of symmetric bilinear forms, real quadratic forms. Triangularization theorem, primary decomposition theorem, Jordan canonical forms. Assessment: Final Examination: 70% Continuous Assessment: 30% Medium of Instruction: English Humanity Skill: CS1, CT3, LL1

References: 1. Kenneth Hoffman, Ray Kunze (1971), Linear Algebra,

Pearson Prentice Hall, Inc. 2. Jin Ho Kwak, Sungpyo Hong (2004), Linear Algebra,

Brikhauser,. (2nd ed.). 3. Harvey E. Rose (2002), Linear Algebra : A Pure

Mathematical Approach, Birkhauser Verlag. 4. Vivek Sahai, Vikas Bist (2002), Linear Algebra, Alpha

Science International Ltd. 5. Seymour Lipschutz (1986). Theory and Problems of

Linear Algebra, McGraw-Hill, Inc. SJEM3415 MATRIX THEORY (4 CREDITS) Prerequisite: SJEM2211 Rank and nullity of matrices. Inner product spaces, the Gram-Schmidt process, least squares problems, ortogonal matrices. Diagonalization for real symmetric matrices, quadratic forms, semi positive definite matrices. The singular value decomposition. Generalized inverses and linear systems, Moore-Penrose inverses. Assessment: Final Examination: 70% Continuous Assessment: 30% Medium of Instruction: English Humanity Skill: CS1, CT3, LL2 References: 1. Anton, H. & Busby, R. C. (2002), Contemporary Linear

Algebra, Wiley Publishers. 2. Horn, R. A. & Johnson, C. R. (1985), Matrix Analysis,

Cambridge University Press. 3. Noble, B. & Daniel, I. W. (1988), Applied Linear

Algebra and Its Applications, Prentice Hall (3rd ed.). 4. Searle, S. R. (1982), Matrix Algebra Useful for

Statistics, John Wiley & Sons, Inc. 5. Bapat, R. B. (2000), Linear Algebra and Linear Models,

Springer (2nd ed.). SJEM3416 ALGEBRA II

Groups-Isomorphism theorems. Permutation groups. Group actions, p-groups. Rings-Maximal and prime ideals, polynomial rings. Field extensions. Finite fields.. Assessment: Final Examination: 70% Continuous Assessment: 30% Medium of Instruction: English Humanity Skill: CT3, LL2

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References: 1. Durbin, J. R. (1985), Modern Algebra, An Introduction,

John Wiley (2nd ed.). 2. Fraleigh, J. B. (1994), A First Course in Abstract

Algebra, Addison-Wesley (5th ed.). 3. Herstein, I. N. (1990), Abstract Algebra, Macmillan (2nd

ed.). SJEM3417 RING THEORY Ring, subrings and ideals, modules, internal direct sum, external direct product, nil and nilpotent ideals, prime and maximal ideals, Jacobson and prime radicals, semiprimitive and semiprime rings, rings with chain condition, primitive rings, group rings. Assessment: Final Examination: 70% Continuous Assessment: 30% Medium of Instruction: English Humanity Skill: CS1, CT3, LL2 References: 1. Burton, D. M. (1970), A First Course in Rings and

Ideals, Addison-Wesley Publ. Co. 2. Herstein, I. N. (1968), Noncommutative Rings, Carus

Mathematical Monographs No. 15, Math Assoc. of America.

3. Beachy, J. A. (1999), Introductory Lectures on Rings and Modules, London Maths. Soc. Student Texts 47, Cambridge University Press.

SJEM3418 GROUP THEORY The three isomorphism theorems. Cyclic groups. Direct product of groups. Classification of group up to order 8. Finitely generated abelian groups. Soluble groups and nilpotent groups. Assessment: Final Examination: 70% Continuous Assessment: 30% Medium of Instruction: English Humanity Skill: CT3, LL2 References:

1. Ledermann, W., Weir, A. J. & Jeffery, A. (1997), Introduction to Group Theory, Addision Wesley Pub. Co. (2nd ed.).

2. Rotman, J. J. (1995), An Introduction to The Theory of Groups", Springer-Verlag, New York (4th ed.).

3. Robinson, D. J. S. (1996), A Course In The Theory Of Groups, Springer-Verlag, New York (2nd ed.).

SJEM3419 DIFFERENTIAL GEOMETRY Vector algebra on Euclidean space. Lines and planes. Change of coordinates. Differntial geometry of curves. Frenet Equations. Local theory of surfaces in Euclidean space. First and second fundamental forms. Gaussian curvatures and mean curvatures. Geodesics. Gauss-Bonnet Theorem. Assessment: Final Examination: 60% Continuous Assessment: 40% Medium of Instruction: English Humanity Skill: CS1, CT3, LL1 References: 1. Lipschutz, M. (1969), Schaum’s Outline of Differential

Geometry, McGraw-Hill. 2. Oprea, J. (2004), Differential Geometry And Its

Applications, Prentice Hall (2nd ed.). 3. Kuhnel, W. (2005), Differential Geometry: Curves,

Surfaces, Manifolds, Amer. Math. Soc. (2nd ed.). SJEM3420 TOPOLOGY Topological Spaces. Continuity, connectedness and compactness. Separation axioms and countability . Metric spaces. Product spaces. Assessment: Final Examination: 60% Continuous Assessment: 40% Medium of Instruction: English Humanity Skill: CS1, CT2, LL1 References: 1. Pervin, W. J. (1974), Foundation of General Topology,

Academic Press. 2. Lipschutz, S. (1965), General Topology, Schaum's

Outline Series. 3. Abu Osman Md Tap (1989), Topologi, DBP. SJEM3421 COMPLEX ANALYSIS Taylor and Laurent series. Singularities and zeroes. Residue Theory. Evaluation of certain Integrals. Arguments Principle, Rouche’s theorem. Maximum Modulus Principle. Poisson’s Integral Formula. Infinite Products. Entire Functions. Assessment: Final Examination: 60% Continuous Assessment: 40% Medium of Instruction: English Humanity Skill: CS3, CT3, LL2

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References: 1. John H. Mathews & Russell W. Howell (2006),

Complex Analysis: for Mathematics and Engineering, Jones & Bartlett Pub. Inc (5th ed.).

2. Saff, E. B. & Snider, A. D. (2003), Fundamental of Complex Analysis, Pearson Education Inc.

3. Wunsh, A. D. (2005), Complex Variables with Applications, Pearson Education Inc.

4. Markushevich, A. I. (1985), Theory of Functions of Complex Variables, Chelsea Publ. Co.

SJEM3422 REAL ANALYSIS Riemann integral. Integrable functions. Properties of the Riemann integral. Integration in relation to differentiation. Differentiation of integrals. Improper integrals. Sequences and series of functions. Pointwise and uniform convergence. Properties of uniform convergence. Limit superior and limit inferior. Power series, radius of convergence. Taylor series. Assessment: Final Examination: 60% Continuous Assessment: 40% Medium of Instruction: English Humanity Skill: CS1, CT3, LL1 References: 1. Witold A.J. Kosmala (2004), A Friendly Introduction to

Analysis, Single and Multivariable, Pearson International (2nd Ed.).

2. Schroder, B. S (2008), Mathematical Analysis: A Concise Introduction, John-Wiley.

3. Richardson, L. F. (2008), Advanced Calculus: An Introduction To Linear Analysis, John-Wiley.

4. Edward D. Gaughan (1998), Introduction to Analysis, Brook/Cole Publishing Co. (5th Ed.)

5. Haggarty, R. (1993), Fundamentals of Mathematical Analysis, Addison-Wesley Pub. Co. (2nd Ed.)

SJEM3430 WAVELETS AND THEIR APPLICATIONS Functions and Function Spaces, Fourier Transform, Sampling, Continuous Wavelet Transform, Multi-resolution Analysis (MRA), Discrete Wavelet Transform, Orthogonal Wavelet Systems, Wavelet Toolbox, Applications to data compression, de-noising and others. Assessment: Final Examination: 50% Continuous Assessment: 50% Medium of Instruction: English Humanity Skill: CT3, LL1

References: 1. Gilbert Strang & Truong Nguyen (1996), Wavelets and

Filter Banks, Wellesley College (2nd rev ed.). 2. Soman, K. P. & Ramachandran, K. I. (2005), Insight

Into Wavelets: From Theory to Practice, Prentice-Hall of India.

3. Stéphane Mallat (1999), A Wavelet Tour of Signal Processing, Academic Press (2nd ed.).

4. James S. Walker (2008), A Primer on Wavelets & Their Scientific Applications, Chapman & Hall/CRC (2nd ed.).

5. Wavelet Toolbox User’s Guide (2006), The MathWorks, Inc.

SJEM3431 INTRODUCTION TO QUANTUM MECHANICS WITH COMPUTERS Introduction to Quantum mechanics. The wave-function and its interpretation. One-dimensional time-independent Schrodinger equation. Solution for the case of the infinite-and finite-square well, harmonic oscillator potential, and free-particle case. Formalism of quantum mechanics. Two- and three-dimensional systems. The hydrogen atom. The concept of spin. Assessment: Final Examination: 50% Continuous Assessment: 50% Medium of Instruction: English Humanity Skill: CS3, CT3, LL1 References: 1. David J. Griffiths (1995), Introduction to Quantum

Mechanics, Prentice-Hall. 2. David K. Ferry (2001), Quantum Mechanics: An

Introduction For Device Physicists And Electrical Engineers, Institute of Physics Publ. (2nd ed.).

3. Rubin Landau & Manuel Paez (1997), Computational Physics: Problem Solving With Computers, John Wiley.

4. Jasprit Singh (1997), Quantum Mechanics: Fundamentals & Applications to Technology, Wiley-Interscience.

5. Alejandro Garcia (2000), Numerical Methods for Physics, Prentice-Hall (2nd ed.).

SJEM3432 CRYPTOGRAPHY Basic concept of cryptography, data security, complexity theory and number theory. Encryption algorithms: Secret key cryptography, public key cryptography, hash functions. Applications of cryptographic algorithms. Assessment: Final Examination: 60% Continuous Assessment: 40% Medium of Instruction: Malay / English Humanity Skill: CS3, CT3, TS1, LL1

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References: 1. Trappe, W. & Washington, L. C. (2006), Introduction to

Cryptography with Coding Theory, Pearson Prentice Hall (2nd ed.).

2. Stallings, W. (2006), Cryptography and Network Security: Principles And Practice., Englewood Cliffs (NJ): Prentice Hall (4th ed.).

3. Schneider, B. (1996), Applied Cryptography, New York: John Wiley and Sons, 2nd ed.).

4. Denning, D. E. (1982), Cryptography and Data Security, Addison Wesley.

5. Stinson, D. R. (1995), Cryptography: Theory and Practice, CRC Press.

SJEM3433 COMPUTATIONAL FLUID DYNAMICS Derivation of conservation equations for mass, momentum and energy. Scaling and simplification of Navier-Stokes equation to Bernoulli’s equation, Stokes’ equation and boundary layer equation. Initial- and boundary-conditions. Simple analytical solutions and approximate solutions. Numerical solutions: finite-element, finite-difference and finite-volume methods. Assessment: Final Examination: 50% Continuos Assessment: 50% Medium of Instruction: Malay / English Humanity Skill: CS4, CT5, TS1, LL3 References: 1. Richardson, S. M. (1989), Fluid Mechanics,

Hemisphere Pub. Corp. 2. Peterson, A. R. (1987), A First Course in Fluid

Dynamics, CUP. 3. Anderson, J. D. (1995), Computational Fluid

Dynamics, McGraw- Hill. 4. Smith G. D. (1978), Numerical Solution of PDE: Finite

Difference Methods, OUP. 5. Joel H. Ferziger & Milovan Peric (1997),

Computational Methods for Fluid Dynamics, Springer. SJEM3434 ANALYSIS OF MATHEMATICAL MODELS Building of Mathematical Models: identifying variables, obtain relationship between variables – ordinary differential equations and systems of ode. Analysis of models analytically and qualitatively. Bifurcations. Phase plane analysis, stability. Assessment: Final Examination: 50% Continuous Assessment: 50% Medium of Instruction: Malay / English Humanity Skill: CS4, CT5, TS1, LL1

References: 1. Nagle, R. K., Saff, E. B. & Snoder, A. D. (2008),

Fundamentals of Differential Equations and Boundary Value Problems with IDE CD, Pearson Higher Education, (5th ed.).

2. Borelli, R. I. & Coleman, C. S. Differential Equations: A Modeling Perspective, John Wiley (2nd ed.).

SJEM3435 – NUMERICAL METHODS AND ANALYSIS Approximation methods: Discrete least square approximation, orthogonal polynomials, Chebyshev polynomials. Eigenvalue problem: Power method, Householder’s methods. The QR algorithm. Initial value problem of Ordinary Differential Equations: Euler’s method, higher order Taylor method, Runge-Kutta methods. Multistep methods. Multistep methods. Convergence and stability analysis, error control. Assessment: Continuous Assessment: 40% Final Examination: 60% Medium of Instruction: English Humanity Skill: CS3, CT3, LL2 References: 1. Atkinson, K. E. (1993), Elementary Numerical Analysis,

John Wiley & Sons, (2nd ed.). 2. Burden, R. L. & Faires, J. D. (2001), Numerical

Analysis, Brooks/Cole, USA, (7th ed.). 3. Brian Bradie, (2006), A Friendly Introduction to

Numerical Analysis, Pearson Education, New Jersey, SJEM3436 PRODUCTION AND INVENTORY SYSTEM The importance of inventory in management. Advanced EOQ models. Inventory model for time-dependent demand: linear increase or decrease cases. Exact and approximate methods by minimizing ordering and holding costs. Applications to real-world problems. Assessment: Final Examination: 60% Continuous Assessment: 40% Medium of Instruction: Malay Humanity Skill: CS2, CT3, LL1 References:

1. Hamdy A. Taha (2007), An Introduction to Operational Research, New York, Mcmillan (8th ed.).

2. Naddor, E. (1966), Inventory Systems, J. Wiley. 3. Hadley G. & Whitin T. M. (1963), Analysis of Inventory

Systems, Prentice-Hall, Inc., Englewood Cliffs, New Jersey.

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4. Waters, C. D. J. (2003), Inventory Control and Management, University of Calgary, Canada.

5. Hillier, Frederick S. (2005), Introductory to Operations Research, New York, McGraw-Hill (8th ed.).

SJEM3437 HEURISTIC METHODS Introduction. Descent Heuristics: random solutions, greedy solutions, exchange heuristics. Improvement Heuristics: Local optimization, iterated local search, simulated annealing, tabu search. Artificial Intelligence: Genetic algorithm, evolutionary algorithm, artificial neural network. Evaluating heuristics. NP Completeness. Assessment: Final Examination: 60% Continuous Assessment: 40% Medium of Instruction: Malay / English Humanity Skill: CT4, LL2 References: 1. Michalewicz, Z. & D. B. Fogel (2005), How To Solve It:

Modern Heuristics, Springer-Verlag,. 2. Osman I. & Kelly, P. (1996), Meta-Heuristics: Theory

and Applications: Kluwer. 3. Rich, E. & Knight, K. (1991), Artificial Intelligence,

McGraw-Hill Inc, International Edition. 4. Goldberg, D. E. (1989), Genetic Algorithms in Search,

Optimization and Machine Learning, Addison-Wesley. 5. Z. Michalewicz, (1992), Genetic Algorithms + Data

Structures = Evolution Programmes, Springer-Verlag. SJEM3438 MATHEMATICAL PROGRAMMING Linear Programming: the matrix of simplex method and revised simplex method, sensitivity analysis and parametric linear programming. Integer programming: pure, mixed and 0-1. Cutting plane, and branch and bound methods. Goal programming (multiple objectives): graphical solution, sequential simplex and modified simplex methods. Other selected mathematical programming models and applications. Assessment: Final Examination: 60% Continuous Assessment: 40% Medium of Instruction: Malay Humanity Skill: CS4, CT3, TS2, LL2 References: 1. Markland, R. E & Sweigart, J. R (1987), Quantitative

Methods: Applications to Managerial Decision Making, John Wiley & Sons.

2. Moore, L. J., Lee, S. M. & Taylor, B. W. (1993), Management Science, Allyn and Bacon (4th ed.).

3. Taha, H. A (1992), Operations Research: An Introduction, Macmillan Pub. Co. (edisi Bahasa Malaysia oleh USM-DBP) (5th ed.).

4. Winston, W. L (1994), Operations Research: Applications and Algorithms, Duxbury Press (3rd ed.).

SJEM3439 INDUSTRIAL OPERATIONAL RESEARCH Network: Formulation of selected network models. Flow network: shortest distance, minimum spanning tree, maximum (minimum) flow and maximum flow-minimum cost. Algorithm, examples and selected applications. Activity network: Critical path method (CPM). Project evaluation and review technique and review technique (PERT) Algortithm, examples and selected applications. Assessment: Final Examination: 60% Continuous Assessment: 40% Medium of Instruction: Malay Humanity Skill: CS4, CT3, TS2, LL2 References: 1. Groebner, D. F & Shannon, P. W. (1991), Introduction

to Management Science, Dallen-Macmillan-Maxwell, International Edition.

2. Lipin, L. L (1994), Quantitative Methods for Business Decisions (with cases), Dryden Press (6th ed.).

3. Taylor, B. W (1993), Introduction to Management Sciene, Allyn and Bacon.

SJEM3440 COMPUTATIONAL GEOMETRY Vector algebra, introduction to differential geometry, design surfaces for Bezier surfaces, triangular Bezeir surfaces, B-Spline, rational Bezier and Coons surfaces. Assessment: Final Examination: 60% Continuous Assessment: 40% Medium of Instruction: Malay / English Humanity Skill: CS3, CT3, TS1, LL1 References: 1. Michael E. Mortenson (1985), Geometric Modeling,

John Wiley & Sons,. 2. Christoph M. Hoffman, (1989), Geometric & Solid

Modeling: An Introduction, Morgan Kaufmann, San Mateo, California.

3. Hill, F. S. (2001), Computer Graphics Using OpenGL, Prentice Hall (2nd ed.).

4. Farin, G. (1988), Curves and Surfaces for Computer Aided Geometric Design, Academic Press, Boston

5. Hoschek, J. & Lasser, D. (1993), Fundamentals of Computer Aided Geometric Design, Ak Peters Ltd.

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SJEM3441 SCIENTIFIC COMPUTING 1. Functions, arrays, strings, pointers, data structures, file

processing. 2. Computation of special functions such as Legendre

polynomials, Bessel and Neumann functions. Gaussian quadrature. Numerical solution of systems of linear equations. Introduction to numerical solution of partial differential equations, e.g. heat and wave equations. FTCS, Crank-Nicholson algorithms, etc.

Assessment: Final Examination: 50% Continuous Assessment: 50% Medium of Instruction: English Humanity Skill: CS3, CT3, TS2, LL2 References: 1. Friedman, F. L. & Koffman, Elliot B. (1997), Problem

Solving, Abstraction and Design Using C++, Addison-Wesley.

2. Thomson, A Structured Programming Approach using C-, Computer Science (3rd ed.).

3. Rubin H. Landau (2008), A Survey of Computational Physics: Introductory Computational Science, Princeton Press.

4. W. H. Press (2007), Numerical Recipe. 5. David R. Kincaid & E. Ward Cheney (2002), Numerical

Analysis, Mathematics of Scientific Computing (3rd ed.).

SJEM3450 INTRODUCTION TO MULTIVARIATE

ANALYSIS The use/application of Multivariate analysis. Managing and Handling Multivariate data. Matrix theory. Random vectors and Matrices. Multivariate Normal Distribution. Wishart distribution and Hotellings distribution. Selected topics from Graphical methods, Regression Analysis, Correlation, Principle Components, Factor Analysis, Discriminant analysis and Clustering Methods Assessment: Final Examination: 60% Continuous Assessment: 40% Medium of Instruction: English Humanity Skill: CS2, CT3, LL2, EM1 References: 1. Johnson, K. A. & Wichern, D. W. (2002), Applied

Multivariate Analysis, Prentice-Hall International, (5th ed.).

2. C. Chatfield & A. J. Collins (1980), An Introduction to Multivariate Analysis, Chapman & Hall.

3. Anderson, T. A. (1984), An Introduction to Multivariate Statistical Analysis, Wiley (2nd ed.).

SJEM3451 COMPUTER INTENSIVE METHODS IN STATISTICS

Computer generation of uniform and non-uniform random variables. Monte Carlo evaluation of integrals, variance reduction. Empirical distribution; bootstrap and jackknife methods, bootstrap estimates of standard deviation and bias, bootstrap confidence intervals. Empirical likelihood, missing data, Expectation-Maximization algorithm, Markov Chain Monte Carlo methods.

Assessment: Final Examination: 60% Continuous Assessment: 40% Medium of Instruction: English Humanity Skill: CS3, CT3, LL2 References: 1. Roberts, C.P. & Casella, G. (200), Monte Carlo

Statistical Methods, Springer. 2. Ross, S.M. (1991), A Course In Simulation, Maxwell-

Macmillan.

SJEM3452 APPLIED STOCHASTIC PROCESSES

Fundamental matrix. Time reversible Markov chains. Poisson processes. Birth and death processes. Random walk and Brownian motion. Application to real-world phenomena and finance.

Assessment: Final Examination: 60% Continuous Assessment: 40% Medium of Instruction: English Humanity Skill: CS3, CT3, LL2 References: 1. Taylor, H. M. & Karlin, S. (1994), An introduction to

stochastic modeling, Academic Press. 2. Kao, E. P. C. (1997), An Introduction To Stochastic

Processes, Duxbury Press. 3. Ross, S. M. (2000), An introduction to probability

models, Academic Press (7th ed.). 4. Ross, S. M. (1996), Stochastic processes, John Wiley

(2nd ed.).

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SJEM3453 TIME SERIES AND FORECASTING METHODS

Introduction to time series: data, properties, examples. Introduction to forecasting: Forecasting methods, errors in forecasting, choosing a forecasting techniques, qualitative and quantitative forecasting techniques. Time series regression: Modelling trend, detecting autocorrelation, type of seasonal variation, modelling seasonal variation, growth curve models, handling first-order autocorrelation Averaging methods: Moving average, Simple exponential smoothing, tracking signals, Holt’s method, Holt-Winters Methods, damped trend exponential method. Box-Jenkins Methods: Stationary data and non-stationary data, difference, autocorrelation function and partial autocorrelation functions, non-seasonal modeling (ARIMA), diagnostic checking, forecasting. ARCH and GARCH models. Assessment: Final Examination : 60% Continuous Assessment : 40% Medium of Instruction: English Humanity Skill: CS3, CT3, LL2 References: 1. Box, G. E. P., Jenkins, G. W., & Reinsel, G. (1994)

Time Series Analysis, Forecasting And Control, Prentice Hall, (3rd ed.).

2. Makridakis, S., Wheelwright, S. C. & Hyndman, R. J. (1998) Forecasting Methods and Application, Wiley.

3. Lazim, M. A. (2001), Introductory Business Forecasting, A Practical Approach, Univision Press.

4. Evans, M. K. (2003), Practical Business Forecasting, Blackwell.

5. Bowerman, B. L., O'Connel, R. T. & Boehler, A. B. (2005), Forecasting, Time Series and Regression, Duxbury.

SJEM3454 FURTHER TOPICS IN REGRESSION

ANALYSIS Multiple Linear Regression Model: Simultaneous Inference, criteria for selecting model, influence diagnostics and multi-collinearity. Introduction to logistic regression and Poisson regression: maximum likelihood estimates of the parameters, lack of fit test, tests based on deviance and score. Assessment: Final Examination: 60% Continuous Assessment: 40% Medium of Instruction: English Humanity Skill: CS2, CT2, LL3

References: 1. Bowerma, L. & O’Connel, R. T. (1990), Linear

Statistical Models, PWS-Kent 1 (2nd ed.) 2. Weisberg, S. (1985), Applied Linear Regression, Wiley

(2nd ed.). 3. Agesti, Alan (1990), Categorical Data Analysis. John

Wiley. 4. P. McCullagh & J. A. Nelder, (1989), Generalized

Linear Models, Chapman & Hall (2nd ed.). SJEM3455 DATA ANALYSIS II Introduction to different kind of data; Generalizing the linear regression models including nonlinear regression model, Linear regression in time series data, logistic regression and Poisson regression models for categorical response data and selected topics Practical survey sampling: Selected case study, design of study, questionnaires, collecting data, data analysis, oral and written presentation Statistical consulting :Theoretical and practical aspects of statistical consulting, Communication skill Report writing Assessment: Continuous Assessment : 50% report and presentation : 50% Medium of Instruction: English Humanity Skill: CS4, CT3, TS5 References: 1. S-Plus (2000), Guide to Statistics Volume 1 and II,

Mathsoft Corporation. 2. Cramer, D. (2003), Advanced Quantitative Data

Analysis, Open University Press. 3. Evans, J. R. & Olson, D. L. (2007), Statistics, Data

Analysis, and Decision Modeling, Prentice Hall. 4. Miller, D. C. & Salkind, J. (1983), Handbook of

Research Design and Social Measurements, Sage Publication.

5. Derr, J. (2000), Statistical Consulting: A Guide To Effective Communication, Pacific Grove: Duxbury.

SJEM3456 INTRODUCTION TO SURVEY SAMPLING Techniques of statistical sampling with applications in the analysis of sample survey data. Topics include simple random sampling, stratified sampling, systematic sampling, cluster sampling, two-stage sampling and ratio and regression estimates. Assessment: Continuous Assessment : 40% Examination : 60% Medium of Instruction: English Humanity Skill: CT4, LL2

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References: 1. Scheaffer, R. L. (2006), Elementary Survey Sampling,

Duxbury (6th ed.). 2. Thompson, S. K. (2002), Sampling, Wiley, (2nd ed.). 3. Lohr, Sharon L. (1999), Sampling: Design and

Analysis, Duxbury. 4. Cochran, W. (1977), Sampling Techniques, Wiley (3rd

ed.). SJEM3457 STATISTICAL PROCESS Methods and philosophy of statistical process control. Control charts for variables and attributes. CUSUM and EWMA charts. Process capability analysis. Acceptance sampling, rectifying inspection. Lot-by-lot acceptance sampling by attributes. Acceptance sampling by variables. Assessment: Continuous Assessment : 40% Examination : 60% Medium of Instruction: English Humanity Skill: CS3, CS3, TS2, LL2 References: 1. Montgomery, D. C. (2005), Introduction to Statistical

Quality Control, Wiley (5th ed.). 2. Kenett, R. S. & Zacks, S. (1998), Modern Industrial

Statistics: Design and control of quality and reliability, Duxbury Press.

3. Duncan, A. J. (1986), Quality Control and industrial Statistics, Irwin (5th ed.).

SJEM3458 INTRODUCTION TO DATA Description: Introduction to statistical methods and tools for analysis of very large data sets and discovery of interesting and unexpected relationships in the data. Measurement and data exploration: types of measurement, distance measure, data quality. Data exploration: summarizing and visualizing data; principal component, multidimensional scaling. Data analysis and uncertainty: handling uncertainty; statistical inference; sampling. Data mining algorithms: classification and clustering- CART; Artificial Neural Network; support vector machine; association rules mining. Modelling: model structures; curse of dimensionality; score functions; optimization methods; descriptive and predictive modeling. Data organization. Assessment: Continuous Assessment: 40% Examination: 60% Medium of Instruction: English Humanity Skill: CS3, CT3, LL2 References: 1. Adriaans, P. & Zantige, D. (1996), Data Mining,

Addison-Wesley.

2. Hand, D., Mannila, H. & Smyth, P. (2001), Principles of Data Mining, MIT Press.

SJEM3459 BIOINFORMATICS Analysis of Sequences: Measures of similarity in sequences, dynamic programming, pairwise and multiple alignments. Statistical modelling of DNA/protein sequences: profiles, hidden Markov Models, Expectation - Maximization (EM) algorithm, Markov chain Monte Carlo sampling. Prediction of Molecular Structure: RNA secondary structure prediction, covariance models; protein folding; protein threading. Analysis of Microarrays: Classification, Clustering, analysis of large scale gene expression data sets, feature selection. Assessment: Final Examination: 60% Continuous Assessment: 40% Medium of Instruction: English Humanity Skill: CS3, CT3, LL2 References: 1. Neil C. Jones, Pavel A. Pevzner (2004), An

Introduction to Bioinformatics Algorithms, Computational Molecular Biology

2. Bishop M. J., Rawlings C.J. (Eds.) (1997), DNA And Protein Sequence Analysis. A Practical approach.IRL Press, Oxford.

3. Richard Durbin Sean R. Eddy, Anders Krogh, Graeme Mitchison, Probabilistic Models of Proteins and Nucleic Acids, Biological Sequence Analysis.

4. David W. Mount, Bioinformatics, Sequence and Genome Analysis.

5. Warren J. Ewens, Statistical Methods in Bioinformatics: An Introduction (Statistics for Biology and Health)

SJEM3460 DESIGN AND ANALYSIS OF EXPERIMENTS Philosophy related to statistical designed experiments. Completely randomized one-factor design. Randomized block designs. Latin squares. Incomplete block designs. Factorial designs. Confounding. Fractional factorial designs. Assessment: Continuous Assessment : 40% Examination : 60% Medium of Instruction: English Humanity Skill: CT4, TS1, LL2 References: 1. Montgomery, D. C. (2004), Design and Analysis of

Experiments, John Wiley (6th ed.).

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2. Box, G. E. P., Hunter, W. G. & Hunter, J. S. (2005), Statistics for Experimenters, John Wiley (2nd ed.).

3. Tabachnick, B. G., Fidell, L. S., (2007), Experimental Designs Using Anova, Duxbury.

4. Myers, R. H. (1990), Classical and Modern Regression Analysis with Applications. Duxbury (2nd ed.).

SJEM3461 JAVA METHODS FOR STATISTICS AND

ACTUARIAL SCIENCE JAVA programming language: Object, class and method. Sample java programs which make use of Java methods to 1. perform data manipulation, matrix operations and

nonlinear optimization. 2. perform computation and simulations in Brownian

motion models, Levy processes, CIR model and other models.

3. find the premiums of investment-linked insurance policies.

4. find approximately aggregate claims distribution and ruin probabilities.

5. find provision of risk margin for adverse deviation (PRAD) of claim liabilities for general insurance business.

Assessment: Final Examination: 60% Continuous Assessment: 40% Medium of Instruction: English Humanity Skill: CS2, CT2, LL1 References: 1. Philip Barker (2007), Java Methods for Financial

Engineering, Applications in Finance and Investment, Springer-Verlag London Limited.

2. Everitt, B. S. Introduction To Optimization Methods And Their Application In Statistics, Chapman and Hall.

3. Deitel, H. M. & Deitel, P. J. (1995), Java How To Program, Prentice-Hall.

4. Hurbbard, John R. (2004), Programming with JAVA (Schaum's Outline Series), McGraw- Hill International Editions.

SJEM3462 ANALYSIS OF FAILURE AND SURVIVAL

DATA Survival distributions, hazard models. Reliability of systems, stochastic models. Censoring and life-tables. The product-limit estimator. Parametric survival models under censoring. Cox proportional hazards model and other basic models with covariates. Assessment: Final Examination: 60% Continuous Assessment: 40% Medium of Instruction: English Humanity Skill: CS1, CT2, LL1

References: 1. Beasley, E. M., Realibility for Engineers: An

Introduction, Macmillan. 2. Henley, E.J. & Kumamoto, H., Reliability Engineering

and Risk Assessment, Prentice Hall. 3. Sherwin, D. J. & Bossche, A., The Reliability,

Availability and Productiveness of Systems, Chapman & Hall.

4. Miller, Rupert G. (1981), Survival Analysis, John Willey.

5. London, Dick (1998), Survival Models and their Estimation. ACTEX Publications.

SJER2211 INTEREST THEORY AND DERIVATIVES Measures of interest and problems solving involving interest. Expansion of basic principles of interest to more complicated financial transactions. Annuity-certain, Amortization and sinking fund; bond and security. Introduction to derivatives, forwards, futures, short and long positions, call and put options, spreads, collars, hedging, arbitrage and swaps. Assessment: Final Examination: 60% Continuous Assessment: 40% Medium of Instruction: English Humanity Skill: CS2, CT2, LL1 References: 1. Broverman, Samuel A.(2004), Mathematics of

investment and credit 3rd ed. Winsted, Conn. : ACTEX. 2. Kellison G. (1991), Theory of Interst, 2nd Ed.,

Homewood IL:Irwin. 3. Cissell & Cissell (1969), Mathematics of finance, 3rd

Ed., Houghton Mifflin. 4. Shao & Shao (1997), Mathematics for management

and finance, 8th Ed., ITP. 5. Robert, L.M. (2006) Derivatives markets, second

edition, Addison Wesley. SJER2212 MICROECONOMICS Fundamental principles of economics; price theory which covers the demand model, supply model and equilibrium point; shape of demand curve and consumer behavior; substitution effects and income; shape of supply curve and behavior of firms; theory of production and cost of production; analysis of competitive markets in the short term; monopoly and oligopoly. Assessment: Final Examination: 60% Continuous Assessment: 40% Medium of Instruction: English Humanity Skill: CS2, CT2, LL1

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References: 1. Gregory Mankiw N. (2008), Principles of

Microeconomics, 5th edition South western. 2. Taylor, John B (1998), Principles of Microeconomics,

2nd ed, Boston, Houghton Mifflin. 3. Pindyck, R.S. and Rubinfeld, D.L. (1995),

Microeconomics, ed., Maxwell Macmillan. 4. Katz, Michael L. and Rosen, Harvey S. (1999),

Microeconomics, ed. 5. Landsburg, Price Theory S.E. (2002) and Applications,

5th ed., International Thomson Publishing. SJER2213 MACROECONOMICS Macroeconomic issues and problems; fundamental concepts of national income; method of calculating national income; simple Keynesian model; derivation of IS curve, LM curve, aggregate demand curve, and aggregate supply curve; relationship between interest rates, monetary demand, consumption and investments; relationship between price levels, monetary demand, aggregate demand and aggregate supply in a Keynesian model. Assessment: Final Examination: 60% Continuous Assessment: 40% Medium of Instruction: English Humanity Skill: CS2, CT2, TS1, LL1 References: 1. Mc Eachern (2007). Macroeconomics; A

Contemporary approach. 7th ed. Thomson. 2. Richard T. Froyen (1999), Macroeconomics: Theories

and Policies, 6th ed., Prentice Hall. 3. Wachtel, P., Macroeconomics, Society of Actuaries.

Study Note 2-21-00 (Third or Fourth Printing). 4. Rudiger Dornbusch & Stanley Fischer 1998,

Macroeconomics, 7th ed., McGraw-Hill. 5. Case, Karl E. (2007) Principles of Macroeconomics,

Pearson Prentice Hall. SJER2214 INTRODUCTION TO ACCOUNTING Basic principles of accounting – including the role of accounting standards. Different types of business entity. Basic structure of company accounts. Interpretation and limitation of company accounts. Assessment: Final Examination: 60% Continuous Assessment: 40% Medium of Instruction: English Humanity Skill: CS2, CT1, LL1 References: 1. Reimers, Jane L. (2007), Financial Accounting,

Pearson Prentice Hall. 2. Hermanson, R.H. and Edwards J.D. Irwin (1995),

Financial Accounting: A Business Perspective, 6th ed.

3. Hoggett, J., and Edwards. L (1996), Financial Accounting in Australia, 3rd ed., Queensland: John Wiley and Sons.

4. Kirkwood, L., Ryan C., Falt J., and Stanley T. (1993), Accounting: An Introductory Perspective. 3rd ed., Melbourne: Longman Cheshire.

5. Meigs, W.B., and Meigs R.F. (1995), Financial Accounting. 8th ed., New York: McGraw Hill.

SJER2215 INTRODUCTORY LIFE CONTINGENCIES Survival distributions and life tables, life assurances, life annuities, commutation functions for assurances and annuities, continuous assurances and annuities, increasing assurances and annuities. Assessment: Final Examination: 60% Continuous Assessment: 40% Medium of Instruction: English Humanity Skill: CS2, CT1, LL1 References: 1. Nesbitt, Cecil, Jones, Hickman, Gerber, Bowers

(1997), Actuarial Mathematics, 2nd ed., Soc. Actuaries.

2. Neil, A. (1997), Life Contingencies: London. 3. Robert W. Batten (1977), Life Contingencies,

Heinemann: London. 4. Jordan, Chester Wallance (1975), Society of Actuaries

Textbook on Life Contingencies, The Society of Actuarial.

5. Cunningham Robin J., Henzog Thomas N., and Landon Richard L. (2005), Models for Quantifying Risk, ACTEX Publications Inc.

SJER3191 INDUSTRIAL TRAINING IN ACTUARIAL

SCIENCE Subject to the training offered by the relevant company. Assessment: Written report : 70% Presentation : 30% Medium of Instruction: English Humanity Skill: CS2, CT2, TS2, LL1, EM1 SJER3216 FURTHER LIFE CONTINGENCIES Net premium, gross premium, modelling additional risk, participating policy and bonus, gross and net premium policy value, multiple life function, multiple decrement model. Assessment: Final Examination: 60% Continuous Assessment: 40% Medium of Instruction: English

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Humanity Skill: CS2, CT1, LL1 References: 1. Nesbitt, Cecil, Jones, Hickman, Gerber & Bowers

(1997), Actuarial Mathematics, Soc. Actuaries (2nd ed.).

2. Neil, A. (1977), Life Contingencies, Heinemann: London.

3. Batten, Robert W. (1999) Life Contingency and Ruin Theory for the Actuarial Student, Actuarial Bookstore.

4. Jordan, Chester Wallance (1975), Society of Actuaries Textbook on Life Contingencies, The Society of Actuarial.

5. Cunningham Robin J., Henzog Thomas N., and Landon Richard L. (2005), Models for Quantifying Risk, ACTEX Publications Inc.

SJER3217 INVESTMENT AND FINANCIAL ANALYSIS I This course introduces students to the concepts and applications of investment such as securities trading and mutual funds, concepts of risk and return and their applications to Markowitz portfolio selection. Students also will be exposed to the calculation of bond prices and yields and management of bond portfolio. Students will be able to discuss the Capital asset pricing Model (APM) and Arbitrage Pricing Theory (APT) . Lastly students can evaluate and manage active portfolio management by using Jensen, Treynor and Sharp model. Assessment: Final Examination: 60% Continuous Assessment: 40% Medium of Instruction: English Humanity Skill: CS2, CT1, TS1, LL1 References: 1. Bodie, Z., Kane, A. & Marcus, A. J. (2002),

Investments, McGraw-Hill/Irwin (5th ed.). 2. Fabozzi, F. J. (2001), The Handbook of Fixed Income

Securities McGraw-Hill (6th ed.). 3. Hull, J. C. (2000), Options, Futures and other

Derivatives, Prentice Hall (5th ed.). 4. Babbel, D. & Merrill, C. (1996), Valuation of Interest-

Sensitive Financial Instruments, Frank J. Fabozzi Associates, (Second Printing).

5. Panjer et al, H. H. (1998), Financial Economics with Applications to Investments Insurance and Pensions, The Actuarial Foundation.

SJER3218 INTRODUCTION TO GENERAL INSURANCE Introduction to insurance and utility theory; types of general insurance products : motor, fire, property and others ,rating factors; data on claims, loss payments and premiums; ingredients of ratemaking: loss development factors, expenses, credibility factors, investment income, projected loss cost per unit exposure, gross rate; calculation of overall average rate change: Loss cost method and loss ratio method, risk classification differentials, balance back

Assessment: Final Examination: 60% Continuous Assessment: 40% Medium of Instruction: English Humanity Skill: CS2, CT1, LL1 References: 1. Brown, Robert L. & Gottlieb, Leon R. (2001),

Introduction to Ratemaking and Loss reserving for Property and Casualty Insurance, ACTEX Publications (2nd ed.).

2. Wiser, R. F., Cookley, J. E. & Gardner A. (2001), Loss Reserving, Foundations of Casualty Actuarial Science, Casualty Actuarial Society (4th ed.).

3. Bellis et al (2003), Understanding Actuarial Management: The Actuarial Control Cycle, Institute of Actuaries of Australia.

4. CAS (2001), Foundation of Casualty Actuarial Science, Casualty Actuarial Society, (4th ed.).

5. Lam (2003), Enterprise Risk Management: From Incentives to Controls, John Wiley.

SJER4221 LIFE INSURANCE AND TAKAFUL Insurance products and unit-linked insurance; Group Life insurance; Operation of a Life Insurance company: underwriting, claims, marketing and distribution methods; Profit testing ; Takaful insurance; Regulations: Insurance Act, taxation and role of Bank Negara. Assessment: Final Examination: 60% Continuous Assessment: 40% Medium of Instruction: English Humanity Skill: CS2, CT1, TS1, LL1 References: 1. Insurance Act (1997). 2. Mohd Ma’sum Billah, (2003), Islamic Insurance

(Takaful), Ilmiah Publisher Sdn. Bhd. 3. Black, K. J. & Skipper, H. J. (1994), Life Insurance. Ed.

Ke-12, New Jersey: Prentice-Hall. 4. Mohd Fadzli Yusof (2006), Mengenali Takaful, Ibs

Buku. 5. Pengiran Noor Asmawi Pengiran Haji Ahmad (2005),

Takaful: Kepentingan dan Hukum-Hukum Perlaksanaannya, Dewan Bahasa dan Pustaka Brunei.

SJER4222 INVESTMENT AND FINANCIAL ANALYSIS II Valuation and application of options; Binomial option pricing techniques, Brownian Motion and Ito’s Lemma, Black-Scholes model; Exotic options; Financial risk management, delta-hedging. Assessment: Final Examination: 60% Continuous Assessment: 40%

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Medium of Instruction: English Humanity Skill: CS2, CT1, TS1, LL1 References: 1. Hull, J. C. (2000), Options, Futures and other

Derivatives, Prentice Hall (5th ed). 2. Babbel, D. & Merrill, C. (1996), Valuation of Interest-

Sensitive Financial Instruments, (Second Printing), Frank J. Fabozzi Associates.

3. Robert, L. M. (2006), Derivatives Markets, Addison Wesley (2nd ed.).

4. Bodie, Z., Kane, A., & Marcus, A. J. (2002) Investments, McGraw-Hill/Irwin, (5th ed.).

5. Fabozzi, F. J. (2001), The Handbook of Fixed Income Securities, McGraw-Hill, (6th ed).

SJER4223 LOSS RESERVING, ACCOUNTING AND

REINSURANCE FOR PROPERTY AND CASUALTY INSURANCE

Definition of reserving terms; paid loss and incurred loss development; loss reserving methods: case reserves, expected loss ratio, chain ladder, average cost per claim and Bornhuetter-Ferguson method, discounting loss reserves; other reserves: unearned premium reserve and additional unexpired risk reserve; insurance accounting principles; types of reinsurance and reserving for reinsurance. Assessment: Final Examination: 60% Continuous Assessment: 40% Medium of Instruction: English Humanity Skill: CS2, CT1, LL1 References: 1. Brown, Robert L., & Gottlieb, Leon R., (2001),

Introduction to Ratemaking and Loss reserving for Property and Casualty Insurance, ACTEX Publications (2nd ed.).

2. Wiser, R. F., Cookley, J. E. & Gardner A. (2001), Loss Reserving, Foundations of Casualty Actuarial Science, Casualty Actuarial Society (4th ed.).

3. Bellis et al, (2003), Understanding Actuarial Management: The Actuarial Control Cycle, Institute of Actuaries of Australia.

4. CAS, (2001), Foundation of Casualty Actuarial Science, Casualty Actuarial Society, (4th ed.).

5. Lam, (2003), Enterprise Risk Management: From Incentives to Controls, John Wiley.

SJER4271 GROUP PRESENTATIONS ON SELECTED

TOPICS IN ACTUARIAL SCIENCE AND FINANCE

Speakers from various areas such as insurance, finance and banking, investments, KLSE and Bank Negara will be invited to give talks on a regular basis. This course will be examined based on group presentations on selected topics

of Actuarial Science and Finance covered by the invited speakers. Assessment: Continuous Assessment : 100 % Medium of Instruction: English Humanity Skill: CS2, CT1, TS1, LL1 SJER4323 CREDIBILITY AND RUIN THEORY Limited fluctuation and greatest accuracy credibility theory. The Bayesian and credibility premiums. The Buhlmann and Buhlmann-Straub models. Exact credibility. Empirical Bayes parameter estimation. The adjustment coefficment and the Cramer-Lundberg ruin inequality. The maximum aggregate loss and the general solution Assessment: Final Examination: 60% Continuous Assessment: 40% Medium of Instruction: English Humanity Skill: CS2, CT2, LL2 References: 1. Herzog, T. N. (1999), Introduction to Credibility Theory,

Actex. (3rd ed.). 2. Klugman, S. A., Panjer, H. H. & Willmot, G. G. (2004)

Loss Models: From Data To Decisions, John Wiley & Sons (2nd ed.).

3. Nesbitt, Cecil, Jones, Hickman, Gerber & Bowers, (1997), Actuarial Mathematics, Soc. Actuaries (2nd ed.).

4. Daykin, Pentikainenn & Pesonen, (1994), Practical Risk Theory for Actuaries, Chapman and Hall,

5. Grandell & Jan, (1991), Aspects of Risk Theory, Springer-Verlag.

SJER4324 INTRODUCTION TO RISK THEORY Insurance economics; short term individual risk model; collective risk model for a single period; collective risk model for an extended period; applications of risk theory. Assessment: Final Examination: 60% Continuous Assessment: 40% Medium of Instruction: English Humanity Skill: CS2, CT2, LL2 References: 1. Nesbitt, Cecil, Jones, Hickman, Gerber & Bowers

(1997), Actuarial Mathematics, Soc. Actuaries, (2nd ed.).

2. Daykin, Pentikainenn, &, Pesonen (1994), Practical Risk Theory for Actuaries, Chapman and Hall.

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3. Gjessing & Hakon (1997), Present Value Distributions with Applications to Ruin Theory and Stochastic Equations, University of Copenhagen, Laboratory of Actuarial Mathematics.

4. Batten, Robert & Richard London (1999), (Risk Management and Insurance). A Guide for the Actuarial Student: Life Contingencies and Ruin Theory. Winsted, CT: ACTEX Publications.

5. Klugman, S. A., Panjer, H. H., Willmot, G. G. (2004), Loss Models: From Data to Decisions, John Wiley & Sons, (2nd ed.).