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Faculty of Science Handbook, Session 2017/2018

References: SIM2006 COMPLEX VARIABLES
1. Erickson, M.J. (2013). Introduction to Combinatorics,
nd
Wiley (2 edition). Complex number system. Complex function, limits,
2. Chen, C.C. & Koh, K.M. (1992). Principles and continuity, differentiability and analytic function. Cauchy-
Techniques in Combinatorics, World Scientific. Riemann equations, Harmonic functions. Mapping and
3. Lovasz, L., Pelikan, J. & Vesztergombi, K. (2003). other properties of elementary functions. Complex
Discrete Mathematics : Elementary and Beyond, Integration, Cauchy’s Theorem, Cauchy’s Integral Formula.
Springer.
4. Matousek J. & Nesetril J. (2008). Invitationd to Assessment:
Discrete Mathematics: Oxford Leniv. Press (2nd Continuous Assessment: 40%
edition). Final Examination: 60%

Medium of Instruction:
SIM2004 ALGEBRA I English
Groups and subgroups. Order of an element and order of a Humanity Skill:
subgroup. Lagrange’s theorem. Normal subgroups and CT3, LL2
factor groups. Homomorphisms and isomorphisms, Rings,
integral domains and fields. Subrings and subfields. Ideals References:
and quotient rings. Rings of polynomials. The Division 1. Churchill, R.V. & Brown, J.W. (2013). Complex
algorithm and Euclidean algorithm in polynomial rings. Variables and Applications, McGraw-Hill Book Co (9 th
Unique factorization theorem. ed).
2. Mathews John H. and Howell, Russell W. (2012).
Assessment: Complex Analysis: for Mathematics and Engineering,
th
Continuous Assessment: 40% Jones & Bartlett Pub. Inc. (6 ed).
Final Examination: 60% 3. Nguyen Huu Bong (1994). Analisis Kompleks dan
Penerapan, Dewan Bahasa dan Pustaka.
Medium of Instruction: 4. Howie, John M. (2007). Complex Analysis. Springer,
rd
English (3 ed).
Humanity Skill:
CT3, LL2 SIM2007 APPRECIATION OF MATHEMATICS

References: Students will be put into groups. Each group will be given 2
1. Gilbert, L., Gilbert, J. (2014). Elements of Modern mathematical tasks to work on. These tasks will come from
Algebra, Brooks/Cole (8 edition). a variety of topics selected from, but not limited to: algebra,
th
2. Durbin, J.R. (2008). Modern Algebra, An Introduction, geometry, combinatorics, applied and computational
th
John Wiley (6 edition). mathematics, probability and statistics, science &
3. Judson, T.W. (2014). Abstract Algebra, Theory and technology, mathematics and society, management
Applications, Open Source. science, finance mathematics, actuarial sciences, history
and philosophy. Students collectively will use
tools/elements of mathematics to undertake each task. In
SIM2005 INTRODUCTION TO ANALYSIS undertaking these tasks, students are required to carry out
to a certain extend some literature survey, background
Sequences. Infinite series, convergence. Tests of reading and explore some elementary research problems.
convergence. Absolute and conditional convergence. During guided learning sessions, students are also
Rearrangement of series. Topology of the real line. expected to critique, analyse, argue logically and deduce
Compactness. Properties of continuous functions. Uniform findings. Each group is required to produce and present
continuity. Derivative of a function. Properties of reports for the tasks given.
differentiable functions. Mean Value Theorems. Higher
order derivatives. L’Hospital’s Rules. Assessment:
Participation in discussion,
Assessment: Communication & Presentation: 25%
Continuous Assessment: 40% Peer Review: 10%
Final Examination: 60% Teamwork & Ethics: 15%
Project Report: 50%
Medium of Instruction:
English Medium of Instruction:
English
Humanity Skill:
CS3, CT3, LL2 Humanity Skill:
CS4, TS3, LL2, EM2, LS2
References:
1. Lay, R. (2014). Analysis with an introduction to proof,
Pearson (5 edition). SIM2008 THEORY OF DIFFERENTIAL EQUATIONS
th
2. Kosmala, W. (2004). A Friendly Introduction to
Analysis, Pearson (2nd edition). The existence and uniqueness theorem. Solutions to the
3. Haggarty, R. (1993). Fundamentals of Mathematical system of linear differential equations with constant
Analysis. Addison-Wesley Publ. Co. (2nd edition). coefficients. Automatic linear system and linear
4. Bartle, R.G. & Sherbert, D.R. (2011). Introduction to approximation of dimension two, types of critical points,
Real Analysis, John Wiley & Sons Inc (4th edition). stability.
5. Pownall, M.W. (1994). Real Analysis: A First Course
with Foundations, Wm. C. Brown Publ. Co. Assessment:
Continuous Assessment: 40%
Final Examination: 60%

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