Page 105 - handbook 20152016

Faculty of Science Handbook, Session 2015/2016

5. Ma, S.L. and Tan, V. (2006). Linear Algebra I, Pearson Assessment:
nd
Prentice Hall (2 edition). Continuous Assessment: 40%
Final Examination: 60%

SIM2003 INTRODUCTION TO COMBINATORICS Medium of Instruction:
English
Ordered and equivalence relations, binomial and
multinomial theorems, recurrence relations, principle of Humanity Skill:
inclusion and exclusion, Latin squares, magic squares, CS3, CT3, LL2
basic properties of graphs, circuits and cycles in graphs,
trees and their applications. References:
1. Lay, R. (2014). Analysis with an introduction to proof,
th
Assessment: Pearson (5 edition).
Continuous Assessment: 40% 2. Kosmala, W. (2004). A Friendly Introduction to
Final Examination: 60% Analysis, Pearson (2nd edition).
3. Haggarty, R. (1993). Fundamentals of Mathematical
Medium of Instruction: Analysis. Addison-Wesley Publ. Co. (2nd edition).
English 4. Bartle, R.G. & Sherbert, D.R. (2011). Introduction to
Real Analysis, John Wiley & Sons Inc (4th edition).
Humanity Skill: 5. Pownall, M.W. (1994). Real Analysis: A First Course
CS3, CT3, LL2 with Foundations, Wm. C. Brown Publ. Co.

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

SIM2004 ALGEBRA I Medium of Instruction:
English
Groups and subgroups. Order of an element and order of a
subgroup. Lagrange’s theorem. Normal subgroups and Humanity Skill:
factor groups. Homomorphisms and isomorphisms, Rings, CT3, LL2
integral domains and fields. Subrings and subfields. Ideals
and quotient rings. Rings of polynomials. The Division References:
algorithm and Euclidean algorithm in polynomial rings. 1. Churchill, R.V. & Brown, J.W. (2013). Complex
th
Unique factorization theorem. Variables and Applications, McGraw-Hill Book Co (9
ed).
Assessment: 2. Mathews John H. and Howell, Russell W. (2012).
Continuous Assessment: 40% Complex Analysis: for Mathematics and Engineering,
th
Final Examination: 60% Jones & Bartlett Pub. Inc. (6 ed).
3. Nguyen Huu Bong (1994). Analisis Kompleks dan
Medium of Instruction: Penerapan, Dewan Bahasa dan Pustaka.
English 4. Howie, John M. (2007). Complex Analysis. Springer,
rd
(3 ed).
Humanity Skill:
CT3, LL2
SIM2007 APPRECIATION OF MATHEMATICS
References:
1. Gilbert, L., Gilbert, J. (2014). Elements of Modern Students will be put into groups. Each group will be given 2
th
Algebra, Brooks/Cole (8 edition). mathematical tasks to work on. These tasks will come from
2. Durbin, J.R. (2008). Modern Algebra, An Introduction, a variety of topics selected from, but not limited to: algebra,
th
John Wiley (6 edition). geometry, combinatorics, applied and computational
3. Judson, T.W. (2014). Abstract Algebra, Theory and mathematics, probability and statistics, science &
Applications, Open Source. technology, mathematics and society, management
science, finance mathematics, actuarial sciences, history
and philosophy. Students collectively will use
SIM2005 INTRODUCTION TO ANALYSIS tools/elements of mathematics to undertake each task. In
undertaking these tasks, students are required to carry out
Sequences. Infinite series, convergence. Tests of to a certain extend some literature survey, background
convergence. Absolute and conditional convergence. reading and explore some elementary research problems.
Rearrangement of series. Topology of the real line. During guided learning sessions, students are also
Compactness. Properties of continuous functions. Uniform expected to critique, analyse, argue logically and deduce
continuity. Derivative of a function. Properties of findings. Each group is required to produce and present
differentiable functions. Mean Value Theorems. Higher reports for the tasks given.
order derivatives. L’Hospital’s Rules.

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