Page 106 - handbook 20152016

Faculty of Science Handbook, Session 2015/2016

Assessment: Eulerian graphs, trees, planar graphs, graph colouring and
Participation in discussion, chromatic polynomials, Hamiltonian graphs, matching
Communication & Presentation: 25% theory, directed graphs and the shortest path problem,
Peer Review: 10% network theory.
Teamwork & Ethics: 15%
Project Report: 50% Assessment:
Continuous Assessment: 40%
Medium of Instruction: Final Examination: 60%
English
Medium of Instruction:
Humanity Skill: English
CS4, TS3, LL2, EM2, LS2
Humanity Skill:
CT3, LL2
SIM2008 THEORY OF DIFFERENTIAL EQUATIONS
References:
The existence and uniqueness theorem. Solutions to the 1. Koh, K.M., Dong, F., Ng, K.L. and and Tay, E.G.
system of linear differential equations with constant (2015). Graph Theory: Undergraduate Mathematics,
coefficients. Automatic linear system and linear World Scientific.
approximation of dimension two, types of critical points, 2. Chartrand, G. and Lesniak, L. (2010). Graphs and
th
stability. digraphs, CRC Press (5 edition).
3. Gross, J.L., Yellan, J. and Zhang, P. (2013).
Assessment: Handbook of Graph Theory (Discrete Mathematics
nd
Continuous Assessment: 40% and its Applications), CRC Press (2 edition).
Final Examination: 60%

Medium of Instruction: SIM3002 COMBINATORIAL MATHEMATICS
English
Theory of Enumeration: Topics will be chosen from:
Humanity Skill: Permutation and Combination, advanced counting
CS3, CT5, LL2 numbers, generating functions, principle of inclusion and
exclusion.
References:
1. Zill D.G., Wright, W.S. & Cullen, M.R. (2013). Combinatorial Designs: Topics will be chosen from: Block
Differential Equations with Boundary-value Problems, designs, balanced incomplete block designs, Steiner triple
th
Brooks/Cole Cengage Learning (8 edition). system, Hadamard matrices, pigeonhole principle and
2. Chicone, C. (2006). Ordinary Differential Equations Ramsey theory for graphs.
nd
with Applications, Springer (2 edition).
3. Logan. J.D. (2011). A First Course in Differential Assessment: 40%
Continuous Assessment:
Equations, Springer (2nd edition). Final Examination: 60%

Medium of Instruction:
SIM2009 GEOMETRY English

Euclidean Geometry, congruence, parallelism, similarity, Humanity Skill:
isometry, Incidence geometry of the sphere, motions of the CS3, CT3, LL2
sphere.
References:
Assessment: 1. Brualdi, R. A. (2009). Introductory Combinatorics,
Continuous Assessment: 40% North Holland Publ. Co. (5 edition).
th
Final Examination: 60% 2. Stanley, R.P. (2011). Enumerative Combinatorics,
Volume 1, Cambridge University Press (2 edition).
nd
Medium of Instruction: 3. Liu, C.L. (1968). Introduction to Combinatorial
English Mathematics, Computer Science Series, McGraw Hill
Book Co.
Humanity Skill: 4. Street, A.P. and Wallis, W.D. (1997). Combinatorial
CS3, CT3, LL2 Theory: An Introduction, The Charles Babbage
Research Center, Manitoba, Canada.
References: 5. Tucker, A. (2012). Applied Combinatorics, John Wiley
1. Ryan P.J. (1986). Euclidean and non-Euclidean and Sons (6 edition).
th
geometry, Cambridge Univ. Press.
2. Kumaresan S. (2005). An expedition to geometry,
Hindustan Book Agency SIM3003 NUMBER THEORY
3. Henle, M. (2001). Modern Geometries: Non-
Euclidean, Projective, and Discrete Geometry, Prime Numbers. The Division Algorithm and Unique
nd
Pearson (2 edition). Factorization Theorem for Integers. Linear Diophantine
4. Kappraff, J. (2014). A Participatory Approach to Equations. Theory of congruence and the Chinese
Modern Geometry, World Scientific. Remainder Theorem. RSA encryption. Quadratic reciprocity
and the Legendre symbol. Arithmetic functions. Primitive
roots.
SIM3001 GRAPH THEORY
Assessment:
Graph theory and its applications. Continuous Assessment: 40%
Topics will be selected from the following : Final Examination: 60%

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