Page 43 - tmp

Faculty of Science Handbook, Session 2017/2018

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.
with Applications, Springer (2 edition).
nd
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
Pearson (2 edition). Factorization Theorem for Integers. Linear Diophantine
nd
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%
Eulerian graphs, trees, planar graphs, graph colouring and
chromatic polynomials, Hamiltonian graphs, matching Medium of Instruction:
theory, directed graphs and the shortest path problem, English
network theory.
Humanity Skill:
Assessment: CS3, CT5, LL2
Continuous Assessment: 40%
Final Examination: 60% References:
1. Burton, D. (2010). Elementary Number Theory,
Medium of Instruction: McGraw Hill Publ. Co. (7 edition).
th
English
2. Rosen, K. H. (2010) Elementary Number Theory and
th
Humanity Skill: Its Applications, Pearson Addison Wesley (6 edition).
CT3, LL2 3. Davenport, H. (2008). The Higher Arithmetic,
Cambridge University Press (8 edition).
th
References: 4. Baker, A. (1985). A Concise Introduction to the Theory
1. Koh, K.M., Dong, F., Ng, K.L. and and Tay, E.G. of Numbers, Cambridge University Press.
(2015). Graph Theory: Undergraduate Mathematics, 5. Baker, A. (2012). A Comprehensive Course in Number
World Scientific. Theory, Cambridge University Press.
2. Chartrand, G. and Lesniak, L. (2010). Graphs and
th
digraphs, CRC Press (5 edition).
3. Gross, J.L., Yellan, J. and Zhang, P. (2013). SIM3004 ADVANCED LINEAR ALGEBRA
Handbook of Graph Theory (Discrete Mathematics
and its Applications), CRC Press (2 edition). Inner product spaces, the Gram-Schmidt orthogonalization
nd
process and orthogonal complements. Orthogonal
41