Page 45 - handbook 20162017

Faculty of Science Handbook, Session 2016/2017

SIM2008 THEORY OF DIFFERENTIAL EQUATIONS References:
1. Koh, K.M., Dong, F., Ng, K.L. and and Tay, E.G.
The existence and uniqueness theorem. Solutions to the (2015). Graph Theory: Undergraduate Mathematics,
system of linear differential equations with constant World Scientific.
coefficients. Automatic linear system and linear 2. Chartrand, G. and Lesniak, L. (2010). Graphs and
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approximation of dimension two, types of critical points, digraphs, CRC Press (5 edition).
stability. 3. Gross, J.L., Yellan, J. and Zhang, P. (2013).
Handbook of Graph Theory (Discrete Mathematics
nd
Assessment: and its Applications), CRC Press (2 edition).
Continuous Assessment: 40%
Final Examination: 60%
SIM3002 COMBINATORIAL MATHEMATICS
Medium of Instruction:
English Theory of Enumeration: Topics will be chosen from:
Permutation and Combination, advanced counting
Humanity Skill: numbers, generating functions, principle of inclusion and
CS3, CT5, LL2 exclusion.
References: Combinatorial Designs: Topics will be chosen from: Block
1. Zill D.G., Wright, W.S. & Cullen, M.R. (2013). designs, balanced incomplete block designs, Steiner triple
Differential Equations with Boundary-value Problems, system, Hadamard matrices, pigeonhole principle and
Brooks/Cole Cengage Learning (8 edition). Ramsey theory for graphs.
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2. Chicone, C. (2006). Ordinary Differential Equations
nd
with Applications, Springer (2 edition). Assessment:
3. Logan. J.D. (2011). A First Course in Differential Continuous Assessment: 40%
60%
Final Examination:
Equations, Springer (2nd edition).
Medium of Instruction:
English
SIM2009 GEOMETRY
Humanity Skill:
Euclidean Geometry, congruence, parallelism, similarity, CS3, CT3, LL2
isometry, Incidence geometry of the sphere, motions of the
sphere. References:
1. Brualdi, R. A. (2009). Introductory Combinatorics,
Assessment: North Holland Publ. Co. (5 edition).
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Continuous Assessment: 40% 2. Stanley, R.P. (2011). Enumerative Combinatorics,
Final Examination: 60% Volume 1, Cambridge University Press (2 edition).
nd
3. Liu, C.L. (1968). Introduction to Combinatorial
Medium of Instruction: Mathematics, Computer Science Series, McGraw Hill
English Book Co.
4. Street, A.P. and Wallis, W.D. (1997). Combinatorial
Humanity Skill: Theory: An Introduction, The Charles Babbage
CS3, CT3, LL2 Research Center, Manitoba, Canada.
5. Tucker, A. (2012). Applied Combinatorics, John Wiley
References: and Sons (6 edition).
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1. Ryan P.J. (1986). Euclidean and non-Euclidean
geometry, Cambridge Univ. Press.
2. Kumaresan S. (2005). An expedition to geometry, SIM3003 NUMBER THEORY
Hindustan Book Agency
3. Henle, M. (2001). Modern Geometries: Non- Prime Numbers. The Division Algorithm and Unique
Euclidean, Projective, and Discrete Geometry, Factorization Theorem for Integers. Linear Diophantine
nd
Pearson (2 edition). Equations. Theory of congruence and the Chinese
4. Kappraff, J. (2014). A Participatory Approach to Remainder Theorem. RSA encryption. Quadratic reciprocity
Modern Geometry, World Scientific. and the Legendre symbol. Arithmetic functions. Primitive
roots.
SIM3001 GRAPH THEORY Assessment:
Continuous Assessment: 40%
Graph theory and its applications. Final Examination: 60%
Topics will be selected from the following :
Eulerian graphs, trees, planar graphs, graph colouring and Medium of Instruction:
chromatic polynomials, Hamiltonian graphs, matching English
theory, directed graphs and the shortest path problem,
network theory. Humanity Skill:
CS3, CT5, LL2
Assessment:
Continuous Assessment: 40% References:
Final Examination: 60%
1. Burton, D. (2010). Elementary Number Theory,
McGraw Hill Publ. Co. (7 edition).
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Medium of Instruction: 2.
English Rosen, K. H. (2010) Elementary Number Theory and
Its Applications, Pearson Addison Wesley (6 edition).
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Humanity Skill: 3. Davenport, H. (2008). The Higher Arithmetic,
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CT3, LL2 Cambridge University Press (8 edition).
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