Page 121 - Handbook Bachelor Degree of Science Academic Session 20202021

Faculty of Science Handbook, Academic Session 2020/2021

SIM2009 GEOMETRY Soft Skills:
CS3, CTPS3, LL2
Euclidean Geometry, congruence, parallelism, similarity,
isometry, Incidence geometry of the sphere, motions of the References:
sphere. 1. Brualdi, R. A. (2009). Introductory combinatorics (5
th
ed.). Pearson Prentice Hall.
Assessment: 2. Stanley, R.P. (2011). Enumerative combinatorics (2
nd
Continuous Assessment: 40% ed.). (Vol. 1). Cambridge University Press.
Final Examination: 60% 3. Liu, C.L. (1968). Introduction to combinatorial
mathematics, Computer science series. McGraw Hill
Medium of Instruction: Book Co.
English 4. Street, A.P., & Wallis, W.D. (1997). Combinatorial
theory: An introduction. Manitoba, Canada: The
Soft Skills: Charles Babbage Research Center.
CS3, CTPS3, LL2 5. Tucker, A. (2012). Applied combinatorics (6 ed.).
th
John Wiley and Sons.
References:
1. Ryan P.J. (1986). Euclidean and non-Euclidean
geometry. Cambridge Univ. Press. SIM3003 NUMBER THEORY
2. Kumaresan S. (2005). An expedition to geometry.
Hindustan Book Agency Prime Numbers. The Division Algorithm and Unique
3. Henle, M. (2001). Modern geometries: Non-Euclidean, Factorization Theorem for Integers. Linear Diophantine
nd
projective, and discrete geometry (2 ed.). Pearson. Equations. Theory of congruence and the Chinese
4. Kappraff, J. (2014). A participatory approach to modern Remainder Theorem. RSA encryption. Quadratic reciprocity
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, Medium of Instruction:
trees, planar graphs, graph colouring and chromatic English
polynomials, Hamiltonian graphs, matching theory, directed
graphs and the shortest path problem, network theory. Soft Skills:
CS3, CTPS5, LL2
Assessment:
Continuous Assessment: 40% References:
Final Examination: 60% 1. Burton, D. (2010). Elementary number theory (7 ed.).
th
McGraw Hill Publ. Co.
Medium of Instruction: 2. Rosen, K. H. (2010) Elementary number theory and its
English applications (6 ed.). Pearson Addison Wesley.
th
3. Davenport, H. (2008). The higher arithmetic (8 ed.).
th
Soft Skills: Cambridge University Press.
CTPS3, LL2 4. Baker, A. (1985). A concise introduction to the theory of
numbers. Cambridge University Press.
References:
1. Koh, K.M., Dong, F., Ng, K.L., & Tay, E.G. (2015). 5. Baker, A. (2012). A comprehensive course in number
theory. Cambridge University Press.
Graph theory: Undergraduate mathematics. World
Scientific.
2. Chartrand, G., & Lesniak, L. (2010). Graphs and
th
digraphs (5 ed.). CRC Press. SIM3004 ADVANCED LINEAR ALGEBRA
3. Gross, J.L., Yellan, J., & Zhang, P. (2013). Handbook Inner product spaces, the Gram-Schmidt orthogonalization
of graph theory (Discrete mathematics and its process and orthogonal complements. Orthogonal
nd
applications) (2 ed.). CRC Press.
operators, unitary operators, self-adjoint operators and
positive definite operators. Dual spaces, bilinear forms.
SIM3002 COMBINATORIAL MATHEMATICS Diagonalization of symmetric bilinear forms, real quadratic
forms. Triangularization theorem, primary decomposition
theorem, Jordan canonical forms.
Theory of Enumeration: Topics will be chosen from:
Permutation and Combination, advanced counting numbers,
generating functions, principle of inclusion and exclusion. Assessment: 40%
Continuous Assessment:
Final Examination: 60%
Combinatorial Designs: Topics will be chosen from: Block
designs, balanced incomplete block designs, Steiner triple
system, Hadamard matrices, pigeonhole principle and Medium of Instruction:
Ramsey theory for graphs. English
Soft Skills:
Assessment: CS3, CTPS3, LL2
Continuous Assessment: 40%
Final Examination: 60%
Medium of Instruction:
English

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