Page 159 - FINAL_HANDBOOK_20242025

Faculty of Science Handbook, Academic Session 2024/2025

SIM2021 permutations and
OPTIMIZATION combinations, Catalan
TECHNIQUES numbers, Stirling numbers and
partition numbers.
Unconstraint optimization,
necessary and sufficient Existential combinatorics:
conditions for an extremum pigeonhole principle, Ramsey
point. Constraint optimization. theory of graphs and systems
Type of constraint. A variation of distinct representatives.
of techniques for solving
nonlinear problems. Combinatorial designs: block
designs, balanced incomplete
Assessment: block designs, Steiner triple
Continuous Assessment: 40% systems and Hadamard
Final Examination: 60% matrices.

Assessment:
SIM3001 Continuous Assessment: 40%
GRAPH THEORY Final Examination: 60%

Graph theory and its
applications. SIM3003
NUMBER THEORY
Topics will be selected from the
following: Eulerian graphs, Prime numbers. The division
trees, planar graphs, graph algorithm and unique
colouring and chromatic factorization theorem for
polynomials, Hamiltonian integers. Linear diophantine
graphs, matching theory, equations. Theory of
directed graphs and the congruence and the Chinese
shortest path problem, network Remainder Theorem. RSA
theory. encryption. Quadratic
reciprocity and the Legendre
Assessment: symbol. Arithmetic functions.
Continuous Assessment: 40% Primitive roots.
Final Examination: 60%
Assessment:
Continuous Assessment: 40%
SIM3002 Final Examination: 60%
COMBINATORIAL
MATHEMATICS

Enumerative combinatorics:

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