Page 141 - FULL FINAL HANDBOOK 20232024

Faculty of Science Handbook, Academic Session 2023/2024

factor groups; group homomorphisms. systems. Liapunov’s method. Applications
Ring Theory – rings, integral domains and fields; Assessment:
subrings, ideals and quotient rings; ring Continuous Assessment: 40%
homomorphisms; polynomial rings, the Division Final Examination: 60%
algorithm and Euclidean algorithm in polynomial rings.
Assessment:
Continuous Assessment: 40% SIM2020 MANAGEMENT MATHEMATICS
Final Examination: 60%
Output function: Theory and some concepts. Break even
model. Maximum profit for monopoly and oligopoly
markets. Inventory model. EOQ Model, reordering point,
SIM2015 INTRODUCTION TO ANALYSIS finite input rate, shortage and discount quantity.
Probabilistic model, safety stock and efficiency level.
Sequences. Topology of the real line. Compactness.
Properties of continuous functions. Uniform continuity.
Derivative of a function. Properties of differentiable Assessment:
functions. Mean Value Theorems. Higher order Continuous Assessment: 40%
derivatives. L’Hospital’s Rules. Final Examination: 60%
Assessment:
Continuous Assessment: 40%
Final Examination: 60% SIM2021 OPTIMIZATION TECHNIQUES
Unconstraint optimization, necessary and sufficient
condtions for an extremum point. Constraint
SIM2016 COMPLEX VARIABLES optimization. Type of constraint. A variation of
techniques for solving nonlinear problems.
Complex numbers, complex functions, limits, continuity.
Differentiable and analytic functions, Cauchy-Riemann Assessment:
equations, harmonic functions. Sequences and series of Continuous Assessment: 40%
complex numbers, convergence tests, power series. Final Examination: 60%
Elementary functions: the complex exponential function,
complex logarithms, complex exponents, trigonometry
functions. Complex integrals, contour integrals, the
Cauchy-Goursat theorem, the fundamental theorems of SIM3001 GRAPH THEORY
integration, Cauchy’s integral formula, Cauchy’s integral
formula for derivatives and Morera’s theorem. Graph theory and its applications.
Assessment: Topics will be selected from the following:
Continuous Assessment: 40% Eulerian graphs, trees, planar graphs, graph colouring
Final Examination: 60% and chromatic polynomials, Hamiltonian graphs,
matching theory, directed graphs and the shortest path
problem, network theory.
SIM2017 GEOMETRY Assessment:
Continuous Assessment: 40%
Euclidean Geometry, congruence, parallelism, similarity, Final Examination: 60%
isometry, Incidence geometry of the hyperbolic plane,
motions of the sphere.
Assessment: SIM3002 COMBINATORIAL MATHEMATICS
Continuous Assessment: 40%
Final Examination: Enumerative combinatorics: permutations and
60% combinations, Catalan numbers, Stirling numbers and
partition numbers.
Existential combinatorics: pigeonhole principle, Ramsey
SIM2018 PARTIAL DIFFERENTIAL EQUATIONS theory of graphs and systems of distinct representatives.
Fourier series, introduction to partial differential Combinatorial designs: block designs, balanced
equations, method of characteristics, separation of incomplete block designs, Steiner triple systems and
variables, Laplace transform method. Hadamard matrices.
Assessment: Assessment:
Continuous Assessment: 40% Continuous Assessment: 40%
Final Examination: 60% Final Examination: 60%
SIM2019 SYSTEMS OF ORDINARY SIM3003 NUMBER THEORY
DIFFERENTIAL EQUATIONS
Prime numbers. The division algorithm and unique
Linear systems of first-order equations. Homogeneous factorization theorem for integers. Linear diophantine
linear systems. Nonhomogeneous linear systems. equations. Theory of congruence and the Chinese
Remainder Theorem. RSA encryption. Quadratic
Nonlinear autonomous systems. Stability. Locally linear reciprocity and the Legendre symbol. Arithmetic
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