Page 140 - FULL FINAL HANDBOOK 20232024

Faculty of Science Handbook, Academic Session 2023/2024

integrals, Jacobians. method, Hermite interpolation, cubic spline interpolation.
Basic set theory. Functions, bijective functions, inverse Roots of nonlinear equation: bisection method, fixed-
functions. Finite and infinite sets, countable and point iteration, Newton – Raphson method, secant
uncountable sets. The Real Number system. Bounds, method.
supremum and infimum. Archimedean property. Rational
and irrational numbers. Properties of real numbers. Numerical differentiation: Forward, backward and central
Sequences of real numbers, convergence. Limit finite difference methods.
Theorems. Monotone sequences, Cauchy sequences
and subsequences. Basic topology of the real line: Open Numerical Integration: trapezoidal, Simpson’s,
and closed sets, accumulation points. Romberg’s methods. Composite methods.
Assessment: System of linear equations. Matrix factorization, LU
Continuous Assessment: 40% factorization.
Final Examination: 60%
Assessment:
Continuous Assessment: 40%
Final Examination: 60%
SIM2002 LINEAR ALGEBRA
Vector spaces and subspaces, null spaces, sums and
direct sums of subspaces. Linear independences, SIM2011 STRUCTURED PROGRAMMING
bases, dimension, the subspaces dimension theorem,
row and column spaces, rank, ordered bases, Algorithms: Structured programming – sequence,
coordinates, changes of basis. Linear transformations, decision statement and loops. Object-oriented design.
kernel and range, the rank-nullity theorem,
isomorphisms, matrix representations. Eigenvalues, Programming: fundamental data types – int, double,
eigenvectors, characteristic polynomials, char. Operators, precedence order. Pre-processor
diagonalizability, the Cayley-Hamilton Theorem. directives. In-built functions. User-defined functions –
pass by value and reference. One- and two-dimensional
Assessment: arrays.
Continuous Assessment: 40%
Final Examination: 60% Introduction to user-defined data types – structures and
classes.
Applications of numerical methods: integer and floating
SIM2007 APPRECIATION OF MATHEMATICS point arithmetic, root finding, solutions of ordinary
differential equations. Use of random number generator.
This course exposes students to some aesthetic aspects
of mathematics that they may not have encountered in Assessment:
other mathematics courses. The main aim is to promote Continuous Assessment: 50%
appreciation of the beauty of mathematics and the role Final Examination: 50%
mathematics plays in society. The topics chosen for this
course come from a variety of different areas, for
example, mathematical puzzles and games, famous
solved or unsolved mathematical problems and their SIM2012 BASIC OPERATIONS RESEARCH
history, mathematicians and their work, mathematics
and music, mathematics and origami, mathematics in Introduction to the problems in operations research,
technology and mathematics in nature. Students will be modelling, formulation and examples. Linear
put into groups and each group will work on a project programming, transportation and assignment problems.
related to any of the topics discussed in the lectures. Integer programming, game theory and dynamic
Students collectively will use elements of mathematics to programming.
undertake the project. Each group is also required to
identify and plan activities for a community partnership Assessment:
that will not only help them to enhance their Continuous Assessment: 40%
understanding or gain a different perspective of their Final Examination: 60%
project but will also be beneficial to the community
partner. Each student will be required to record a
reflection of their experiences before, during and after
the field work at the community partner and to submit SIM2013 INTRODUCTION TO COMBINATORICS
their record with the group project report at the end of the
semester. Students are also required to do a group Ordered and equivalence relations, binomial and
presentation based on the project. multinomial theorems, recurrence relations, principle of
inclusion and exclusion, generating functions, Latin
Assessment: squares, magic squares, basic properties of graphs,
Continuous Assessment: 100% circuits and cycles in graphs, trees and their applications.
Assessment:
Continuous Assessment: 40%
SIM2010 NUMERICAL COMPUTATION Final Examination: 60%
Computer arithmetic: floating-point numbers, round off
error, machine precision, overflow/underflow, numerical
cancellation, truncation error. SIM2014 ALGEBRA I
Taylor polynomials and limits. Group Theory - abstract groups, subgroups, cyclic and
dihedral groups; order of an element and of a subgroup,
Interpolation: Lagrange interpolation, divided difference Lagrange’s theorem; cosets, normal subgroups and
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