Page 159 - FINAL_HANDBOOK_20252026

Faculty of Science Handbook, Academic Session 2025/2026

topology of the real line: Open and closed discussed in the lectures. Students
sets, accumulation points. collectively will use elements of
mathematics to undertake the project. Each
Assessment: group is also required to identify and plan
Continuous Assessment: 40% activities for a community partnership that
Summative Assessment: 60% will not only help them to enhance their
understanding or gain a different
SIM2002 perspective of their project but will also be
LINEAR ALGEBRA beneficial to the community partner. Each
student will be required to record a
Vector spaces and subspaces, null spaces, reflection of their experiences before,
sums and direct sums of subspaces. Linear during and after the fieldwork at the
independences, bases, dimensions, the community partner and to submit their
subspace dimension theorem, row and record with the group project report at the
column spaces, ranks, ordered bases, end of the semester. Students are also
coordinates, changes of basis. Linear required to do a group presentation based
transformations, kernel and range, the on the project.
rank-nullity theorem, isomorphisms, matrix
representations. Eigenvalues, eigenvectors, Assessment:
characteristic polynomials, Continuous Assessment:100%
diagonalizability, the Cayley-Hamilton
Theorem. SIM2010
NUMERICAL COMPUTATION
Assessment:
Continuous Assessment: 40% Computer arithmetic: floating-point
Summative Assessment: 60% numbers, round-off error, machine
precision, overflow/underflow, numerical
SIM2007 cancellation, truncation error.
APPRECIATION OF MATHEMATICS
Taylor polynomials and limits.
This course exposes students to some
aesthetic aspects of mathematics that they Interpolation: Lagrange interpolation,
may not have encountered in other divided difference method, Hermite
mathematics courses. The main aim is to interpolation, cubic spline interpolation.
promote appreciation of the beauty of
mathematics and the role mathematics Roots of nonlinear equation: bisection
plays in society. The topics chosen for this method, fixed-point iteration, Newton–
course come from a variety of different Raphson method, secant method.
areas, for example, mathematical puzzles
and games, famous solved or unsolved Numerical differentiation: Forward,
mathematical problems and their history, backward and central finite difference
mathematicians and their work, methods.
mathematics and music, mathematics and
origami, mathematics in technology and Numerical Integration: trapezoidal,
mathematics in nature. Students will be put Simpson’s, Romberg’s methods. Composite
into groups and each group will work on a methods.
project related to any of the topics

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