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Faculty of Science Handbook, Academic Session 2025/2026
SIM3006 SIM3009
ALGEBRA II DIFFERENTIAL GEOMETRY
The isomorphism theorems, various Vector algebra on Euclidean space. Lines
subgroups such as the centre and and planes. Change of coordinates.
commutator subgroups, finitely generated Differential geometry of curves. Frenet
abelian groups, automorphism groups, Equations. Local theory of surfaces in
permutation groups, and p-groups. Euclidean space. First and second
fundamental forms. Gaussian curvatures
The maximal and prime ideals, polynomial and mean curvatures. Geodesics. Gauss-
rings, irreducible polynomials and the Bonnet Theorem.
unique factorization theorem.
Assessment:
Assessment: Continuous Assessment: 40%
Continuous Assessment: 40% Summative Assessment: 60%
Summative Assessment: 60%
SIM3010
SIM3007 TOPOLOGY
RING THEORY
Topological spaces. Continuity,
Subrings, subfields and ideals; internal connectedness and compactness.
direct sum and external direct product; nil Separation axioms and countability. Metric
ideals, nilpotent ideals; modules and spaces. Product spaces.
submodules; prime ideals, maximal ideals;
prime radical and Jacobson radical; Assessment:
semiprime and semiprimitive rings; rings Continuous Assessment: 40%
with chain conditions; group rings. Summative Assessment: 60%
Assessment: SIM3011
Continuous Assessment: 40% COMPLEX ANALYSIS
Summative Assessment: 60%
Infinite series expansions: convergence and
SIM3008 divergence and region of convergence.
GROUP THEORY Taylor and Laurent theorems. Classification
of isolated singularities. Zeroes and poles.
The three isomorphism theorems. Cyclic Calculus of residues; calculation of definite
groups. Direct product of groups. integrals. Residue theory. Evaluation of
Introduction to the three Sylow’s certain integrals. Argument principle,
Theorems. Classification of groups up to Rouche’s Theorem. Maximum modulus
order 8. Finitely generated abelian groups. principle. Conformal mappings.
Nilpotent and soluble groups.
Assessment:
Assessment: Continuous Assessment: 40%
Continuous Assessment: 40% Summative Assessment: 60%
Summative Assessment: 60%
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