Page 161 - FINAL_HANDBOOK_20242025

Faculty of Science Handbook, Academic Session 2024/2025

SIM3007 SIM3009
RING THEORY DIFFERENTIAL GEOMETRY

This course includes both Vector algebra on Euclidean
commutative and non- space. Lines and planes.
commutative rings. Topics that Change of coordinates.
will be discussed include Differential geometry of curves.
subrings, subfields and ideals; Frenet Equations. Local theory
internal direct sum and external of surfaces in Euclidean space.
direct product; nil ideals, First and second fundamental
nilpotent ideals; modules and forms. Gaussian curvatures
submodules; prime ideals, and mean curvatures.
maximal ideals; prime radical Geodesics. Gauss-Bonnet
and Jacobson radical; Theorem.
semiprime and semiprimitive
rings; rings with chain Assessment:
conditions; group rings. Continuous Assessment: 40%
Final Examination: 60%
Assessment:
Continuous Assessment: 40%
Final Examination: 60% SIM3010
TOPOLOGY

SIM3008 Topological Spaces.
GROUP THEORY Continuity, connectedness and
compactness. Separation
The three isomorphism axioms and countability. Metric
theorems. Cyclic groups. Direct spaces. Product spaces.
product of groups. Introduction
to the three Sylow’s Theorems. Assessment:
Classification of groups up to Continuous Assessment: 40%
order 8. Finitely generated Final Examination: 60%
abelian groups. Permutation
groups.
SIM3011
Assessment: COMPLEX ANALYSIS
Continuous Assessment: 40%
Final Examination: 60% Infinite series expansions:
convergence and divergence
and region of convergence.
Taylor and Laurent theorems.
Classification of isolated
singularities. Zeroes and poles.

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