Course Archives Theoretical Statistics and Mathematics Unit
Course: Group Theory
Level: Undergraduate
Time: Currently not offered
Syllabus
Past Exams


Syllabus:

i) Equivalence relations and partitions, Zorns lemma, Axiom of choice, Principle of mathematical induction.
ii) Groups, subgroups, homomorphisms, Modular arithmetic, quotient groups, isomorphism theorems.
iii) Groups acting on sets, Sylows theorems, Permutation groups,Semidirect products.
iv) Classification of groups of small order.
v) Notion of solvable groups and proof of simplicity of An (for n > 4).
vi) Matrix groups O(2); U(2); SL(2;R), Matrix exponential.

Reference Texts:

(a) M. Artin: Algebra.
(b) S. D. Dummit and M. R. Foote: Abstract Algebra.
(c) I. N. Herstein: Topics in Algebra.
(d) K. Hoffman and R. Kunze: Linear Algebra.
(e) J. A. Gallian: Contemporary Abstract Algebra.

Evaluation:
Midterm 30 marks
Assignments 20 marks
Final Exam 50 marks
Total 100 marks


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Past Exams
Midterm
23.pdf

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