Course Archives Theoretical Statistics and Mathematics Unit | ||||||||
Course: Group Theory Level: Undergraduate Time: Currently not offered |
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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:
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Midterm
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