Course Archives Theoretical Statistics and Mathematics Unit

Course: Group Theory Instructor: Sury B Room: G26 Level: Undergraduate Time: Currently 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 35 marks Assignments 15 marks Final Exam 50 marks Total 100 marks Top of the page Past Exams

Midterm 23.pdf Semestral 23.pdf Supplementary and Back Paper 23.pdf Top of the page

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