Abstract Algebra I
MW 4:35-5:55, Skiles 246
OFFICE HOURS: Tues 11-12 or by appointment.
Textbook:
Topics in Algebra by I.M. Herstein.
Topics covered:
Week 1:
Equivalence relations, mappings, definition of
groups, subgroups, homomorphisms, cosets, examples. Sections 1.2, 2.1-2.4.
Week 2:
More examples. Counting. Sections 2.5-2.6.
Week 3:
Homomorphisms, Normal Subgroups, Quotient Groups, Cauchy's Theorem.
Sections 2.6-2.7.
Week 4:
Automorphisms, Cayley's Theorem, Permutation groups.
Sections 2.8-2.10.
Week 5:
Sylow theorems. Sections 2.11-12.
Assignments:
Assignment 1 (due Mon, Sept 10). Page 35: Problems 1,2,3,10,21,22,24,25,26.
Page 46: Problems 1,2,3,4,5,6.
Assignment 2 (due Wed, Sept 26).
Page 48: Problems 18, 21, 22,23, 29,30,31.
Page 53: Problems 1-6, 8-11.
Assignment 3 (due Mon, Oct 15).
Page 64: Problems 1-5.
Page 80: Problems 1-5, 7,
Page 90: Problems 2, 5, 7, 8, 9, 10.
Mid-term: Mon, Oct 15, in class.
Assignment 4 (due Wed, Nov 7).
Page 102: Problems 7,8,13,21,22,23.
Assignment 5 (due Mon, Novv 26 ).
Page 116: Problems 1,4,5. Page 152: Problems 1,2,3.
Saugata Basu