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Notice Board
Topics covered in the class.
Sept. 10: Introduction; Sets, mappings.
Sept. 12: Mappings, Binary operations, Binary relation.
Sept. 17: Bijections, Binary relations, Division Algorithm.
Sept. 19: Divisibility, greatest common divisor, Euclidean algorithm.
Sept. 24: Unique factorization, congruences.
Sept. 26: Solve linear congruence, congruence classes, monoids.
Test # 1
Oct. 1: Examples of Monoids.
Oct. 3: Free monoids and Deterministic Finite Automata.
Oct. 8: no class.
Oct. 10: regular language.
Oct. 15: Groups, examples and properties.
Oct. 17: properties, subgroups, cyclic groups.
Test #2.
Oct. 22: Cyclic groups.
Oct. 24: Order of elements, multiplicative subgroup of complex numbers.
Oct. 29: permutation groups.
Oct. 31: Cosets and Lagrange's Theorem.
Test #3.
Nov. 5: Converse of Lagrange's Theorem, Euler's Theorem, RSA.
Nov. 7: Homomorphism, Isomorphism, and Cayley's Theorem.
Nov. 12: Direct product. Normal subgroup.
Nov. 14: Normal subgroup, quotient groups, Kernel.
Test #4.
Nov. 19: Homomorphisms, Fundamental theorem of homomorphisms.
Nov. 21: Isomorphism thoerems, Rings.
Nov. 26: Ideals and quotient rings
Nov. 28: Homomorphism and isomorphism thoerems, Maximal/prime ideals.
Tutorials
Tutotial #1:
Chapter 1: 17, 20, 22, 25, 26.
Tutorial #2:
Chapter 2: 15 (a) (f), 18, 27, 30.
Tutorial #3: posted in WebCT.
Tutorial #4: Chapter 4: 5, 8, 32, 37, 43; Chapter 5: 2 (a) (i).
Tutorial #5: Chapter 6: 1, 5 (a) (b), 7, 11; Chapter 7: 7 (a), 8(a); Chapter 9: 3, 4.
Tutorial #6: Chapter 10: 1 (a) (b) (e); Chapter 11: 4, 8, 19, find all homomorphic images of Z_{6}; Chapter 16: 1 (b) (c) (g), 12.
Suggested Exercises.
Chapter 1: 1-29.
Chapter 2: 1, 5, 15, 16, 18, 22-31.
Chapter 3: 1, 19-23, 24-54,
Chapter 4: 1-12, 13-43.
Chapter 5: 1-6, 20-27.
Chapter 6: 1-6, 11-21.
Chapter 7: 7-10.
Chapter 9: 1-11, 14-17, 26-28, 46-48, 52.
Chapter 10: 1-10
Chapter 11: 1-6, 8-13, 19
Chapter 16: 1-3, 11-12.
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