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Notice Board
My office hour: Tuesday 10:30-11:30am, Thursday, 3:00-4:00pm, HP4368.
TA: Georgios Tzanakis, office hours: Tuesday 3-4pm, HP 4354
Topics covered in the class.
Sept. 8: Introduction; Sets, mappings.
Sept. 13: Mappings, equivalence relation.
Sept. 15: equivalence classes, division algorithm
Sept. 20: gcd, Euclidean algorithm, congruence, monoids
Sept. 22: monoids, deterministic finite automaton.
Test #1
Sept. 27: groups
Sept. 29: more examples of groups, basic properties.
Oct. 4: Exponents/multiples, subgroups.
Oct. 6: Cyclic groups.
Oct. 11: multiplicative subgroups of complex numbers; n-th roots of unity.
Oct. 13: permutation groups.
Test #2.
Oct. 18: permutation groups, alternating groups, Dihedral groups.
Oct. 20: Dihedral groups, motion group of a cube.
Oct. 25: motion group of a cube, conjugates, cosets.
Oct. 27: Lagrange' Theorem and applications.
Test #3.
Nov. 1: Lagrange's Theorem, Fermat's Theorem, Euler's Theorem, classical cryptography.
Nov. 3: RSA, isomorphism.
Nov. 8: Isomorphism, Cayley's Theorem.
Nov. 10: Direct products, normal subgroups.
Test #4
Nov. 15: Normal subgroups and quotient groups.
Nov. 17: Quotient groups and fundamental theorem of homomorphism.
Nov. 22: Rings.
Nov. 24: Ideals and Integral domain.
Nov. 29: quotient rings, maximal ideals and prime ideals.
Dec. 1: Polynomial rings, irreducible polynomials, construction of finite fields.
Tutorials:
Tutorial #1:
Chapter 1: 17, 20, 22, 25.
Tutorial #2:
Chapter 3:
#1, 7, 10, 12, 27.
Tutorial #3:
Chapter 3: #32, 40, 43, 47.
Chapter 4: #5, 8.
Tutorial #4:
Chapter 4: 32, 37, 43.
Chapter 5: 2 (a) (i), 4, 13, 30.
Tutorial #5:
Chapter 6: 5(a), (b), 12.
Chapter 7: 7(a), 8(a).
Chpater 9: 5.
Suggested Exercises.
Chapter 1: 1-29.
Chapter 2: 1, 5, 12-31.
Chapter 3: 1-32, 33-54.
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.
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