Detailed Schedule -- Algebraic Structures, Section 3

Fall 2012, Prof. Little

As always, topics may be added, deleted, or rearranged during the course of the semester. Any changes will be announced in class and here.

DateClass Topic Reading (Gilbert and Gilbert)
8/29 Course Intro, Sets 1.1, Appendix on Logic
8/31 More on Sets 1.1, Appendix on Logic
9/3 Mappings 1.2
9/5 More on Mappings 1.2
9/7 Additional properties; PS 1 due; Definitions Quiz 1 1.3
9/10 Binary operations 1.4
9/12 More on binary operations 1.4
9/14 Permutations and Inverses; PS 2 due; Definitions Quiz 2 1.5
9/17 More on permutations and Inverses 1.5
9/19 Matrices and matrix operations 1.6
9/21 Matrices and matrix operations; PS 3 due; Definitions Quiz 3 1.6
9/24 Relations 1.7
9/26 Equivalence relations and their properties 1.7
9/28 Exam 1 (Appendix on Logic, 1.1-1.6)
10/1 The integers and mathematical induction 2.1, 2.2
10/3 More on mathematical induction 2.2
10/5 Spare Day; PS 4 due; Definitions Quiz 4
10/8,10,12 No Class -- Columbus Day Break
10/15 Integer division 2.3
10/17 Divisibility 2.3
10/19 GCD and Euclid's algorithm; PS 5 due; Definitions Quiz 5 2.4
10/22 Prime factorization 2.4
10/24 Congruences 2.5
10/26 Congruence Classes and Zn; PS 6 due; Definitions Quiz 6 2.6
10/29 The RSA public-key cryptosystem 2.8
10/31 More on RSA 2.8
11/2 Exam 2 (Sections 1.7, 2.1 - 2.6)
11/5 Begin groups 3.1
11/7 More on groups 3.1
11/9 Subgroups; PS 7 due ; Definitions Quiz 7 3.2
11/12 Cyclic subgroups; exponents 3.2
11/14 Cyclic groups 3.3
11/16 More on cyclic groups; PS 8 due ; Definitions Quiz 8 3.3
11/19 Isomorphisms of groups 3.4
11/21,23 No Class -- Thanksgiving Break 3.5
11/26 Homomorphisms of groups 3.5
11/28 Permutation groups 4.1
11/30 Cayley's Theorem; PS 9 due; Definitions Quiz 9 4.1
12/3 Cayley's Theorem 4.2
12/5 Exam 3 (Chapter 3, 4.1)
12/7 Course wrap-up 4.3
The final exam for this course will be given at 11:30am on Saturday, December 15.

Last modified: October 17, 2012