Detailed Schedule -- Algebraic Structures, Section 1

Fall 2006, 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)
8/30 Course Intro, Sets 1.1, Appendix on Logic
9/1 More on Sets 1.1, Appendix on Logic
9/4 Mappings 1.2
9/6 More on Mappings 1.2
9/8 Additional properties; Definitions Quiz 1 1.3
9/11 Binary operations 1.4
9/13 More on binary operations 1.4
9/15 Permutations and Inverses; Definitions Quiz 2 1.5
9/18 More on permutations and Inverses 1.5
9/20 Matrices and matrix operations 1.6
9/22 Matrices and matrix operations; Definitions Quiz 3 1.6
9/25 Relations 1.7
9/27 Equivalence relations and their properties 1.7
9/29 Exam 1 (Appendix on Logic, 1.1-1.6)
10/2 The integers and mathematical induction 2.1, 2.2
10/4 More on mathematical induction 2.2
10/6 Spare Day; Definitions Quiz 4
10/9 No Class -- Columbus Day Break
10/11 Integer division 2.3
10/13 Divisibility; Definitions Quiz 5 2.3
10/16 GCD and Euclid's algorithm 2.4
10/18 Prime factorization 2.4
10/20 Congruences; Definitions Quiz 6 2.5
10/23 Congruence Classes and Zn 2.6
10/25 The RSA public-key cryptosystem 2.8
10/27 More on RSA; Definitions Quiz 7 2.8
10/30 Begin groups 3.1
11/1 Exam 2 (1.7, Chapter 2)
11/3 More on groups 3.1
11/6 Subgroups 3.2
11/8 Cyclic subgroups; exponents 3.2
11/10 Cyclic groups; Definitions Quiz 8 3.3
11/13 More on cyclic groups 3.3
11/15 Isomorphisms of groups 3.4
11/17 Homomorphisms of groups; Definitions Quiz 9 3.5
11/20 Permutation groups 4.1
11/22,24 No Class -- Thanksgiving Break 4.1
11/27 Cayley's Theorem 4.2
11/29 Permutation groups in science and art 4.3
12/1 Exam 3 (Chapter 3, 4.1)
12/4 Course wrap-up
The final exam for this course will be given at 8:30 am on Wednesday, December 13, 2006.

Last modified: August 21, 2006