Date |
Topics covered |
Read before class
|
August 22 |
Sets and operations on them |
Hammack 1.1-1.8 |
August 24 |
Logic, truth tables, Worksheet 1 |
Hammack 2.1-2.6 |
August 29 |
Statements in logic |
Hammack 2.7-2.12 |
August 31 |
Proofs: Introduction and first techniques |
Hammack 4.1-4.5 |
September 5 |
Proofs by contrapositive |
Hammack 5.1-5.3 |
September 7 |
Proofs by contradiction |
Hammack 6.1-6.4 |
September 12 |
More on proofs |
Hammack 7.1-7.4 |
September 14 |
Set-theoretic proofs |
Hammack 8.1-8.3 |
September 19 |
Review |
|
September 21 |
Midterm 1 |
|
September 26 |
Induction |
Hammack 10.1-10.3 |
September 28 |
Relations, equivalence relations, partitions, integers modulo n |
Hammack 11.1-11.5 |
October 3 |
Functions, properties of functions, the pigeonhole principle |
Hammack 12.1-12.3 |
October 5 |
Compositions of functions, inverse functions, images and inverse images of functions |
Hammack 12.4-12.6 |
October 10 |
Fall Recess, no class |
|
October 12 |
Cardinality, countable sets, uncountable sets |
Hammack 13.1-13.2 |
October 17 |
Comparing cardinalities, the Cantor-Bernstein-Schröder theorem |
Hammack 13.3-13.4 |
October 19 |
Groups |
Judson 3.1-3.2 |
October 24 |
Properties of groups, subgroups, and Cyclic groups
| Judson 3.3, 4.1 |
October 26 |
Review |
|
October 31 |
Midterm 2 |
|
November 2 |
Symmetric groups and dihedral groups |
Judson 5.1-5.2 |
November 7 |
Cosets, Lagrange's theorem |
Judson 6.1-6.2 |
November 9 |
Fermat's Little Theorem, Euler's Totient Theorem |
Judson 6.3 |
November 14 |
Limits of sequences |
Ross 2.7-2.8 |
November 16 |
Limit theorems |
Ross 2.9 |
November 21 |
Monotone sequences, Cauchy sequences |
Ross 2.10 |
November 23 |
Thanksgiving, no classes |
|
November 28 |
Subsequences |
Ross 2.11 |
November 30 |
Continuity |
Ross 3.17-3.18 |
December 5 |
Review for final exam |
|