As always, topics may be added, deleted, or rearranged during the course of the semester. Any changes will be announced in class and here.
Date | Class Topic | Reading (Course text) |
---|---|---|
8/30 | Course intro, statements and negations | 1.1 |
9/1 | Logical connectives | 1.2 |
9/4 | Quantifiers | 1.3 |
9/6 | Truth tables and applications | 1.4 |
9/8 | Sets and set operations PS 1 due; Quiz 1 | 2.1 |
9/11 | Partitions and mappings | 2.2 |
9/13 | Writing proofs | 2.3 |
9/15 | More on writing proofs; PS 2 due; Quiz 2 | 2.3 |
9/18 | The Peano axioms for the natural numbers | 3.1 |
9/20 | Mathematical induction | 3.2 |
9/22 | Counting principles PS 3 due; Quiz 3 | 3.3 |
9/25 | Constructing the natural numbers and the integers | 3.4 and 3.5 |
9/27 | Properties of the Integers | 4.1 |
9/29 | Exam 1 | Chapters 1 - 3 |
10/2 | Integer division algorithm | 4.2 |
10/4 | GCD's and Euclid's algorithm | 4.3 |
10/6 | Spare Day; PS 4 due; Quiz 4 | |
10/9,11,13 | No Class -- Columbus Day Break | |
10/16 | Prime numbers and coprimality | 5.1 |
10/18 | Prime factorization | 5.2 |
10/20 | Congruence (mod n) PS 5 due; Quiz 5 | 6.1 |
10/23 | Multiplicative inverses | 6.2 |
10/25 | Linear congruences | 6.3 |
10/27 | Fermat's Little Theorem; PS 6 due; Quiz 6 | 6.4 |
10/30 | The RSA public-key cryptosystem | 6.4 |
11/1 | Mappings and relations | 7.1, 7.2 |
11/3 | Exam 2 | (Chapters 4 - 6) |
11/6 | Composition and inverses | 7.3 |
11/8 | Equivalence relations | 7.4 |
11/10 | Binary operations PS 7 due; Quiz 7 | 8.1, 8.2 |
11/13 | Axioms for the real numbers | 9.1 |
11/15 | Integer powers, binomial theorem | 9.3 |
11/17 | Sets of real numbers, upper and lower bounds PS 8 due; Quiz 8 | 10.1, 10.2 |
11/20 | Suprema | 10.3 |
11/22,24 | No Class -- Thanksgiving Break | |
11/27 | Sequences, series, and convergence | 11.1, 11.2 |
11/29 | Convergence criteria | 11.3 |
12/1 | Algebraic properties of limits PS 9 due; Quiz 9 | 11.4 |
12/4 | Subsequences | 11.4 |
12/6 | Exam 3 | (Chapters 7 - 9) |
12/8 | More on infinite series | 11.5 |
Last modified: October 12, 2017