| Lec. | Date | Section | Topic |
|---|---|---|---|
| 1 | 8/21 | 1.1 | Introduction. Division Theorem. |
| 2 | 8/23 | 1.1 | The greatest common divisor. |
| 3 | 8/25 | 1.1 | Euclidean Algorithm. Relatively prime numbers. |
| 4 | 8/28 | 1.2 | Mathematical Induction. Worksheet pdf |
| 5 | 8/30 | 1.2 | Mathematical Induction. Worksheet pdf |
| 6 | 9/1 | 1.2 | Recursively defined sequences. Strong induction. |
| - | 9/4 | - | Labor Day - No Classes |
| 7 | 9/6 | 1.3 | Prime numbers. |
| 8 | 9/8 | 1.3 | Unique Factorization Theorem. |
| 9 | 9/11 | 1.4 | Congruence classes. |
| 10 | 9/13 | 1.4 | Invertible elements and zero-divisors in Zn. |
| 11 | 9/15 | 1.4 | Worksheet pdf |
| 12 | 9/18 | 1.5 | Solving linear congruences. |
| 13 | 9/20 | 1.5 | Chinese Remainder Theorem. |
| 14 | 9/22 | 1.6 | The order of a mod n. |
| 15 | 9/25 | 1.6 | Fermat’s Theorem. Euler’s phi-function. |
| 16 | 9/27 | 1.6 | Euler’s phi-function. Euler’s Theorem. |
| 17 | 9/29 | 1.6 | Public key code. |
| 18 | 10/2 | Exam 1 covering Chapter 1. Study guide pdf | |
| 19 | 10/4 | 2.1 | Sets. |
| 20 | 10/6 | 2.1 | Sets. Worksheet pdf |
| 21 | 10/9 | 2.2 | Functions: surjective, injective, bijective. |
| 22 | 10/11 | 2.2 | Composition. The inverse function. |
| 23 | 10/13 | 2.2 | Cardinality of sets. |
| 24 | 10/16 | Cardinality of sets. Optional reading pdf | |
| 25 | 10/18 | 2.3 | Relations: examples and properties. |
| 26 | 10/20 | 2.3 |
Presentation by John Meier
PSU library info More on relations. Partial order. |
| 27 | 10/23 | 2.3 3.1 |
Equivalence relation. Propositions. Negation. |
| 28 | 10/25 | 3.1 | Conjunction, disjunction, implication, equivalence. |
| 29 | 10/27 | 3.2 | Quantifiers. |
| 30 | 10/30 | Sections 3.1 and 3.2 Worksheet pdf | |
| 31 | 11/1 | 3.3 | Some proof strategies. |
| 32 | 11/3 | Chapter 2 Worksheet pdf | |
| 33 | 11/6 | Exam 2 covering Chapters 2, 3. Study guide pdf | |
| 34 | 11/8 | 4.3 | Groups: definition, examples, and non-examples. Worksheet pdf |
| 35 | 11/10 | 4.3 | More examples of groups: matrices and symmetries. |
| 36 | 11/13 | 4.3 4.1 |
More on Symmetries. Permutations. |
| 37 | 11/15 | 4.2 | Order and sign of a permutation. |
| 38 | 11/17 | 4.2 | Transpositions. Subgroups. Project is due! |
| 11/19-25 | Thanksgiving Holiday - no classes | ||
| 39 | 11/27 | 5.1 | The order of an element. |
| 40 | 11/29 | 5.1,3 | Cyclic groups. Worksheet pdf |
| 41 | 12/1 | 5.3 | Group isomorphism. |
| 42 | 12/4 | 4.4 | Rings and fields. |
| 43 | 12/6 | Subgroups, rings, and fields. Worksheet pdf | |
| 44 | 12/8 | Groups. Worksheet pdf |
The Final Exam will be on Monday, Dec. 11, 10:10 a.m. - noon
in 105 Wagner.
Study guide pdf