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 Z_{n}. |
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