### Math 311M     Fall 2017   Schedule

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