Math 2001 Fall 16

## MATH 2001: Introduction to Discrete Mathematics (Fall 2016)

Syllabus

### Final Exam:

Wednesday 12/14, 4:30-7 pm, in class
Exam problems might look something like this: review problems

### Office hours:

Tuesday 3-4 pm Wednesday 11-12 am Friday 10-11 am

### Schedule

Numbers refer to sections in Hammack, Book of Proof.
1. 08/22: arithmetic sum, infinitely many primes, Goldbach conjecture, continuum hypothesis
2. 08/24: sets (1.1)
3. 08/26: cartesian products (1.2)
4. 08/29: subsets (1.3), power set (1.4) union, intersection, difference (1.5)
5. 08/31: complement (1.6), laws of set operations, Venn diagrams (1.7)
6. 09/02: proving identities for sets
7. 09/07: infinite unions and intersections (1.8), Russell's paradoxon (1.10)
8. 09/09: poison, latex
9. 09/12: logic, and, or, not (2.1) truthtables (2.5), logical equivalence (2.6)
10. 09/14: if (2.3)
11. 09/16: review for midterm
12. 09/19: MIDTERM
13. 09/21: iff (2.4), quantifiers (2.7)
14. 09/23: permutations, factorial, binomial theorem
15. 09/26: inclusion-exclusion
16. 09/26: inclusion-exclusion
17. 09/30: (un)ordered collections with/without repetiton
18. 10/03: primes, divisibility
19. 10/05: division algorithm
20. 10/07: extended Euclidean algorithm
21. 10/10: Bezout's identity
22. 10/12: direct proof, contrapositive, contradiction
23. 10/14: irrationality of root 2
24. 10/17: modular arithmetic
25. 10/19: Diffie-Hellmann key exchange
26. 10/21: induction 10.1
27. 10/24: REVIEW
28. 10/26: MIDTERM
29. 10/28: discussion of midterm, strong induction, minimal counterexample
30. 10/31: Fundamental Theorem of Arithmetic (10.1)
31. 11/02: gcd, lcm
32. 11/04: relations, functions, reflexive, symmetric, anti-symmetric, transitive (11.1)
33. 11/07: partial orders, equivalence relations (11.2)
34. 11/09: partitions (11.3)
35. 11/11: integers mod n (11.4)
36. 11/14: functions (12)
37. 11/16: injective, surjective, bijective
38. 11/18: pigeon hole principle
39. 11/28: composition, inverse functions
40. 11/30: inverse functions
41. 12/02: inverse functions
42. 12/05: cardinality of sets, countably infinite (13.1)
43. 12/07: uncountable sets (13.2)
44. 12/09: REVIEW

### Assignments

1. due 08/24 [pdf] [tex]
2. due 09/02 [pdf] [tex]
3. due 09/09 [pdf] [tex]
4. due 09/16 [pdf] [tex]
5. due 09/23 [pdf] [tex]
6. due 09/30 [pdf] [tex]
7. due 10/07 [pdf] [tex]
8. due 10/14 [pdf] [tex]
9. due 10/21 [pdf] [tex]
10. due 10/28 [pdf] [tex]
11. due 11/04 [pdf] [tex]
12. due 11/11 [pdf] [tex]
13. due 11/18 [pdf] [tex]
14. due 12/02 [pdf] [tex]
15. due 12/07 [pdf] [tex]

### Handouts

1. Sets vs Logic [pdf] [pdf]
2. Combinatorics [pdf] [tex]
3. Integers [pdf] [tex]
4. Review [pdf] [tex]

### Scientific writing

There is a variety of word-processing software for writing Mathematics. LaTeX is the most widespread. You can use it with many text editors or via some cloud-based service, like ShareLaTeX.
Here are the first files that we produced in class [pdf] [tex]
You can use files from the homework assignments as templates for your writing as well.