Math 2001 Fall 15

## MATH 2001: Introduction to Discrete Mathematics (Fall 2015)

Syllabus

### New office hours:

Tuesday, 10 - 11 am Wednesday, 2 - 3 pm Thursday, 10 - 11 am

### Schedule

1. 08/24: arithmetic sum, infinitely many primes, Goldbach conjecture, continuum hypothesis
2. 08/26: intro to sets (1.1) , Cartesian product (1.2)
3. 08/28: subsets (1.3), power set (1.4), union, intersection, difference (1.5)
4. 08/31: complement (1.6), laws of set operations, Venn diagrams (1.7)
5. 09/02: proving identities for sets
6. 09/04: infinite unions and intersections (1.8)
7. 09/09: Russell's paradoxon (1.10), strategy for poison
8. 09/11: statements (2.1), logical connectives (2.2)
9. 09/14: if (2.3), truth tables (2.5), logical equivalence (2.6)
10. 09/16: iff (2.4)
11. 09/18: quantifiers (2.7)
12. 09/21: negating quantifiers
13. 09/23: counting, Towers of Hanoi
14. 09/25: lists, permutations (3.1,, 3.2)
15. 09/27: binomials (3.3)
16. 09/30: first midterm
17. 10/02: binomial theorem (3.4)
18. 10/05: inclusion-exclusion (3.5)
19. 10/07: combinations with repetitions
20. 10/09: integers, divisibility, direct proofs (4.2, 4.3)
21. 10/12: gcd, lcm, Euclidean algorithm
22. 10/14: division algorithm, proof by contradiction
23. 10/16: Bezout's identity, contrapositive proof
24. 10/19: checking for primes, proof methods
26. 10/23: congruences (5.2)
27. 10/26: induction, sums (10)
28. 10/28: Bernoulli's inequality
29. 10/30: strong induction
30. 11/02: fundamental theorem of arithmetic
31. 11/04: second midterm
32. 11/06: gcd, lcm
33. 11/09: relations and their properties (11.1, 11.5)
34. 11/11: partial orders, equivalences (11.2)
35. 11/13: partitions (11.3)
36. 11/16: integers mod n (11.4), Diffie-Hellman key exchange
37. 11/18: functions (12)
38. 11/20: injective, surjective, bijective
39. 11/30: composition
40. 12/02: inverse functions
41. 12/04: inverse functions
42. 12/07: cardinality of sets, countably infinite (13.1)
43. 12/09: uncountable sets (13.2)
44. 12/11: REVIEW
The numbering refers to sections in Hammack: Book of Proof.