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

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

The numbering refers to sections in
Hammack: Book of Proof.
### Assignments

- due 09/02
- due 09/09
- due 09/16 and solutions
- due 09/23
- due 10/02
- due 10/09
- due 10/16
- due 10/23
- due 10/30
- due 11/06
- due 11/13
- due 11/20
- due 12/04
- due 12/09

### Handouts

- sets/logic
- combinatorics
- integers
- review