University Homepage School Homepage School Contacts School Search

DMMR: Course Schedule and Lecture Slides 2019

Lecture slides will typically be available from this web page a day or two before the lecture. The slides from last year will give a good idea about what's coming up.

Week	Lectures	Readings
1	Sep 16: Lecture 1: Introduction and Course Admin Sep 17: Lecture 2: Predicates, Quantifiers and Proof Techniques Sep 19: Lecture 3: Predicates, Quantifiers and Proof Techniques	Rosen Chapter 1
2	Sep 23: Lecture 4: Sets, Functions, Relations, Sequences and Sums Sep 24: Lecture 5: Sets, Functions, Relations, Sequences and Sums Sep 26: Lecture 6: Sets, Functions, Relations, Sequences and Sums	Rosen Sections 2.1-2.4, 9.1, 9.4 and 9.5
3	Sep 30: Lecture 7: Relations, Sequences and Sums Oct 01: Lecture 8: Cardinality Oct 03: Lecture 9: Cardinality	Rosen Sections 9.4, 9.5 and 2.5.
4	Oct 07: Lecture 10: Induction Oct 08: Lecture 11: Induction Oct 10: Lecture 12: Arithmetic Modulo m, Primes	Rosen Sections 5.1, 5.2, then 4.1.
5	Oct 14: Lecture 13: Greatest Common Divisors Oct 15: Lecture 14: Multiplicative Inverses and Some Cryptography Oct 17: Lecture 15: Multiplicative Inverses and Some Cryptography	Rosen Sections 4.3, 4.4 and 4.6
6	Oct 21: Lecture 16: Basic Counting, and the Pigeonhole Principle Oct 22: Lecture 17: Permutations & Combinations, Binomial Coefficients Oct 24: Lecture 18: Generalized Permutations & Combinations	Rosen chapter 6
7	Oct 28: Lecture 19: Graphs: basic definitions and examples Oct 29: Lecture 20: Bipartite Graphs and Matching Oct 31: Lecture 21: Graph Isomorphism; Paths and Connectivity; Euler paths/circuits	Rosen chapter 10
8	Nov 4: Lecture 22: Euler and Hamiltonian paths/circuits (continued); shortest paths; Nov 5: Lecture 23: Shortest Paths and Dijkstra's algorithm; Graph Coloring Nov 7: Lecture 24: Trees	Rosen chapter 10 & 11
9	Nov 11: Lecture 25: Introduction to Discrete Probability; some important distributions; Nov 12: Lecture 26: Conditional probabability; Bayes' theorem Nov 14: Lecture 27: Random variables, Expectation, and Variance	Rosen chapter 7
10	Nov 18: Lecture 28: Markov's and Chebyshev's Inequalities; Examples in probability: the birthday problem; Nov 19: Lecture 29: Examples in probability: ramsey numbers Nov 21: Lecture 30: review lecture	Rosen chapter 7

Study guide