# DMMR: Course Schedule and Lecture Slides 2016

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.
1 Sep 19: Lecture 1: Introduction and Course Admin
Sep 21: Lecture 2: Predicates, Quantifiers and Proof Techniques
Sep 22: Lecture 3: Predicates, Quantifiers and Proof Techniques
Rosen Chapter 1
2 Sep 26: Lecture 4: Sets, Functions, Relations, Sequences and Sums
Sep 28: Lecture 5: Sets, Functions, Relations, Sequences and Sums
Sep 29: Lecture 6: Sets, Functions, Relations, Sequences and Sums
Rosen Sections 2.1-2.4, 9.1, 9.4 and 9.5
3 Oct 03: Lecture 7: Cardinality
Oct 05: Lecture 8: Cardinality
Oct 06: Lecture 9: Induction
Rosen Sections 2.5, then 5.1 and 5.2
4 Oct 10: Lecture 10: Induction
Oct 12: Lecture 11: Arithmetic Modulo m, Primes
Oct 13: Lecture 12: Greatest Common Divisors
Rosen Section 4.1, then 4.3, 4.4 and 4.6
5 Oct 17: Lecture 13: Multiplicative Inverses and Some Cryptography
Oct 19: Lecture 14: Algorithms
Oct 20: Lecture 15: Algorithms
Rosen Section 4.6, then 3.1-3.3 and Appendix 3
6Oct 24: Lecture 16: Basic Counting, and the Pigeonhole Principle
Oct 26: Lecture 17: Permutations & Combinations, Binomial Coefficients
Oct 27: Lecture 18: Generalized Permutations & Combinations
Rosen chapter 6
7Oct 31: Lecture 19: Graphs: basic definitions and examples
Nov 2: Lecture 20: Bipartite Graphs and Matching
Nov 3: Lecture 21: Graph Isomorphism; Paths and Connectivity; Euler paths/circuits
Rosen chapter 10
8 Nov 7: Lecture 22: Euler and Hamiltonian paths/circuits (continued); shortest paths;
Nov 9: Lecture 23: Shortest Paths and Dijkstra's algorithm; Graph Coloring
Nov 10: Lecture 24: Trees
Rosen chapter 10 & 11
9 Nov 14: Lecture 25: Introduction to Discrete Probability; some important distributions;
Nov 16: Lecture 26: Conditional probabability; Bayes' theorem
Nov 17: Lecture 27: Random variables, Expectation, and Variance
Rosen chapter 7
10 Nov 21: Lecture 28: Markov's and Chebyshev's Inequalities; Examples in probability: the birthday problem;
Nov 23: Lecture 29: Examples in probability: ramsey numbers
Nov 24: Lecture 30: review lecture
Rosen chapter 7

#### Study guide

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