Lectures

The Book Sections column lists the sections of the book that contain that day's material. The first sections are for the 3rd edition of the book, and the sections in parentheses are for the 4th edition.

January 25

 Set, Element, Subset, Empty Set, Bijective Proof 5.1 (6.1)

January 27

 Set builder notation, Cardinality, Set Operations, Set Equality, Element Method 5.1-5.2 (6.1-6.2)

January 30

 Cartesian Product, Universal and Existential Quantifiers, Proof by Contradiction 2.1, 3.6, 5.1 (3.1, 4.6, 6.1)

February 1

 Relation, Reflexive, Symmetric, Transitive, Equivalence Relation, Equivalence Classes 10.1-10.3 (8.1-8.3)

February 3

 Equivalence Classes, Parity, Functions, Injective, Surjective, Bijective 7.1-7.2 (7.1-7.2)

February 6

 Domain, Range, Codomain, If and only if, Bijective Proof, Power Set 1.2, 7.1-7.2 (2.2, 7.1-7.2)

February 8

 Bijective Proof, Direct Proof, Division into Cases, Proof by Contradiction, Inductive Proof 3.1-3.6, 7.2 (4.1-4.6, 7.2)

February 10

 Summation and Product notation, Induction, Strong Induction, Divisibility, Primes 3.3, 4.1-4.3 (4.3, 5.1-5.3)

February 13

 Division Algorithm, GCD, Relatively Prime, Euclidean Algorithm, Mersenne Primes, Twin Primes, Goldbach Conjecture 3.1, 3.7-3.8, 10.4 (4.1, 4.7-4.8, 8.4)

February 15

 Modulo Relation, Modular Arithmetic, Solving Congruences, Multiplicative Inverse 10.4 (8.4)

February 17

 Chinese Remainder Theorem, Fermat's Little Theorem 10.4 (8.4)

February 22

 Public key cryptography, RSA 10.4 (8.4)

February 24

 Midterm Exam

February 27

 Logic: not, or, and, xor, Conditional, Biconditional, Converse, Inverse, Contrapositive, Tautology and Contradiction, Logical Equivalence 1.1-1.2 (2.1-2.2)

February 29

 Predicate Logic, Quantifiers, Intro to Formal Proofs 2.1-2.2 (3.1-3.2)

March 2

 Argument, Valid Argument, Modus Ponens, Modus Tollens, Hypothetical Syllogism 1.3 (2.3)

March 5

 Inference with Quantifiers, Inference Proof, Logical Basis of Proof Techniques, Chessboard tiling 1.3 (2.3)

March 7

 Boolean Algebra, Logic Circuits 1.4, 5.3 (2.4, 6.4)

March 9

 Clock input, S-R Latch, D Latch, Flip-Flop Notes

March 12

 Combinatorics, Product Rule, Sum Rule, Permutations, Factorial, Binomial Coefficient 6.2-6.4, 6.7 (9.2-9.3, 9.5, 9.7)

March 14

 Counting possible functions between 2 sets, Binomial Coefficients, Binomial Theorem 6.7 (9.7)

March 16

 Combinatorial Proofs, Binomial Coefficient Symmetry, Pascal's Identity, Pascal's Triangle, Dots and Bars, Inclusion-Exclusion 6.3, 6.6-6.7 (9.3, 9.7)

March 19

 Derangements, Pigeonhole Principle 7.3, 8.2 (9.3-9.4)

March 21

 Generalized Pigeonhole Principle, Strong Form of Pigeonhole Principle 7.3 (9.4)

March 23

 Big O/Omega/Theta 9.2 (11.2)

April 2

 Finite Probability Space, Uniform Probability Distribution, Conditional Probability 6.8-6.9 (9.9)

April 4

 Conditional Probability, Law of Total Probability, Bayes' Rule, Extended Bayes' Rule 6.9 (9.9)

April 6

 Midterm Exam

April 9

 Bayesian Spam Filters, Random Variables, Expectation, Linearity of Expectation See Documents page for probability notes

April 11

 Linearity of Expectations, Independence of Random Variables See Documents page for probability notes

April 13

 Variance, Binomial Distribution See Documents page for probability notes

April 16

 Variance, Markov Bound, Chebyshev's Bound, Weak Law of Large Numbers See Documents page for probability notes

April 18

 Graph Theory, Isomorphism, Degree, Regular Graph, Bipartite Graph, Complete Graph 11.1-11.4 (10.1-10.4)

April 20

 Postman Problem, Eulerian Circuits 11.2 (10.2)

April 23

 Hamiltonian Cycles, Subgraph, Spanning Subgraph, Induced Subgraph, Trees 11.1-11.5 (10.1-10.5)

April 25

 Prufer Sequence

April 27

 Multigraph, Graph Coloring, Planarity, Subdivision, Kuratowiski Theorem, 4-color Theorem 11.2-11.6 (10.2-10.7)

April 30

 Euler's Formula, 6-Color Theorem 11.2 (10.2)

May 2

 Markov Process, Finite Markov Chain, Random Text Generation