lectures
Lectures

Class notes will generally not be posted. Lecture topics are tentative.

Date Topics Book Sections
January 24 Introduction, Set, Element, Subset, Empty Set, Bijective Proof I

class notes

4.1, 4.4

January 27 Proposition, Predicate, Theorem, Direct Proof, Proof by Contradition 1.1, 1.2, 1.3, 1.5, 1.8
January 29 Set-Builder Notation, Cardinality, Set Operations, Element Method, Proof by Cases, Proof by Counterexample 1.7, 2.2, 4.1, 5.1
January 31 Cartesian Product, Quantification I, Power Set, Relations, Set Equality, Set Identities 3.6, 4.1, 4.4
February 3 Properties of Relations, Equivalence Relations, Equivalence Classes, Set Partitions 9.11, 9.12
February 5 Functions, Injectivity, Surjectivity, Bijectivity I 4.4
February 7 Bijective Proof II, Bijectivity II, Cardinality of Sets, Countable Infinity 4.4, 5.1, 5.2, 15
February 10 Induction I 6.1
February 12 Induction II, Strong Induction, Divisibility, Division Algorithm 6.2, 6.3, 8.1
February 14 Induction III, Primes, Fundamental Theory of Arithmetic, Summation and Product Notation 8.3
February 17 GCD, Division Algorithm, Divisibility, Euclidean Algorithm 8.2
February 19 Modular Arithmetic I 8.5
February 21 Modular Arithmetic II, Fermat's Little Theorem 8.6
February 24 Euler's Totient Function, Euler-Fermat Theorem 8.7
February 26 RSA Encryption
February 28 Logical Operators, Conditional, Proposition, Predicate, Truth Tables
March 3 Biconditional, Inverse, Converse, Contrapositive, Tautology, Contradiction, Quantification II
March 5 Logical Algebra, Combinational Circuits
March 7 Binary Representation, Half-Adder, Full-Adder, Feedback Circuits
March 10 R/S Latch, D Latch, D Flip Flop, Clocks, Memory Circuits
March 12 Counting, Product Rule, Permutations I, Factorials
March 14 Sum Rule, Permutations II, Binomial Theorem
March 17 Binomial Identities, Multinomial Coefficients, Inclusion/Exclusion I
March 19 Inclusion/Exclusion II, Derangements
March 21 Pigeonhole Principle, Stars and Bars Problem
March 31 Asymptotics, Big-O, Big-Omega, Big-Theta
April 2 Algorithms, Time Complexity
April 4 Probability, Sample Space, Event, Distributions
April 7 Product rule, Generalized Product Rule, Independence
April 9 Bayes' Rule, Law of Total Probability, Extended Bayes' Rule
April 11 Random Variables I, Expected Value II, Linearity of Expectation
April 14 Random Variables II, Expected Value II, Binomial Distribution
April 16 Variance, Independence, Random Variables III
April 18 Markov/Chebyshev Bounds, Intro to Graph Theory (Vertex, Edge, Path, Degree, Simplicity, Completeness, Connectivity)
April 21 Euler Paths, Circuits, Isomorphism
April 23 Hamiltonian Circuits, Trees, Spanning Trees, Prufer Code
April 25 Planar Graphs, Counting Trees
April 28 Graph Coloring, Four Color Theorem, Euler's Formula
April 30 Markov Process, Finite Markov Chain, Random Text Generation