Lectures

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Lectures

Class notes will generally not be posted. Lecture topics are tentative. You are highly encouraged to attend all classes.

Date Topics Book Sections
January 21 Introduction, Set, Element, Subset, Empty Set, Bijective Proof I

4.1, 4.4

January 23 Proposition, Predicate, Theorem, Direct Proof, Proof by Contradition 1.1, 1.2, 1.3, 1.5, 1.8
January 26 Set-Builder Notation, Cardinality, Set Operations, Element Method, Proof by Cases, Power Set, Disproof by Counterexample 1.7, 2.2, 4.1, 5.1
January 28 Cartesian Product, Quantification I, Power Set, Relations 3.6, 4.1, 4.2, 4.4
January 30 Properties of Relations, Equivalence Relations, Equivalence Classes, Set Partitions 9.11, 9.12
February 2 Functions, Injectivity, Surjectivity, Bijectivity I 4.3, 4.4
February 4 Bijective Proof II, Bijectivity II, Cardinality of Sets, Countable Infinity 4.4, 5.1, 5.2, 15
February 6 Induction I 6.1
February 9 No Class
February 11 Induction II, Strong Induction 6.2, 6.3
February 13 Divisibility, Primes, Division Algorithm 2.3, 8.1
February 18 GCD, Euclidean Algorithm, Relative Primes 8.2, 8.3, 8.7
February 20 Modular Arithmetic I 8.5
February 23 Modular Arithmetic II, Fermat's Little Theorem 8.6
February 25 Euler's Totient Function, Encryption 8.7
February 27 RSA Encryption 8.8
March 2 Logical Operators, Conditional, Proposition, Predicate, Truth Tables 3.1
March 4 Biconditional, Inverse, Converse, Contrapositive, Tautology, Contradiction, Quantification II, Logical Algebra 3.3, 3.4
March 6 Combinational Circuits Binary Representation, Half-Adder I Not in book!
March 9 Half Adder II, Full-Adder, Feedback Circuits Not in book!
March 11 RS-Latch, Clocks, D-Latch I Not in book!
March 13 D-Latch II Not in book!
March 16 Counting, Product Rule, Permutations I, Factorials, Binomial Coefficient 15.1, 15.3, 15.5
March 18 Permutations II, Binomial Theorem 15.2, 15.7
March 20 Inclusion/Exclusion, Derangements 15.12
March 30 Pigeonhole Principle, Strong Pigeonhole Principle 15.10
April 1 The Donut Problem, Asymptotics, Big-O, Big-Omega, Big-Theta 14.7
April 3 Algorithms, Time Complexity Not in book!
April 6 Probability, Sample Space, Event, Distributions 17.1, 17.2, 17.3
April 8 Product rule, Generalized Product Rule, Independence 17.4, 17.6
April 10 Bayes' Rule, Law of Total Probability, Extended Bayes' Rule 17.5
April 13 Random Variables I, Expected Value II, Binomial Distribution, Linearity of Expectation 18.1, 18.2, 18.4, 18.5
April 15 Random Variables II, Expected Value II, Variance I 18.3, 18.4
April 17 Variance II, Independence, Random Variables III, Markov Bounds 18.2, 19.3, 19.4
April 20 Chebyshev Bounds, Intro to Graph Theory (Vertex, Edge, Path, Degree, Simplicity, Completeness, Connectivity) 19.2, 19.3, 11.1
April 22 Euler Paths, Circuits, Isomorphism Prob 9.12, 11.4
April 24 Hamiltonian Circuits, Trees, Spanning Trees, Prufer Code 11.8, 11.11
April 27 Planar Graphs, Counting Trees 12.1, 12.2
April 29 Graph Coloring, Four Color Theorem, Euler's Formula 11.7, 12.3, 12.6
May 1 Markov Process, Finite Markov Chain, Random Text Generation Not in book!