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 | |

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, 4.4 |

January 30 | Properties of Relations, Equivalence Relations, Equivalence Classes, Set Partitions | 9.11, 9.12 |

February 2 | Functions, Injectivity, Surjectivity, Bijectivity I | 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 |
6.2, 6.3, 8.1 |

February 11 | Induction II, Strong Induction | 8.3 |

February 13 | Divisibility, Primes, Division Algorithm | 8.2 |

February 18 | GCD, Euclidean Algorithm, Relative Primes | 8.5 |

February 20 | Modular Arithmetic I | 8.6 |

February 23 | Modular Arithmetic II, Fermat's Little Theorem | 8.7 |

February 25 | Euler's Totient Function, Encryption | 8.8 |

February 27 | RSA Encryption | 3.1 |

March 2 | Logical Operators, Conditional, Proposition, Predicate, Truth Tables | 3.3 |

March 4 | Biconditional, Inverse, Converse, Contrapositive, Tautology, Contradiction, Quantification II, Logical Algebra | 3.3 |

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 | 15.3 |

March 18 | Permutations II, Binomial Theorem | 15.2, 15.7 |

March 20 | Inclusion/Exclusion, Derangements | 15.7, 15.12 |

March 30 | Pigeonhole Principle, Strong Pigeonhole Principle | 15.10 |

April 1 | Stars and Bars 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 |

April 10 | Bayes' Rule, Law of Total Probability, Extended Bayes' Rule | 17.5 |

April 13 | Random Variables I, Expected Value II, Linearity of Expectation | 18.1, 18.2, 18.4 |

April 15 | Random Variables II, Expected Value II, Binomial Distribution | 18.3, 18.4 |

April 17 | Variance, Independence, Random Variables III | 18.2, 19.3 |

April 20 | Markov/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 | 11.1 |

April 27 | Planar Graphs, Counting Trees | 12.1, 12.2 |

April 29 | Graph Coloring, Four Color Theorem, Euler's Formula | 12.3, 1.1 |

May 1 | Markov Process, Finite Markov Chain, Random Text Generation | Not in book! |