Tuesday |
Thursday |
| Jan. 27 Lecture #1: Basic counting Counting vs Analytic Arguemtents Homework Due: |
Jan. 29 Lecture #2: Moving on a Grid Sampling with Replacement Homework Due: Homework #1: C Problems |
| Feb. 3 Lecture #3: Multinomial Coefficents Binomial Theorem Homework Due: |
Feb. 5 Quiz 1 Lecture #4: Power in Simple Games Pigeonhole Principle Homework Due: R 2.15,2.19 Homework #2: C Problems |
| Feb. 10 Lecture #5: Shapley Shubik Pigeonhole Principle |
Feb. 12 Quiz 2 Lecture #6: Generlized Pigeonhole Principle Homework Due: R 3.1 Homework #3: C 2.8: 14 C 2.11: 4,6 C 2.14: 2b,13,16ad C 2.15: 1bc,2bc,3,5,8,12 C Problems NC 2.9: 3,9 NC 2.11: 10,11 NC 2.14: 16bc |
| Feb. 17 Lecture #7: Erdos-Szekeres Theorem Graph Theory Homework Due: R 3.2 |
Feb. 19 Quiz 3 Lecture #8: Connectedness Euclidian Paths Homework Due: Homework #4: C 2.19: 1ac,2ac,5,7,10,13,18,22,23 C Problems NC 2.19: 1bd,2bd,20 |
| Feb. 24 Directed Graphs Homework Due: R 3.3 |
Feb. 26 Quiz 4 Lecture #9: Relations Homework Due: R 4.1 Homework #5: C 2.19: 19,24,27 C 3.1: 4 C Problems |
| March 3 Lecture #10: Order Relations Questions for the Exam Homework Due: R 4.2-4.3 |
March 5 Exam #1 Topics: TBA Homework Due: Homework #6: C 3.2: 9,10,13 C 4.1: 16,19,20,25 C Problems NC 3.2: 19,20,22,29 NC 4.1: 6,21,22 |
| March 10 Lecture #11: Weak Orders Utility Funtions |
March 12 Quiz 5 Lecture #12: Strict Weak Orders Extentions of Partial Orders Szpilrajn's Theorem Homework Due: Homework #7: C 4.1: 7,8,10,11,12 4.2: 1ab,2ab,7ab,14 C Problems NC 4.1:18 NC 4.2: 5,6,13,15 |
| March 17 Lecture #13: Proof of Szpilrajn's Theorem Utility Functions for Posets |
March 19 Quiz 6 Lecture #14: Chains and Antichains Homework Due: Homework #8: C 4.2: 20,21,27 C Problems NC 4.2: 13,16,17,22,29 |
| March 24 No Class |
March 26 Lecture #15: Dilworth's Theorem |
| March 31 Spring Break |
April 2 Spring Break |
| April 7 Lecture #16: Rolling Dice Introduction to Generating Functions |
April 9 Quiz 7 Lecture #17: Generating Functions Homework Due: R 5.1 Homework #9: C 4.3: 2,3,4acdf,5,8,13,17,18,19 NC 1,4be,10 |
| April 14 Lecture #18: Products of Generating Functions Homework Due: R 5.2 |
April 16 Exam #2 Topics: TBA Homework Due: Homework #10: C 5.2: 3acf,6 C Problems NC 5.2: 3bde |
| April 21 Lecture #19: Fibonacci Sequence Partitions Homework Due: R 5.3 |
April 23 Quiz 8 Lecture #20: Exponential Generating Functions Homework Due: R 5.7 Homework #11: C 5.3: 9,10,11 C Problems NC 5.3: 1 |
| April 28 Lecture #21: Banzhaf Power Index Bell's Number Homework Due: R 6.3 |
April 30 Lecture #22: Exponential Generating Function for Bell's Number Inclusion Exclusion Principle Homework Due: R 7.1 Homework #12: C 5.5: 1abf,2bcf,3 C Problems NC 5.5: 1cde,4ade,6f |
| May 5 Quiz 9 Lecture #23: Phi of n Derangement's and the Hat Problem Homework Due: |
May 7 Lecture #24: Questions for Exam Homework Due: Homework #13: NC 5.7: 1,2,4,5 NC 7.1: 1,2,3,11,12,13,17 NC Problems |