The Secondt Midterm will be held on Friday, November 21, in class. The test will cover Chapters 5, 6, and 7.
You may bring in the review sheet (witout practice problems) and one sheet of notes (one paper, 8.5" x 11.5", both
sides).
The
First Midterm will be held on Wednesday, October 15, in class. The test will cover Chapters 2, 3, and 4.
You may bring in the review sheet and one sheet of notes (one paper, 8.5" x 11.5", both
sides).
Homework 1 due 9/8: Sec. 2.4: Ex. 1, 4, 10, 17, 18, 20.
Homework 3 due 9/22: Sec. 3.3 Ex. 7(a,b,c,d), 10, 11, 17, 21, 37, 38, 39.
Homework 4 due 9/29: Sec. 4.6 Ex. 3 (first 15 permutations), 6(b), 7(b), 9 (bonus), 12(a), 13, 15(c,d) , 16(c,d), 18, 21(a or b).
Homework 5 due 10/06: Sec. 4.6 Ex. 27, 29, 31, 34(b), 36, 43, 50; Sec. 5.8 Ex. 1, 2, 3 (you do not need to refer to the counting function from Ch.1).
Homework 6 due 10/13: Sec. 5.8 Ex. 5, 7, 9, 11, 12, 13, 15, 23(c,d), 24, 25, 37.
Homework 7 due 10/20: Sec. 5.8 Ex. 16, 28, 39, 41, 45, 46.
Homework 8 due 10/27: Sec. 5.8 Ex. 32, 34, 49(a,b); Sec. 6.7 Ex. 2, 3.
Homework 9 due 11/03: Sec. 6.7 Ex. 5, 6 , 8, 13, 22, 23.
Homework 10 due 11/10: Sec. 6.7 Ex. 24(c), 26; Sec. 7.8 Ex. 1(c,d), 9, 14, 15, 24, 26.
Homework 11 due 11/19: hw11.pdf (you have to use ordinary or exponential generating functions in this homework)
Homework 12 due 12/10: Sec. 14.4 Ex. 7, 8, 11, 17, 19, 26, 29, 35, 37, 38, 39.
| Week | Monday | Wednesday | Friday |
| 1 | 8/25 Introduction |
8/27 2.1 Pigeonhole principle (simple form) |
8/29
2.2 Pigeonhole principle (strong form) |
| 2 | 9/1 NO CLASS! |
9/3 2.3 Ramsey's theorem survey, R(4,5), 16 |
9/5 Chapter 2 review |
| 3 | 9/8 3.1 Counting Principles |
9/10 3.2 Permutations of sets |
9/12 3.3 Combinations of sets |
| 4 | 9/15 3.4 Permutations of multiset |
9/17 3.5 Combinations of multisets |
9/19 Chapter 3 review |
| 5 | 9/22 4.1, 4.2 Generating permutations |
9/24 4.3 Generating combinations |
9/26 4.4 Generating r-permutations |
| 6 | 9/29 4.5 Partial Orders |
10/1 4.5 (cont.) Equivalence Relations |
10/3 5.1 Binomial coefficients |
| 7 | 10/6 5.2 Binomial theorem |
10/8 5.3 Identities |
10/10 5.5. Multinomial theorem |
| 8 | 10/13 Review |
10/15 Midterm 1 |
10/17 5.6 Newton's binomial theorem |
| 9 | 10/20 5.4 Sperner's theorem |
10/22 5.7 Dilworth's Theorem |
10/24 6.1, 6.2 Inlusion - Exclusion |
| 10 | 10/27 6.3 Derangements |
10/29 6.5 Non-consecutive permutations; Surjective functions |
10/31 6.4 Perrmutations with forbidden positions 7.1 Recurrence relations |
| 11 | 11/3 7.2 Linear homogeneous recurrence relations |
11/5 7.3 Nonhomogeneous recurrence relations |
11/7 7.4 (Ordinary) generating functions |
| 12 | 11/10 7.5 Operations on generating functions; applications |
11/12 7.7 Exponential generating functions |
11/14 Exponential generating functions (cont.) |
| 13 | 11/17 8.1 Catalan Numbers |
11/19 Review |
11/21 Midterm 2 |
| 14 | 12/1 |
12/3 |
12/5 |
| 15 | 12/18 |
12/10 |
12/12 |
