1 |
Jan 10 |
Introduction; A proof involving sqrt and floor |
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2 |
Jan 12 |
Induction |
1.1,1.2 |
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HW1 posted. |
3 |
Jan 14 |
Tromino Tilings |
1.1,1.2 |
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Jan 17 |
MLK Day: no class |
- |
- |
- |
HW2 posted. |
4 |
Jan 19 |
More tilings; Recurrence relations |
1.3 |
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5 |
Jan 21 |
Recurrence relations II |
1.3 |
quiz1.pdf |
quiz1-soln.pdf |
Quiz 1 in class |
6 |
Jan 24 |
Bad proof example; unrolling a recurrence |
1.3 |
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HW2 due. HW3 posted. |
7 |
Jan 26 |
Pigeonhole principle |
2.1 |
quiz2.pdf |
quiz2-soln.pdf |
Quiz 2 in class. |
8 |
Jan 28 |
Erdos--Szekeres Theorem; Groupwork |
2.1 |
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- |
9 |
Jan 31 |
Groupwork (continued) |
2.1 |
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HW3 due. HW4 posted. |
10 |
Feb 2 |
Graphs and Multigraphs |
2.2 |
- |
- |
- |
11 |
Feb 4 |
Test 1: Classes 1 through 9; Sec. 1.1-1.3, 2.1 |
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test1.pdf |
test1-soln.pdf |
- |
12 |
Feb 7 |
Bipartite graphs; graph isomorphism; Ramsey Theory |
2.2,2.3 |
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- |
HW4 due. HW5 posted. |
13 |
Feb 9 |
Ramsey Numbers r(n,m) |
2.3 |
quiz4.pdf |
quiz4-soln.pdf |
Quiz 4 in class. |
14 |
Feb 11 |
Handshaking lemma; r(3,4) at most 9 |
2.3 |
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15 |
Feb 14 |
Multicolor Ramsey numbers; Graph Ramsey Theory |
2.3,2.4 |
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HW5 due. HW6 posted. |
16 |
Feb 16 |
Schur, Van der Waerden Numbers |
2.4 |
quiz5.pdf |
quiz5-soln.pdf |
Quiz 5 in class. |
17 |
Feb 18 |
r(C_4,C_4); Counting: Addition, Multiplication Principles |
2.4,3.1 |
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18 |
Feb 21 |
Counting examples; Subtraction Principle |
3.1 |
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HW6 due. HW7 posted. |
19 |
Feb 23 |
Probability: Introduction |
3.2 |
quiz6.pdf |
quiz6-soln.pdf |
Quiz 6 in class. |
20 |
Feb 25 |
Group Activity: Max Run of Heads |
3.2.1 |
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21 |
Feb 28 |
Permutations; Falling Factorials |
4.1 |
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HW7 due. |
22 |
Mar 2 |
Combinations; Binomial Coefficients |
4.2 |
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23 |
Mar 4 |
Test 2: Classes 10 through 21; 2.2-2.4; 3.1, 3.2, 4.1 |
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test2.pdf |
test2-soln.pdf |
- |
24 |
Mar 7 |
Binomial coefficient examples; decks of cards |
4.2 |
- |
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HW8 posted.
|
25 |
Mar 9 |
Group activity: probability of all aces in one hand |
4.2 |
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26 |
Mar 11 |
Multinomial coefficients |
4.3 |
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27 |
Mar 21 |
Combinations of multisets |
4.4 |
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HW8 due. HW9 posted. |
28 |
Mar 23 |
Counting solutions; combinatorial proofs |
4.4,5.1 |
quiz8.pdf |
quiz8-soln.pdf |
Quiz 8 in class |
29 |
Mar 25 |
Combinatorial proofs II |
5.1 |
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- |
HW8 due. HW9 posted. |
30 |
Mar 28 |
Pascal's Triangle; binomial coefficient bounds |
5.1.2-5.1.3 |
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HW9 due. HW10 posted. |
31 |
Mar 30 |
Ramsey Numbers: quantitative upper bounds |
5.1.4 |
quiz9.pdf |
quiz9-soln.pdf |
Quiz 9 in class. |
32 |
Apr 1 |
Ramsey Numbers: quantitative lower bounds |
5.1.4 |
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- |
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33 |
Apr 4 |
Ramsey Numbers: quantitative lower bounds II; Binomial Theorem |
5.1.4, 5.2 |
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- |
HW10 due. HW11 posted. |
34 |
Apr 6 |
Inclusion/Exclusion |
8.1 |
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- |
- |
35 |
Apr 8 |
Test 3: Classes 22 through 33; 4.2-4.4, 5.1, 5.2, 8.1 |
- |
test3.pdf |
test3-soln.pdf |
- |
36 |
Apr 11 |
Ordinary Generating Functions |
9.1 |
- |
- |
HW11 due. HW12 posted. |
37 |
Apr 13 |
OGFs and Recurrence Relations |
9.2 |
quiz11.pdf |
quiz11-soln.pdf |
Quiz 11 in class. |
38 |
Apr 18 |
Fibonacci Formula Derivation |
9.2 |
- |
- |
HW12 due. HW13 posted. |
39 |
Apr 20 |
Graph Coloring |
10.7 |
quiz12.pdf |
quiz12-soln.pdf |
Quiz 12 in class. |
40 |
Apr 22 |
Graph Coloring II |
10.7 |
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- |
- |
41 |
Apr 25 |
Group Activity: Mycielski's Construction |
10.7 |
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HW13 due. |
42 |
Apr 27 |
Large girth, large chromatic number; Degeneracy; Chromatic polynomial |
10.7 |
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- |
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43 |
Apr 29 |
Review |
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May 3 |
Final Exam: Tues May 3, 11:00am-1:00pm |
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