| 1 |
Introduction
Pigeonhole Principle |
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| 2 |
Mathematical Induction |
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| 3 |
Permutations |
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| 4 |
Binomial Theorem |
Problem set 1 due |
| 5 |
Compositions
Integer Partitions |
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| 6 |
Set Partitions |
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| 7 |
Cycles in Permutations
Stirling Numbers |
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| 8 |
Exam 1 |
Problem set 2 due |
| 9 |
Inclusion-exclusion Principle |
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| 10 |
Inclusion-exclusion (cont.)
Mobius Inversion |
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| 11 |
Recurrence Relations |
Problem set 3 due |
| 12 |
Generating Functions |
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| 13 |
Generating Functions (cont.) |
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| 14 |
Catalan Numbers |
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| 15 |
Generating Functions (cont.) |
Problem set 4 due |
| 16 |
Exam 2 |
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| 17 |
Graphs
Eulerian Walks
Hamiltonian Cycles |
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| 18 |
Trees
Counting Trees |
Problem set 5 due |
| 19 |
Matrix-tree Theorem |
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| 20 |
Matrix-tree Theorem (cont.) |
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| 21 |
Matrix-tree Theorem and Eulerian Digraphs |
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| 22 |
Bipartite Graphs and Matchings |
Problem set 6 due |
| 23 |
Planar Graphs
Polyhedra
Maps |
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| 24 |
Chromatic Polynomials |
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| 25 |
Exam 3 |
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| 26 |
Polya Counting
Ramsey Theory
Probabilistic Method |
Problem set 7 due |