Combinatorics

  1. Advanced Counting Techniques
    1. The Principle of Inclusion-Exclusion
      1. Statement and Motivation
        1. Two Sets Case
          1. Three Sets Case
            1. General Formula for n Sets
              1. Venn Diagram Interpretation
                1. Applications
                  1. Counting Surjective Functions
                    1. Derangement Problems
                      1. Elements with Multiple Properties
                        1. Euler's Totient Function
                      2. The Pigeonhole Principle
                        1. Simple Pigeonhole Principle
                          1. Generalized Pigeonhole Principle
                            1. Strong Form of Pigeonhole Principle
                              1. Applications
                                1. Existence Proofs
                                  1. Bounds and Extremal Arguments
                                    1. Number Theory Applications
                                      1. Geometric Applications

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                                  5. The Binomial Theorem

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                                  7. Recurrence Relations