Discrete Mathematics

  1. Combinatorics
    1. Fundamental Counting Principles
      1. Addition Principle
        1. Basic Addition Rule
          1. Mutually Exclusive Events
            1. Applications and Examples
            2. Multiplication Principle
              1. Basic Multiplication Rule
                1. Sequential Choices
                  1. Applications and Examples
                  2. Inclusion-Exclusion Principle
                    1. Two-Set Case
                      1. Three-Set Case
                        1. General Formula
                          1. Applications to Counting Problems
                          2. Pigeonhole Principle
                            1. Basic Pigeonhole Principle
                              1. Generalized Pigeonhole Principle
                                1. Applications and Examples
                              2. Permutations
                                1. Basic Permutations
                                  1. Permutations without Repetition
                                    1. Formula and Calculation
                                    2. Permutations with Restrictions
                                      1. Permutations with Repetition
                                        1. Circular Permutations
                                          1. Permutations with Forbidden Positions
                                          2. Partial Permutations
                                            1. r-Permutations
                                              1. Formula and Applications
                                            2. Combinations
                                              1. Basic Combinations
                                                1. Combinations without Repetition
                                                  1. Binomial Coefficients
                                                    1. Formula and Calculation
                                                    2. Combinations with Repetition
                                                      1. Stars and Bars Method
                                                        1. Multiset Combinations
                                                        2. Properties of Combinations
                                                          1. Symmetry Property
                                                            1. Pascal's Identity
                                                              1. Other Identities
                                                            2. Binomial Theorem and Identities
                                                              1. Binomial Theorem
                                                                1. Statement and Proof
                                                                2. Pascal's Triangle
                                                                  1. Construction and Properties
                                                                    1. Patterns in Pascal's Triangle
                                                                    2. Binomial Identities
                                                                      1. Vandermonde's Identity
                                                                        1. Hockey Stick Identity
                                                                          1. Sum Identities
                                                                        2. Advanced Counting Techniques
                                                                          1. Generating Functions
                                                                            1. Ordinary Generating Functions
                                                                              1. Operations on Generating Functions
                                                                                1. Applications to Counting
                                                                                2. Recurrence Relations
                                                                                  1. Linear Homogeneous Recurrences
                                                                                    1. Characteristic Equation Method
                                                                                      1. Non-homogeneous Recurrences
                                                                                        1. Fibonacci Sequence
                                                                                          1. Applications and Examples
                                                                                          2. Derangements
                                                                                            1. Definition and Formula
                                                                                              1. Inclusion-Exclusion Derivation
                                                                                              2. Stirling Numbers
                                                                                                1. Stirling Numbers of the Second Kind
                                                                                                  1. Stirling Numbers of the First Kind

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                                                                                              2. Set Theory and Basic Structures

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                                                                                              4. Number Theory