Discrete Mathematics

  1. Discrete Probability
    1. Probability Foundations
      1. Sample Spaces
        1. Finite Sample Spaces
          1. Events and Outcomes
            1. Event Operations
            2. Probability Axioms
              1. Kolmogorov Axioms
                1. Basic Properties
                  1. Probability Assignment
                  2. Counting and Probability
                    1. Equally Likely Outcomes
                      1. Classical Probability
                        1. Combinatorial Probability
                      2. Conditional Probability
                        1. Definition and Calculation
                          1. Conditional Probability Formula
                            1. Multiplication Rule
                              1. Tree Diagrams
                              2. Independence
                                1. Independent Events
                                  1. Mutual Independence
                                    1. Pairwise Independence
                                    2. Bayes' Theorem
                                      1. Statement and Proof
                                        1. Prior and Posterior Probabilities
                                        2. Law of Total Probability
                                          1. Partition of Sample Space
                                        3. Random Variables
                                          1. Discrete Random Variables
                                            1. Definition and Examples
                                              1. Probability Mass Function
                                                1. Cumulative Distribution Function
                                                2. Expected Value
                                                  1. Definition and Calculation
                                                    1. Linearity of Expectation
                                                      1. Expected Value of Functions
                                                      2. Variance and Standard Deviation
                                                        1. Definition and Calculation
                                                          1. Properties of Variance
                                                            1. Computational Formulas
                                                            2. Common Discrete Distributions
                                                              1. Bernoulli Distribution
                                                                1. Binomial Distribution
                                                                  1. Geometric Distribution
                                                                    1. Poisson Distribution
                                                                  2. Applications and Advanced Topics
                                                                    1. Markov Chains
                                                                      1. State Spaces and Transitions
                                                                        1. Transition Matrices
                                                                          1. Steady-State Behavior
                                                                          2. Probabilistic Algorithms
                                                                            1. Randomized Algorithms
                                                                              1. Monte Carlo Methods
                                                                                1. Las Vegas Algorithms
                                                                                2. Information Theory Basics
                                                                                  1. Entropy
                                                                                    1. Information Content
                                                                                      1. Applications to Coding

                                                                                  Previous

                                                                                  6. Trees

                                                                                  Go to top

                                                                                  Next

                                                                                  8. Algorithms and Complexity