Operations Research

  1. Mathematical Preliminaries
    1. Linear Algebra Review
      1. Vectors and Vector Operations
        1. Vector Representation
          1. Vector Addition and Subtraction
            1. Scalar Multiplication
              1. Dot Product and Cross Product
                1. Vector Norms
                2. Matrices and Matrix Operations
                  1. Matrix Representation
                    1. Matrix Addition and Subtraction
                      1. Scalar Multiplication
                        1. Matrix Multiplication
                          1. Matrix Transpose
                            1. Matrix Inverse
                              1. Determinants
                                1. Special Matrices
                                2. Systems of Linear Equations
                                  1. Gaussian Elimination
                                    1. Gauss-Jordan Elimination
                                      1. Cramer's Rule
                                        1. Existence and Uniqueness of Solutions
                                          1. Homogeneous Systems
                                          2. Vector Spaces and Linear Independence
                                            1. Vector Space Properties
                                              1. Linear Independence
                                                1. Basis and Dimension
                                                  1. Rank of a Matrix
                                                    1. Null Space and Column Space
                                                  2. Probability Theory Review
                                                    1. Sample Spaces and Events
                                                      1. Definitions and Notation
                                                        1. Set Operations
                                                          1. Probability Axioms
                                                          2. Conditional Probability and Independence
                                                            1. Conditional Probability Definition
                                                              1. Independence of Events
                                                                1. Bayes' Theorem
                                                                  1. Law of Total Probability
                                                                  2. Random Variables
                                                                    1. Discrete Random Variables
                                                                      1. Continuous Random Variables
                                                                        1. Functions of Random Variables
                                                                        2. Probability Distributions
                                                                          1. Probability Mass Functions
                                                                            1. Probability Density Functions
                                                                              1. Cumulative Distribution Functions
                                                                                1. Common Discrete Distributions
                                                                                  1. Binomial Distribution
                                                                                    1. Poisson Distribution
                                                                                      1. Geometric Distribution
                                                                                      2. Common Continuous Distributions
                                                                                        1. Normal Distribution
                                                                                          1. Exponential Distribution
                                                                                            1. Uniform Distribution
                                                                                          2. Expected Value and Variance
                                                                                            1. Properties of Expectation
                                                                                              1. Variance and Standard Deviation
                                                                                                1. Covariance and Correlation
                                                                                                  1. Moment Generating Functions
                                                                                                2. Calculus Review
                                                                                                  1. Differential Calculus
                                                                                                    1. Limits and Continuity
                                                                                                      1. Derivatives and Rules
                                                                                                        1. Partial Derivatives
                                                                                                          1. Chain Rule
                                                                                                          2. Optimization Concepts
                                                                                                            1. Critical Points
                                                                                                              1. First-Order Conditions
                                                                                                                1. Second-Order Conditions
                                                                                                                  1. Constrained Optimization
                                                                                                                  2. Integral Calculus
                                                                                                                    1. Definite and Indefinite Integrals
                                                                                                                      1. Integration Techniques
                                                                                                                        1. Multiple Integrals

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                                                                                                                    1. Introduction to Operations Research

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                                                                                                                    3. Linear Programming