Operations Research and Optimization

  1. Mathematical Foundations for Optimization
    1. Linear Algebra Essentials
      1. Vectors and Vector Operations
        1. Vector Definitions and Notation
          1. Vector Addition and Subtraction
            1. Scalar Multiplication
              1. Dot Product and Cross Product
                1. Vector Norms
                2. Matrices and Matrix Operations
                  1. Matrix Definitions and Types
                    1. Square Matrices
                      1. Diagonal Matrices
                        1. Identity Matrices
                          1. Symmetric Matrices
                            1. Matrix Addition and Subtraction
                              1. Scalar Multiplication
                                1. Matrix Multiplication
                                  1. Matrix Transpose
                                    1. Matrix Inverse
                                      1. Determinants
                                      2. Systems of Linear Equations
                                        1. Matrix Representation
                                          1. Gaussian Elimination
                                            1. LU Decomposition
                                              1. Existence and Uniqueness of Solutions
                                                1. Homogeneous Systems
                                                2. Vector Spaces and Subspaces
                                                  1. Vector Space Properties
                                                    1. Subspace Definition
                                                      1. Basis and Dimension
                                                        1. Null Space
                                                          1. Column Space
                                                            1. Row Space
                                                            2. Linear Independence and Dependence
                                                              1. Linear Combinations
                                                                1. Spanning Sets
                                                                  1. Basis Vectors
                                                                    1. Rank of a Matrix
                                                                      1. Orthogonality and Orthonormality
                                                                    2. Calculus Essentials
                                                                      1. Single Variable Calculus
                                                                        1. Limits and Continuity
                                                                          1. Derivatives
                                                                            1. Chain Rule
                                                                              1. Optimization Conditions
                                                                              2. Multivariable Calculus
                                                                                1. Partial Derivatives
                                                                                  1. Gradient Vectors
                                                                                    1. Directional Derivatives
                                                                                      1. Chain Rule for Multiple Variables
                                                                                      2. Second-Order Derivatives
                                                                                        1. Hessian Matrices
                                                                                          1. Second Derivative Test
                                                                                            1. Positive and Negative Definite Matrices
                                                                                              1. Eigenvalues and Eigenvectors
                                                                                              2. Convexity and Concavity
                                                                                                1. Convex Functions
                                                                                                  1. Concave Functions
                                                                                                    1. Properties of Convex Sets
                                                                                                      1. First-Order Conditions for Convexity
                                                                                                        1. Second-Order Conditions for Convexity
                                                                                                      2. Probability and Statistics Essentials
                                                                                                        1. Probability Theory Fundamentals
                                                                                                          1. Sample Spaces and Events
                                                                                                            1. Probability Axioms
                                                                                                              1. Conditional Probability
                                                                                                                1. Independence
                                                                                                                  1. Bayes' Theorem
                                                                                                                  2. Random Variables
                                                                                                                    1. Discrete Random Variables
                                                                                                                      1. Continuous Random Variables
                                                                                                                        1. Probability Mass Functions
                                                                                                                          1. Probability Density Functions
                                                                                                                            1. Cumulative Distribution Functions
                                                                                                                            2. Common Probability Distributions
                                                                                                                              1. Discrete Distributions
                                                                                                                                1. Bernoulli Distribution
                                                                                                                                  1. Binomial Distribution
                                                                                                                                    1. Poisson Distribution
                                                                                                                                      1. Geometric Distribution
                                                                                                                                      2. Continuous Distributions
                                                                                                                                        1. Uniform Distribution
                                                                                                                                          1. Normal Distribution
                                                                                                                                            1. Exponential Distribution
                                                                                                                                              1. Gamma Distribution
                                                                                                                                            2. Expected Value and Variance
                                                                                                                                              1. Expected Value Properties
                                                                                                                                                1. Variance and Standard Deviation
                                                                                                                                                  1. Covariance and Correlation
                                                                                                                                                    1. Moment Generating Functions
                                                                                                                                                    2. Statistical Inference
                                                                                                                                                      1. Point Estimation
                                                                                                                                                        1. Interval Estimation
                                                                                                                                                          1. Confidence Intervals
                                                                                                                                                            1. Hypothesis Testing
                                                                                                                                                              1. Type I and Type II Errors
                                                                                                                                                                1. P-values and Significance Levels

                                                                                                                                                            Previous

                                                                                                                                                            1. Introduction to Operations Research

                                                                                                                                                            Go to top

                                                                                                                                                            Next

                                                                                                                                                            3. Linear Programming