Algebra

**1. Linear Equations and Systems**- Solving Linear Equations; Slope-Intercept Form; Point-Slope Form; Standard Form; Linear Systems.**2. Quadratic Equations**- Standard Form; Factoring; Quadratic Formula; Completing the Square; Vertex Form; Quadratic Systems.**3. Inequalities**- Linear Inequalities in the Number Line; Linear Inequalities in the Plane; Quadratic Inequalities; Systems of Inequalities.**4. Polynomials**- Standard Form and End Behavior; Zeros; Rational Roots and Synthetic Division; Sketching Graphs.**5. Rational Functions**- Polynomial Long Division; Horizontal Asymptotes; Vertical Asymptotes; Graphing with Horizontal and Vertical Asymptotes; Graphing with Slant and Polynomial Asymptotes.**6. Non-Polynomial Functions**- Radical Functions; Exponential and Logarithmic Functions; Absolute Value; Trigonometric Functions; Piecewise Functions.**7. Transformations of Functions**- Shifts; Rescalings; Reflections; Inverse Functions; Compositions.

Calculus

**1. Limits and Derivatives**- Evaluating Limits; Limits by Logarithms, Squeeze Theorem, and Euler's Consant; Derivatives and the Difference Quotient; Power Rule; Chain Rule; Properties of Derivatives; Derivatives of Non-Polynomial Functions; Finding Local Extrema; Differentials and Approximation; L'Hôpital's Rule.**2. Integrals**- Antiderivatives; Finding Area; Substitution; Integration by Parts; Improper Integrals.**3. Differential Equations**- Separation of Variables; Slope Fields and Euler Approximation; Substitution; Characteristic Polynomial; Undetermined Coefficients; Integrating Factors; Variation of Parameters.**4. Series**- Geometric Series; Tests for Convergence; Taylor Series; Manipulating Taylor Series; Solving Differential Equations with Taylor Series.

Linear Algebra

**1. Vectors**- N-Dimensional Space; Dot Product and Cross Product; Lines and Planes; Span, Subspaces, and Reduction; Elimination as Vector Reduction.**2. Volume**- N-Dimensional Volume Formula; Volume as the Determinant of a Square Linear System; Shearing, Cramer’s Rule, and Volume by Reduction; Higher-Order Variation of Parameters.**3. Matrices**- Linear Systems as Transformations of Vectors by Matrices; Matrix Multiplication; Rescaling, Shearing, and the Determinant; Inverse Matrices.**4. Eigenspace**- Eigenvalues, Eigenvectors, and Diagonalization; Recursive Sequence Formulas via Diagonalization; Generalized Eigenvectors and Jordan Form; Matrix Exponential and Systems of Linear Differential Equations.

Machine Learning

*To be written!*

**1. The Pseudoinverse**- Linear Regressor; Polynomial Regressor; Linear Combination of Nonlinear Functions; Logistic Regressor; Pitfalls.**2. Gradient Descent**- Partial Derivatives and the Gradient; Algebraic Functions; Non-Algebraic Functions; Linear Regressor; Logistic Regressor; Logistic Classifier; Pitfalls.**3. Non-Parametric Models**- K-Nearest Neighbors; Decision Trees; Random Forests.**4. Validation**- Overfitting, Underfitting, and the Bias-Variance Tradeoff; Cross-Validation; Normalization; Feature Selection.**5. Neural Networks**- Multivariable Chain Rule; Forward Propagation, Activation Functions, and Weight Updates; Computing Gradients via Chain Rule; Computing Gradients via Path Enumeration; Computing Gradients via Backpropagation.**6. Bayesian Methods**- Probability Distributions; Bayes' Theorem; Maximum Likelihood; Naive Bayes; Prior and Posterior Distributions; Maximum a Posteriori.**7. Unsupervised Learning**- K-Means Clustering; Principal Component Analysis.