Mathematics and Statistics for the Quantitative Sciences

Section I. Applied Mathematics. The Plot (so you don't lose it). 1. Functions. 1.1. Anatomy of a Function. 1.2. Modeling With Mathematics. 1.3. Constants and Linear Functions. 1.4. Polynomials. 1.5. Exponentials And Logarithms. 1.6. Functions in Higher Dimensions. 1.7. Contour Diagrams. 1.8. Models In Two Dimensions. 1.9. Variables vs Parameters. 2. Derivatives. 2.1. The Tangent Line. 2.2. Approximating Derivatives of Functions. 2.3. Limits. 2.4. Limits And Derivates. 2.5. Derivative Formulas. 2.6. The Product Rule. 2.7. The Chain Rule. 2.8. Mixing Rules. 2.9. Critical Values. 2.10. Constrained Optimization. 2.11. Elasticity. 2.12. Partial Derivatives. 3. Linear Algebra. 3.1. Vectors. 3.2. Matrices. 3.3. Multiplication: Numbers and Matrices. 3.4. Multiplication: Matrix and Vectors. 3.5. Multiplication: Matrix and Matrix. 3.6. Leslie Matrices. 3.7. The Determinant. 3.8. Eigenvalues & Eigenvectors. 4. Derivatives in Multiple Dimensions. 4.1. Applications. 4.2. Distribution Fitting, Probability and Likelihood. 5. Differential Equations. 5.1. Solving Basic Differential Equations; With an Example. 5.2 Equilibria and Stability. 5.3 Equilibria and Linear Stability in Higher Dimensions. 5.4. The Jacobian. 6. Integration. 6.1. Accumulated Change. 6.2. The Fundamental Theorem of Calculus. 6.3. The Anti-Derivative. 6.4. Fundamental Theorem of Calculus Revisited. 6.5. Properties Of Integrals. 6.6. Integration by Parts. 6.7. Substitution. Section II. Applied Stats & Data Science. Some Context to Anchor Us. Math vs. the World. 7. Data and Summary Statistics. 7.1. What Is Data? 7.2. Data In Python. 7.3. Summary Statistics. 7.4. Ethical and Moral Considerations: Part 1. 7.5. Mean vs. Median vs. Mode. 7.6. Variance & Standard Deviation. 7.7. Ethical And Moral Considerations: Episode 2. 7.8. An Example. 7.9. The Empirical Rule. 8. Visualizing Data. 8.1. Plotting In Python. 8.2. Scatter Plots. 8.3. Outliers. 8.4. Correlation. 8.6. The Anatomy of a Technical Document. 8.7. Bad Plots and Why They're Bad. 9. Probability. 9.1. Ethical and Moral Considerations: A Very Special Episode. 9.2. Counting. 9.3. Permutations. 9.4. Combinations. 9.5. Combinations With Replacement. 9.6. Probability. 9.7. Properties of Probabilities. 9.8. More Notation. 9.9. Conditional Probability. 9.10. Bayes' Theorem. 9.11. The Prosecutor's Fallacy. 9.12. The Law of Total Probability. 10. Probability Distributions. 10.1. Discrete Probability Distributions. 10.2. The Binomial Distribution. 10.3. Trinomial Distribution. 10.4. Cumulative Probability Distributions. 10.5. Continuous Probability. 10.6. Continuous vs Discrete Probability Distributions. 10.7. Probability Density Functions. 10.8. The Normal Distribution. 10.9. Other Useful Distributions. 10.10. Mean, Median, Mode, Variance. 10.11. Summing To Infinity. 10.12. Probability and Python. 10.13. Practice Problems. 11. Fitting Data. 11.1. Defining Relationships. 11.2. Data and Lines. 11.3. Distribution Fitting & Likelihood. 11.4. Dummy Variables. 11.5. Logistic Regression. 11.6. Logistic Regression in Python. 11.7. Iterated Logistic Regression. 11.8. Random Forest Classification. 11.9. Bootstrapping & Confidence Intervals. 11.10. T-Statistics. 11.11. The Dichotomous Nature of P-Values. A. A Crash Course in Python.