Mathematics and Statistics for the Quantitative Sciences

Cover
	Half Title
Title Page
Copyright Page
Dedication
	Contents
Preface
Author Bio
SECTION I: Applied Mathematics
	The Plot (so you don’t lose it)
	CHAPTER 1: Functions
		1.1. ANATOMY OF A FUNCTION
		1.2. MODELLING 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
	CHAPTER 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
	CHAPTER 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
	CHAPTER 4: Derivatives in Multiple Dimensions
		4.1. APPLICATIONS
		4.2. DISTRIBUTION FITTING, PROBABILITY, AND LIKELIHOOD
	CHAPTER 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
	CHAPTER 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 Versus The World
	CHAPTER 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 AND STANDARD DEVIATION
		7.7. ETHICAL AND MORAL CONSIDERATIONS: EPISODE 2
		7.8. AN EXAMPLE
		7.9. THE EMPIRICAL RULE
	CHAPTER 8: Visualizing Data
		8.1. PLOTTING IN PYTHON
		8.2. SCATTER PLOTS
		8.3. OUTLIERS
		8.4. HISTOGRAMS
		8.5. THE ANATOMY OF A TECHNICAL DOCUMENT
		8.6. BAD PLOTS AND WHY THEY’RE BAD
	CHAPTER 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
	CHAPTER 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, AND VARIANCE
		10.11. SUMMING TO INFINITY
		10.12. PROBABILITY AND PYTHON
		10.13. PRACTICE PROBLEMS
	CHAPTER 11: Fitting Data
		11.1. DEFINING RELATIONSHIPS
		11.2. DATA AND LINES
		11.3. DISTRIBUTION FITTING AND 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 AND CONFIDENCE INTERVALS
		11.10. T-STATISTICS
		11.11. THE DICHOTOMOUS NATURE OF P-VALUES
APPENDIX A: A Crash Course in Python
	A.I. VARIABLES
	A.II. KEYWORDS
	A.III. CONDITIONALS
	A.IV. LOOPS
	A.V. IMPORT
	A.VI. FUNCTIONS
	A.VII. A SIMPLE PYTHON PROGRAM
Bibliography
Index