# Contents

The beauty of mathematics only shows itself

to more patient followers.— Maryam Mirzakhani

## Volume I

### Variables

Number Systems

Proof

Coordinates

Discrete Graphs

Continuous Graphs

Domain and Range

Linear Equations

### Linear Systems

Systems of Equations

Boolean Algebra

Conditionals

Loops

Systems of Inequalities

### Functions

Maps

Functions

Combination and Composition

Inversion

Rate of Change

Limits

Derivatives

### Probability

Random Walks

Monte Carlo Simulation

Sequences and Series

Lists

Counting

Events

Rules of Probability

Probability Density Functions

Cumulative Distribution Functions

Integrals

### Data Science

Statistical Questions

Categorical and Quantitative Data

Data Visualization

Summary Statistics

Modeling and Prediction

Privacy and Data Collection

## Volume II

### Complex Numbers

Quadratic Equations

Imaginary and Complex Numbers

Lines

Angles

Triangles

The Pythagorean Theorem

Function Iteration

Fractals

### Trigonometry

Trigonometric Ratios

Unit Circle

Trigonometric Functions

Polar Coordinates

Euler’s Formula

Fourier Transforms

### Analytic Geometry

Parametric Equations

Conic Sections

Systems of Nonlinear Equations

Scientific Computing

### Linear Algebra

Vector Arithmetic

Elementary Row Operations

Gauss-Jordan Elimination

Matrix Arithmetic

Linear Transformations

Matrix Equations

Synchronization

### Machine Learning

Classification and Regression

Neurons

Gradients

The Chain Rule

Backpropagation

Neural Networks

Pose Estimation

Case Study: ImageNet