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