RAW Math

Mathematics Book

Introduction to Quaternions

21 Feb · Robert Eisele

Introduction to Quaternions

Hamiltonian quaternions extend the complex numbers into a non-commutative algebra built from the imaginary units i, j, and k. The treatment develops...

Polynomial Equations

Logic Minimization

Introduction to the Quine-McCluskey Algorithm

Rotations

Quaternions

Introduction to Quaternions

Complex Numbers

Introduction to Complex Numbers

Rational Numbers

Introduction to Rational Numbers

Real Numbers

Introduction to Real Numbers

PID Controllers

Introduction to PID Controllers

Bit Manipulation

Regression

Introduction to Regression

Surface Geometry

Introduction to the First Fundamental Form

Curves and Splines

Instance-Based Learning

Introduction to k-Nearest Neighbors

Vehicle Kinematics

Special Functions

Introduction to the Gamma Function

Differential Calculus

Vector Operations

Linear Programming

Introduction to Linear Programming

Parsing

Introduction to the CYK Algorithm

Inverse Kinematics

Inverse Kinematics of a 3-DOF Spider Robot Leg

Stirling's Approximation

Introduction to Stirling's Approximation

Set-Theoretic Foundations

Polynomials

Introduction to Polynomials

Continuity

Introduction to Continuity

Limits

Introduction to Limits

Function Classes

Introduction to Monotone, Bounded Variation, and Convex Functions

Monte Carlo Integration

Introduction to Monte Carlo integration

Integral Calculus

Algebraic Structures

Introduction to Algebraic Structures

Number Systems

Introduction to Number Systems

Directional Statistics

Rasterization

Introduction to Rasterization Algorithms

Vector Basics

Introduction to Vectors

Fast Exponentiation

Introduction to Exponentiation by Squaring

Prime Numbers

Natural Numbers and Integers

Introduction to Natural Numbers and Integers

Divisibility and GCD

Introduction to Greatest Common Divisor

Modular Arithmetic

Introduction to Modulo and Divisibility

Set Theory

Introduction to Sets

Collision Detection

Introduction to 2D Hit-Testing

Matrix Operations

Introduction to Matrix Multiplication

Shader Functions

GLSL Functions

Order Statistics

Second Smallest Element in an Array

Graph Algorithms

Introduction to Minimum Spanning Trees

Sequence Alignment

Introduction to Needleman-Wunsch Algorithm

Spectral Graph Theory

Spectral Theory

Counting Principles

Introduction to Combinatorics

Numerical Methods

Randomized Algorithms

Introduction to the Fisher-Yates Shuffle

Classification

Introduction to Linear Discriminant Analysis

Sequences

Introduction to Sequences

Local Regression

Introduction to LOESS and LOWESS

Root Finding

Introduction to Newton's Method

Newton-Type Methods

Introduction to the Gauss-Newton Method

Digital Filters

Series

Introduction to Series

Continued Fractions

Introduction to Continued Fractions

Probabilistic Data Structures

Introduction to Bloomfilters

Taylor Series

Introduction to Taylor Series

Power Series

Introduction to Power Series

Metaheuristics

Introduction to Simulated Annealing

Gradient Methods

Introduction to Gradient Descent

Linear Systems

Introduction to Gauss-Jordan Elimination

Matrix Inversion

Introduction to Matrix Inverse

Matrices

Introduction to Matrices

Rolling Variance

Efficient and Accurate Rolling Variance

Cryptography

Introduction to Diffie-Hellman Key Exchange

Searching

Introduction to Binary Search

Lambert W Function

Introduction to Lambert W function

Numerical Stability

Introduction to the Log-Sum-Exp Trick in Machine Learning

Solutions to Coding Challenges