 ยง  Read  Use / Do 
 1 
The Arithmetic of Braids
Combing Braids

Exercises  The Arithmetic of Braids

 2 
The Arithmetic of Permutations (and Commutators)

Exercises  The Arithmetic of Permutations

 3 
Powers, Exponents, and their Dependencies

Exercises  Powers, Exponents, and their Dependencies

 4 
Roots  A Story of Two Notations

Exercises  Roots  A Story of Two Notations

 5 
The Triangle of Power and Logarithms

Exercises  The Triangle of Power and Logarithms
Exercises  Review Set A

 6 
Functions and Mapping Diagrams/Transformation Figures

Exercises  Functions

 7 
Alternate Bases and Polynomials

Exercises  Alternate Bases and Polynomials

 8 
The Binomial Theorem
Factoring and Eisenstein's Criterion

Exercises  Factoring, the Binomial Theorem, and Eisenstein's Criterion

 9 
Developing an Algorithm to Divide Polynomials
The Remainder, Factor, and Rational Roots Theorems

Exercises  Developing an Algorithm to Divide Polynomials

 10 
Clocks, Groups, and Commutative Rings

Exercises  Clocks, Groups, and Commutative Rings

 11 
The Field of Rational Expressions

Exercises  The Field of Rational Expressions

 12 
Extending Fields and Related Root Tricks

Exercises  Extending Fields and Related Root Tricks

 13 
Roots of Polynomials, the ZeroProduct Property, and Sign Analysis

Exercises  Roots of Polynomials, the ZeroProduct Property, and Sign Analysis
Exercises  Review Set B

 14 
Graphs of Simple Functions, their Inverses, and Compositions

Exercises  Graphs of Simple Functions, their Inverses, and Compositions

 15 
The Socks and Shoes Principle

Exercises  The Socks and Shoes Principle
Exercises  Graphing With Transformations

 16 
Equivalent Equations

Exercises  Equivalent Equations
Exercises  Solving Equations (Mixed Review)

 17 
PiecewiseDefined Functions
Relations and Lambert's W Function
Linear Functions & Mobius Transformations

Exercises  PiecewiseDefined Functions
Exercises  Relations and Lambert's W Function
Exercises  Linear Functions & Mobius Transformations

 18 
Quadratic Equations, PoShen Loh's Method, Depressed Terms, and Viete's Formulas

Exercises  Quadratic Equations, PoShen Loh's Method, Depressed Terms, and Viete's Formulas
Exercises  Solving Equations (Mixed Review 2)

 19 
Another Extended Field: The Complex Numbers

Exercises  Another Extended Field: The Complex Numbers

 20 
Measuring Angles of Rotation in a Dimensionless Way
Complex Numbers Birth the Trigonometric Functions!
Trigonometric Identities & More Complex Connections
Graphing Trigonometric Functions and Their Inverses

Exercises  Measuring Angles of Rotation
Exercises  Evaluating Trigonometric Functions
Exercises  Trigonometric Identities
Exercises  Inverse Trigonometric Functions
Exercises  Graphing Trigonometric Functions
Exercises  Solving Trigonometric Equations
Exercises  Review of Trigonometry

 21 
Solving the General Cubic Equation
How Imaginary Numbers were Invented (Source: Veritasium)

 22 
Solving the General Quartic Equation

 23 
The Fundamental Theorem of Algebra

 24 
The "Natural" Base and Hyperbolic Trigonometry


 25 
Abel's Impossibility Theorem
