ยงReadUse / Do
1 The Arithmetic of Braids Exercises - The Arithmetic of Braids
2 Combing Braids
3 The Arithmetic of Permutations (and Commutators) Exercises - The Arithmetic of Permutations
4 Powers, Exponents, and their Dependencies Exercises - Powers, Exponents, and their Dependencies
5 Roots - A Story of Two Notations Exercises - Roots - A Story of Two Notations
6 The Triangle of Power and Logarithms Exercises - The Triangle of Power and Logarithms
Exercises - Review Set A
7 Functions and Mapping Diagrams/Transformation Figures Exercises - Functions
8 Alternate Bases and Polynomials Exercises - Alternate Bases and Polynomials
9 Factoring, the Binomial Theorem, and Eisenstein's Criterion Exercises - Factoring, the Binomial Theorem, and Eisenstein's Criterion
10 Developing an Algorithm to Divide Polynomials Exercises - Developing an Algorithm to Divide Polynomials
11 Clocks, Groups, and Commutative Rings Exercises - Clocks, Groups, and Commutative Rings
12 The Field of Rational Expressions Exercises - The Field of Rational Expressions
13 Extending Fields and Related Root Tricks Exercises - Extending Fields and Related Root Tricks
14 Roots of Polynomials, the Zero-Product Property, and Sign Analysis Exercises - Roots of Polynomials, the Zero-Product Property, and Sign Analysis
Exercises - Review Set B
15 Graphs of Simple Functions, their Inverses, and Compositions Exercises - Graphs of Simple Functions, their Inverses, and Compositions
16 The Socks and Shoes Principle Exercises - The Socks and Shoes Principle
17 Equivalent Equations Exercises - Equivalent Equations
18 Restricting Relations & Piecewise-Defined Functions
Linear Functions & Mobius Transformations
Exercises - Restricting Relations & Piecewise-Defined Functions
Exercises - Linear Functions & Mobius Transformations
19 Quadratic Equations, Po-Shen Loh's Method, Depressed Terms, and Viete's Formulas Exercises - Quadratic Equations, Po-Shen Loh's Method, Depressed Terms, and Viete's Formulas
20 Another Extended Field: The Complex Numbers Exercises - Another Extended Field: The Complex Numbers
21 Complex Numbers Birth Trigonometry! Exercises - Trigonometry
Exercises - Review of Trigonometry
22 Solving the General Cubic Equation
How Imaginary Numbers were Invented (Source: Veritasium)
23 Solving the General Quartic Equation
24 The Fundamental Theorem of Algebra
25 The "Natural" Base and Hyperbolic Trigonometry
Exercises - The "Natural" Base
26 Abel's Impossibility Theorem