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 1 
The Arithmetic of Braids

Exercises  The Arithmetic of Braids

 2 
Combing Braids

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 3 
The Arithmetic of Permutations

Exercises  The Arithmetic of Permutations

 4 
Powers, Exponents, and their Dependencies

Exercises  Powers, Exponents, and their Dependencies

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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

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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 ZeroProduct Property, and Sign Analysis

Exercises  Roots of Polynomials, the ZeroProduct 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

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Equivalent Equations

Exercises  Equivalent Equations

 18 
Restricting Relations & PiecewiseDefined Functions
Linear Functions & Mobius Transformations

Exercises  Restricting Relations & PiecewiseDefined Functions
Exercises  Linear Functions & Mobius Transformations

 19 
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

 20 
Another Extended Field: The Complex Numbers

Exercises  Another Extended Field: The Complex Numbers

 21 
Complex Numbers Birth Trigonometry!

Exercises  Trigonometry

 22 
Solving the General Cubic Equation
How Imaginary Numbers were Invented (Watch This!)

 23 
Solving the General Quartic Equation

 24 
The Fundamental Theorem of Algebra

 25 
The "Natural" Base and Hyperbolic Trigonometry

 26 
Abel's Impossibility Theorem
