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