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Index
Cover page
Halftitle page
Series page
Title page
Copyright page
Contents
Preface
List of illustrations
Chapter 1: Numbers and algebra
The backstory of algebra
The number system
Number factorization
Chapter 2: The laws of algebra
Rules, tricks, and traps
Powers, indices, and the Binomial Theorem
The rules governing arithmetic
Chapter 3: Linear equations and inequalities
Single equations with one unknown
Simultaneous equations
Inequalities
Lincoln Fair problem
Chapter 4: Quadratic equations
Factorization and completing the square
The quadratic formula
Chapter 5: The algebra of polynomials and cubic equations
General polynomials
Complex numbers
Factorization of polynomials
Solution of the cubic
Chapter 6: Algebra and the arithmetic of remainders
Groups, rings, and fields
Modular arithmetic: rules of engagement
Solving linear congruences
Chapter 7: Introduction to matrices
Matrices and their operations
Networks
Geometric applications
Chapter 8: Matrices and groups
Inverses and groups
Matrix inverses
Chapter 9: Determinants and matrices
Determinants
Properties of determinants
Eigenvalues and eigenvectors
Similarity and diagonalization
Chapter 10: Vector spaces
More on abelian groups
Vector spaces
Finite fields
Further reading
Index
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