**A Concrete Approach To Abstract Algebra**

##### Contents

- What This Book Is About And Who This Book Is For
- Algebra
- Finding Roots Of Polynomials
- Existence Of Roots Of Polynomials
- Solving Linear Equations
- Geometry
- Ruler And Compass Constructions
- Trigonometry
- Rational Values Of Trigonometric Functions
- Precalculus
- Recognizing Polynomials Using Data
- Calculus
- Partial Fraction Decomposition
- Detecting Multiple Roots Of Polynomials
- Exercises For Chapter
- Proof And Intuition
- The Well Ordering Principle
- Proof By Contradiction
- Mathematical Induction
- Mathematical Induction—First Version
- Mathematical Induction—First Version Revisited
- Mathematical Induction—Second Version
- Exerc ises For Sections
- A Concrete Approach To Abstract Algebra

##### Functions And Binary Operations

- Exercises For Section
- The Integers
- Prime Numbers
- Unique Factorization
- Division Algorithm
- Exercises For Sections
- Greatest Common Divisors
- Euclidean Algorithm
- Exercises For Sections
- The Rational Numbers And The Real Numbers
- Rational Numbers
- Intermediate Value Theorem
- Exercises For Sections
- Equivalence Relations
- Exercises For Section
- The Complex Numbers
- Complex Numbers
- Fields And Commutative Rings
- Complex Conjugation
- Automorphisms And Roots Of Polynomials
- Groups Of Automorphisms Of Commutative Rings
- Exercises For Section
- A Concrete Approach To Abstract Algebra