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
Exercises 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
The Fundamental Theorem Of Algebra
Representing Real Numbers And Complex Numbers Geometrically
Rectangular And Polar Form
Demoivre’s Theorem And Roots Of Complex Numbers
A Proof Of The Fundamental Theorem Of Algebra
The Integers Modulo N
Definitions And Basic Properties
Zero Divisors And Invertible Elements
The Euler Φ Function
Polynomials With Coefficients In Zn
Group Theory
Definitions And Examples
I Commutative Rings And Fields Under Addition
II Invertible Elements In Commutative Rings Under Multiplication
III Bijections Of Sets
Exercises For Section
Theorems Of Lagrange And Sylow
Exercises For Section
Solvable Groups
Exercises For Section
Symmetric Groups
Exercises For Section
Polynomials Over The Integers And Rationals
Integral Domains And Homomorphisms Of Rings
Exercises For Section
A Concrete Approach To Abstract Algebra
Rational Root Test And Irreducible Polynomials
Exercises For Section
Gauss’ Lemma And Eisenstein’s Criterion
Exercises For Section
Reduction Modulo P
Exercises For Section
Roots Of Polynomials Of Degree Less Than
Finding Roots Of Polynomials Of Small Degree
A Brief Look At Some Consequences Of Galois’ Work
Rational Values Of Trigonometric Functions
Values Of Trigonometric Functions
Exercises For Section
A Concrete Approach To Abstract Algebra
A Concrete Approach To Abstract Algebra Pdf
What Is Abstract Algebra
History Of Abstract Algebra
Concrete And Abstract Ideas
Algebra Abstract And Concrete
Concrete Semi-Concrete And Abstract Math
A Concrete Introduction To Higher Algebra
Concrete To Abstract Math
Concrete Representational Abstract (Cra) Approach
A Concrete Approach To Abstract Algebra
Concrete Abstract Representational
Concrete And Abstract Mathematics
Abstract Algebra With A Concrete Introduction
A Concrete Introduction To Higher Algebra Pdf
J A Concrete
Concrete Abstract Math
Concrete To Abstract Learning
Math Concrete To Abstract
Math Concrete Representational Abstract
Concrete Representational-Abstract Nctm
Concrete Approach Meaning
Concrete And Abstract Concept
Concrete To Abstract Examples
Abstract Algebra Examples
Concrete To Abstract Meaning In Teaching
From Concrete To Abstract Meaning
The Concrete Tetrahedron
Uconn Abstract Algebra
Ucla Abstract Algebra
Abstract Math Vs. Concrete Math
Concrete Abstract Representational Math
Concrete Semi-Concrete And Abstract Math
What Is A Concrete Representation In Math
Concrete Approach Meaning
Is Math A Concrete Subject
Concrete To Abstract Math
Concrete To Abstract Learning
Concrete Abstract Math
Concrete Abstract Representational
Concrete Abstract Representational Math
Concrete And Abstract Mathematics
What Does Concrete To Abstract Mean