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# A Concrete Approach To Abstract Algebra

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
• 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