Description

Book Synopsis

Examines familiar objects like integers, rational numbers, real numbers, complex numbers, complex conjugation and polynomials. This title shows how most of the concepts within an abstract algebra course are actually tools used to solve difficult, but well-known problems. It builds on relatively familiar material (Integers and polynomials).

Table of Contents

Introduction; What This Book Is about and Who This Book Is for; Proof and Intuition; The Integers; Rational Numbers and the Real Numbers; The Complex Numbers; The fundamental Theorem of Algebra; The Integers Modulo n; Group Theory; Polynomials over the Integers and Rationals; Roots of Polynomials of Degree Less than 5; Rational Values of Trigonometric Functions; Polynomials over Arbitrary Fields; Difference Functions and Partial Fractions; An Introduction to Linear Algebra and Vector Spaces; Degrees and Galois Groups of Field Extensions; Geometric Constructions; The Insolvability of the Quintic; Bibliography; Index

A Concrete Approach to Abstract Algebra

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    A Paperback by Jeffrey Bergen

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      Book details

      Publisher Elsevier
      Published 6 March 2010
      ISBN-13 9780123749413
      978-0123749413
      ISBN-10 0123749417
      Also in:
      Algebra Number theory

      Description

      Book Synopsis

      Examines familiar objects like integers, rational numbers, real numbers, complex numbers, complex conjugation and polynomials. This title shows how most of the concepts within an abstract algebra course are actually tools used to solve difficult, but well-known problems. It builds on relatively familiar material (Integers and polynomials).

      Table of Contents

      Introduction; What This Book Is about and Who This Book Is for; Proof and Intuition; The Integers; Rational Numbers and the Real Numbers; The Complex Numbers; The fundamental Theorem of Algebra; The Integers Modulo n; Group Theory; Polynomials over the Integers and Rationals; Roots of Polynomials of Degree Less than 5; Rational Values of Trigonometric Functions; Polynomials over Arbitrary Fields; Difference Functions and Partial Fractions; An Introduction to Linear Algebra and Vector Spaces; Degrees and Galois Groups of Field Extensions; Geometric Constructions; The Insolvability of the Quintic; Bibliography; Index

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