Description

Book Synopsis
Offers a new approach to laying a foundation for abstract mathematics. Prior experience with proofs is not assumed, and the book takes time to build proof-writing skills in ways that will serve students through a lifetime of learning and creating mathematics.

Table of Contents
  • Preliminaries: Introduction to proofs
  • Sets and subsets
  • Divisors
  • Examples of groups: Modular arithmetic
  • Symmetries
  • Permutations
  • Matrices
  • Introduction to groups: Introduction to groups
  • Groups of small size
  • Matrix groups
  • Subgroups
  • Order of an element
  • Cyclic groups, Part I
  • Cyclic groups, Part II
  • Group homomorphisms: Functions
  • Isomorphisms
  • Homomorphisms, Part I
  • Homomorphisms, Part II
  • Quotient groups: Introduction to cosets
  • Lagrange's theorem
  • Multiplying/adding cosets
  • Quotient group examples
  • Quotient group proofs
  • Normal subgroups
  • First isomorphism theorem
  • Introduction to rings: Introduction to rings
  • Integral domains and fields
  • Polynomial rings, Part I
  • Polynomial rings, Part II
  • Factoring polynomials
  • Quotient rings: Ring homomorphisms
  • Introduction to quotient rings
  • Quotient ring $\mathbb{Z}_7[x]/ \langle x^2-1\rangle$
  • Quotient ring $\mathbb{R}[x]/ \langle x^2 +1\rangle$
  • $F[x]/ \langle g(x)\rangle$ is/isn't a field, Part I
  • Maximal ideals
  • $F[x]/ \langle g(x)\rangle$ is/isn't a field, Part II
  • Appendices: Proof of the GCD theorem
  • Composition table for $D_4$
  • Symbols and notations
  • Essential theorems
  • Index: Index of terms

A Friendly Introduction to Abstract Algebra

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    A Paperback by Ryota Matsuura

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      Book details

      Publisher American Mathematical Society
      Published 8/30/2022 12:00:00 AM
      ISBN-13 9781470468811
      978-1470468811
      ISBN-10 1470468816
      Also in:
      Algebraic geometry

      Description

      Book Synopsis
      Offers a new approach to laying a foundation for abstract mathematics. Prior experience with proofs is not assumed, and the book takes time to build proof-writing skills in ways that will serve students through a lifetime of learning and creating mathematics.

      Table of Contents
      • Preliminaries: Introduction to proofs
      • Sets and subsets
      • Divisors
      • Examples of groups: Modular arithmetic
      • Symmetries
      • Permutations
      • Matrices
      • Introduction to groups: Introduction to groups
      • Groups of small size
      • Matrix groups
      • Subgroups
      • Order of an element
      • Cyclic groups, Part I
      • Cyclic groups, Part II
      • Group homomorphisms: Functions
      • Isomorphisms
      • Homomorphisms, Part I
      • Homomorphisms, Part II
      • Quotient groups: Introduction to cosets
      • Lagrange's theorem
      • Multiplying/adding cosets
      • Quotient group examples
      • Quotient group proofs
      • Normal subgroups
      • First isomorphism theorem
      • Introduction to rings: Introduction to rings
      • Integral domains and fields
      • Polynomial rings, Part I
      • Polynomial rings, Part II
      • Factoring polynomials
      • Quotient rings: Ring homomorphisms
      • Introduction to quotient rings
      • Quotient ring $\mathbb{Z}_7[x]/ \langle x^2-1\rangle$
      • Quotient ring $\mathbb{R}[x]/ \langle x^2 +1\rangle$
      • $F[x]/ \langle g(x)\rangle$ is/isn't a field, Part I
      • Maximal ideals
      • $F[x]/ \langle g(x)\rangle$ is/isn't a field, Part II
      • Appendices: Proof of the GCD theorem
      • Composition table for $D_4$
      • Symbols and notations
      • Essential theorems
      • Index: Index of terms

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