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Introduction to Abstract Algebra by Samir Siksek

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Introduction to Abstract Algebra written by Samir Siksek . This is an other great mathematics book cover the following topics of Problem Solving.

  • Chapter I. Prologue
    Who Am I? A Jolly Good Read!, Proofs, Acknowledgements and Corrections

  • Chapter II. FAQ

  • Chapter III. Algebraic Reorientation
    Sets, Binary Operations, Vector Operations, Operations on PolynomialsComposition of Functions, Composition Tables, Commutativity and Associativity, Where are the Proofs?, The Quaternionic Number System (do not read)

  • Chapter IV. Matrices—Read On Your Own
    What are Matrices?, Matrix Operations, Where do matrices come from?, How to think about matrices?, Why Column Vectors?, Multiplicative Identity and Multiplicative Inverse, Rotations

  • Chapter V. Groups
    The Definition of a Group, First Examples (and Non-Examples), Abelian Groups, Symmetries of a Square

  • Chapter VI. First Theorems
    Getting Relaxed about Notation, Additive Notation

  • Chapter VII. More Examples of Groups
    Matrix Groups I, Congruence Classes

  • Chapter VIII. Orders and Lagrange’s Theorem
    The Order of an Element, Lagrange’s Theorem—Version

  • Chapter IX. Subgroups
    What Were They Again?, Criterion for a Subgroup, Roots of Unity, Matrix Groups II, Differential Equations, Non-Trivial and Proper Subgroups, Lagrange’s Theorem—Version 2

  • Chapter X. Cyclic Groups and Cyclic Subgroups
    Lagrange Revisited, Subgroups of Z

  • Chapter XI. Isomorphisms

  • Chapter XII. Cosets
    Geometric Examples, Solving Equations, Index, The First Innermost Secret of Cosets, The Second Innermost Secret of Cosets, Lagrange Super-Strength

  • Chapter XIII. Quotient Groups
    Congruences Modulo Subgroups, Congruence Classes and Cosets, R/Z, R/Q, Well-Defined and Proofs

  • Chapter XIV. Symmetric Groups
    Motivation, Injections, Surjections and Bijections, The Symmetric Group, A Nice Application of Lagrange’s Theorem, Cycle Notation, Permutations and Transpositions, Even and Odd Permutations

  • Chapter XV. Rings
    Definition, Examples, Subrings, The Unit Group of a Ring, The Unit Group of the Gaussian Integers 117

  • Chapter XVI. Fields

  • Chapter XVII. Congruences Revisited
    Units in Z/mZ, Fermat’s Little Theorem, Euler’s Theorem, Vale Dicere

  • Appendices
  • Appendix A. 2012 Introduction to Abstract Algebra Paper
  • Appendix B. 2013 Introduction to Abstract Algebra Paper
  • Appendix C. 2014 Introduction to Abstract Algebra Paper
  • Appendix D. 2015 Introduction to Abstract Algebra Paper
  • Appendix E. The Forgotten Joys of Analytic Irresponsibility
  • E.1. The Mathematical Equivalent of an X-Rated DVD
  • E.2. Nothing to see here—move along please
  • Download free pdf Introduction to Abstract Algebra by Samir Siksek
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