A Friendly Introduction to Abstract Algebra
eBook - PDF

A Friendly Introduction to Abstract Algebra

  1. English
  2. PDF
  3. Available on iOS & Android
eBook - PDF

A Friendly Introduction to Abstract Algebra

About this book

A Friendly Introduction to Abstract Algebra 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.The author's pedagogical philosophy is that when students abstract from a wide range of examples, they are better equipped to conjecture, formalize, and prove new ideas in abstract algebra. Thus, students thoroughly explore all concepts through illuminating examples before formal definitions are introduced. The instruction in proof writing is similarly grounded in student exploration and experience. Throughout the book, the author carefully explains where the ideas in a given proof come from, along with hints and tips on how students can derive those proofs on their own.Readers of this text are not just consumers of mathematical knowledge. Rather, they are learning mathematics by creating mathematics. The author's gentle, helpful writing voice makes this text a particularly appealing choice for instructors and students alike. The book's website has companion materials that support the active-learning approaches in the book, including in-class modules designed to facilitate student exploration.

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Yes, you can access A Friendly Introduction to Abstract Algebra by Ryota Matsuura in PDF and/or ePUB format, as well as other popular books in Mathematics & Mathematics General. We have over one million books available in our catalogue for you to explore.

Table of contents

  1. Cover
  2. Title page
  3. Copyright
  4. Contents
  5. Preface
  6. Unit I: Preliminaries
  7. Chapter 1. Introduction to Proofs
  8. Chapter 2. Sets and Subsets
  9. Chapter 3. Divisors
  10. Unit II: Examples of Groups
  11. Chapter 4. Modular Arithmetic
  12. Chapter 5. Symmetries
  13. Chapter 6. Permutations
  14. Chapter 7. Matrices
  15. Unit III: Introduction to Groups
  16. Chapter 8. Introduction to Groups
  17. Chapter 9. Groups of Small Size
  18. Chapter 10. Matrix Groups
  19. Chapter 11. Subgroups
  20. Chapter 12. Order of an Element
  21. Chapter 13. Cyclic Groups, Part I
  22. Chapter 14. Cyclic Groups, Part II
  23. Unit IV: Group Homomorphisms
  24. Chapter 15. Functions
  25. Chapter 16. Isomorphisms
  26. Chapter 17. Homomorphisms, Part I
  27. Chapter 18. Homomorphisms, Part II
  28. Unit V: Quotient Groups
  29. Chapter 19. Introduction to Cosets
  30. Chapter 20. Lagrange’s Theorem
  31. Chapter 21. Multiplying/Adding Cosets
  32. Chapter 22. Quotient Group Examples
  33. Chapter 23. Quotient Group Proofs
  34. Chapter 24. Normal Subgroups
  35. Chapter 25. First Isomorphism Theorem
  36. Unit VI: Introduction to Rings
  37. Chapter 26. Introduction to Rings
  38. Chapter 27. Integral Domains and Fields
  39. Chapter 28. Polynomial Rings, Part I
  40. Chapter 29. Polynomial Rings, Part II
  41. Chapter 30. Factoring Polynomials
  42. Unit VII: Quotient Rings
  43. Chapter 31. Ring Homomorphisms
  44. Chapter 32. Introduction to Quotient Rings
  45. Chapter 33. Quotient Ring Z ₇[𝑥]/⟨𝑥²-1⟩
  46. Chapter 34. Quotient Ring R [𝑥]/⟨𝑥²+1⟩
  47. Chapter 35. 𝐹[𝑥]/⟨𝑔(𝑥)⟩ Is/Isn’t a Field, Part I
  48. Chapter 36. Maximal Ideals
  49. Chapter 37. 𝐹[𝑥]/⟨𝑔(𝑥)⟩ Is/Isn’t a Field, Part II
  50. Appendix A. Proof of the GCD Theorem
  51. Appendix B. Composition Table for 𝐷₄
  52. Appendix C. Symbols and Notations
  53. Appendix D. Essential Theorems
  54. Index of Terms
  55. Back Cover