Abstract Algebra

Abstract Algebra

by Jonathan K. Hodge, Steven Schlicker, Ted Sundstrom
Released December 2013
Publisher(s): Chapman and Hall/CRC
ISBN: 9781466567085

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Book description

Emphasizing active learning, this text not only teaches abstract algebra but also provides a deeper understanding of what mathematics is, how it is done, and how mathematicians think. The book can be used in both rings-first and groups-first abstract algebra courses.

Table of contents

  1. Front Cover
  2. Contents (1/3)
  3. Contents (2/3)
  4. Contents (3/3)
  5. Note to Students
  6. Preface
  7. I. The Integers
    1. 1. The Integers: An Introduction (1/2)
    2. 1. The Integers: An Introduction (2/2)
    3. 2. Divisibility of Integers (1/3)
    4. 2. Divisibility of Integers (2/3)
    5. 2. Divisibility of Integers (3/3)
    6. 3. Greatest Common Divisors (1/2)
    7. 3. Greatest Common Divisors (2/2)
    8. 4. Prime Factorization (1/2)
    9. 4. Prime Factorization (2/2)
  8. II. Other Number Systems
    1. 5. Equivalence Relations and Zn (1/4)
    2. 5. Equivalence Relations and Zn (2/4)
    3. 5. Equivalence Relations and Zn (3/4)
    4. 5. Equivalence Relations and Zn (4/4)
    5. 6. Algebra in Other Number Systems (1/3)
    6. 6. Algebra in Other Number Systems (2/3)
    7. 6. Algebra in Other Number Systems (3/3)
  9. III. Rings
    1. 7. An Introduction to Rings (1/3)
    2. 7. An Introduction to Rings (2/3)
    3. 7. An Introduction to Rings (3/3)
    4. 8. IntegerMultiples and Exponents (1/3)
    5. 8. IntegerMultiples and Exponents (2/3)
    6. 8. IntegerMultiples and Exponents (3/3)
    7. 9. Subrings, Extensions, and Direct Sums (1/4)
    8. 9. Subrings, Extensions, and Direct Sums (2/4)
    9. 9. Subrings, Extensions, and Direct Sums (3/4)
    10. 9. Subrings, Extensions, and Direct Sums (4/4)
    11. 10. Isomorphism and Invariants (1/3)
    12. 10. Isomorphism and Invariants (2/3)
    13. 10. Isomorphism and Invariants (3/3)
  10. IV. Polynomial Rings
    1. 11. Polynomial Rings (1/4)
    2. 11. Polynomial Rings (2/4)
    3. 11. Polynomial Rings (3/4)
    4. 11. Polynomial Rings (4/4)
    5. 12. Divisibility in Polynomial Rings (1/3)
    6. 12. Divisibility in Polynomial Rings (2/3)
    7. 12. Divisibility in Polynomial Rings (3/3)
    8. 13. Roots, Factors, and Irreducible Polynomials (1/3)
    9. 13. Roots, Factors, and Irreducible Polynomials (2/3)
    10. 13. Roots, Factors, and Irreducible Polynomials (3/3)
    11. 14. Irreducible Polynomials (1/4)
    12. 14. Irreducible Polynomials (2/4)
    13. 14. Irreducible Polynomials (3/4)
    14. 14. Irreducible Polynomials (4/4)
    15. 15. Quotients of Polynomial Rings (1/4)
    16. 15. Quotients of Polynomial Rings (2/4)
    17. 15. Quotients of Polynomial Rings (3/4)
    18. 15. Quotients of Polynomial Rings (4/4)
  11. V. More Ring Theory
    1. 16. Ideals and Homomorphisms (1/5)
    2. 16. Ideals and Homomorphisms (2/5)
    3. 16. Ideals and Homomorphisms (3/5)
    4. 16. Ideals and Homomorphisms (4/5)
    5. 16. Ideals and Homomorphisms (5/5)
    6. 17. Divisibility and Factorization in Integral Domains (1/2)
    7. 17. Divisibility and Factorization in Integral Domains (2/2)
    8. 18. From Z to C (1/4)
    9. 18. From Z to C (2/4)
    10. 18. From Z to C (3/4)
    11. 18. From Z to C (4/4)
  12. VI. Groups
    1. 19. Symmetry (1/3)
    2. 19. Symmetry (2/3)
    3. 19. Symmetry (3/3)
    4. 20. An Introduction to Groups (1/3)
    5. 20. An Introduction to Groups (2/3)
    6. 20. An Introduction to Groups (3/3)
    7. 21. Integer Powers of Elements in a Group (1/2)
    8. 21. Integer Powers of Elements in a Group (2/2)
    9. 22. Subgroups (1/3)
    10. 22. Subgroups (2/3)
    11. 22. Subgroups (3/3)
    12. 23. Subgroups of Cyclic Groups (1/2)
    13. 23. Subgroups of Cyclic Groups (2/2)
    14. 24. The Dihedral Groups (1/2)
    15. 24. The Dihedral Groups (2/2)
    16. 25. The Symmetric Groups (1/3)
    17. 25. The Symmetric Groups (2/3)
    18. 25. The Symmetric Groups (3/3)
    19. 26. Cosets and Lagrange’s Theorem (1/3)
    20. 26. Cosets and Lagrange’s Theorem (2/3)
    21. 26. Cosets and Lagrange’s Theorem (3/3)
    22. 27. Normal Subgroups and Quotient Groups (1/5)
    23. 27. Normal Subgroups and Quotient Groups (2/5)
    24. 27. Normal Subgroups and Quotient Groups (3/5)
    25. 27. Normal Subgroups and Quotient Groups (4/5)
    26. 27. Normal Subgroups and Quotient Groups (5/5)
    27. 28. Products of Groups (1/3)
    28. 28. Products of Groups (2/3)
    29. 28. Products of Groups (3/3)
    30. 29. Group Isomorphisms and Invariants (1/6)
    31. 29. Group Isomorphisms and Invariants (2/6)
    32. 29. Group Isomorphisms and Invariants (3/6)
    33. 29. Group Isomorphisms and Invariants (4/6)
    34. 29. Group Isomorphisms and Invariants (5/6)
    35. 29. Group Isomorphisms and Invariants (6/6)
    36. 30. Homomorphisms and Isomorphism Theorems (1/3)
    37. 30. Homomorphisms and Isomorphism Theorems (2/3)
    38. 30. Homomorphisms and Isomorphism Theorems (3/3)
    39. 31. The Fundamental Theorem of Finite Abelian Groups (1/3)
    40. 31. The Fundamental Theorem of Finite Abelian Groups (2/3)
    41. 31. The Fundamental Theorem of Finite Abelian Groups (3/3)
    42. 32. The First Sylow Theorem (1/3)
    43. 32. The First Sylow Theorem (2/3)
    44. 32. The First Sylow Theorem (3/3)
    45. 33. The Second and Third Sylow Theorems (1/2)
    46. 33. The Second and Third Sylow Theorems (2/2)
  13. VII. Special Topics
    1. 34. RSA Encryption (1/2)
    2. 34. RSA Encryption (2/2)
    3. 35. Check Digits (1/2)
    4. 35. Check Digits (2/2)
    5. 36. Games: NIM and the 15 Puzzle (1/3)
    6. 36. Games: NIM and the 15 Puzzle (2/3)
    7. 36. Games: NIM and the 15 Puzzle (3/3)
    8. 37. Finite Fields, the Group of Units in Zn, and Splitting Fields (1/4)
    9. 37. Finite Fields, the Group of Units in Zn, and Splitting Fields (2/4)
    10. 37. Finite Fields, the Group of Units in Zn, and Splitting Fields (3/4)
    11. 37. Finite Fields, the Group of Units in Zn, and Splitting Fields (4/4)
    12. 38. Groups of Order 8 and 12: Semidirect Products of Groups (1/3)
    13. 38. Groups of Order 8 and 12: Semidirect Products of Groups (2/3)
    14. 38. Groups of Order 8 and 12: Semidirect Products of Groups (3/3)
  14. A. Functions (1/3)
  15. A. Functions (2/3)
  16. A. Functions (3/3)
  17. B. Mathematical Induction and theWell-Ordering Principle (1/5)
  18. B. Mathematical Induction and theWell-Ordering Principle (2/5)
  19. B. Mathematical Induction and theWell-Ordering Principle (3/5)
  20. B. Mathematical Induction and theWell-Ordering Principle (4/5)
  21. B. Mathematical Induction and theWell-Ordering Principle (5/5)

Product information

  • Title: Abstract Algebra
  • Author(s): Jonathan K. Hodge, Steven Schlicker, Ted Sundstrom
  • Release date: December 2013
  • Publisher(s): Chapman and Hall/CRC
  • ISBN: 9781466567085