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Abstract Algebra by Dan Saracino

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Textbook:: Abstract Algebra: A First Course
Author:: Dan Saracino
Edition:: 2nd
Context:: MATH 3230, MATH 3231
When:: Fall 2024, Spring 2025
Depth:: Comprehensive
Sections:: Section 0-15 (3230), Section 16-26 (3231)

Content Covered

  1. Sets and Induction
  2. Binary Operations
  3. Groups
  4. Fundamental Theorems about Groups
  5. Powers of an Element; Cyclic Groups
  6. Subgroups
  7. Direct Products
  8. Functions
  9. Symmetric Groups
  10. Equivalence Relations; Cosets
  11. Counting the Elements of a Finite Group
  12. Normal Subgroups
  13. Homomorphisms
  14. Homomorphisms and Normal Subgroups
  15. Direct Products and Finite Abelian Groups
  16. Sylow Theorems
  17. Rings
  18. Subrings, Ideals, and Quotient Rings
  19. Ring Homomorphisms
  20. Polynomial
  21. From Polynomial to Fields
  22. Unique Factorization Domains

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