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Abstract Algebra: A First Course (2nd Edition) by Dan Saracino



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Abstract Algebra: A First Course (2nd Edition) written by Dan Saracino , Colgate University, Hamilton, New York, United States. This book is intended for use in a junior/senior level course in abstract algebra. The main change from the first edition is the addition of five new sections on field extensions and Galois theory, providing enough material for a two semester course. More minor changes include the simplification of some points in the presentation, the addition of some new exercises and the updating of some historical material.

Abstract Algebra: A First Course (2nd Edition) written by Dan Saracino . cover the following topics.

  • 0. Sets and Induction
    1. Binary Operation
    2. Groups
    3. Fundamnetal Theorems about groups
    4. Power of an Element, Cyclic Groups
    5. SubGroups
    6. Direct Product
    7. Functions
    8. Symmetric Groups
    9. Quivalence Relations, Cosets
    10. Countring the Elements of a Finite Group
    11. Normal Subgroups
    12. Homomorphisms
    13. Homomorphisms and Normal Subgroups
    14. Direct Products and Finite Abelian Groups
    15. Sylow Theorems
    16. Rings
    17. Subrings, Ideals and Quotient Rings
    18. Ring Homomorphisms
    19. Polynomials
    20. From Polynomials to Fields
    21. Unique Factorization Domains
    22. Extensions of Fields
    23. Constructions with Straightedge and Compass
    24. Normal and Separable Extensions
    25. Galois Theory
    26. Solvability

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