Includes index.

1. The natural numbers -- 2. The integers -- 3. Modular arithmetic -- 4. Polynomials with rational coefficients -- 5. Factorization of polynomials -- 6. Rings -- 7. Subrings and unity -- 8. Integral domains and fields -- 9. Polynomials over a field -- 10. Associates and irreducibles -- 11. Factorization and ideals -- 12. Principal ideal domains -- 13. Primes and unique factorization -- 14. Polynomials with integer coefficients -- 15. Euclidean domains -- 16. Ring homomorphisms -- 17. The kernel -- 18. Rings of cosets -- 19. The isomorphism theorem for rings -- 20. Maximal and prime ideals -- 21. The Chinese remainder theorem -- 22. Symmetries of figures in the plane -- 23. Symmetries of figures in space -- 24. Abstract groups -- 25. Subgroups -- 26. Cyclic groups -- 27. Group homomorphisms -- 28. Group isomorphisms -- 29. Permutations and Cayley's theorem -- 30. More about permutations -- 31. Cosets and Lagrange's theorem -- 32. Groups of cosets -- 33. The isomorphism theorem for groups -- 34. The alternating groups -- 35. Fundamental theorem for finite Abelian groups -- 36. Solvable groups -- 37. Constructions with compass and straightedge -- 38. Constructibility and quadratic field extensions -- 39. The impossibility of certain constructions -- 40. Vector spaces I -- 41. Vector spaces II -- 42. Field extensions and Kronecker's theorem -- 43. Algebraic field extensions -- 44. Finite extensions and constructibility revisited -- 45. The splitting field -- 46. Finite fields -- 47. Galois groups -- 48. The fundamental theorem of Galois theory -- 49. Solving polynomials by radicals.

"As stated in the title, this book is designed for a first course. It requires only a typical calculus sequence as a prerequisite and does not assume any familiarity with linear algebra or complex number."--BOOK JACKET.