A concrete approach to abstract algebra : from the integers to the insolvability of the quintic

"Beginning with a concrete and thorough examination of familiar objects like integers, rational numbers, real numbers, complex numbers, complex conjugation and polynomials, in this unique approach, the author builds upon these familiar objects and then uses them to introduce and motivate advanced concepts in algebra in a manner that is easier to understand for most students."--BOOK JACKET. Ch. 1. What This Book Is about and Who This Book Is for -- Ch. 2. Proof and Intuition -- Ch. 3. Integers -- Ch. 4. Rational Numbers and the Real Numbers -- Ch. 5. Complex Numbers -- Ch. 6. Fundamental Theorem of Algebra -- Ch. 7. Integers Modulo n -- Ch. 8. Group Theory -- Ch. 9. Polynomials over the Integers and Rationals -- Ch. 10. Roots of Polynomials of Degree Less than 5 -- Ch. 11. Rational Values of Trigonometric Functions -- Ch. 12. Polynomials over Arbitrary Fields -- Ch. 13. Difference Functions and Partial Fractions -- Ch. 14. Introduction to Linear Algebra and Vector Spaces -- Ch. 15. Degrees and Galois Groups of Field Extensions -- Ch. 16. Geometric Constructions -- Ch. 17. Insolvability of the Quintic