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Full Description
A Concrete Approach to Abstract AlgebraInsolvability of the Quintic, Second Edition provides a primer and reference on abstract algebra for readers whose interests lie in mathematics and information and physical sciences. Adopting the unique `rings first' approach, the work provides a gentle transition into abstract structures that will make abstract algebra more natural to interested readers. In addition to introducing the major concepts of modern algebra, the book covers numerous applications which are intended to illustrate the concepts and convince the reader of the utility and relevance of algebra today. This Second Edition features 40% new or revised content, including complete and self-contained proofs of the fundamental theorems of algebra and the Insolvability of the Quintic, and new coverage of commutative rings and linear transformations.
Contents
1. What this book is about and who this book is for 2. Proof and Intuition 3. The Integers 4. The Rational Numbers and the Real Numbers 5. The Complex Numbers 6. The Integers 7. Group Theory: A First Look 8. Roots and Factorization of Polynomials over the integrals 9. Polynomials over arbitrary fields 10. Difference Functions and Partial Fractions 11. An Introduction to Linear Algebra and Vector Spaces 12. Degrees and Galois Groups of Field Extensions 13. Geometric Constructions 14. Group Theory: Solvable and Symmetric Groups 15. Insolvability of the Quintic 16. Values of Trigonometric Functions 17. Additional Topics
