A Concrete Approach to Abstract Algebra
From the Integers to the Insolvability of the Quintic
2nd Edition
Will be published approx. on 1. August 2029
Book
Paperback/Softback
976 pages
978-0-12-805148-1 (ISBN)
Description
A Concrete Approach to Abstract Algebra: From the Integers to the Insolvability 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.
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.
More details
Edition
2nd edition
Language
English
Place of publication
San Diego
United States
Publishing group
Elsevier Science Publishing Co Inc
Target group
College/higher education
(senior) Undergraduate students in algebraic and discrete mathematics seeking to move to graduate studies or into teaching who use the work as a foundational reference. Readers from across the physical sciences seeking to use algebraic structures with exact proofs. Application specialists routinely called on to use integers, group theory and complex algebraic structures.
Product notice
Paperback (trade)
Unsewn / adhesive bound
Dimensions
Height: 235 mm
Width: 191 mm
ISBN-13
978-0-12-805148-1 (9780128051481)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Other editions
Previous edition
Jeffrey Bergen
A Concrete Approach to Abstract Algebra
From the Integers to the Insolvability of the Quintic
Book
03/2010
Academic Press
€94.50
Shipment within 10-15 days
Person
Jeffrey Bergen (DePaul, Chicago), received his B.S. in Mathematics from Brooklyn College in 1976. He received his M.S. in 1977 and Ph.D. in 1981 from the University of Chicago. His DePaul career began in 1981, where he continues to do research in the branch of abstract algebra known as noncommutative ring theory. His research has received external support from the English Speaking Union, the National Science Foundation, and the National Security Agency. He has given lectures in 7 countries and co-authored papers with 16 mathematicians around the world. In 2001, he received the Excellence in Teaching Award from the College of Liberal Arts and Sciences and, in 2007, received their Cortelyou-Lowery Award for Excellence.
Content
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 Numbers6. 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
2. Proof and Intuition
3. The Integers
4. The Rational Numbers and the Real Numbers
5. The Complex Numbers6. 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