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A Concrete Approach to Abstract Algebra: From the Integers to the Insolvability of the Quintic  무료배송

 
지은이 : Jeffrey Bergen
출판사 : Academic Press
페이지수 : 720
ISBN : 9780123749413
예상출고일 : 입금확인후 2일 이내
주문수량 :
도서가격 : 45,000원 ( 무료배송 )
적립금 : 1,350 Point
     

 

A Concrete Approach to Abstract Algebra begins 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 familar objects and then uses them to introduce and motivate advanced concepts in algebra in a manner that is easier to understand for most students. The text will be of particular interest to teachers and future teachers as it links abstract algebra to many topics wich arise in courses in algebra, geometry, trigonometry, precalculus and calculus.  The final four chapters present the more theoretical material needed for graduate study.


Ancillary list: * Online ISM- http://textbooks.elsevier.com/web/manuals.aspx?isbn=9780123749413 * Online SSM- http://www.elsevierdirect.com/product.jsp?isbn=9780123749413 * Ebook- http://www.elsevierdirect.com/product.jsp?isbn=9780123749413



  • Presents a more natural 'rings first' approach to effectively leading the student into the the abstract material of the course by the use of motivating concepts from previous math courses to guide the discussion of abstract algebra
  • Bridges the gap for students by showing how most of the concepts within an abstract algebra course are actually tools used to solve difficult, but well-known problems
  • Builds on relatively familiar material (Integers, polynomials) and moves onto more abstract topics, while providing a historical approach of introducing groups first as automorphisms
  • Exercises provide a balanced blend of difficulty levels, while the quantity allows the instructor a latitude of choices

A Concrete Approach to Abstract Algebra begins 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 familar objects and then uses them to introduce and motivate advanced concepts in algebra in a manner that is easier to understand for most students. The text will be of particular interest to teachers and future teachers as it links abstract algebra to many topics wich arise in courses in algebra, geometry, trigonometry, precalculus and calculus.  The final four chapters present the more theoretical material needed for graduate study.

1. What This Book Is about and Who This Book Is for
2. Proof and Intuition
3. The Integers
4. Rational Numbers and the Real Numbers
5. The Complex Numbers
6. The fundamental Theorem of Algebra
7. The Integers Modulo n
8. Group Theory
9. Polynomials over the Integers and Rationals
10. Roots of Polynomials of Degree Less than 5
11. Rational Values of Trigonometric Functions
12. Polynomials over Arbitrary Fields
13. Difference Functions and Partial Fractions
14. An Introduction to Linear Algebra and Vector Spaces
15. Degrees and Galois Groups of Field Extensions
16. Geometric Constructions
17. The Insolvability of the Quintic
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