A Concrete Approach to Abstract Algebra: From the Integers to the Insolvability of the Quintic
A Concrete Approach to Abstract Algebra presents a solid and highly accessible introduction to abstract algebra by providing details on the building blocks of abstract algebra.
It begins with a concrete and thorough examination of familiar objects such as integers, rational numbers, real numbers, complex numbers, complex conjugation, and polynomials. The author then builds upon these familiar objects and uses them to introduce and motivate advanced concepts in algebra in a manner that is easier to understand for most students. Exercises provide a balanced blend of difficulty levels, while the quantity allows the instructor a latitude of choices. The final four chapters present the more theoretical material needed for graduate study.
This text will be of particular interest to teachers and future teachers as it links abstract algebra to many topics which arise in courses in algebra, geometry, trigonometry, precalculus, and calculus.
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Chapter 4 The Rational Numbers and the Real Numbers
Chapter 5 The Complex Numbers
Chapter 6 The Fundamental Theorem of Algebra
Chapter 7 The Integers Modulo n
Chapter 8 Group Theory
Chapter 11 Rational Values of Trigonometric Functions
Chapter 12 Polynomials over Arbitrary Fields
Chapter 13 Difference Functions and Partial Fractions
Chapter 14 An Introduction to Linear Algebra and Vector Spaces
Chapter 15 Degrees and Galois Groups of Field Extensions
Chapter 16 Geometric Constructions
Chapter 17 Insolvability of the Quintic