Abstract algebra An interactive approach Edition by William Paulsen ISBN 1498719766 978-1498719766

Abstract algebra An interactive approach Edition by  William Paulsen – Ebook PDF Instant Download/Delivery: 1498719766, 978-1498719766
Full download Abstract algebra An interactive approach Edition  after payment

Product details: 

ISBN 10: 1498719766 
ISBN 13: 978-1498719766

Author: William Paulsen 

The new edition of Abstract Algebra: An Interactive Approach presents a hands-on and traditional approach to learning groups, rings, and fields. It then goes further to offer optional technology use to create opportunities for interactive learning and computer use.

This new edition offers a more traditional approach offering additional topics to the primary syllabus placed after primary topics are covered. This creates a more natural flow to the order of the subjects presented. This edition is transformed by historical notes and better explanations of why topics are covered.

This innovative textbook shows how students can better grasp difficult algebraic concepts through the use of computer programs. It encourages students to experiment with various applications of abstract algebra, thereby obtaining a real-world perspective of this area.

Each chapter includes, corresponding Sage notebooks, traditional exercises, and several interactive computer problems that utilize Sage and Mathematica® to explore groups, rings, fields and additional topics.

This text does not sacrifice mathematical rigor. It covers classical proofs, such as Abel’s theorem, as well as many topics not found in most standard introductory texts. The author explores semi-direct products, polycyclic groups, Rubik’s Cube®-like puzzles, and Wedderburn’s theorem. The author also incorporates problem sequences that allow students to delve into interesting topics, including Fermat’s two square theorem.

Table of contents: 

Preliminaries

1 Integer Factorization
2 Functions
3 Modular Arithmetic
4 Rational and Real Numbers

Understanding the Group Concept

5 Introduction to Groups
6 Modular Congruence
7 The Definition of a Group

The Structure within a Group

8 Generators of Groups
9 Defining Finite Groups in Sage
10 Subgroups

Patterns within the Cosets of Groups

11 Left and Right Cosets
12 Writing Secret Messages
13 Normal Subgroups
14 Quotient Groups

Mappings between Groups

15 Isomorphisms
16 Homomorphisms
17 The Three Isomorphism Theorems

Permutation Groups

18 Symmetric Groups
19 Cycles
20 Cayley’s Theorem
21 Numbering the Permutations

Building Larger Groups from Smaller Groups

22 The Direct Product
23 The Fundamental Theorem of Finite Abelian Groups
24 Automorphisms
25 Semi-Direct Products

The Search for Normal Subgroups

26 The Center of a Group
27 The Normalizer and Normal Closure Subgroups
28 Conjugacy Classes and Simple Groups
29 The Class Equation and Sylow’s Theorems

Solvable and Insoluble Groups

30 Subnormal Series and the Jordan-Hölder Theorem
31 Derived Group Series
32 Polycyclic Groups
33 Solving the Pyraminx™

Introduction to Rings

34 The Definition of a Ring
35 Entering Finite Rings into Sage
36 Some Properties of Rings

The Structure within Rings

37 Subrings
38 Quotient Rings and Ideals
39 Ring Isomorphisms
40 Homomorphisms and Kernels

Integral Domains and Fields

41 Polynomial Rings
42 The Field of Quotients
43 Complex Numbers
44 Ordered Commutative Rings

Unique Factorization

45 Factorization of Polynomials
46 Unique Factorization Domains
47 Principal Ideal Domains
48 Euclidean Domains

Finite Division Rings

49 Entering Finite Fields in Sage
50 Properties of Finite Fields
51 Cyclotomic Polynomials
52 Finite Skew Fields

The Theory of Fields

53 Vector Spaces
54 Extension Fields
55 Splitting Fields

Galois Theory

56 The Galois Group of an Extension Field
57 The Galois Group of a Polynomial in ℚ
58 The Fundamental Theorem of Galois Theory
59 Applications of Galois Theory

People also search for:

abstract algebra explained
    
abstract algebra example
    
abstract algebra topics
    
what is abstract algebra
    
abstract algebra an inquiry based approach

 

Tags:

William Paulsen,Abstract algebra,An interactive approach