This work is intended as an upper-division laboratory supplement for courses in abstract algebra. It consists of several Mathematica packages that the authors have programmed as a foundation with two collections of labs for group theory and ring theory built on this base. Additionally, there is a "u
Exploring Abstract Algebra With Mathematica®
✍ Scribed by Allen C. Hibbard, Kenneth M. Levasseur (auth.)
- Publisher
- Springer-Verlag New York
- Year
- 1999
- Tongue
- English
- Leaves
- 476
- Edition
- 1
- Category
- Library
No coin nor oath required. For personal study only.
✦ Synopsis
• What is Exploring Abstract Algebra with Mathematica? Exploring Abstract Algebra with Mathematica is a learning environment for introductory abstract algebra built around a suite of Mathematica packages enti tled AbstractAlgebra. These packages are a foundation for this collection of twenty-seven interactive labs on group and ring theory. The lab portion of this book reflects the contents of the Mathematica-based electronic notebooks con tained in the accompanying CD-ROM. Students can interact with both the printed and electronic versions of the material in the laboratory and look up details and reference information in the User's Guide. Exercises occur in the stream of the text of labs, providing a context in which to answer. The notebooks are designed so that the answers to the questions can either be entered into the electronic notebook or written on paper, whichever the instructor prefers. The notebooks support versions 2. 2 and 3. 0-4. 0 and are compatible with all platforms that run Mathematica. This work can be used to supplement any introductory abstract algebra text and is not dependent on any particular text. The group and ring labs have been cross referenced against some of the more popular texts. This information can be found on our web site at http://www . central. edu/eaarn. htrnl (which is also mirrored at http://www . urnl. edu/Dept/Math/eaarn/eaarn. htrnl). If your favorite text isn't on our list, it can be added upon request by contacting either author.
✦ Table of Contents
Front Matter....Pages i-xiii
Front Matter....Pages 1-1
Using Symmetry to Uncover a Group....Pages 3-10
Determining the Symmetry Group of a Given Figure....Pages 11-16
Is This a Group?....Pages 17-19
Let’s Get These Orders Straight....Pages 20-31
Subversively Grouping Our Elements....Pages 32-44
Cycling Through the Groups....Pages 45-52
Permutations....Pages 53-63
Isomorphisms....Pages 64-73
Automorphisms....Pages 74-80
Direct Products....Pages 81-87
Cosets....Pages 88-94
Normality and Factor Groups....Pages 95-100
Group Homomorphisms....Pages 101-110
Rotational Groups of Regular Polyhedra....Pages 111-116
Front Matter....Pages 117-117
Introduction to Rings and Ringoids....Pages 119-126
Introduction to Rings, Part 2....Pages 127-133
An Ideal Part of Rings....Pages 134-139
What Does ℤ[ i ] / < a + b i > Look Like?....Pages 140-147
Ring Homomorphisms....Pages 148-155
Polynomial Rings....Pages 156-166
Front Matter....Pages 117-117
Factoring and Irreducibility....Pages 167-181
Roots of Unity....Pages 182-189
Cyclotomic Polynomials....Pages 190-199
Quotient Rings of Polynomials....Pages 200-208
Quadratic Field Extensions....Pages 209-214
Factoring in ℤ[√ d ]....Pages 215-226
Finite Fields....Pages 227-233
Front Matter....Pages 235-235
Introduction to Abstract Algebra....Pages 237-251
Groupoids....Pages 252-320
Ringoids....Pages 321-392
Morphoids....Pages 393-413
Additional Functionality....Pages 414-443
Back Matter....Pages 445-469
✦ Subjects
Algebra;Analysis;Algorithms;Math Applications in Computer Science;Mathematical Methods in Physics;Numerical and Computational Physics
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