[No longer freely available] Applied Abstract Algebra

Introduces a wide range of abstract algebra with relevant and interesting applications, from error-correcting codes to cryptography to the group theory of Rubik's cube. Also covers topics such as the Euclidean algorithm, encryption, and permutations.

**Tag(s):**
Linear Algebra

**Publication date**: 01 Jun 2004

**ISBN-10**:
0801878225

**ISBN-13**:
n/a

**Paperback**:
344 pages

**Views**: 19,332

**Type**: Textbook

**Publisher**:
The Johns Hopkins University Press

**License**:
n/a

**Post time**: 03 Sep 2006 11:36:31

[No longer freely available] Applied Abstract Algebra

Introduces a wide range of abstract algebra with relevant and interesting applications, from error-correcting codes to cryptography to the group theory of Rubik's cube. Also covers topics such as the Euclidean algorithm, encryption, and permutations.

Book Excerpts:

This text is based on notes which have been used in teaching at Texas A&M at Commerce, and at the US Naval Academy, for several semesters. The notes were used to to teach three different courses. One, a first course in modern algebra, emphasizing applications and once-a-week computer labs, to students who have only had a "fundamentals in mathematics" course and a matrix theory course. This course covered some of chapters 1, 2, 3, 4 and 5. The second course was a course on error-correcting codes. This course covered chapters 2 and 3 in more detail, and chapter 6. The third course was given to a class consisting mostly of computer science graduate students.

This book covers basic topics such as the Euclidean algorithm, encryption, and permutations. Hamming codes and Reed-Solomon codes used on today's CDs are also discussed. The authors present examples as diverse as "Rotation," available on the Nokia 7160 cell phone, bell ringing, and the game of NIM.

On one hand this book aims to teach some undergraduate modern algebra with an emphasis on applications. These applications are mostly focused on error-correcting codes, the Rubik's cube and cryptography. Each chapter has exercises in GAP (a free computer algebra system) and MAGMA (a non-commercial but not free computer algebra system). Both have extensive capabilities to do modern algebra. Since many of the applications are oriented to communications, it is natural to use computers to understand these applications. In fact, for coding theory and cryptography, many systems use such large parameters that working practical "by hand" is virtually impossible and computers are not just useful but required. Moreover, most chapters end with some "special projects", which might be useful for a student class project.

On the other hand, it can be used to teach an undergraduate course in error-correcting codes or an upper level course in computer science. The GAP and MAGMA exercises are especially helpful for giving the student a grasp of examples. After such a course, the student should be prepared to move onto a more serious treatment.

This text is based on notes which have been used in teaching at Texas A&M at Commerce, and at the US Naval Academy, for several semesters. The notes were used to to teach three different courses. One, a first course in modern algebra, emphasizing applications and once-a-week computer labs, to students who have only had a "fundamentals in mathematics" course and a matrix theory course. This course covered some of chapters 1, 2, 3, 4 and 5. The second course was a course on error-correcting codes. This course covered chapters 2 and 3 in more detail, and chapter 6. The third course was given to a class consisting mostly of computer science graduate students.

This book covers basic topics such as the Euclidean algorithm, encryption, and permutations. Hamming codes and Reed-Solomon codes used on today's CDs are also discussed. The authors present examples as diverse as "Rotation," available on the Nokia 7160 cell phone, bell ringing, and the game of NIM.

On one hand this book aims to teach some undergraduate modern algebra with an emphasis on applications. These applications are mostly focused on error-correcting codes, the Rubik's cube and cryptography. Each chapter has exercises in GAP (a free computer algebra system) and MAGMA (a non-commercial but not free computer algebra system). Both have extensive capabilities to do modern algebra. Since many of the applications are oriented to communications, it is natural to use computers to understand these applications. In fact, for coding theory and cryptography, many systems use such large parameters that working practical "by hand" is virtually impossible and computers are not just useful but required. Moreover, most chapters end with some "special projects", which might be useful for a student class project.

On the other hand, it can be used to teach an undergraduate course in error-correcting codes or an upper level course in computer science. The GAP and MAGMA exercises are especially helpful for giving the student a grasp of examples. After such a course, the student should be prepared to move onto a more serious treatment.

Tweet

About The Author(s)

No information is available for this author.

No information is available for this author.

Book Categories

Computer Science
Introduction to Computer Science
Introduction to Computer Programming
Algorithms and Data Structures
Artificial Intelligence
Computer Vision
Machine Learning
Neural Networks
Game Development and Multimedia
Data Communication and Networks
Coding Theory
Computer Security
Information Security
Cryptography
Information Theory
Computer Organization and Architecture
Operating Systems
Image Processing
Parallel Computing
Concurrent Programming
Relational Database
Document-oriented Database
Data Mining
Big Data
Data Science
Digital Libraries
Compiler Design and Construction
Functional Programming
Logic Programming
Object Oriented Programming
Formal Methods
Software Engineering
Agile Software Development
Information Systems
Geographic Information System (GIS)

Mathematics
Mathematics
Algebra
Abstract Algebra
Linear Algebra
Number Theory
Numerical Methods
Precalculus
Calculus
Differential Equations
Category Theory
Proofs
Discrete Mathematics
Theory of Computation
Graph Theory
Real Analysis
Complex Analysis
Probability
Statistics
Game Theory
Queueing Theory
Operations Research
Computer Aided Mathematics

Supporting Fields
Web Design and Development
Mobile App Design and Development
System Administration
Cloud Computing
Electric Circuits
Embedded System
Signal Processing
Integration and Automation
Network Science
Project Management

Operating System
Programming/Scripting
Ada
Assembly
C / C++
Common Lisp
Forth
Java
JavaScript
Lua
Rexx
Microsoft .NET
Perl
PHP
R
Python
Rebol
Ruby
Scheme
Tcl/Tk

Miscellaneous
Sponsors