Abstract algebra is a branch of mathematics that studies the structure of mathematical systems and the relationships between objects in those systems. It is a critical subject for students who are studying mathematics, computer science, engineering, and other related fields.

Richard Klima, Neil Sigmon, and Ernest Stizinger have written a comprehensive and accessible study of applied abstract algebra with the third edition of their book, Applied Abstract Algebra with Maple and MATLAB. The book is designed to help students learn about abstract algebra and how to apply it to real-world problems.

One of the unique features of this book is its integration of Maple and MATLAB software. The authors use these software programs to illustrate and explore the concepts presented in the book. This makes it easier for students to understand and apply the techniques presented, and it provides hands-on experience with mathematical software that is widely used in many fields.

**TABLE OF CONTENTS**

**Preliminary Mathematics**

- Permutation Groups
- Cosets and Quotient Groups
- Rings and Euclidean Domains
- Finite Fields
- Finite Fields with Maple
- Finite Fields with MATLAB
- The Euclidean Algorithm

**2 Block Designs**

- General Properties
- Hadamard Matrices
- Hadamard Matrices with Maple
- Hadamard Matrices with MATLAB
- Difference Sets
- Difference Sets with Maple
- Difference Sets with MATLAB

**3 Error-Correcting Codes**

- General Properties
- Hadamard Codes
- Reed-Muller Codes
- Reed-Muller Codes with Maple
- Reed-Muller Codes with MATLAB
- Linear Codes
- Hamming Codes with Maple
- Hamming Codes with MATLAB

**4 BCH Codes**

- Construction
- Error Correction
- BCH Codes with Maple
- Construction
- Error Correction
- BCH Codes with MATLAB
- Construction
- Error Correction

**5 Reed-Solomon Codes**

- Construction
- Error Correction
- Error Correction Method Proof
- Reed-Solomon Codes with Maple
- Construction
- Error Correction
- Reed-Solomon Codes with MATLAB
- Construction
- Error Correction
- Reed-Solomon Codes in Voyager 2

**6 Algebraic Cryptography **

- Two Elementary Cryptosystems
- Shift Ciphers
- Affine Ciphers
- Shift and Affine Ciphers with Maple
- Shift Ciphers
- Affine Ciphers
- Shift and Affine Ciphers with MATLAB
- Shift Ciphers
- Affine Ciphers
- Hill Ciphers
- Hill Ciphers with Maple
- Hill Ciphers with MATLAB
- The Two-Message Problem

**7 Vigen`ere Ciphers**

- Encryption and Decryption
- Cryptanalysis
- The Index of Coincidence
- Determining the Keyword Length
- Determining the Keyword
- Vigen`ere Ciphers with Maple
- Encryption and Decryption
- Cryptanalysis
- Vigen`ere Ciphers with MATLAB
- Encryption and Decryption
- Cryptanalysis

**8 RSA Ciphers**

- Preliminary Mathematics
- Encryption and Decryption
- RSA Ciphers with Maple
- RSA Ciphers with MATLAB
- Efficiency and Security Issues
- Primality Testing
- Integer Factorization
- Modular Exponentiation
- Digital Signatures
- The Diffie-Hellman Key Exchange with RSA
- Discrete Logarithms with Maple
- Discrete Logarithms with MATLAB

**9 Elliptic Curve Cryptography**

- ElGamal Ciphers
- ElGamal Ciphers with Maple
- ElGamal Ciphers with MATLAB
- Elliptic Curves
- Elliptic Curves with Maple
- Elliptic Curves with MATLAB
- Elliptic Curve Cryptography
- Elliptic Curve Cryptography with Maple
- Elliptic Curve Cryptography with MATLAB

**10** **The Advanced Encryption Standard **

- Text Setup
- The S-Box
- Key Generation
- The Initial Key
- The Key Schedule
- Encryption
- The AES Layers
- ByteSub
- ShiftRow
- MixColumn
- AddRoundKey
- Decryption
- AES with Maple
- Construction of Initial Parameters
- The Encryption Layers
- The Decryption Layers
- Encryption and Decryption
- AES with MATLAB
- Construction of Initial Parameters
- The Encryption Layers
- The Decryption Layers
- Encryption and Decryption

**11 P ́olya Theory**

- Group Actions
- Burnside’s Theorem
- The Cycle Index
- The Pattern Inventory
- The Pattern Inventory with Maple
- The Pattern Inventory with MATLAB
- Switching Functions

**12 Graph Theory **

- The Cycle Index of Sn
- The Cycle Index of Sn with Maple
- The Cycle Index of Sn with MATLAB
- Counting Undirected Graphs
- Counting Undirected Graphs with Maple
- Counting Undirected Graphs with MATLAB

**13 Symmetry in Western Music**

- Group Actions and Scales
- Group Actions and Chords
- Group Actions and Chords with Maple
- Group Actions and Chords with MATLAB
- Cayley Graphs for Z12
- Twelve-Tone Rows
- Twelve-Tone Rows with Maple
- Twelve-Tone Rows with MATLAB

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Another great feature of this book is its clear writing style. The authors present the concepts in a straightforward and easy-to-understand manner, making it accessible to students of all levels. The book also includes numerous examples and exercises, as well as explanations of key concepts, to help students understand and practice the techniques presented.

The book covers a wide range of topics in abstract algebra, including groups, rings, fields, and modules. Each chapter is designed to build upon the concepts presented in previous chapters, so students can gradually develop their understanding of the subject. This makes it a great resource for students who are just starting to study abstract algebra, as well as for those who want to deepen their understanding of the subject.

We are pleased to announce that the third edition of Applied Abstract Algebra with Maple and MATLAB by Richard Klima, Neil Sigmon, and Ernest Stizinger is available in PDF format, so students can easily download and access it. Whether you prefer to study on your own or with a teacher, this book is a valuable resource for anyone who wants to learn about applied abstract algebra and how to apply it to real-world problems.

In conclusion, Applied Abstract Algebra with Maple and MATLAB is a comprehensive and accessible study of abstract algebra and its applications. Its integration of mathematical software, clear writing style, and numerous examples and exercises make it an ideal resource for students, teachers, and anyone looking to improve their understanding of abstract algebra.