Algebras and Representations MATH 3193 2016 1st edition by Alison Parker, Oliver King

Algebras and Representations MATH 3193 (2016 1st Edition) by Alison Parker and Oliver King is a textbook designed for students studying algebra and its applications in the field of mathematics. The book focuses on the theory and representations of algebraic structures, providing both theoretical foundations and practical applications. Here is a description of the key content and structure of the book:

Book Description:

This textbook explores the subject of algebras and their representations, which are fundamental concepts in modern abstract algebra. The book is primarily aimed at undergraduate mathematics students who have a solid background in basic algebra, linear algebra, and abstract mathematics. The material is structured to take students from fundamental concepts to more advanced topics in algebraic structures and their representations.

Key Features:

1. Introduction to Algebras:

   • The text begins by introducing the basics of algebras, including various types of algebras such as associative algebras, Lie algebras, and matrix algebras.
   • Concepts such as modules, vector spaces, and subalgebras are explored in detail.

2. Representations of Algebras:

   • A major focus is on how algebras can act on vector spaces through representations.
   • The book covers different representation theories, including finite-dimensional representations, irreducibility, and characters.

3. Structure Theory:

   • The book delves into the structure of algebras, discussing the Jordan canonical form, Wedderburn’s theorem, and other critical results in algebra.

4. Applications:

   • Throughout the book, the authors provide practical examples to show how algebraic structures are used in various mathematical and applied contexts, including physics, computer science, and other branches of mathematics.

5. Exercises and Examples:

   • A wide range of exercises are provided, allowing students to test their understanding and apply what they have learned.
   • Solutions or hints are often given to help students through more difficult problems.

6. Clear Exposition and Approach:

   • The authors are known for their clear and engaging writing style, making complex topics accessible without oversimplifying important details.
   • The book is structured to be a comprehensive reference, starting from introductory topics and progressing to more advanced material.

Intended Audience:

• This textbook is aimed primarily at mathematics undergraduates, particularly those taking courses in abstract algebra, linear algebra, and algebraic structures.
• It can also serve as a reference for more advanced students or researchers in the field of algebra and its applications.