Vision Group Theory by Nathan Carter is a comprehensive and well-written textbook that covers the essential concepts of group theory. This book is designed for students of mathematics who are interested in learning about the fundamental theories and applications of group theory. The book provides a clear and in-depth explanation of the concepts, making it an ideal resource for students at all levels of mathematical proficiency.
The author has included numerous examples and exercises throughout the text to help students understand and apply the concepts they are learning. Additionally, the book is well-organized and easy to navigate, making it a great resource for students who are studying on their own.
One of the key strengths of Vision Group Theory is its accessibility. The author has made every effort to ensure that the language used in the book is clear and concise, making it easy for students to understand the material. The book also provides a visual approach to the subject, using illustrations and diagrams to help students understand complex concepts.
TABLE OF CONTENTS
What is a group?
- A famous toy
- Considering the cube
- The study of Symmetry
- Rules of a Group
What do groups look like?
- Mapmaking
- A not-so-famous toy
- Mapping a Group
- Cayley Diagrams
- A Touch more Abstract
Why study Groups?
Algebra at last
- Where have all the actions gone?
- Combine, Combine, Combine
- Multiplication Tables
- The Classic Definition
Five Families
- Cyclic Groups
- Abelian Groups
- Dihedral Groups
- Symmetric and Alternating Groups
Subgroups
What do Multiplication tables say about Cayley Diagrams?
- Seeing Subgroups
- Revealing Subgroups
- Cosets
- Lagrange’s Theorem
Products and Quotients
- The Direct Product
- Semidirect Products
- Normal Subgroups and Quotients
- Normalizers
- Conjugacy
The Power of Homomorphisms
- Embeddings and Quotient Maps
- The Fundamental Homomorphism Theorem
- Modular Arithematic
- Direct Products and Relatively Prime Numbers
- The Fundamental Theorem of Abelian Groups
- Semidirect Products Revisited
Sylow Theory
- Group Actions
- Approaching Sylow: Cauchy’s Theorem
- p-groups
- Sylow Theorem
Galois Theory
- The big Question
- More big Questions
- Visualizing Field Extensions
- Irreducible Polynomials
- Galois Groups
- The heart of Galois Theory
- Unsolvability
The book is also available in PDF format, allowing students to easily access and study the material from their computer or mobile device. This is especially useful for students who are unable to attend physical classes or who prefer to study at their own pace. With the PDF format, students can easily search for specific information, make notes, and highlight important sections of the text.
In conclusion, Vision Group Theory by Nathan Carter is an excellent resource for students who are interested in learning about group theory. The book provides a clear and comprehensive overview of the subject, making it an ideal resource for students at all levels of mathematical proficiency. And with the availability of the book in PDF format, students can easily access and study the material at their convenience.
