Abstract Algebra is a math book written by David S Dummit. The book focuses on teaching the readers about abstract algebra and at the same time, letting the readers experience the beauty of the interwoven network of mathematical aspects. The start of the boom is from a basic explanation of algebraic terms and from there on, the story continues.
Abstract Algebra Pdf Review:
The writer starts with basics of algebra and then dives into the complexities of the subject. He then shows how different fields of math are integrated into algebra and how these various fields make a mesh of information and mystery. The author has also added many exercises in the book so that the reader can understand better and can also teat their knowledge. Not only does the reader understand how this algebra is done, he also sees the beauty of mathematics especially the field of abstract algebra which is filled with lattices, structures, rings and so much more.
Abstract Algebra Pdf Features:
- The author has used as many examples as he possibly could because he wants to pump the readers to feel passionate about the subject.
- He has used many examples in which algebra is used so that every aspect of the topic can be discussed.
- There is also a chapter that gives an introduction to Representation theory for the readers to be familiar with that too.
Table of Contents:
Part I: Group Theory.
- Introduction to Groups.
- Quotient Group and Homomorphisms.
- Group Actions.
- Direct and Semidirect Products and Abelian Groups.
- Further Topics in Group Theory.
Part II: Ring Theory.
- Introduction to Rings.
- Euclidean Domains, Principal Ideal Domains and Unique Factorization Domains.
- Polynomial Rings.
Part III: Modules and Vector Spaces.
- Introduction to Module Theory.
- Vector Spaces.
- Modules over Principal Ideal Domains.
Part IV: Field Theory and Galois Theory.
- Field Theory.
- Galois Theory.
Part V: An Introduction to Commutative Rings, Algebraic Geometry and Homological Algebra.
- Commutative Rings and Algebraic Geometry.
- Artinian Rings, Discrete Valuation Rings, and Dedekind Domains.
- Introduction to Homological Algebra and Group Cohomology.
Part VI: Introduction to the Representation Theory of Finite Groups.
- Representation Theory and Character Theory.
- Examples and Applications of Character Theory.
Appendix I: Cartesian Products and Zorn’s Lemma.
Appendix II: Category Theory.
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