Best Abstract Algebra Books for Beginners to Sharpen Their Analytical Knowledge
Abstract Algebra is the set of advanced topics of algebra that deal with abstract algebraic structures rather than the usual number systems. Concerned with algebraic structures such as groups, rings, vector spaces, and algebras, it is one of the basic pillars of modern mathematics. Here you will get some of the best Abstract Algebra books if you want to achieve a good mathematical maturity and to build mathematical thinking and skill.
This Book Features:
- An introductory chapter traces concepts of abstract algebra from their historical roots
- Plenty of math exercises
- Chapters including solutions to mathematical equations with detailed explanation
- Major theorems of modern algebra in simple terms
This is an amazing book for the first introduction to modern algebra. It is primarily intended for an abstract algebra course whose main purpose is to enable students to do computations and write proofs. Gallian's text stresses the importance of obtaining a solid introduction to the traditional topics of abstract algebra, while at the same time presenting it as a contemporary and very much an active subject which is currently being used by working physicists, chemists, and computer scientists. This Abstract Algebra book is very well organized with lots of examples of problems which is nice for such a difficult subject. Very thorough introduction for those who need a better foundation in the basics of the algebraic theory.
CONTEMPORARY ABSTRACT ALGEBRA Provides:
- Basic overview of advanced mathematics
- Illustrative and well-constructed Math exercises with solution manuals
- Undergraduate algebra courses including groups, rings, and fields
- Major theorems of modern algebra in simple terms
ABSTRACT ALGEBRA is an amazing book with so many examples of algebra in a logical order. It provides the basis for the integration of all the crazy subdivisions of abstract algebra under the unifying context of Category Theory. There is a vast amount of exercises and proofs ranging from the very easy to quite difficult and detailed enough for beginners to understand. This is a superb textbook on algebra that is notable for its extremely clear and well-organized presentation.
There is a solid introduction to representation theory via group rings and Wedderburn's theorem - an approach which is really more useful for applications than a pure group-theoretic introduction might have been.
A great resource for those learning graduate algebra.
# Chapter 1-6: Group Theory
# Chapter 7-9: Ring Theory
# Chapter 10-12: Module Theory
# Chapter 13-14: Field and Galois Theory
# Chapter 15-17: Algebraic Geometry, Commutative Algebra, and Homological Algebra
# Chapter 18-19: Representation Theory
A First Course in Abstract Algebra is an in-depth introduction to abstract algebra. Focused on groups, rings, and fields, this textbook gives students a firm foundation for more specialized work by emphasizing an understanding of the nature of algebraic structures. All the chapter exercises of this book are broken down in 3 categories: computations, concepts, and theory. The book is an extremely good introduction to how to prove theorems for those who have not yet done it before. The theorem, exercises, and proofs of this book are well organized and well written. A great resource for all readers interested in abstract algebra.
Pure Mathematics for Beginners is an excellent book for beginners who would like to learn what pure mathematics is. It consists of a series of lessons in Logic, Set Theory, Abstract Algebra, Number Theory, Real Analysis, Topology, Complex Analysis, and Linear Algebra. The 16 lessons in this book cover basic through intermediate material from each of these 8 topics. In addition, all the proof-writing skills that are essential for advanced study in mathematics are covered and reviewed extensively.
All concepts and theorems are explained clearly and followed by plenty of examples. All the problems come with detailed solutions and extra explanations.
This book is very useful for understanding the mathematics used in proving theorems in the mathematical treatments of quantum mechanics and is great for self-study since it provides clear and thorough solutions to the problems which can be consulted after working through the problems on your own.
This Math Book Features:
- 16 lessons in 8 subject areas
- A friendly but rigorous treatment of all the mathematics covered
- Additional analyses before and after proofs to help students gain a deep understanding of the subject matter with the minimum amount of effort
- A problem set after each lesson containing problems arranged by difficulty level
- An introductory college course in higher mathematics.
- High school teachers working with advanced math students.
- High school and college students wishing to see the type of mathematics they would be exposed to as a math major.
The Second Edition of this ABSTRACT ALGEBRA maintains the clear exposition, logical organization, and accessible breadth of coverage that have been its hallmarks. It plunges directly into algebraic structures and incorporates an unusually large number of examples to clarify abstract concepts as they arise.
Proofs of theorems do more than just prove the stated results. Most of the exercises range from easy to moderately difficult and ask for understanding of ideas rather than flashes of insight.
The new edition introduces five new sections on field extensions and Galois theory, increasing its versatility by making it appropriate for a two-semester as well as a one-semester course.
It manages to express the subject in a way that is concise and thorough. This book divides up abstract algebra into a bunch of short lessons that are easy to digest.