Best Abstract Algebra Books
Here you will get Best Abstract Algebra Books For you.This is an up-to-date list of recommended books.
1. Algebra Part 1 (Quickstudy Reference Guides – Academic)
Author: by Inc. BarCharts
Published at: QuickStudy; Chrt edition (November 11, 2002)
For a subject that is a challenge at all levels of education, this chart covers principles for basic algebra, intermediate algebra and college algebra courses.
2. Math Without Numbers
Author: by Milo Beckman
Published at: Dutton (January 5, 2021)
An illustrated tour of the structures and patterns we call “math” The only numbers in this book are the page numbers. Math Without Numbers is a vivid, conversational, and wholly original guide to the three main branches of abstract mathtopology, analysis, and algebrawhich turn out to be surprisingly easy to grasp.
This book upends the conventional approach to math, inviting you to think creatively about shape and dimension, the infinite and infinitesimal, symmetries, proofs, and how these concepts all fit together. What awaits readers is a freewheeling tour of the inimitable joys and unsolved mysteries of this curiously powerful subject.
Like the classic math allegory Flatland, first published over a century ago, or Douglas Hofstadter’s Godel, Escher, Bach forty years ago, there has never been a math book quite like Math Without Numbers. So many popularizations of math have dwelt on numbers like pi or zero or infinity.
This book goes well beyond to questions such as: How many shapes are there? Is anything bigger than infinity? And is math even true? Milo Beckman shows why math is mostly just pattern recognition and how it keeps on surprising us with unexpected, useful connections to the real world.
3. Algebra, Part 2 (Quick Study)
Author: by S. B. Kizlik
Published at: Barcharts Inc; Lam Crds edition (April 1, 2002)
Algebra 2 is the advanced QuickStudy guide specially designed for students who are already familiar with Algebra 1.
4. Graph Paper Composition Notebook: Quad Ruled 5×5, Grid Paper for Math & Science Students (8.5 x 11)
Author: by Math Wizo
Published at: Independently published (July 1, 2019)
5×5 Graph Paper Composition Notebook:Perfect for math, science, school, college, drawing, writing, to-do lists, and more! About this notebook:Length: 103 Pages – Surprise Gift on the Last PagePaper: Good Quality White, Quad Ruled PaperSize: 8.5 x 11 IN / 21.59 x 27. 94 CMCover: High Quality Matte Soft CoverBinding: Professional Paperback Binding, Non-Perforated PagesScroll up and click ‘buy’ to get yours now!
5. Quantum Mechanics: The Theoretical Minimum
Author: by Leonard Susskind
Published at: Basic Books; Illustrated edition (May 12, 2015)
First he taught you classical mechanics. Now, physicist Leonard Susskind has teamed up with data engineer Art Friedman to present the theory and associated mathematics of the strange world of quantum mechanics. In this follow-up to the New York Times best-selling The Theoretical Minimum, Susskind and Friedman provide a lively introduction to this famously difficult field, which attempts to understand the behavior of sub-atomic objects through mathematical abstractions.
Unlike other popularizations that shy away from quantum mechanics’ weirdness, Quantum Mechanics embraces the utter strangeness of quantum logic. The authors offer crystal-clear explanations of the principles of quantum states, uncertainty and time dependence, entanglement, and particle and wave states, among other topics, and each chapter includes exercises to ensure mastery of each area.
Like The Theoretical Minimum, this volume runs parallel to Susskind’s eponymous Stanford University-hosted continuing education course. An approachable yet rigorous introduction to a famously difficult topic, Quantum Mechanics provides a tool kit for amateur scientists to learn physics at their own pace.
6. Abstract Algebra, 3rd Edition
Author: by David S. Dummit
Published at: Wiley; 3rd edition (July 14, 2003)
This revision of Dummit and Foote’s widely acclaimed introduction to abstract algebra helps students experience the power and beauty that develops from the rich interplay between different areas of mathematics. The book carefully develops the theory of different algebraic structures, beginning from basic definitions to some in-depth results, using numerous examples and exercises to aid the student’s understanding.
With this approach, students gain an appreciation for how mathematical structures and their interplay lead to powerful results and insights in a number of different settings. The text is designed for a full-year introduction to abstract algebra at the advanced undergraduate or graduate level, but contains substantially more material than would normally be covered in one year.
Portions of the book may also be used for various one-semester topics courses in advanced algebra, each of which would provide a solid background for a follow-up course delving more deeply into one of many possible areas: algebraic number theory, algebraic topology, algebraic geometry, representation theory, Lie groups, etc.
7. Special Relativity and Classical Field Theory: The Theoretical Minimum
Author: by Leonard Susskind
Published at: Basic Books; Reprint edition (May 7, 2019)
The third volume in the bestselling physics series cracks open Einstein’s special relativity and field theory Physicist Leonard Susskind and data engineer Art Friedman are back. This time, they introduce readers to Einstein’s special relativity and Maxwell’s classical field theory.
Using their typical brand of real math, enlightening drawings, and humor, Susskind and Friedman walk us through the complexities of waves, forces, and particles by exploring special relativity and electromagnetism. It’s a must-read for both devotees of the series and any armchair physicist who wants to improve their knowledge of physics’ deepest truths.
8. A Book of Abstract Algebra: Second Edition (Dover Books on Mathematics)
Author: by Charles C Pinter
Published at: Dover Publications; Second edition (January 14, 2010)
Accessible but rigorous, this outstanding text encompasses all of the topics covered by a typical course in elementary abstract algebra. Its easy-to-read treatment offers an intuitive approach, featuring informal discussions followed by thematically arranged exercises. Intended for undergraduate courses in abstract algebra, it is suitable for junior- and senior-level math majors and future math teachers.
This second edition features additional exercises to improve student familiarity with applications. An introductory chapter traces concepts of abstract algebra from their historical roots. Succeeding chapters avoid the conventional format of definition-theorem-proof-corollary-example; instead, they take the form of a discussion with students, focusing on explanations and offering motivation.
Each chapter rests upon a central theme, usually a specific application or use. The author provides elementary background as needed and discusses standard topics in their usual order. He introduces many advanced and peripheral subjects in the plentiful exercises, which are accompanied by ample instruction and commentary and offer a wide range of experiences to students at different levels of ability.
9. Algebra (Graduate Texts in Mathematics (211))
Author: by Serge Lang
Published at: Springer; 3rd edition (January 8, 2002)
This book is intended as a basic text for a one year course in algebra at the graduate level or as a useful reference for mathematicians and professionals who use higher-level algebra. This book successfully addresses all of the basic concepts of algebra.
For the new edition, the author has added exercises and made numerous corrections to the text. From MathSciNet’s review of the first edition: “The author has an impressive knack for presenting the important and interesting ideas of algebra in just the “right” way, and he never gets bogged down in the dry formalism which pervades some parts of algebra.”
10. CLEP® College Algebra Book + Online (CLEP Test Preparation)
Author: by Stu Schwartz
Published at: Research & Education Association; Eighth Edition, Revised (July 22, 2013)
Earn College Credit with REA’s Test Prep for CLEP College Algebra Everything you need to pass the exam and get the college credit you deserve. CLEP is the most popular credit-by-examination program in the country, accepted by more than 2,900 colleges and universities.
For over 15 years, REA has helped students pass the CLEP exam and earn college credit while reducing their tuition costs. Our CLEP test preps are perfect for adults returning to college (or attending for the first time), military service members, high-school graduates looking to earn college credit, or home-schooled students with knowledge that can translate into college credit.
There are many different ways to prepare for the CLEP. What’s best for you depends on how much time you have to study and how comfortable you are with the subject matter. Our test prep for CLEP College Algebra and the free online tools that come with it, will allow you to create a personalized CLEP study plan that can be customized to fit you: your schedule, your learning style, and your current level of knowledge.
11. Algebra: 100 Fully Solved Equations To Explain Everything You Need To Know To Master Algebra! (Content Guide Included)
Author: by Math Wizo
Published at: Independently published (December 31, 2018)
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12. A First Course in Abstract Algebra, 7th Edition
Author: by John Fraleigh
Published at: Pearson; 7th edition (November 6, 2002)
Considered a classic by many, A First Course in Abstract Algebra, Seventh Edition is an in-depth introduction to abstract algebra. Focused on groups, rings and fields, this text gives students a firm foundation for more specialized work by emphasizing an understanding of the nature of algebraic structures.
KEY TOPICS: Sets and Relations; GROUPS AND SUBGROUPS; Introduction and Examples; Binary Operations; Isomorphic Binary Structures; Groups; Subgroups; Cyclic Groups; Generators and Cayley Digraphs; PERMUTATIONS, COSETS, AND DIRECT PRODUCTS; Groups of Permutations; Orbits, Cycles, and the Alternating Groups; Cosets and the Theorem of Lagrange; Direct Products and Finitely Generated Abelian Groups; Plane Isometries; HOMOMORPHISMS AND FACTOR GROUPS; Homomorphisms; Factor Groups; Factor-Group Computations and Simple Groups; Group Action on a Set; Applications of G-Sets to Counting; RINGS AND FIELDS; Rings and Fields; Integral Domains; Fermat’s and Euler’s Theorems; The Field of Quotients of an Integral Domain; Rings of Polynomials; Factorization of Polynomials over a Field; Noncommutative Examples; Ordered Rings and Fields; IDEALS AND FACTOR RINGS; Homomorphisms and Factor Rings; Prime and Maximal Ideas; Grbner Bases for Ideals; EXTENSION FIELDS; Introduction to Extension Fields; Vector Spaces; Algebraic Extensions; Geometric Constructions; Finite Fields; ADVANCED GROUP THEORY; Isomorphism Theorems; Series of Groups; Sylow Theorems; Applications of the Sylow Theory; Free Abelian Groups; Free Groups; Group Presentations; GROUPS IN TOPOLOGY; Simplicial Complexes and Homology Groups; Computations of Homology Groups; More Homology Computations and Applications; Homological Algebra; Factorization; Unique Factorization Domains; Euclidean Domains; Gaussian Integers and Multiplicative Norms; AUTOMORPHISMS AND GALOIS THEORY; Automorphisms of Fields; The Isomorphism Extension Theorem; Splitting Fields; Separable Extensions; Totally Inseparable Extensions; Galois Theory; Illustrations of Galois Theory; Cyclotomic Extensions; Insolvability of the Quintic; Matrix Algebra MARKET: For all readers interested in abstract algebra.
13. Abstract Algebra: A Student-Friendly Approach
Author: by Laura L. Dos Reis
Published at: CreateSpace Independent Publishing Platform; 1st edition (March 18, 2017)
If you are studying abstract algebra independently or are having trouble understanding your professor, this is the book for you. It not only makes learning abstract algebra easy, it also gets you to think mathematically and to do mathematics while reading the book.
It covers all the traditional topics in an introductory course. Its only prerequisite is high school algebra.
14. Abstract Algebra: A First Course
Author: by Dan Saracino
Published at: Waveland Pr Inc; 2nd edition (August 29, 2008)
The Second Edition of this classic text 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; Saracino examines them so readers gain a better impression of where the proofs come from and why they proceed as they do. 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.
15. Categories for the Working Mathematician (Graduate Texts in Mathematics (5))
Author: by Saunders Mac Lane
Published at: Springer; 2nd edition (September 25, 1998)
An array of general ideas useful in a wide variety of fields. Starting from the foundations, this book illuminates the concepts of category, functor, natural transformation, and duality. It then turns to adjoint functors, which provide a description of universal constructions, an analysis of the representations of functors by sets of morphisms, and a means of manipulating direct and inverse limits.
These categorical concepts are extensively illustrated in the remaining chapters, which include many applications of the basic existence theorem for adjoint functors. The categories of algebraic systems are constructed from certain adjoint-like data and characterised by Beck’s theorem. After considering a variety of applications, the book continues with the construction and exploitation of Kan extensions.
This second edition includes a number of revisions and additions, including new chapters on topics of active interest: symmetric monoidal categories and braided monoidal categories, and the coherence theorems for them, as well as 2-categories and the higher dimensional categories which have recently come into prominence.
16. Lie Groups, Lie Algebras, and Representations: An Elementary Introduction (Graduate Texts in Mathematics, 222)
Author: by Brian Hall
Published at: Springer; 2nd ed. 2015, Corr. 2nd printing 2016 edition (May 22, 2015)
as of Mar 28, 2021
This textbook treats Lie groups, Lie algebras and their representations in an elementary but fully rigorous fashion requiring minimal prerequisites. In particular, the theory of matrix Lie groups and their Lie algebras is developed using only linear algebra, and more motivation and intuition for proofs is provided than in most classic texts on the subject.
In addition to its accessible treatment of the basic theory of Lie groups and Lie algebras, the book is also noteworthy for including:a treatment of the BakerCampbellHausdorff formula and its use in place of the Frobenius theorem to establish deeper results about the relationship between Lie groups and Lie algebrasmotivation for the machinery of roots, weights and the Weyl group via a concrete and detailed exposition of the representation theory of sl(3;C)an unconventional definition of semisimplicity that allows for a rapid development of the structure theory of semisimple Lie algebrasa self-contained construction of the representations of compact groups, independent of Lie-algebraic argumentsThe second edition of Lie Groups, Lie Algebras, and Representations contains many substantial improvements and additions, among them: an entirely new part devoted to the structure and representation theory of compact Lie groups; a complete derivation of the main properties of root systems; the construction of finite-dimensional representations of semisimple Lie algebras has been elaborated; a treatment of universal enveloping algebras, including a proof of the PoincarBirkhoffWitt theorem and the existence of Verma modules; complete proofs of the Weyl character formula, the Weyl dimension formula and the Kostant multiplicity formula.