92 Best Abstract Algebra Books of All Time
We've researched and ranked the best abstract algebra books in the world, based on recommendations from world experts, sales data, and millions of reader ratings. Learn more
Featuring recommendations from Eric Weinstein, and 1 other experts. 1
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... more
An introductory chapter traces concepts of abstract algebra from their historical... more
2
From the bestselling author of The Theoretical Minimum, a DIY introduction to the math and science of quantum mechanics.
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... more
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... more
Recommended by Eric Weinstein, and 1 others. Eric Weinstein[Eric Weinstein recommended this book on Twitter.] (Source)
3
Widely acclaimed algebra text. This book is designed to give the reader insight into the power and beauty that accrues from a 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 reader's understanding. In this way, readers gain an appreciation for how mathematical structures and their interplay lead to powerful results and insights in a number of different settings.
* The emphasis throughout has been to... more
* The emphasis throughout has been to... more
5
Joseph Gallian is a well-known active researcher and award-winning teacher. His Contemporary Abstract Algebra, 6/e, includes challenging topics in abstract algebra as well as numerous figures, tables, photographs, charts, biographies, computer exercises, and suggested readings that give the subject a current feel and makes the content interesting and relevant for students. less
6
A funny, insightful, and self-contained guide to Einstein's relativity theory and classical field theories--including electromagnetism
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... more
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... more
7
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. 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,... more
8
Abstract Algebra: Theory and Applications is an open-source textbook written by Tom Judson that is designed to teach the principles and theory of abstract algebra to college juniors and seniors in a rigorous manner. Its strengths include a wide range of exercises, both computational and theoretical, plus many nontrivial applications. The first half of the book presents group theory, through the Sylow theorems, with enough material for a semester-long course. The second-half is suitable for a second semester and presents rings, integral domains, Boolean algebras, vector spaces, and fields,... more
9
Algebra 2 is the advanced QuickStudy guide specially designed for students who are already familiar with Algebra 1.
6-page laminated guide includes:
- real number lines
- graphing & lines
- types of functions
- sequences & series
- conic sections
- problems & solutions
- and much more less
6-page laminated guide includes:
- real number lines
- graphing & lines
- types of functions
- sequences & series
- conic sections
- problems & solutions
- and much more less
10
"Lang's Algebra changed the way graduate algebra is taught, retaining classical topics but introducing language and ways of thinking from category theory and homological algebra. It has affected all subsequent graduate-level algebra books." NOTICES OF THE AMS
"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." MATHEMATICAL REVIEWS
This book is intended as a basic text for a one-year course in algebra at the... more
"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." MATHEMATICAL REVIEWS
This book is intended as a basic text for a one-year course in algebra at the... more
Don't have time to read the top Abstract Algebra books of all time? Read Shortform summaries.
Shortform summaries help you learn 10x faster by:
- Being comprehensive: you learn the most important points in the book
- Cutting out the fluff: you focus your time on what's important to know
- Interactive exercises: apply the book's ideas to your own life with our educators' guidance.
11
Linear algebra and matrix theory are fundamental tools in mathematical and physical science, as well as fertile fields for research. This new edition of the acclaimed text presents results of both classic and recent matrix analysis using canonical forms as a unifying theme, and demonstrates their importance in a variety of applications. The authors have thoroughly revised, updated, and expanded on the first edition. The book opens with an extended summary of useful concepts and facts and includes numerous new topics and features, such as: - New sections on the singular value and CS... more
12
New edition includes extensive revisions of the material on finite groups and Galois Theory. New problems added throughout. less
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The second edition of a book designed to introduce mathematics students to abstract algebra. less
Recommended by Eric Weinstein, and 1 others. Eric Weinstein[Eric Weinstein recommended this book on Twitter.] (Source)
16
This text covers topics in algebraic geometry and commutative algebra with a strong perspective toward practical and computational aspects. The first four chapters form the core of the book. A comprehensive chart in the Preface illustrates a variety of ways to proceed with the material once these chapters are covered. In addition to the fundamentals of algebraic geometry the elimination theorem, the extension theorem, the closure theorem and the Nullstellensatz this new edition incorporates several substantial changes, all of which are listed in the Preface. The largest revision incorporates... more
18
Symmetry is a classic study of symmetry in mathematics, the sciences, nature, and art from one of the twentieth century's greatest mathematicians. Hermann Weyl explores the concept of symmetry beginning with the idea that it represents a harmony of proportions, and gradually departs to examine its more abstract varieties and manifestations--as bilateral, translatory, rotational, ornamental, and crystallographic. Weyl investigates the general abstract mathematical idea underlying all these special forms, using a wealth of illustrations as support. Symmetry is a work of seminal... more
Recommended by Eric Weinstein, and 1 others. Eric Weinstein[Eric Weinstein recommended this book on Twitter.] (Source)
19
Graduate mathematics students will find this book an easy-to-follow, step-by-step guide to the subject. Rotman's book gives a treatment of homological algebra which approaches the subject in terms of its origins in algebraic topology. In this new edition the book has been updated and revised throughout and new material on sheaves and cup products has been added. The author has also included material about homotopical algebra, alias K-theory. Learning homological algebra is a two-stage affair. First, one must learn the language of Ext and Tor. Second, one must be able to compute these things... more
20
The focus of this book is geometric properties of general sets and measures in Euclidean spaces. Applications of this theory include fractal-type objects, such as strange attractors for dynamical systems, and those fractals used as models in the sciences. The author provides a firm and unified foundation for the subject and develops all the main tools used in its study, such as covering theorems, Hausdorff measures and their relations to Riesz capacities and Fourier transforms. The last third of the book is devoted to the Besicovitch-Federer theory of rectifiable sets, which form in a sense... more
Don't have time to read the top Abstract Algebra books of all time? Read Shortform summaries.
Shortform summaries help you learn 10x faster by:
- Being comprehensive: you learn the most important points in the book
- Cutting out the fluff: you focus your time on what's important to know
- Interactive exercises: apply the book's ideas to your own life with our educators' guidance.
21
Anyone who has studied abstract algebra and linear algebra as an undergraduate can understand this book. The first six chapters provide material for a first course, while the rest of the book covers more advanced topics. This revised edition retains the clarity of presentation that was the hallmark of the previous editions.
From the reviews:
"Rotman has given us a very readable and valuable text, and has shown us many beautiful vistas along his chosen route." --MATHEMATICAL REVIEWS less
From the reviews:
"Rotman has given us a very readable and valuable text, and has shown us many beautiful vistas along his chosen route." --MATHEMATICAL REVIEWS less
22
Howard Georgi is the co-inventor (with Sheldon Glashow) of the SU(5) theory. This extensively revised and updated edition of his classic text makes the theory of Lie groups accessible to graduate students, while offering a perspective on the way in which knowledge of such groups can provide an insight into the development of unified theories of strong, weak, and electromagnetic interactions. less
Recommended by Eric Weinstein, and 1 others. Eric Weinstein[Eric Weinstein recommended this book on Twitter.] (Source)
23
This volume presents modern algebra from first principles and is accessible to undergraduates or graduates. It combines standard materials and necessary algebraic manipulations with general concepts that clarify meaning and importance. This conceptual approach to algebra starts with a description of algebraic structures by means of axioms chosen to suit the examples, for instance, axioms for groups, rings, fields, lattices, and vector spaces. less
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An Introduction to Mathematical Cryptography provides an introduction to public key cryptography and underlying mathematics that is required for the subject. Each of the eight chapters expands on a specific area of mathematical cryptography and provides an extensive list of exercises.
It is a suitable text for advanced students in pure and applied mathematics and computer science, or the book may be used as a self-study. This book also provides a self-contained treatment of mathematical cryptography for the reader with limited mathematical background. less
It is a suitable text for advanced students in pure and applied mathematics and computer science, or the book may be used as a self-study. This book also provides a self-contained treatment of mathematical cryptography for the reader with limited mathematical background. less
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With firm foundations dating only from the 1950s, algebraic topology is a relatively young area of mathematics. There are very few textbooks that treat fundamental topics beyond a first course, and many topics now essential to the field are not treated in any textbook. J. Peter May’s A Concise Course in Algebraic Topology addresses the standard first course material, such as fundamental groups, covering spaces, the basics of homotopy theory, and homology and cohomology. In this sequel, May and his coauthor, Kathleen Ponto, cover topics that are essential for algebraic topologists and... more
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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... more
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... more
28
Over the past twenty-five years K-theory has become an integrated part of the study of C*-algebras. This book gives a very elementary introduction to this interesting and rapidly growing area of mathematics. The authors cover the basic properties of the functors K and K1 and their interrelationship. In particular, the Bott periodicity theorem is proved (Atiyah's proof), and the six-term exact sequence is derived. The theory is well illustrated with 120 exercises and examples, making the book ideal for beginning graduate students in functional analysis, especially operator algebras, and for... more
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Providing a concise introduction to abstract algebra, this work unfolds some of the fundamental systems with the aim of reaching applicable, significant results. less
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"Springer has just released the second edition of Steven Roman's Field Theory, and it continues to be one of the best graduate-level introductions to the subject out there....Every section of the book has a number of good exercises that would make this book excellent to use either as a textbook or to learn the material on your own. All in all...a well-written expository account of a very exciting area in mathematics." --THE MAA MATHEMATICAL SCIENCES DIGITAL LIBRARY less
Don't have time to read the top Abstract Algebra books of all time? Read Shortform summaries.
Shortform summaries help you learn 10x faster by:
- Being comprehensive: you learn the most important points in the book
- Cutting out the fluff: you focus your time on what's important to know
- Interactive exercises: apply the book's ideas to your own life with our educators' guidance.
31
Ludwig Prandtl, with his fundamental contributions to hydrodynamics, ae- dynamics, and gas dynamics, greatly in?uenced the development of ?uid - chanics as a whole, and it was his pioneering research in the ?rst half of the last century that founded modern ?uid mechanics. His book Fu]hrer durch die Str]omungslehre, which appeared in 1942, originated from previous pub- cations in 1913, Lehre von der Flu]ssigkeit und Gasbewegung, and 1931, Abri der Str]omungslehre. The title Fu]hrer durch die Str]omungslehre, or Essentials of Fluid Mechanics, is an indication of Prandtl's intentions to guide... more
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Pure Mathematics for BeginnersPure Mathematics for Beginners 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 proofwriting skills that are essential for advanced study in mathematics are covered and reviewed extensively.Pure Mathematics for Beginners is perfect for
professors teaching an introductory college course in higher... more
professors teaching an introductory college course in higher... more
33
In this volume in his exceptional series of translations of Russian mathematical texts, Richard Silverman has taken Shilov's course in linear algebra and has made it even more accessible and more useful for English language readers.
Georgi E. Shilov, Professor of Mathematics at the Moscow State University, covers determinants, linear spaces, systems of linear equations, linear functions of a vector argument, coordinate transformations, the canonical form of the matrix of a linear operator, bilinear and quadratic forms, Euclidean spaces, unitary spaces, quadratic forms in Euclidean and... more
Georgi E. Shilov, Professor of Mathematics at the Moscow State University, covers determinants, linear spaces, systems of linear equations, linear functions of a vector argument, coordinate transformations, the canonical form of the matrix of a linear operator, bilinear and quadratic forms, Euclidean spaces, unitary spaces, quadratic forms in Euclidean and... more
34
"Elliptic Tales" describes the latest developments in number theory by looking at one of the most exciting unsolved problems in contemporary mathematics--the Birch and Swinnerton-Dyer Conjecture. The Clay Mathematics Institute is offering a prize of $1 million to anyone who can discover a general solution to the problem. In this book, Avner Ash and Robert Gross guide readers through the mathematics they need to understand this captivating problem.
The key to the conjecture lies in elliptic curves, which are cubic equations in two variables. These equations may appear simple, yet... more
The key to the conjecture lies in elliptic curves, which are cubic equations in two variables. These equations may appear simple, yet... more
35
This survey of fundamental algebraic structures employs techniques applicable to mathematics, physics, engineering, and computer science. Topics include relations between groups and sets, the fundamental theorem of Galois theory, and the results and methods of abstract algebra in terms of number theory, geometry, and noncommutative and homological algebra. Solutions. 2006 edition.
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In the fall of 1990, I taught Math 581 at New Mexico State University for the first time. This course on field theory is the first semester of the year-long graduate algebra course here at NMSU. In the back of my mind, I thought it would be nice someday to write a book on field theory, one of my favorite mathematical subjects, and I wrote a crude form of lecture notes that semester. Those notes sat undisturbed for three years until late in 1993 when I finally made the decision to turn the notes into a book. The notes were greatly expanded and rewritten, and they were in a form sufficient to... more
37
This text and reference book on Category Theory, a branch of abstract algebra, is aimed not only at students of Mathematics, but also researchers and students of Computer Science, Logic, Linguistics, Cognitive Science, Philosophy, and any of the other fields that now make use of it. Containing clear definitions of the essential concepts, illuminated with numerous accessible examples, and providing full proofs of all important propositions and theorems, this book aims to make the basic ideas, theorems, and methods of Category Theory understandable to this broad readership. Although it assumes... more
38
This book aims to fill a gap in the literature by introducing Lie theory to junior and senior level undergraduates. In order to achieve this, the author focuses on the so-called "classical groups, '' viewed as matrix groups with real, complex, or quaternion entries. This allows them to be studied by elementary methods from calculus and linear algebra. Each chapter is enhanced with numerous exercises, discussion of further results, and historical comments. less
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Brief, clear, and well written, this introduction to abstract algebra bridges the gap between the solid ground of traditional algebra and the abstract territory of modern algebra. The only prerequisite is high school–level algebra.
Author W. W. Sawyer begins with a very basic viewpoint of abstract algebra, using simple arithmetic and elementary algebra. He then proceeds to arithmetic and polynomials, slowly progressing to more complex matters: finite arithmetic, an analogy between integers and polynomials, an application of the analogy, extending fields, and linear dependence and...
moreAuthor W. W. Sawyer begins with a very basic viewpoint of abstract algebra, using simple arithmetic and elementary algebra. He then proceeds to arithmetic and polynomials, slowly progressing to more complex matters: finite arithmetic, an analogy between integers and polynomials, an application of the analogy, extending fields, and linear dependence and...
40
For two-term undergraduate level courses in Algebra. This text's organizing principle is the interplay between groups and rings, where rings includes the ideas of modules. It contains basic definitions, complete and clear theorems and gives attention to the topics of algebraic geometry, computers, homology and representations. More than merely a succession of definition theorem proofs, this text puts results and ideas in context so that students can appreciate why a certain topic is being studied and where definitions originate. *Coverage of topics not usually found in other texts - e.g.... more
Don't have time to read the top Abstract Algebra books of all time? Read Shortform summaries.
Shortform summaries help you learn 10x faster by:
- Being comprehensive: you learn the most important points in the book
- Cutting out the fluff: you focus your time on what's important to know
- Interactive exercises: apply the book's ideas to your own life with our educators' guidance.
42
Ordered structures have been increasingly recognized in recent years due to an explosion of interest in theoretical computer science and all areas of discrete mathematics. This book covers areas such as ordered sets and lattices. A key feature of ordered sets, one which is emphasized in the text, is that they can be represented pictorially. Lattices are also considered as algebraic structures and hence a purely algebraic study is used to reinforce the ideas of homomorphisms and of ideals encountered in group theory and ring theory. Exposure to elementary abstract algebra and the rotation of... more
43
This book is designed to introduce the reader to the theory of semisimple Lie algebras over an algebraically closed field of characteristic 0, with emphasis on representations. A good knowledge of linear algebra (including eigenvalues, bilinear forms, euclidean spaces, and tensor products of vector spaces) is presupposed, as well as some acquaintance with the methods of abstract algebra. The first four chapters might well be read by a bright undergraduate; however, the remaining three chapters are admittedly a little more demanding. Besides being useful in many parts of mathematics and... more
44
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 Baker Campbell Hausdorff formula and its use in place of... more
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 Baker Campbell Hausdorff formula and its use in place of... more
46
Das vorliegende, nunmehr zum neunten Male herausgebrachte Werk von B. L. VAN DER W AERDEN nimmt unter den mathematischen Lehrbiichem eine auBergewohnliche Stellung ein. Selten nur hat in der Vergangenheit ein Lehrbuch eine iihnlich groBe Wirkung auf das mathematische Leben ausgeiibt wie dieses. Seit seinem ersten Erscheinen im Sommer 1930, also vor nunmehr 63 Jahren, haben Generationen von Mathematikem nach ihm die Algebra gelemt, zumindest im deutschsprachigen Bereich. Fiir zahllose Studenten bedeutete es Eintritt und Aufnahme in die hOhere Mathematik, fur viele war es die erste Stufe zu... more
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The purpose of this book is to prepare the reader for coping with abstract mathematics. The intended audience is both students taking a first course in abstract algebra who feel the need to strengthen their background, and those from a more applied background who need some experience in dealing with abstract ideas. Learning any area of abstract mathematics requires not only ability to write formally but also to think intuitively about what is going on and to describe that process clearly and cogently in ordinary English. Ash tries to aid intuition by keeping proofs short and as informal as... more
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This volume is a collection of scholarly articles on the Mach Principle, the impact that this theory has had since the end of the 19th century, and its role in helping Einstein formulate the doctrine of general relativity. 20th-century physics is concerned with the concepts of time, space, motion, inertia and gravity. The documentation on all of these makes this book a reference for those who are interested in the history of science and the theory of general relativity less
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Intended for beginning graduate-level courses, this text introduces various aspects of the theory of abstract algebra. The book is also suitable as independent reading for interested students at that level as well as a primary source for a one-semester course that an instructor may supplement to expand to a full year. Author Richard S. Pierce, a Professor of Mathematics at Seattle's University of Washington, places considerable emphasis on applications of the theory and focuses particularly on lattice theory.
After a preliminary review of set theory, the treatment presents the basic... more
After a preliminary review of set theory, the treatment presents the basic... more
Don't have time to read the top Abstract Algebra books of all time? Read Shortform summaries.
Shortform summaries help you learn 10x faster by:
- Being comprehensive: you learn the most important points in the book
- Cutting out the fluff: you focus your time on what's important to know
- Interactive exercises: apply the book's ideas to your own life with our educators' guidance.
51
In addition to many new problems for practice and challenge, this edition of a self-contained graduate text on abstract algebra contains an introduction to lattices, a new chapter on tensor products and a discussion of the new (1993) approach to the celebrated Lasker-Noether theorem. less
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This well-organized volume develops the elementary ideas of both group theory and representation theory in a progressive and thorough fashion. Designed to allow students to focus on any of the main fields of application, it is geared toward advanced undergraduate and graduate physics and chemistry students. 1963 edition. Appendices. less
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Number theory and algebra play an increasingly significant role in computing and communications, as evidenced by the striking applications of these subjects to such fields as cryptography and coding theory. This introductory book emphasises algorithms and applications, such as cryptography and error correcting codes, and is accessible to a broad audience. The mathematical prerequisites are minimal: nothing beyond material in a typical undergraduate course in calculus is presumed, other than some experience in doing proofs - everything else is developed from scratch. Thus the book can serve... more
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Galois theory is the culmination of a centuries-long search for a solution to the classical problem of solving algebraic equations by radicals. In this book, Bewersdorff follows the historical development of the theory, emphasizing concrete examples along the way. As a result, many mathematical abstractions are now seen as the natural consequence of particular investigations. Few prerequisites are needed beyond general college mathematics, since the necessary ideas and properties of groups and fields are provided as needed. Results in Galois theory are formulated first in a concrete,... more
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Volume II of a pair of classic texts — and standard references for a generation — this book comprises all of the subjects of first-year graduate algebra. In addition to the immediate introduction and constant use of categories and functors, it revisits many topics from Volume I with greater depth. 1989 edition. less
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A comprehensive presentation of abstract algebra and an in-depth treatment of the applications of algebraic techniques and the relationship of algebra to other disciplines, such as number theory, combinatorics, geometry, topology, differential equations, and Markov chains. less
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This book provides a comprehensive introduction into the classical topic of projective geometry. It explains how metric concepts may be best understood in projective terms and explores the beauty of the interplay of geometry, algebra and combinatorics." less
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This upper-division laboratory supplement for courses in abstract algebra consists of several Mathematica packages programmed as a foundation for group and ring theory. Additionally, the "user's guide" illustrates the functionality of the underlying code, while the lab portion of the book reflects the contents of the Mathematica-based electronic notebooks. Students interact with both the printed and electronic versions of the material in the laboratory, and can look up details and reference information in the user's guide. Exercises occur in the stream of the text of the lab, which provides a... more
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A description of 148 algorithms fundamental to number-theoretic computations, in particular for computations related to algebraic number theory, elliptic curves, primality testing and factoring. The first seven chapters guide readers to the heart of current research in computational algebraic number theory, including recent algorithms for computing class groups and units, as well as elliptic curve computations, while the last three chapters survey factoring and primality testing methods, including a detailed description of the number field sieve algorithm. The whole is rounded off with a... more
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Higher category theory is generally regarded as technical and forbidding, but part of it is considerably more tractable: the theory of infinity-categories, higher categories in which all higher morphisms are assumed to be invertible. In Higher Topos Theory, Jacob Lurie presents the foundations of this theory, using the language of weak Kan complexes introduced by Boardman and Vogt, and shows how existing theorems in algebraic topology can be reformulated and generalized in the theory's new language. The result is a powerful theory with applications in many areas of mathematics. more
Don't have time to read the top Abstract Algebra books of all time? Read Shortform summaries.
Shortform summaries help you learn 10x faster by:
- Being comprehensive: you learn the most important points in the book
- Cutting out the fluff: you focus your time on what's important to know
- Interactive exercises: apply the book's ideas to your own life with our educators' guidance.
61
Appropriate for one- or two-semester algebra courses
This title is part of the Pearson Modern Classics series. Pearson Modern Classics are acclaimed titles at a value price. Please visit www.pearsonhighered.com/math-classics... for a complete list of titles.
Algebra, 2nd Edition, by Michael Artin, provides comprehensive coverage at the level of an honors-undergraduate or introductory-graduate course. The second edition of this classic text... more
This title is part of the Pearson Modern Classics series. Pearson Modern Classics are acclaimed titles at a value price. Please visit www.pearsonhighered.com/math-classics... for a complete list of titles.
Algebra, 2nd Edition, by Michael Artin, provides comprehensive coverage at the level of an honors-undergraduate or introductory-graduate course. The second edition of this classic text... more
62
'Rings, Fields and Groups' gives a stimulating and unusual introduction to the results, methods and ideas now commonly studied on abstract algebra courses at undergraduate level. The author provides a mixture of informal and formal material which help to stimulate the enthusiasm of the student, whilst still providing the essential theoretical concepts necessary for serious study.
Retaining the highly readable style of its predecessor, this second edition has also been thoroughly revised to include a new chapter on Galois theory plus hints and solutions to many of the 800 exercises... more
Retaining the highly readable style of its predecessor, this second edition has also been thoroughly revised to include a new chapter on Galois theory plus hints and solutions to many of the 800 exercises... more
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Aimed at the novice rather than the connoisseur and stressing the role of examples and motivation, this text is suitable not only for use in a graduate course, but also for self-study in the subject by interested graduate students. More than 400 exercises testing the understanding of the general theory in the text are included in this new edition. less
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Contains worked-out solutions to odd-numbered problems. less
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Galois theory is a mature mathematical subject of particular beauty. Any Galois theory book written nowadays bears a great debt to Emil Artin's classic text "Galois Theory," and this book is no exception. While Artin's book pioneered an approach to Galois theory that relies heavily on linear algebra, this book's author takes the linear algebra emphasis even further. This special approach to the subject together with the clarity of its presentation, as well as the choice of topics covered, has made the first edition of this book a more than worthwhile addition to the literature on Galois... more
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This book guides undergraduate students in the use of Maxima--a computer algebra system--in solving problems in classical mechanics. It functions well as a supplement to a typical classical mechanics textbook.
When it comes to problems that are too difficult to solve by hand, computer algebra systems that can perform symbolic mathematical manipulations are a valuable tool. Maxima is particularly attractive in that it is open-source, multiple-platform software that students can download and install free of charge. Lessons learned and capabilities developed using... more
When it comes to problems that are too difficult to solve by hand, computer algebra systems that can perform symbolic mathematical manipulations are a valuable tool. Maxima is particularly attractive in that it is open-source, multiple-platform software that students can download and install free of charge. Lessons learned and capabilities developed using... more
68
This textbook is an introduction to the theory of Hilbert spaces and its applications. The notion of a Hilbert space is a central idea in functional analysis and can be used in numerous branches of pure and applied mathematics. Dr. Young stresses these applications particularly for the solution of partial differential equations in mathematical physics and to the approximation of functions in complex analysis. Some basic familiarity with real analysis, linear algebra and metric spaces is assumed, but otherwise the book is self-contained. The book is based on courses given at the University of... more
69
This graduate-level text is intended for initial courses in algebra that begin with first principles but proceed at a faster pace than undergraduate-level courses. It employs presentations and proofs that are accessible to students, and it provides numerous concrete examples.
Exercises appear throughout the text, clarifying concepts as they arise; additional exercises, varying widely in difficulty, are included at the ends of the chapters. Subjects include groups, rings, fields and Galois theory, modules, and structure of rings and algebras. Further topics encompass infinite Abelian... more
Exercises appear throughout the text, clarifying concepts as they arise; additional exercises, varying widely in difficulty, are included at the ends of the chapters. Subjects include groups, rings, fields and Galois theory, modules, and structure of rings and algebras. Further topics encompass infinite Abelian... more
70
A teenage genius and his teacher take readers on a wild ride to the extremes of mathematics
Everyone has stared at the crumpled page of a math assignment and wondered, where on Earth will I ever use this? It turns out, Earth is precisely the place. As teen math prodigy Agnijo Banerjee and his teacher David Darling reveal, complex math surrounds us. If we think long enough about the universe, we're left not with material stuff, but a ghostly and beautiful set of equations. Packed with puzzles and paradoxes, mind-bending concepts, and surprising solutions, Weird... more
Everyone has stared at the crumpled page of a math assignment and wondered, where on Earth will I ever use this? It turns out, Earth is precisely the place. As teen math prodigy Agnijo Banerjee and his teacher David Darling reveal, complex math surrounds us. If we think long enough about the universe, we're left not with material stuff, but a ghostly and beautiful set of equations. Packed with puzzles and paradoxes, mind-bending concepts, and surprising solutions, Weird... more
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73
Linear algebra is a living, active branch of mathematics which is central to almost all other areas of mathematics, both pure and applied, as well as to computer science, to the physical, biological, and social sciences, and to engineering. It encompasses an extensive corpus of theoretical results as well as a large and rapidly-growing body of computational techniques. Unfortunately, in the past decade, the content of linear algebra courses required to complete an undergraduate degree in mathematics has been depleted to the extent that they fail to provide a sufficient theoretical or... more
74
Matrix algebra has been called "the arithmetic of higher mathematics" [Be]. We think the basis for a better arithmetic has long been available, but its versatility has hardly been appreciated, and it has not yet been integrated into the mainstream of mathematics. We refer to the system commonly called 'Clifford Algebra', though we prefer the name 'Geometric Algebm' suggested by Clifford himself. Many distinct algebraic systems have been adapted or developed to express geometric relations and describe geometric structures. Especially notable are those algebras which have been used for this... more
75
AT-theory was introduced by A. Grothendieck in his formulation of the Riemann- Roch theorem (cf. Borel and Serre [2]). For each projective algebraic variety, Grothendieck constructed a group from the category of coherent algebraic sheaves, and showed that it had many nice properties. Atiyah and Hirzebruch [3] con sidered a topological analog defined for any compact space X, a group K{X) constructed from the category of vector bundles on X. It is this ''topological J DEGREES-theory" that this book will study. Topological DEGREES-theory has become an important tool in topology. Using- theory,... more
76
This traditional treatment of abstract algebra is designed for the particular needs of the mathematics teacher. Readers must have access to a Computer Algebra System (C. A. S.) such as Maple, or at minimum a calculator such as the TI 89 with C. A. S. capabilities. KEY TOPICS: Includes "To the Teacher" sections that Draw connections from the number theory or abstract algebra under consideration to secondary mathematics. Provides historical context with "From the Past" sections in each chapter. Features "Worksheets" that outline the framework of a topic in most chapters. ... more
77
Helpful illustrations and exercises included throughout this lucid coverage of group theory, Galois theory and classical ideal theory stressing proof of important theorems. Includes many historical notes. Mathematical proof is emphasized. Includes 24 tables and figures. Reprint of the 1971 edition. less
78
This introduction to Boolean algebra explores the subject on a level accessible even to those with a modest background in mathematics. The first chapter presents the algebra of sets from an intuitive point of view, followed by a formal presentation in chapter two of Boolean algebra as an abstract algebraic system, with no reference to applications.
Succeeding chapters offer concise accounts of applications to symbolic logic, focusing on topics of logic common to elementary mathematics and discussing concepts of valid argument and indirect proofs. Additional topics include the algebra of... more
Succeeding chapters offer concise accounts of applications to symbolic logic, focusing on topics of logic common to elementary mathematics and discussing concepts of valid argument and indirect proofs. Additional topics include the algebra of... more
79
This beautiful and eloquent text transformed the graduate teaching of algebra in Europe and the United States. It clearly and succinctly formulated the conceptual and structural insights which Noether had expressed so forcefully and combined it with the elegance and understanding with which Artin had lectured. This text is a reprinted version of the original English translation of the first volume of B.L. van der Waerden's Algebra. less
80
Since the characterization of generators of C0 semigroups was established in the 1940s, semigroups of linear operators and its neighboring areas have developed into an abstract theory that has become a necessary discipline in functional analysis and differential equations. This book presents that theory and its basic applications, and the last two chapters give a connected account of the applications to partial differential equations. less
Don't have time to read the top Abstract Algebra books of all time? Read Shortform summaries.
Shortform summaries help you learn 10x faster by:
- Being comprehensive: you learn the most important points in the book
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81
This classic, written by two young instructors who became giants in their field, has shaped the understanding of modern algebra for generations of mathematicians and remains a valuable reference and text for self study and college courses. less
82
If classical Lie groups preserve bilinear vector norms, what Lie groups preserve trilinear, quadrilinear, and higher order invariants? Answering this question from a fresh and original perspective, Predrag Cvitanovic takes the reader on the amazing, four-thousand-diagram journey through the theory of Lie groups. This book is the first to systematically develop, explain, and apply diagrammatic projection operators to construct all semi-simple Lie algebras, both classical and exceptional.
The invariant tensors are presented in a somewhat unconventional, but in recent years... more
The invariant tensors are presented in a somewhat unconventional, but in recent years... more
83
Designed to offer undergraduate mathematics majors insights into the main themes of abstract algebra, this text contains ample material for a two-semester course. Its extensive coverage includes set theory, groups, rings, modules, vector spaces, and fields. Loaded with examples, definitions, theorems, and proofs, it also features numerous practice exercises at the end of each section.
Beginning with sets, relations, and functions, the text proceeds to an examination of all types of groups, including cyclic groups, subgroups, permutation groups, normal subgroups, homomorphism, factor... more
Beginning with sets, relations, and functions, the text proceeds to an examination of all types of groups, including cyclic groups, subgroups, permutation groups, normal subgroups, homomorphism, factor... more
84
This lively introduction to measure theory and Lebesgue integration is motivated by the historical questions that led to its development. The author stresses the original purpose of the definitions and theorems, highlighting the difficulties mathematicians encountered as these ideas were refined. The story begins with Riemann's definition of the integral, and then follows the efforts of those who wrestled with the difficulties inherent in it, until Lebesgue finally broke with Riemann's definition. With his new way of understanding integration, Lebesgue opened the door to fresh and productive... more
85
The companion title, Linear Algebra, has sold over 8,000 copies
The writing style is very accessible
The material can be covered easily in a one-year or one-term course
Includes Noah Snyder's proof of the Mason-Stothers polynomial abc theorem
New material included on product structure for matrices including descriptions of the conjugation representation of the diagonal group less
The writing style is very accessible
The material can be covered easily in a one-year or one-term course
Includes Noah Snyder's proof of the Mason-Stothers polynomial abc theorem
New material included on product structure for matrices including descriptions of the conjugation representation of the diagonal group less
86
Explains algebra clearly through theory and example
Renews the reader's aquaintance with school mathematics before taking them progressively further
Elucidates the laws governing algebra in order to reveal the elegance and power of equations and inequalities
Provides an accessible account of algebra for the general reader
Part of the bestselling Very Short Introductions series - over seven million sold worldwide
Algebra marked the beginning of modern mathematics, moving it beyond arithmetic, which involves calculations featuring given numbers, to problems where some... more
Renews the reader's aquaintance with school mathematics before taking them progressively further
Elucidates the laws governing algebra in order to reveal the elegance and power of equations and inequalities
Provides an accessible account of algebra for the general reader
Part of the bestselling Very Short Introductions series - over seven million sold worldwide
Algebra marked the beginning of modern mathematics, moving it beyond arithmetic, which involves calculations featuring given numbers, to problems where some... more
87
* Stanley represents a broad perspective with respect to two significant topics from Combinatorial Commutative Algebra:
1) The theory of invariants of a torus acting linearly on a polynomial ring, and
2) The face ring of a simplicial complex
* In this new edition, the author further develops some interesting properties of face rings with application to combinatorics less
1) The theory of invariants of a torus acting linearly on a polynomial ring, and
2) The face ring of a simplicial complex
* In this new edition, the author further develops some interesting properties of face rings with application to combinatorics less
88
Contains complete worked solutions to all regular exercises and computer exercises in the text; additional test questions and their solutions; an online laboratory manual for the computer algebra system GAP, with exercises tied to the book and an instructor answer key; and links on the author's website to true/false questions, flash cards, essays, software downloads, and other abstract algebra-related materials. less
89
From a Geometrical Point of View explores historical and philosophical aspects of category theory, trying therewith to expose its significance in the mathematical landscape. The main thesis is that Klein's Erlangen program in geometry is in fact a particular instance of a general and broad phenomenon revealed by category theory. The volume starts with Eilenberg and Mac Lane's work in the early 1940's and follows the major developments of the theory from this perspective. Particular attention is paid to the philosophical elements involved in this development. The book ends with a presentation... more
90
A Course in the Theory of Groups is a comprehensive introduction to the theory of groups - finite and infinite, commutative and non-commutative. Presupposing only a basic knowledge of modern algebra, it introduces the reader to the different branches of group theory and to its principal accomplishments. While stressing the unity of group theory, the book also draws attention to connections with other areas of algebra such as ring theory and homological algebra.
This new edition has been updated at various points, some proofs have been improved, and lastly about thirty additional... more
This new edition has been updated at various points, some proofs have been improved, and lastly about thirty additional... more
Don't have time to read the top Abstract Algebra books of all time? Read Shortform summaries.
Shortform summaries help you learn 10x faster by:
- Being comprehensive: you learn the most important points in the book
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91
Applied Abstract Algebra with MapleTM and MATLAB(R) provides an in-depth introduction to real-world abstract algebraic problems. This popular textbook covers a variety of topics including block designs, coding theory, cryptography, and counting techniques, including Polya's and Burnside's theorems. The book also includes a concise review of all prerequisite advanced mathematics.
The use of sophisticated mathematical software packages such as MapleTM and MATLAB(R) allows students to work though realistic examples without having to struggle with extensive... more
The use of sophisticated mathematical software packages such as MapleTM and MATLAB(R) allows students to work though realistic examples without having to struggle with extensive... more
92
In elementary introductions to mathematical analysis, the treatment of the logical and algebraic foundations of the subject is necessarily rather skeletal. This book attempts to flesh out the bones of such treatment by providing an informal but systematic account of the foundations of mathematical analysis written at an elementary level. This book is entirely self-contained but, as indicated above, it will be of most use to university or college students who are taking, or who have taken, an introductory course in analysis. Such a course will not automatically cover all the material dealt... more
Don't have time to read the top Abstract Algebra books of all time? Read Shortform summaries.
Shortform summaries help you learn 10x faster by:
- Being comprehensive: you learn the most important points in the book
- Cutting out the fluff: you focus your time on what's important to know
- Interactive exercises: apply the book's ideas to your own life with our educators' guidance.