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Abstract Algebra: Structures and Applications, by Stephen Lovett
Download PDF Abstract Algebra: Structures and Applications, by Stephen Lovett
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A Discovery-Based Approach to Learning about Algebraic Structures
Abstract Algebra: Structures and Applications helps students understand the abstraction of modern algebra. It emphasizes the more general concept of an algebraic structure while simultaneously covering applications. The text can be used in a variety of courses, from a one-semester introductory course to a full two-semester sequence.
The book presents the core topics of structures in a consistent order:
- Definition of structure
- Motivation
- Examples
- General properties
- Important objects
- Description
- Subobjects
- Morphisms
- Subclasses
- Quotient objects
- Action structures
- Applications
The text uses the general concept of an algebraic structure as a unifying principle and introduces other algebraic structures besides the three standard ones (groups, rings, and fields). Examples, exercises, investigative projects, and entire sections illustrate how abstract algebra is applied to areas of science and other branches of mathematics.
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�"Lovett (Wheaton College) takes readers through the variegated landscape of algebra, from elementary modular arithmetic through groups, semigroups, and monoids, past rings and fields and group actions, beyond modules and algebras, to Galois theory, multivariable polynomial rings, and Gr�bner bases."
Choice Reviewed: Recommended
- Sales Rank: #229386 in Books
- Published on: 2015-07-17
- Original language: English
- Number of items: 1
- Dimensions: 11.30" h x 1.60" w x 9.10" l, .0 pounds
- Binding: Hardcover
- 720 pages
Review
"… lucid, detailed, and versatile main text comes with a wealth of illustrating examples and very instructive exercises in each single section of the book, and each chapter ends with a section containing project ideas (and hints) to challenge the student to write her or his own investigative or expository papers on related topics. … an excellent introduction to the principles of abstract algebra for upper undergraduate and graduate students, and a valuable source for instructors likewise. No doubt, this text is a highly welcome addition to the already existing plethora of primers on abstract algebra in the mathematical literature."
―Zentralblatt MATH 1323
"This is a text for a serious upper-level undergraduate course in abstract algebra. It adopts a ‘groups first’ approach to the subject, and, although it starts from scratch, winds up covering more than enough material to fill out two semesters. The topic coverage is very extensive for an undergraduate text … The author does an excellent job of balancing theory with applications. … The inclusion of all the topics described above and the large number of exercises, examples and projects make for an undeniably interesting text … a well-written book with interesting features … "
―MAA Reviews, November 2015
About the Author
Stephen Lovett is an associate professor of mathematics at Wheaton College. He is a member of the Mathematical Association of America, American Mathematical Society, and Association of Christians in the Mathematical Sciences. He earned a PhD from Northeastern University. His research interests include commutative algebra, algebraic geometry, differential geometry, cryptography, and discrete dynamical systems.
Most helpful customer reviews
7 of 7 people found the following review helpful.
Fantastic Textbook
By Hunter Dinkins
I am the type of student that learns math best when working with good textbooks at my own pace, and I must say that this is one of the best textbooks I have ever used. The books opens with some introductory set theory and number theory, and then dives into group, rings, and fields. When new concepts are introduced, Lovett generally gives some historical background and motivating examples that help make the topic more approachable. Lots of theorems and proofs are given in the book and are presented with great clarity.
The exercises at the end of each section vary a lot in terms of difficulty. Some exercises are straightforward, while others are quite creative and require a lot of thought (and time) to solve. At the end of each chapter, there is a list of open-ended projects, some of which are quite interesting. There are also several sections that focus on applications of Abstract Algebra to other disciplines, my favorites being the ones on cryptography and constructable numbers.
In my opinion, some strengths of this book are its clarity, organization, and rigor. The sections are very readable and it is easy to refer back to previous chapters to find key topics, as all theorems and definitions are conveniently boxed.
Though the book does not adopt a "teach by example" approach, the examples are strategically-chosen and are very helpful. I have found that a lot math books tend to present theorems and examples in a way that I have to refer back to the examples to remember what the theorems actually mean. This book, however, does not do that and instead challenges the reader to understand examples in the context of theorems, and not the other way around.
Though I used this book for an introductory Abstract Algebra course, I think it would also be very well-suited for self-study and would be easy to use as a reference book. In summary, this is a great book that will challenge you, and you should buy it if you want to have a rewarding experience learning Abstract Algebra.
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