- Series: MAA Problem Book Series
- Hardcover: 297 pages
- Publisher: The Mathematical Association of America; 1 edition (May 12, 2009)
- Language: English
- ISBN-10: 088385757X
- ISBN-13: 978-0883857571
- Product Dimensions: 6.7 x 0.9 x 9.7 inches
- Shipping Weight: 1.6 pounds
- Average Customer Review: 11 customer reviews
- Amazon Best Sellers Rank: #931,415 in Books (See Top 100 in Books)
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Visual Group Theory (MAA Classroom Resource Materials) (MAA Problem Book Series) 1st Edition
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Carter presents the grojp theory portion of abstract algebra in a way that allows student to actually see, using a multitute of examples and applications, the basic concepts of group theory...The numerous images (more than 300) are the heart of the text. As this work enables readers to see, experiment with, and understand the significance of groups, they will accumulate examples of groups and their properties that will serve them well in future endeavors in mathematics. Recommended --J. T. Zerger, Choice
If you teach abstract algebra, then this book should be a part of the resources you use. While the phrase "visual abstract algebra" may seem to be a contradiction, the diagrams in this book are an existence proof to the contrary. They are clear, colorful and concise very easy to understand and sure to aid the students that have difficulty in internalizing the abstract nature of the subject matter. Especially appealing are the colorized tables of groups and their operations.
The approach is a very slow one in the sense that a foundation of common operations and rearrangements that are groups that are first examined with text and images. A large number of exercises are included at the end of each chapter and detailed solutions with colored images found in an appendix.
this book could also serve as a text in a first course in abstract algebra provided that the course is limited to groups only or you used supplementary material for rings and fields. If your course is restricted to groups only, then this is the best book available. --Charles Ashbacher, Journal of Recreational Mathematics
This text approaches the learning of group theory visually. It allows the student to see groups, experiment with groups and understand their significance. It is ideal as a supplement for a first course in group theory or alternatively as recreational reading.
Top customer reviews
There are lots of examples to think about and many problems to work through. Very readable.
The book is well written and well illustrated. I took one night to read through the first 5 chapters, that shows how easy it is to understand the concepts. (It helps, may be, because I had read the Grossman and Magnus book, however the later is not a pre-requisite reading).
I am also very pleased that the author uses Cayley diagrams to show how Subgroups, Cosets and Normal Subgroups could be visualized. This is a real break-through in teaching abstract stuff like Group Theory - a real tough nut to crack for most Math students. Don't forget the inventor of Group - Evariste Galois - had hard time making himself understood by even the greatest mathematicians of his time - Cauchy, Fourier, Poisson, etc.
This is the book to read before anyone attempting to study Group Theory in a formal textbook way.
2. For math hobbyist, it will show you the beauty of mathematics. (This is vague, and sorry I don't want to elaborate on this)
3. For serious math learners, this certainly will not be your only algebra book, but by reading this you will have some useful tools/insights (really really useful insights) in hand when you begin your second book on the subject.
4. The problems in the book are okay~~~~~~~~, but the meat of the book lies in the main readings.
5. Many typos, mistakes, errors, and not conventional and sometimes confusing notations (especially those that have to do with "multiplication", where in a usual (abstract) algebra book ab means b first then a acts on b, but this is not always consistent in this book).
6. But what-the-hell to 5, this will not be your only book, take the things you need and move on. We don't need a diamond to kill a bird, any big enough rock will do the job.