Algebra and Geometry Hardcover – 12 May 2005
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'The presentation is traditional, informal, and relaxed.' Zentralblatt MATH
This text gives a basic introduction and unified approach to algebra and geometry, two of the cornerstones of undergraduate mathematics. The emphasis is constantly on the interaction between these topics. For ease of use by students, the text is divided into short chapters, with exercises at the end of each.See all Product Description
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Top Customer Reviews
This is the one book that I would recommend that anyone in their first year of maths at university should buy.
Les notions sont reprises depuis le début, et chapitre après
chapitre, Beardon nous fait voyager dans plusieurs domaines
mathématiques, avec simplicité et rigueur.
Lorsqu'un résultat est utilisé sans démonstration nous
sommes averti tout de suite, et la vitesse adoptée dans
ce livre me convient parfaitement.
Je ne peux que recommander ce livre pour quiconque désire
se promener dans la géométrie hyperbolique, domaine abordé
dans les derniers chapitres.
Most Helpful Customer Reviews on Amazon.com (beta)
I truly wish I had a course which devoted itself to the complete digestion of this book. I used it for self-study and found that it served me very well. It does not fall easily into the structure of most American math sequences, as these departments are often forced to "modularize" mathematics into semester-bite-sized pieces. I believe that this often has a negative impact on the appreciation of mathematics as a whole, especially at the nexus between doing basic calculus and appreciating proof, rigor and beauty in mathematical structures.
The book may not go into the same depth as, say, Artin's "Algebra", but rather the foundational concepts for the study of algebra and geometry are emphasized in a variety of settings. This is very important as the study of "abstract algebra" is precisely that if you do not have a wide-selection of examples and contexts to draw from. This book has plenty of exercises of varying difficulty, and everything in this book is accessible to the beginning student of mathematics.
Bottom line: If you are someone interested in learning linear algebra, geometry, group theory, Mobius transformations, complex variables all in a rigorous yet introductory level, this is the book for you. Developing a robust mental model for mathematics requires building several thin layers at a time. This means not going too deep too quickly, but rather snorkeling around the entire reef, before you gear up for further exploration.
However, the Kindle edition is scanned so badly from print that it's almost unusable.
For example, in Section 4.2, the scalar product of two vectors x and y is defined thusly:
x dot y = x1<scanner left this mostly blank> + x2y2 + x3y3
Yes, an intelligent person can figure out what's missing. But you shouldn't pay $35 for a book and then need to "fill in the blanks." The entire content should be there.
Any proofreader would have caught that omission, and the eBook contains other similar omissions.
It is a disgrace that Cambridge UP would issue an eBook in such poor condition.