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Algebra and Geometry Hardcover – 12 May 2005

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Product details

  • Hardcover: 340 pages
  • Publisher: Cambridge University Press (12 May 2005)
  • Language: English
  • ISBN-10: 052181362X
  • ISBN-13: 978-0521813624
  • Product Dimensions: 15.2 x 2.2 x 22.8 cm
  • Average Customer Review: 4.3 out of 5 stars  See all reviews (3 customer reviews)
  • Amazon Bestsellers Rank: 523,275 in Books (See Top 100 in Books)
  • See Complete Table of Contents

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'The presentation is traditional, informal, and relaxed.' Zentralblatt MATH

Book Description

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.

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Most Helpful Customer Reviews

7 of 7 people found the following review helpful By Aidan Fox on 30 Aug. 2009
Format: Paperback
The book's preamble suggests that the text is a basic introduction to algebra and geometry. On a pre-calculus level I would not totally agree with this, since the text shows the links between the two topics in terms of group theory. This would seem to be a vital link, but does raise the level of the text away from what I would term a 'basic introduction'. However, that said, it appears to deal with the topics (and the links between them) in a comprehensive fashion.
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20 of 21 people found the following review helpful By Sarah on 16 Mar. 2006
Format: Paperback
As a first year student at Cambridge I found this book completely invaluable. It rigorously covers lots of topics, giving clear step-by-step proofs and explanations. Excellent.
This is the one book that I would recommend that anyone in their first year of maths at university should buy.
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6 of 14 people found the following review helpful By Antoine Zahnd on 12 Oct. 2010
Format: Hardcover
J'ai beaucoup de plaisir à lire ce livre.

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.

Antoine Zahnd
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Most Helpful Customer Reviews on Amazon.com (beta)

Amazon.com: 3 reviews
21 of 22 people found the following review helpful
Excellent first glimpse into the algebraic world 3 Aug. 2007
By Justin Curry - Published on Amazon.com
Format: Paperback Verified Purchase
This book has become a bible of sorts to first-year students studying mathematics at Cambridge. Its quality as a text cannot be doubted, although its usefulness for further years of algebra is limited. This is precisely the book to study from if you are doing vector calculus and differential equations, but still aren't sure about doing mathematics seriously. If you have not taken a course in linear algebra or abstract algebra, buy the paperback copy of this book and start reading right away. Beardon starts with (what I believe is the best way) the study of permutations (think about shuffling a deck of cards) to develop an intuition of the basic notions of a group. From here the fundamentals for further study in mathematics is laid. I won't repeat the table of contents here, as you can look for yourself, but believe me when I say that mastering the concepts in this book will serve you very well.

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.
4 of 4 people found the following review helpful
Excellent explanation of how algebra can be used to describe and manipulate objects in space 26 July 2008
By Charles Ashbacher - Published on Amazon.com
Format: Paperback
This book is an introduction to group theory, complex numbers and linear algebra. In an unusual approach, the first topic covered is group theory, although it is only a small part of a small toe placed in the water. Chapters covering the set of real numbers, complex numbers and three-dimensional vectors follow this. Vector spaces, systems of linear equation, matrices, and eigenvectors are the topics of the next chapters. The final chapters are "Linear maps of Euclidean space", "Groups", "Mobius transformations", "Group actions" and "Hyperbolic geometry."
The overall theme is to unify the two areas of algebra and geometry by showing that space itself can be described algebraically by repeating the use of real numbers to create multiple dimensions. Large numbers of exercises are included at the ends of the sections, making it easy to assign homework or to further study by working longer and deeper. However, no solutions to the problems are included.
While this book certainly is a good one in these areas, I am puzzled as to where it would fit into an undergraduate curriculum. Abstract algebra and linear algebra are separate courses in the curriculum and having a course covering both would certainly be an oddity. However, that criticism aside, the author does an excellent job in explaining how space can be described and transformed by first representing it as a set of vectors and then transforming those vectors.
2 of 3 people found the following review helpful
Excellent book, bad scan into Kindle 27 Dec. 2011
By N.S. Palmer - Published on Amazon.com
Format: Kindle Edition Verified Purchase
Other reviewers have addressed the merits of the book's content, which is excellent.

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.
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