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A Vector Space Approach to Geometry (Dover Books on Mathematics) Paperback – 28 Mar 2003


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Amazon.com: HASH(0x8c95e444) out of 5 stars 8 reviews
39 of 39 people found the following review helpful
HASH(0x8c22ba80) out of 5 stars A useful High School Geometry book for Computer Graphics 23 Dec. 2000
By Shankar N. Swamy - Published on Amazon.com
Format: Paperback
This is essentially a high school geometry book; but with a difference - its fully linear algebra based approach. If you are a beginner in computer graphics, and want to review elements of geometry and linear algebra, you will benefit from studying through this book.
The almost four hundred pages book is remarkably readable and is very consistent at that. There are both worked out examples and exercise problems, for each section - which are very useful for self-study or revision.
If you have never had an introduction to linear algebra before, you may have to supplement this with a linear algebra book. But if you have not had a good course in elementary geometry, and your motivation is getting started with elementary Computer Graphics/CAD and the likes, this is a good book for that.
Interspersed with the subject matter discussed at a elementary level, in a useful, stimulating style are small, interesting discussions on such useful and relatively advanced topics as function spaces, fixed point theorem in affine transformation, simplices, symmetries etc. I rarely have seen any of these topics mentioned in a book aimed at this level.
Highly recommended for freshman undergraduates and those without any mathematics experience who want to start in Graphics, CAD, CAGD and the likes. Recommended also for experienced practitioners in Graphics: it is good to review the fundamentals once in a while, and a well written book that is a quick read helps at that!
34 of 35 people found the following review helpful
HASH(0x8c4009b4) out of 5 stars Perfect for first and second year, or physicists 2 Dec. 2000
By Ken Braithwaite - Published on Amazon.com
Format: Paperback Verified Purchase
The basics of the very deep connection between geometry and vector spaces. If you do undergrad math you will see everything in this book during first and second year. But what this book does is fit those bits together. He does this very nicely at an introductory level. If you are not in math, but need to learn some geometryfor a physics course, this will be a useful book.
It is a formal math book, with axioms, but it is strong on motivation and has some quite amusing examples.
Keywords: tangent spaces, determinants, barycentric, linear transformations.
33 of 35 people found the following review helpful
HASH(0x8f102150) out of 5 stars I never thought vectors could be so interesting! 12 Jun. 2000
By Matthew Scarpino - Published on Amazon.com
Format: Paperback
Having suffered through enough dry, pointless courses in vector algebra and analysis, this book was a genuine pleasure. Requiring no mathematical background whatsoever, Mr. Hausner makes the properties of vectors and matrices (cross-products, determinants, eigenvalues) intuitively obvious. With detailed descriptions and graphics, the science of vectors is made very clear. Further, Mr. Hausner's use of levity and practical examples makes for a very enjoyable read.
26 of 27 people found the following review helpful
HASH(0x8c025ab0) out of 5 stars The best math book I have read 8 Sept. 2000
By Peter S. Shirley - Published on Amazon.com
Format: Paperback Verified Purchase
I have been reading many books on vector analysis, geometry, and linear algebra this year. Many of them have been good, but this book stands alone for deriving the basics of determinants, vector products, geometry, etc. in a clear and intuitive manner along with great examples. A wonderful, wonderful book.
19 of 19 people found the following review helpful
HASH(0x8c7bd588) out of 5 stars Must have if on the road to Linear Algebra 16 Sept. 2005
By Henry Lenzi - Published on Amazon.com
Format: Paperback
This is one beautiful book. The whole book is one long thread about geometry and vectors. To make this review short, I'll say you absolutely *must* have this book if you want to set yourself on the proper track to Linear Algebra. In fact, this book could almost be considered an Analytic Geometry book 'done right.' But be careful: I said almost. By that I mean that some staple AG stuff is missing. For instance, no long discussions about a plane intersecting a sphere, no quadric surfaces. So it does lack the sort of drill exercises you need to succeed in an AG class - but such stuff is not its purported goal, anyway - but then again, your 'vector 6th sense' will increase tremendously with this book. I wish I had discovered this book while I was having my Analytic Geometry. Now I'm taking a Linear Algebra class and I'm glad I found this book.
It also is full of other interesting insights and relations to other topics, including some applications to Calculus (motion) and some topology.
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