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Vector Geometry, by Gilbert De Beauregard Robinson
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This brief undergraduate-level text by a prominent Cambridge-educated mathematician explores the relationship between algebra and geometry. An elementary course in plane geometry is the sole requirement�for Gilbert de B. Robinson's text, which�is the result of several years of teaching and learning the most effective methods from discussions with students.�
Topics include lines and planes, determinants and linear equations, matrices, groups and linear transformations, and vectors and vector spaces. Additional subjects range from conics and quadrics to homogeneous coordinates and projective geometry, geometry on the sphere, and reduction of real matrices to diagonal form. Exercises appear throughout the text, with complete answers at the end.
- Published on: 2012-07-21
- Original language: English
- Number of items: 1
- Dimensions: 9.02" h x .41" w x 5.98" l, .59 pounds
- Binding: Paperback
- 194 pages
Most helpful customer reviews
13 of 13 people found the following review helpful.
I like this book immensely.
By Bruce R. Gilson
The book I got was the original hardbound edition because I could actually get it more cheaply than the recent Dover reprint. But I am happy to see that Dover did reprint this book, because it is probably the best book on its subject matter that I have seen. The only negative comment I might have is that it is a relatively slim book but covers a lot of ground, so it might be too compressed for some students.
Some books introduce vectors as directed line segments, others as ordered n-tuples (where n is the dimensionality of a space). This book very quickly gets to both concepts, and even points out that a vector is really an equivalence class of directed line segments, something I had stated to someone whom I was helping to understand vector algebra, but something I do not recall seeing in any book.
The relationship of projective, affine, and metric Euclidean geometry is covered very well, better than I have seen it elsewhere, and homogeneous coordinates are introduced in a way that I think is better motivated than what I have seen in most books dealing with projective geometry. The relationship between Euclidean, elliptic, and hyperbolic geometry is also covered. Vector methods are used to cover many topics (such as spherical trigonometry and linear programming) that would usually not be introduced in a book entitled "Vector Geometry." The relationship between matrices and vectors is covered as well as in any linear algebra book, and all in all, this book goes far beyond other books that purport to cover the same subject.
I cannot rate this book too highly. As I said, I am glad to see that Dover has reprinted it.
0 of 0 people found the following review helpful.
first book on mathematics at u of toronto
By Elma Miller
1st yr student in maths at U of T. Very condensed, many errors, but highly challenging, difficult but eminently satisfying. Although G de B was not my lecturer, he was still around. I learned much from his book.
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