Mathematics Books

Geometry algorithms and computer graphics uses a lot of math, and many algorithms books assume the reader has some knowledge of basic math (geometry, algebra, trig, etc). The books on this page are not about algorithms; instead they give this math background and more, especially about geometry.


(2003)		Four Colors Suffice: How the Map Problem Was Solved by Robin Wilson
		New: $32.20 List: ~~$41.00~~ Buy Used from: $2.15

	The four-color conjecture, formulated in 1852, was among the most popular unsolved problems in mathematics. It stated that only four country colors are needed in any map so that neighboring countries are always colored differently. The first correct proof was completed in 1976 using a computer to verify almost 2000 special irreducible cases. This book describes the history of this problem, and its solution.


(2002)		Standard Mathematical Tables and Formulas (31st Edition) by Daniel Zwillinger
		New: $50.70 List: ~~$59.95~~ Buy Used from: $40.57

	This is an essential (and reasonably priced) reference work that puts a wealth of well-organized math formulas and tables at your finger tips. It has extensive coverage of discrete math, trigonometry, geometry, linear algebra, calculus, special functions, numerical methods, probability, and statistics. This may be the best of the math formula handbooks with many fundamental geometric computations.


(2002)		Concise Encyclopedia of Mathematics (2nd Edition) by Eric Weisstein
		New: Out of Stock List: $139.95 Buy Used from: $124.00

(2002)		Concise Encyclopedia of Mathematics CD-ROM (2nd Edition) by Eric Weisstein
		New: $95.00 List: ~~$119.95~~

	This excellent "concise" reference work is a mere 1969 pages. It falls short of giving comprehensive encyclopedic coverage of all mathematics, but it is especially complete in the area of geometry. It is also an evolving work with an online site The World of Mathematics run by Eric Weisstein who accepts contributions, all of which he screens and edits. To see just how good this work is, go to the site, and search for the definition of something you are familiar with. There are lots of definitions, formulas, figures, references, and cross-referencing links. This is a great piece of work that is easy to consult.


(2001)		Geometry (Cliffs Quick Review) by Edward Kohn
		New: $9.99 Buy Used from: $2.90

	This is a thorough summary of Euclidean synthetic geometry. Great as a quick review or a compact reference source.


(1999)		Handbook of Discrete and Combinatorial Mathematics edited by Kenneth Rosen, John Michaels, & Jonathan Gross
		New: $101.88 List: ~~$129.95~~

	This is another huge handbook (1248 pages) which comprehensively covers the field of discrete mathematics. It includes large sections on Graph Theory (12 chapters, 108 pages) and Discrete and Computational Geometry (8 chapters, 92 pages). Implementation details are given for many essential algorithms in these areas. In addition, there are many other chapters in fields that can be brought to bear on geometry algorithm solutions. This is a good general reference to own.


(1998)		A Vector Space Approach to Geometry by Melvin Hausner
		New: $17.05 List: ~~$18.95~~ Buy Used from: $7.95

	This is a high school geometry book with a new twist - it's based completely on linear algebra. Its about time. Geometric intuition can be taught as easily, or better, using modern methodologies. And it ends up being immensely more useful to the computer-literate generation. Even if you took classical geometry before, get this book, and re-educate yourself. If you want to learn computer graphics, this book will give you the right tools to succeed.


(1998)		Graph Theory & Its Applications by Jonathan Gross & Jay Yellen
		New: Out of Stock List: $89.95 Buy Used from: $29.91

	This fantastic book gives a comprehensive and cohesive overview of modern graph theory. It has lots of theory (with short proofs) but the emphasis is conceptual and intuitive. It also links the theory to concrete applications with algorithms given by conceptual pseudo-code. Although there are no implementations in a specific programming language, software design issues are addressed. Topics covered include: spanning trees, connectivity, optimal traversal, drawing graphs, coloring graphs, network flows and much more. If you need to write software for graphs, this is a must-have reference. There is a web site for this book www.graphtheory.com.


(1997)		Circles : A Mathematical View (Revised Edition) by Dan Pedoe
		New: $20.95

	This is a revised edition of the mathematical classic originally published in 1957. The late Dan Pedoe was one of the master geometers and math expositors of the 20th century. He brings out the amazing properties of this simple aesthetic geometric figure that has fascinated thinkers for thousands of years.


(1995)		Combinatorial Geometry by Janos Pach & Pankaj Agarwal (Contributor)
		New: $113.00 List: ~~$132.00~~

	This book focuses on arrangements of geometric objects: points, lines, circles, and other convex sets. Some topics covered are: polygon approximation, packings and coverings, cell decomposition, planar and geometric graphs, and geometric discrepancy.


(1991)		Old and New Unsolved Problems in Plane Geometry by Victor Klee and Stan Wagon
		New: $31.95 Buy Used from: $12.95

	This book presents 12 major unsolved problems about plane geometry, and 12 more about number theory. Each problem is discussed in its historical context, and other problems related to it are also presented. It is written in an easy-to-understand style, but does not sacrifice relevant details. There are 2 chapters for each problem, one elementary and then a second advanced one. This book is not about algorithms, but gives insight into the scope and limits of modern geometry. Some of the problems presented are relevant to modern computational geometry. An amusing book which can be recommended as bedtime reading so you can solve the problem in your dreams :-)


(1989)		Introduction to Geometry (2nd Edition) by Donald Coxeter
		New: $74.40 List: ~~$93.95~~ Buy Used from: $68.00

	This book was originally published in 1961, and is a modern classic by the 20th century's foremost master of geometry. It covers a multitude of geometric techniques and computational methods from the mathematician's point of view. Even though it predates widespread use of computers, it is a fundamental reference for modern geometry, and its republication in 1989 attests to this fact. If you are faced with an unfamiliar or difficult geometric problem, this would be the first place to look. It covers all branches of modern geometry with a clear overview of each.


(1988)		Geometry : A Comprehensive Course by Dan Pedoe
		New: $16.46 List: ~~$21.95~~ Buy Used from: $3.30

	Originally published in 1970, this is a classic work by a great geometer of the 20th century. It is math oriented but contains many useful computational methods along with a compendium of geometric facts and insights. It has an interesting first chapter about what one can do with vectors. This book has more extensive information about the properties of circles than any other book we've seen.


(1987)		Mathematical Recreations by Rouse Ball & Donald Coxeter
		New: $11.53 List: ~~$16.95~~ Buy Used from: $3.95

	This timeless classic was originally written by Rouse Ball around 1900, and later updated by the great geometer Donald Coxeter. It includes polyhedron puzzles, chessboard recreations, magic squares, map coloring, and much more. This book is an entertaining stimulus for creative thinking.


(1973)		Regular Polytopes (3rd Edition) by H.S.M. Coxeter
		New: $11.53 List: ~~$16.95~~ Buy Used from: $5.50

	This is Coxeter's landmark treatise on polytopes first published in 1947 (2nd Ed 1963, 3rd Ed 1973). This classic "sequel to Euclid's Elements" completely enumerates all n-dimensional regular polytopes. It also covers quasi-regular solids, honeycombs, star-polytopes, and more. This is a pure math book, but an essential reference for anyone working with symmetric structures (crystals, molecules, etc). It is also a great aid for visualizing multidimensional space.


(1967)		Geometry Revisited by Donald Coxeter & Samuel Greitzer
		New: $24.75 List: ~~$27.50~~ Buy Used from: $23.99

	This classic is a great undergraduate geometry text. It is more focused than Coxeter's all-encompassing Introduction to Geometry, but this actually makes it more suitable for a semester course. Even though it was written more than 30 years ago, one cannot find a better geometry text today. It is also very reasonably priced. Get a copy of this one.