Book Description

The distinctive approach of Henderson and Taimina's volume stimulates readers to develop a broader, deeper, understanding of mathematics through active experience—including discovery, discussion, writing fundamental ideas and learning about the history of those ideas. A series of interesting, challenging problems encourage readers to gather and discuss their reasonings and understanding. The volume provides an understanding of the possible shapes of the physical universe.The authors provide extensive information on historical strands of geometry, straightness on cylinders and cones and hyperbolic planes, triangles and congruencies, area and holonomy, parallel transport, SSS, ASS, SAA, and AAA, parallel postulates, isometries and patterns, dissection theory, square roots, pythagoras and similar triangles,projections of a sphere onto a plane, inversions in circles, projections (models) of hyperbolic planes, trigonometry and duality, 3-spheres and hyperbolic 3-spaces and polyhedra.For mathematics educators and other who need to understand the meaning of geometry. ... Read more

Book Description

The easiest way to solve the hardest problems! Geometry's extensive use of figures and visual calculations make its word problems especially difficult to solve. This book picks up where most textbooks leave off, making techniques for solving problems easy to grasp and offering many illustrative examples to make learning easy. Each year more than two million students take high school or remedial geometry courses. Geometry word problems are abstract and especially hard to solve--this guide offers detailed, easy-to-follow solution procedures. Emphasizes the mechanics of problem-solving. Includes worked-out problems and a 50-question self-test with answers. ... Read more

Reviews (3)

Doesn't live up to its title
This book is, at best, a quick review for those already familiar with the subject. The "word problems" are the same type of basic problems one would find in any geometry textbook; in other words, there are no interesting real-life story problems. To accommodate the book's small size, pictures and diagrams are sacrificed in favor of endless definitions. Example: "Adjacent angles are two angles in a plane that have a common vertex and a common side but no common interior points." This approach makes the book concise, but dry.

Consice review, but has typos
The book has a concise review of geometry. It lists about five to ten related theorems at a time, and then gives about two examples for each. This would be a good review of geometry for someone who is preparing for the SAT or GMAT if there were not so many typos. There are typos such has having the wrong diagram for a given question and listing questions that are not consistent with information in the associated diagrams.

If you are learning geometry for the first time or expect difficulty in re-learning geometry, I would not recommend this book. However, if you need just a quick geometry refresher, then you can probably detect the typos without too much frustration and learn the basic theorems of geometry.

You Need More Practice and More Review? Buy if you must!
This book hardly teaches "how to solve word problem in Geometry". It just crams as much geometry definitions and theorems as it can into small space which can only confuse students that are already confused. In fact, the listing of concepts are not ordered well either.

I almost gave this book 1 star rating since I strongly believed this book DID NOT do the job as its' cover seem to promise. But!...I gave the author some credit for her good intentions and thought about some that it MIGHT benefit...

First, she gives us the shortest Geometry review ever! (I think even Cliff Notes does more)...and points to couple of examples that are somewhat helpful. It adds short exercises (about 10 per chapter) with complete solutions (which is nice). Yes, it may be good for those that want to quickly review (or the quickest review), but there are other books out there that are MUCH more...MUCH better.

I recommend: Geometry the Easy Way by L. Leff. And in many Test Prep. books like those of SAT and GRE contains surprisingly good reviews on Geometry with very insightful problems. I personally like Kaplan's materials.

One more note: The other book of this series "How to Solve Word Problems in Algebra" on the contrary does an excellent job! It really helps. ... Read more

Book Description

Describes orthgonal and related Lie groups, using real or complex parameters and indefinite metrics. Develops theory of spinors by giving a purely geometric definition of these mathematical entities. Covers generalities on the group of rotations in n-dimensional space, the theory of spinors in spaces of any number of dimensions and much more.
... Read more

Reviews (3)

Looking to link Quantum Mechanics with Group Theory?
This book is extremely easy to understand compared to other texts on the subject. It serves well to lead you to other books such as Hermann Weyl's text on Quantum Groups. The author has the most intuitive explanations that I have seen in any other works on the subject. This is extremely useful for me, since I was trained as an electrical engineer, and sometimes I feel that authors of mathematics text get lost in formal definitions in n space; although important I feel that relating them to basic understandable behavior in 3-space is especially useful, and done well in this text. It is my current thought that formulating a certain level of abstraction is necessary for the furthering of mathematics, like what is done with Geometric Algebra, but making these relations clear for myself at least in the physical world has been an important hard earned step. I believe this book to be simply outstanding and recommend it to anyone interested in linking group theory to Quantum Mechanics, especially Engineers who don't want to physically build anything but like math, like myself. On the subject, I used this book to understand the mathematics in the majority of texts on Quantum Mechanics, I approach the equations now, not as an abstract concepts but looking at their space behavior even for n space; Hopefully I will be able to exploit some useful properties of the lie group useful for Quantum Computation. This book is one of my current favorites; I recommend it, but especially to those interested in Quantum Mechanics or Group Theory from a non Mathematics background. Of course this is not a beginning text, but it can be used along side a beginning text such as "Algebraic Structures" or "A course on Group Theory" both from Dover. I have never taken a class on Group Theory but with these texts and about 5 others on Topology and some other subjects along with several on Quantum Computing (my application for leaning group theory) I was able to teach myself what I needed; but group theory is covered in other places, they just don't call it that. This book was the most helpful, the best written and the most intuitive. A classic... The only thing bad about it is that more things have happened in the subject since it was published, but this covers the main points, and is where you may want to start.

Masterpiece based on the original lecture notes of Cartan
This book is a great work on the subject of spinors. Since it is based solely on Elie Cartan's work, the termonology and wording reflects that of the transition coming out of the Post-Victorian math era (i.e., when quaternions and the more abstract mathematics where used for applied calculations in physics, which have been replaced with scalars and vectors). The geometrical definition layed down in the third chapter makes this a very comprehensive book for the newcomer to the subject. Quote page 42., "A spinor is thus a sort of "directed" or "polarized" isotropic vector; a rotation about an axis through an angle of 2pi changes the polarization of this isotropic vector."

Review of theory of spinors
This is an excellent introductory book on spinors, the basic mathematical object used to represent particles with spin.

The author begins by defining the spinor as a form of a square root of a 3 dimensional null vector. Scalars, vectors and tensors are then described by their properties under simple geometrical transformations such as reflection and rotation. The author then represents vectors as 2x2 matrices. The transformational properties of spinors are defined by their relation to vectors and tensors under these same simple transformations. The author then shows how spinors are useful for finding the irreducible representations of the rotation group. These concepts are then extended to higher dimensional spinors. Specific applications are shown for Laplace's equation, the Dirac equation and to general relativity.

The is an introductory, inexpensive, brief and easy to read book. The book also covers a fair amount of ground. It is an excellent first book for the subject. It does not contain modern developments in the field or some elements of the current notational system for representing spinors. Yet, for me it was the first book that gave me a sense of really understanding the significance of the Dirac equation and quantum physic's concept of spin. ... Read more

Book Description

College Geometry offers readers a deep understanding of the basic results in planegeometry and how they are used. Its unique coverage helps readers master Euclidean geometry, in preparation for non- Euclidean geometry. Focus on plane Euclidean geometry, reviewing high school level geometry and coverage of more advanced topicsequips readers with a thorough understanding of Euclidean geometry, needed in order to understand non-Euclideangeometry. Coverage of Spherical Geometry in preparation for introduction of non-Euclidean geometry. A strongemphasis on proofs is provided, presented in various levels of difficulty and phrased in the manner of present-daymathematicians, helping the reader to focus more on learning to do proofs by keeping the material less abstract. For readers pursuing a career in mathematics. ... Read more

Book Description

This comprehensive, best-selling text focuses on the study of many different geometries -- rather than a single geometry -- and is thoroughly modern in its approach. Each chapter is essentially a short course on one aspect of modern geometry, including finite geometries, the geometry of transformations, convexity, advanced Euclidian geometry, inversion, projective geometry, geometric aspects of topology, and non-Euclidean geometries. This edition reflects the recommendations of the COMAP proceedings on Geometry's Future, the NCTM standards, and the Professional Standards for Teaching Mathematics.References to a new companion text, Active Geometry by David A. Thomas encourage students to explore the geometry of motion through the use of computer software. Using Active Geometry at the beginning of various sections allows professors to give students a somewhat more intuitive introduction using current technology before moving on to more abstract concepts and theorems. ... Read more

Reviews (2)

A nice little book
This book covers a broad range of geometries, including convexity and an introduction to topology. It presents revelent definitions followed by intuitive theorems (some with full proofs, others partial).
For a general study in geometry at the university level, this book is quite adequate. It's use of analytic methods and exploratory exercises, makes it an appropriate introduction for the undergraduate who is considering further studies in geometry or analysis.

for students?
This is the required text in my Eucliden Geometry class in college and while for the most part I find this book a useful tool, I often find terms and definitions either underexplained or introduced without definition, which can be frustrating to a student new to the dicipline. It has a very easy-to-follow introduction to non-Euclidean geometies, however, and I recommed the book especially on this level. Overall, however, I feel it could be written in more of a student-friendly manner. ... Read more

Book Description

Some geometry study aids are overly complex and do more harm than good. 501 Geometry Questions provides concise questions and clear answers to familarize students with geometry questions. Standardized tests-takers will find this book an indispensable aid. Math concepts and properties are made clear, including trigonometry basics, angles and lines, ratios, proportion, perimeter, and surface measures. ... Read more

Reviews (1)

Too many errors!
This book would be very helpful and comprehensive if it weren't for so many errors.It's very frustrating to try and learn when parts of a question or answer are wrong (and obviously so).Makes you wonder who, if anyone, double-checked the problems to make sure they worked out correctly. ... Read more

Book Description

Geometry in Action uses Sketchpad™ to awaken student creativity through discovery-based learning. It supplements any college geometry course in which The Geometer's Sketchpad is used. All students must have access to The Geometer's Sketchpad. Each book is packaged with a CD-ROM for students that illustrates what is meant by geometry in action. Students explore 27 sketches prepared by the author to demonstrate Sketchpad's capabilities by dragging points to see shifts in graphs, by animating tesselations to create new patterns, and much, much more! Also included on this CD is the Poincaré Disk, a Sketchpad file used to dig deeper into non-Euclidean geometry with The Geometer's Sketchpad. ... Read more

Book Description

The classification of algebraic surfaces is an intricate and fascinating branch of mathematics, developed over more than a century and still an active area of research today. In this book, Professor Beauville gives a lucid and concise account of the subject, expressed simply in the language of modern topology and sheaf theory, and accessible to any budding geometer. A chapter on preliminary material ensures that this volume is self-contained while the exercises succeed both in giving the flavor of the classical subject, and in equipping the reader with the techniques needed for research. The book is aimed at graduate students in geometry and topology. ... Read more

Book Description

Captain Invincible and his intrepid space-dog, Comet, are on a perilous journey back to Earth!

Throughout their mission, the fearless captain and his canine sidekick encounter asteroids, poisonous gas, and alien beings. But will their knowledge of three-dimensional shapes, including cubes, cones, and pyramids, help our heroes navigate past these obstacles -- and make it safely home?

Reviews (1)

Super book!
Set in a comic book format, this book has been a favorite of my 4 year old son since we bought it. A very simple book, and very appropriate for preschoolers. The writing is a little lame at one point, but my son doesn't care and thoroughly enjoys this book ( and he's learned some simple math concepts without realizing he's been taught). ... Read more

Book Description

Topology of Surfaces, Knots, and Manifolds offers an intuition-based and example-driven approach to the basic ideas and problems involving manifolds, particularly one- and two-dimensional manifolds. A blend of examples and exercises leads the reader to anticipate general definitions and theorems concerning curves, surfaces, knots, and links--the objects of interest in the appealing set of mathematical ideas known as "rubber sheet geometry." The result is a book that provides solid coverage of the mathematics underlying these topics. ... Read more

Reviews (3)

Fun, but not very substantive.
This is a relatively fun romp through some very interesting concepts, but it lacks rigor.The book could have been much stronger if the author had simply developed some of the basic concepts (compactness, connectedness, homeomorphisms, homotopy, etc) rather than do a little hand-waving around a nice illustration.As it stands, this book is only 140 pages long, and does not develop any of its topics (manifolds, surfaces, graphs, knots) adequately.This book is far too weak to serve as a good text.Kinsey's TOPOLOGY OF SURFACES is much stronger, and costs less.Or look as something like Gamelin's INTRO TO TOPOLOGY.Or even Schaum's outline GENERAL TOPOLOGY, which deals with the basics, but is highly readable and rigorous.

Very Misleading Title, Quite Thin, No Rigor, and Overpriced
This book is subtitled "A First Undergraduate Course" but is certainly below undergraduate level.A high school student could easily follow this--which might be a good thing in certain cases--but the rigor is lacking.In fact, there is barely a hint of any rigor whatsoever.It is mostly intuitive arguments and the author often says things like "but we won't bother worrying about mathematical technicalities".It does get you to be able to visualize certain things well, but the visualization techniques can be found in other books also.The book is very thin and a quick read--hardly worth the money they are trying to get for it.If you're really at the undergraduate level and want to learn some topology, try something like Mendelson's "Introduction to Topology" by Dover or one of the excellent topology books in the series "Undergraduate Texts in Mathematics" by Springer.Munkres is also a classic.If you're not an undergraduate in a math related field and just want to know about the ideas behind topology or perhaps see some visualization techniques, try something like "The Shape of Space" by Weeks.Overall I was very disappointed with this text.If you could purchase this book for under $20 it might be worth it, but even then I think the other books I quoted are better in both price and substance.

No math library is complete without this book
This book presents the topology of surfaces, manifolds and knots in a manner that is reachable for undergraduate students with only a knowledge of calculus.Some linear algebra might be helpful.The text is written in a style that is easy to follow and there are superfluous examples.The exercises in the text are well thought out and are not extremely difficult.The exercises complement the text very well.The text makes clear a lot of difficult concepts such as isotopic surfaces as opposed to homeomorphic surfaces.I particularly enjoyed the manner in which the topology of knots was explained.After reading this text, the reader should be able to better visualize the projective plain and even the Klein bottle as it exists in 4-dimensional space.I have not read a text on topology that I enjoyed reading as much since Munkres.This text is a must have for any topologist. ... Read more

Reviews (1)

The great master's way of looking at geometry
About the set: Klein's Elementarmathematik lectures was intended as a survey of mathematics for those who already knew most of the technical detail, especially future teachers, but who perhaps lacked a good understanding of mathematics as a whole. The lack of a broad perspective is probably at least as big a problem today as it was then, so Klein's text is still valuable. Klein also frequently discusses historical and pedagogical aspects, and the tone is quite informal throughout.

About this volume: The first part is an elementary introduction to vector techniques in geometry, which is probably not very interesting for the modern reader. The second part of the book is more interesting. Klein has explained in his preface that he wants to present a unified view of geometry, and here in the second part he shows how many diverse concepts can be brought together under the notion of transformation. This approach paves the way for a discussion of Klein's own Erlanger Programm in part three. This third part is very nice. First there is a "systematic discussion of geometry", where the Erlanger Programm is one of the themes, then there is a discussion of the foundations of geometry. This part of the book makes great pleasure reading, as Klein speaks freely and informally, and sometimes voices his personal opinions. ... Read more

Book Description

With the ever-rising volume worldwide of visual content on computers and communication networks, it becomes increasingly important to understand visual processing, to model and evaluate image formation, and to attempt to interpret image content. "Numerical Geometry of Images" presents an authoritative examination of new computational methods and algorithms in image processing and analysis.In addition to providing the requisite vocabulary for formulating problems, the book describes and utilizes tools from mathematical morphology, differential geometry, numerical analysis, and calculus of variations. Many applications, such as shape reconstruction, color-image enhancement and segmentation, edge integration, path planning, and calculation invariant signatures are explored.

Topics and features:

*Introduces new concepts in geometric image modeling and image interpretation (computer vision)

*Provides the requisite theoretical basis and progresses to using key tools

*Offers a solution to the face-recognition problem by generalizing principles from texture-mapping methods in computer graphics

*Contains numerous helpful exercises and solutions to facilitate learning

*Presents a new perspective on solving classic problems, as well as classic approaches to solving new problems

*Uses industry-proven variational geometric methods and numerical schemes. ... Read more

Reviews (1)

Some additional info.
The book is an extended version of my lecture notes.
Including introduction to variational methods, differential geometry, level sets and fast marching numerical methods,
and geometric active contours for segmentation (with Matlab
pseudo code), 3D face recognition, texture mapping and more
applications.

Thanks to the many who already bought the book.
(its a bit cheaper now at B&N ;-) ... Read more

Book Description

This book is the first to present a new area of mathematical research that combines topology, geometry, and logic. Shmuel Weinberger seeks to explain and illustrate the implications of the general principle, first emphasized by Alex Nabutovsky, that logical complexity engenders geometric complexity. He provides applications to the problem of closed geodesics, the theory of submanifolds, and the structure of the moduli space of isometry classes of Riemannian metrics with curvature bounds on a given manifold. Ultimately, geometric complexity of a moduli space forces functions defined on that space to have many critical points, and new results about the existence of extrema or equilibria follow.

The main sort of algorithmic problem that arises is recognition: is the presented object equivalent to some standard one? If it is difficult to determine whether the problem is solvable, then the original object has doppelgangers-that is, other objects that are extremely difficult to distinguish from it.

Many new questions emerge about the algorithmic nature of known geometric theorems, about "dichotomy problems," and about the metric entropy of moduli space. Weinberger studies them using tools from group theory, computability, differential geometry, and topology, all of which he explains before use. Since several examples are worked out, the overarching principles are set in a clear relief that goes beyond the details of any one problem.

... Read more

Reviews (1)

Not a bad book, but outdated and too simplistic
This book tries to explain Mastercam software to novice students. The chapters and topics are well thought out but don't go into nearly enough depth. One big problem is the book's use of Mastercam V7, which is 4-5 years old. A book published in 2002 should use software from 2002. The screenshots are excellent, but the book would need to double in size and feature the latest software to become a contender in the CAD/CAM marketplace. ... Read more

Book Description

Art gallery theorems and algorithms are so called because they relate to problems involving the visibility of geometrical shapes and their internal surfaces.This book explores generalizations and specializations in these areas.Among the presentations are recently discovered theorems on orthogonal polygons, polygons with holes, exterior visibility, visibility graphs, and visibility in three dimensions. The author formulates many open problems and offers several conjectures, providing arguments which may be followed by anyone familiar with basic graph theory and algorithms. This work may be applied to robotics and artificial intelligence as well as other fields, and will be especially useful to computer scientists working with computational and combinatorial geometry. ... Read more

Book Description

The learn-by-doing way to master Geometry

Why CliffsStudySolver™ Guides?

Go with the name you know and trust
Get the information you need–fast!
Written by teachers and educational specialists

Inside you’ll get the practice you need to learn Geometry, including:

Basic Geometric Concepts

• Points, lines, and planes
• Postulates and theorems
• Line segments, midpoints, and rays
• Angles and angle pairs
• Parallel lines

Shapes and Measurement

• Measuring angle sums
• Triangles, polygons, and circles
• Determining perimeter and area
• Ratio and proportion
• Similar figures
• Solid figures and measurement
• Coordinate geometry

Problem-Solving Tools

• Clear, concise reviews of every topic
• Practice problems in every chapter–with explanations and solutions
• Diagnostic pretest to assess your current skills
• Full-length exam–with answers–that adapts to your skill level

We take great notes–and make learning a snap ... Read more

Book Description

Algebraic geometry is, essentially, the study of the solution of equations and occupies a central position in pure mathematics. With the minimum of prerequisites, Dr. Reid introduces the reader to the basic concepts of algebraic geometry, including: plane conics, cubics and the group law, affine and projective varieties, and nonsingularity and dimension. He stresses the connections the subject has with commutative algebra as well as its relation to topology, differential geometry, and number theory. The book contains numerous examples and exercises illustrating the theory. ... Read more

Reviews (1)

baked just right for the first timers !
There are many good books on the subject of algebraic geometry, so what was the use of one more - asks the author in the preface to this book. But there are none -at the UG level- which for the first time reveal to the younger mathematicians the secrets of this vast and growing subject. The book treats every new concept with the rigour that keeps in mind the level it is meant for, and yet maintains its mathematical "beauty" - setting firmly the basics for those who would want to take up this course at an advanced level as well as keeping the more casual mathematics reader interested. ... Read more

Book Description

Engaging, accessible, and extensively illustrated, this brief, but solid introduction to modern geometry describes geometry as it is understood and used by contemporary mathematicians and theoretical scientists. Basically non-Euclidean in approach, it relates geometry to familiar ideas from analytic geometry, staying firmly in the Cartesian plane. It uses the principle geometric concept of congruence or geometric transformation--introducing and using the Erlanger Program explicitly throughout. It features significant modern applications of geometry--e.g., the geometry of relativity, symmetry, art and crystallography, finite geometry and computation.Covers a full range of topics from plane geometry, projective geometry, solid geometry, discrete geometry, and axiom systems.For anyone interested in an introduction to geometry used by contemporary mathematicians and theoretical scientists. ... Read more

Reviews (1)

This book is not great.
First of all, there are numerous minor errors in the printing; they get to be annoying at best, and extremely confusing at their worst.

The book also is too much of an overview--it makes a good introduction but a poor reference text.It is also very poorly indexed, which can make it hard to find things.The exercises are also poor--many new concepts are introduced in the exercises at the end of the chapters.

The writing is actually pretty good, for the most part.I think that the stuff that is explained in the book is explained well in most places, and the author does a very good job of tieing things together and bringing in historical background and significance of the topics being discussed.

I lastly might add that the name is very misleading--the geometries described in this book were mostly discovered over 100 years ago--there is nothing drastically "modern" about them.

Overall, this book was not prepared for being published--it needs a new edition to correct errors and tie up loose ends. ... Read more

Book Description

In Unbiased Steriology, the authors present a practical guide to making unbiased 3D measurements using microscopy. Stereology is the statistical inference of geometric parameters from spatially sampled information; it is considered unbiased whent he test probes are positioned in an appropriately random manner. Now that unbiased stereology is required for nerve-cell counts in neurotoxicology by the FDA and by many journals before the acceptance of an article or study, this book is essential reading. It includes only those stereological techniques that have been tried and tested by actual application. Although these techniques are essentially mathematical--unbiased stereology is a quantitative rather than qualitative approach to microscopy-the authors do not immerse the reader in complex theories. Instead, they provide simple heuristic explanations and references to the original proof, illustrating the theory with analogies draw from everyday experience. Exercises-provided at the end of each chapter, complete with detailed worked answers-have been developed by the authors or donated by other expert stereologists to give practical experience using the techniques. Specific topis covered include: random sampling and random geometry; the estimation of feature volume, surface, length, number and mean particle size; as well as statistics for stereologists. ... Read more

Reviews (1)

Extremely useful for all interested in true quantification
This is an excellent book for all those interested in true quantification of tissue elements. Here, methods are outlined, amply illustrated and put forward in the form of exercises making it a pleasure even for the novice reader to get an understanding of what stereology is and what it is for. Now, the day seems near when researchers report their results on quantitative tissue features based on stereological estimation procedures. Highly recommended for serious morphologists. ... Read more