Game Programming Gems 6 (Book & CD-ROM) (Game Development Series)

Book Description

Welcome to the sixth volume of the Game Programming Gems series. With team sizes constantly expanding, developers are finding themselves pushed to become increasingly specialized. This makes it important to have cutting-edge, ready-to-use material in your specialization, as well as resources that you can call upon if you need to work outside your area of expertise. Volume 6 has been explicitly designed with your current challenges in mind. With the new generation of machines, players expect higher-fidelity models and animations, fancier physics and graphics effects, and more intelligent AI. All of these capabilities require robust teams and longer schedules, so to help ensure that your games are still delivered on time and on budget, you'll find 50 all new articles written by experts in game technology from many different backgrounds and over twenty countries. This volume also includes a brand new section dedicated to Scripting and Data-Driven Systems, which is focused entirely on the growing trend of removing the programmer from the data-tweaking loop. So, whether you're a new game programmer starting out on this exciting path, a grizzled, industry veteran, or a most welcome visitor, we hope that you will find inspiration, insight, and at least one or two true gems to use in your world!

Customer Reviews:

watch this trend.......2007-04-16

One interesting feature of this book on game programming is how graphics does NOT dominate the discussion. Most books on the subject are chock-a-block with every graphics tip you could imagine. But Dickheiser does not write for the novice. He has gathered a set of papers (chapters) that try to delineate the research boundary. It is a measure of the rising maturity of the field, and the complexity of many games, that graphics is relatively deprecated.

Though I hasten to add that there are still the pretty colour plates of renderings, and several chapters on these methods.

Why is the book symptomatic of the changing trends? In part because graphical methods are starting to saturate. The techniques are now good enough for near-photorealistic impressions. If you look carefully at the non-graphics chapters, you see that they tackle non-trivial problems arising from evermore intricate games. One instance is the use of AI-style decision making methods for how a game proceeds. When well coded, it can give behaviour of characters that is more intelligent, hence yielding a more interesting game. Another chapter looks at the learning process in AI, where a player might change strategies. Here, the research use of Support Vector Machines is suggested as apropos for commercial game development.

Professionally, you should pay attention to the book for the trend it exemplifies. You probably got into game programming because you were attracted by the graphics. But as graphics methods peak, the value added aspect of games is starting to shift towards the story line and how elaborate is the game logic.

Good bag of tricks for advanced game programmers.......2006-04-05

This is the latest volume in the game programming gems series that is now six years old. This book, like the others in the series, is a collection of articles written by industry experts for the advanced game programmer. Because it covers so much ground with little or no background information, I doubt that one reader will be able to appreciate the whole book. The book comes with a CD that has source code for all of the articles, which is very helpful.
I'm a multimedia programmer rather than a game programmer, and I found quite a few nuggets in this edition. Among them was the article on using OpenCV, which is the open source computer vision library, and also the article on CPPUnit, which can be used for unit testing of any type of software, not just games. The section on math and physics was the least helpful. It either set the bar too low with easy articles like "How to do floating point faster than hardware", or set the bar too high with difficult terse articles such as "Real-Time Particle-Based Fluid Simulation". However, if you are into game physics, this section might be something you really enjoy. In the AI section, it seemed like I had seen most of the material before. The last article though was really unique - "Constructing a Goal-Oriented Robot for UnrealTournament Using Fuzzy Sensors, Finite-state Behaviors and Behavior Networks". This is an outstanding article for those interested in robots in games. The whole section on scripting was worthwhile. I especially enjoyed the Script language survey at the front of the section, since this is a moving target with many languages to choose from. The graphics section is quite advanced, and unless "Realtime Rendering" seems like light bedtime reading to you, most of the articles will probably not make much sense. My favorite section of the book was the one on audio for two reasons. First, most game programming books ignor this subject entirely. Second, it is hard to find readable books or articles on the subject with the effects presented in plain language as this section did in all five articles. I notice that Amazon does not show the table of contents, so I do that here:
SECTION 1 GENERAL PROGRAMMING
Introduction 1.1 Game Object Component System 1.2 Closest- String Matching Algorithm 1.3 Implementing Lock-Free Algorithms 1.4 Computer Vision in Games using the OpenCV library 1.5 Using CPPUnit to implement unit testing 1.6 Visualizing Performance Data 1.7 Faster Loading with Access-Based File Reordering 1.8 Stay in the Game: Asset Hotloading for Fast Iteration 1.9 Geographic Grid Registration of Game Objects 1.10 Real-Time Continuous Profiling 1.11 Fingerprinting Prerelease Builds to Deter and Detect Piracy 1.12 The Dynamic Actor Layer

SECTION 2 MATHEMATICS AND PHYSICS
Introduction 2.1 Efficient Sequence Indexing 2.2 How to do floating point faster than hardware. 2.3 Solving linear systems by using the cross product 2.4 Real-Time Particle-Based Fluid Simulation 2.5 Exact Buoyancy for Polyhedra

SECTION 3 ARTIFICIAL INTELLIGENCE
Introduction 3.1 Designing a Multi-layer Pluggable AI Engine Framework 3.2 Smart Scene Load Management using Fuzzy Logic 3.3 Achieving coordination with autonomous NPC's 3.4 Using a Quantified Judgment Model for Engagement Analysis 3.5 Short-term memory using support vector machine (SVM) 3.6 Applying Model-Based Decision-Making Methods to Games 3.7 Constructing a Goal-Oriented Robot for UnrealTournament Using Fuzzy Sensors, Finite-state Behaviors and Behavior Networks

SECTION 4 SCRIPTING SYSTEMS
Introduction 4.1 A Script language survey 4.2 Managing High-Level Scripts Execution within 4.3 Automatic Function Binding for Game Scripting and Networking 4.4 Programming advanced control mechanisms with Lua coroutines 4.5 Binding C/C++ objects to Lua

SECTION 5 GRAPHICS
Introduction 5.1 Automatic Realistic Idle Motion Synthesis for Interactive Characters" 5.2 GPU Terrain Rendering 5.3 Rendering Road Signs Sharply 5.4 Interactive Fluid Dynamics and Rendering on the GPU 5.5 Spatial Partitioning using an Adaptive Binary Tree 5.6 Enhanced Object Culling with (Almost) Oriented Bounding Boxes 5.7 Fast per-pixel lighted scenes with a high number of lights 5.8 Efficient Sky Rendering Techniques 5.9 High Dynamic Range Rendering using OpenGL Frame Buffer Objects 5.10 Skin Splitting for Optimal Skin Rendering

SECTION 6 AUDIO
Introduction 6.1 Real- Time Sound Generation From Deformable Meshes 6.2 Volume Control Through Chained Busses 6.3 Faking Real-time DSP Effects 6.4 A lightweight oscillator for ambient sound generation 6.5 Cheap Doppler effect

SECTION 7 NETWORKING AND MULTIPLAYER
Introduction 7.1 Complex High-Level Systems 7.2 Reliable Peer-to-Peer Gaming Connection Penetrating Firewall and NAT 7.3 Massively Multiplayer Online Prototype (MMOP): Utilizing Second Life for Game Concept Prototyping 7.4 Dynamically Adaptive Streaming of 3D Data for Animated Characters 7.5 Generating globally unique identifiers for game objects About the CD-ROM
Index

Programming Tips from the Pros.......2006-04-04

Intended for the intermediate to advanced game programmer, this is a book that will literally have something for everyone. It contains fifty-two 'gems' that is, articles on how to some particular aspect of game programming. Sophisticated game programming is probably the most complex programming there is. And this book goes into some pretty sophisticated programming details.

For instance:
1.2 Using Multicore Processors - New software that facilitates programming to make the most effective use of dual/triple core CPUs.
2.5 - Exact Buoyancy for Polyhedra - Your game character has built a raft. How does it look like it's floating realistically?
5.9 - Practical Sky Rendering - The sky is so simple, unless, of course you want it to look real. ==There is no question that the main driving force for faster computers is to make for more realistic gaming. And the faster computers allow more sophisticated programming to be done to make the grass wave realistically.

This is probably not a book you're going to sit down and read from cover to cover. You'll probably scan through and read the ones that are applicable to just what you need to do next. But then in a couple of weeks, in a couple of months....

How to Solve Word Problems in Algebra, (Proven Techniques from an Expert)

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Good Delivery
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Algebra made easier
Great beginners book
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How to Solve Word Problems in Algebra, (Proven Techniques from an Expert)
Mildred Johnson , Tim Johnson , Linus Johnson , Dean McRaine , and Sheralyn Johnson
Manufacturer: McGraw-Hill
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Binding: Paperback

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How to Solve Math Word Problems on Standardized Tests: Proven Techniques from an Expert (How to Solve Word Problems)
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ASIN: 0071343075

Book Description

Solving word problems has never been easier than with Schaum's How to Solve Word Problems in Algebra!

This popular study guide shows students easy ways to solve what they struggle with most in algebra: word problems. How to Solve Word Problems in Algebra, Second Edition, is ideal for anyone who wants to master these skills. Completely updated, with contemporary language and examples, features solution methods that are easy to learn and remember, plus a self-test.

Customer Reviews:

Good Delivery.......2007-03-24

Speedy delivery, great condition, and seems to be what the advertisement said it would be..Thanks

Awesome Book.......2007-03-16

My son Sid and I are having a lot of fun solving word problems. It gives me a lot of happiness solving problem and spending time with my son. Father son time well spent.

Algebra made easier.......2007-02-07

This workbook can really help someone taking or tutoring Algebra. It really can help for even grades 7-8. The explanations are usually clear and have good examples. Sometimes it required re-reading, but that may be because of the difficulty of the subject matter.

Great beginners book.......2006-03-10

My son is really getting a lot out of "How to Solve Word Problems in Algebra". He is understanding the material and applying it to his homework and tests.

Good book.......2005-03-24

I'm very happy with this book. It does just what it promises: teaches kids how to solve word problems in beginning-level algebra. I wish I'd had a book like this when I was in school. It gives detailed explanations which are easy to understand.

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makes your head buzz...
Provides a very interesting point of view
A powerful mathematical language for physics and engineering
Compared to what ?
Articulate Path to the Future

Geometric Algebra for Physicists
Chris Doran , and Anthony Lasenby
Manufacturer: Cambridge University Press
ProductGroup: Book
Binding: Hardcover

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New Foundations for Classical Mechanics (Fundamental Theories of Physics)
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On Quaternions and Octonions
Quaternions and Rotation Sequences: A Primer with Applications to Orbits, Aerospace and Virtual Reality
Geometric Algebra for Computer Science: An Object-Oriented Approach to Geometry (The Morgan Kaufmann Series in Computer Graphics)

ASIN: 0521480221

Book Description

As leading experts in geometric algebra, Chris Doran and Anthony Lasenby have led many new developments in the field over the last ten years. This book provides an introduction to the subject, covering applications such as black hole physics and quantum computing. Suitable as a textbook for graduate courses on the physical applications of geometric algebra, the volume is also a valuable reference for researchers working in the fields of relativity and quantum theory.

Customer Reviews:

makes your head buzz..........2007-08-04

I'm reading this book somewhat in parallel with Hestenes' New Foundations for Classical Mechanics. Both are fantastic books (Hestenes' predates this one), and in some parts they are complementary, while of course they overlap in the foundations and many special topics. What is so fascinating about Geometric Algebra and Calculus? I think it's mainly the recognition that many seemingly complicated theorems of mathematical physics really become much clearer - in a sense of getting a guts feeling about the geometry. The method opens a way to look at the same thing from totally different angles: If one can't imagine something based on geometric arguments, one can take the presented formalism and translate it back into geometry, and suddenly things become clear.
Is the book (or that by Hestenes) basic and easy to understand or are they difficult? Certainly they require some work by the reader. To follow the entire book, one really can't do without learning to master the formalism of geometric algebra, which is simple, yet sometimes bizarre. I suspect though that it is only bizarre to the one who "knows it all" already: The student or scientist who has grown familiar with vector spaces, matrix notation and wiggling around with tensor notation, needs to go through the same exercises as the bloody beginner to whom even the idea of a vector may not be clear. In fact, the beginner could be at a real advantage to not being poisoned by vector calculus. For example, take the very basic notation for a geometric product of two multi-vectors: ab = a.b + a^b (the sum of inner and outer product). What's so confusing about it? Nothing, really, after one really understands what "+" here means. But it happens often enough that one only thinks about this product in terms of the right hand side of the equation, because those are totally familiar for anyone who took basic linear algebra, and then ends up making simple things complicated again. I must say that it was like loosing shadows from the eyes to see how the formulations in this book and Hestenes' work explain so well why it is that the quantum mechanical psi function needs to be complex, or better yet what really the i means in physics, and how the entire set of Maxwell equations (all 4 of them) are one simple continuity equation. That's the kind of thing that makes your head buzz. I'm not done with these books, but I have a clear feeling that in the end I will have an entry point to understand QM and parts of general relativity not just formally (especially QM) but really develop a guts feeling for it.
One thing that I'm still a bit missing in any of the books related to geometric algebra is classical continuum mechanics. This may be so because many of the authors are immersed in fields related to cosmology. In this book, one can find a tiny little bit also about elasticity (linear and nonlinear). However, I keep wondering what it would be like to reformulate the entire underlying theory of continuum mechanics (about deforming solids, elastic or viscoelastic or plastic, about fluid flow, about polarized materials, biological active materials, etc). Could something new be learned? I bet it could!

Provides a very interesting point of view.......2007-02-22

Provides a very interesting point of view, absolutely necessary for grasping the bolts and plumbing of modern physics.

The material covered was not present in other texts that I had a look at so this book serves as a good corner stone to build advanced undergraduate and graduate courses on.

A powerful mathematical language for physics and engineering.......2004-08-01

This is a well-written book on a very interesting and important subject: geometric algebra (GA) is a powerful and elegant mathematical language -- based on the works of Hamilton, Grassmann and Clifford -- that is especially well-suited for spacetime physics and several fields of engineering.

The authors adopt David Hestenes' viewpoint of a graded GA as a unified mathematical language that is coordinate-free, thereby stressing the fundamental role of geometric invariants in physics.

In fact, the elementary vector analysis -- which pervades almost all undergraduate (and even) graduate approaches to electrodynamics -- finds its roots in the misguided Gibbsian approach: Gibbs advocated abandoning Hamilton's quaternions and just work with scalar and cross products of vectors. However, the cross product has a major flaw: it only exists in three (or seven) dimensions -- if we require that (i) it should have just two factors, (ii) to be orthogonal to the factors, and (iii) to have length equal to the corresponding parallelogram.

Electrodynamics and relativistic physics, particularly, are elegantly presented through GA and otherwise cumbersome calculations may be circumvented in a simple and insightful way.

Mainstream physics and engineering cannot overlook GA anymore.

Compared to what ?.......2004-01-30

This is truly a great book for any one who is interested in not just physics, but physical reality. Although the ideas expressed therein have a long history and are by no means as uniquely those of its authors as were Albert Einstein's in his day, I believe that they will have comparable lasting value. Moreover the synthesis presented in this book, which builds pre-eminently on the work of Hestenes, is absolutely superb. Interested readers need not take my word for these claims, but are invited to prove it to themselves.

Although the above should be a sufficient review, my experience nevertheless indicates that it is a good idea to warn potentially enthusiastic readers against several common semantic misconceptions, lest they jump to conclusions which prevent them from ever taking that vital first step. Thus let it be clearly understood that Geometric Algebra is NOT:
(1) A replacement for linear/matrix/tensor algebra (on the contrary, it is a very nice complement to these formalisms).
(2) Identical, or even very close, to Emil Artin's earlier excellent book on bilinear forms with the title "Geometric Algebra".
(3) Another name for the enormous field "algebraic geometry" (it is indeed appropriate that the word stemming from "geometry" comes first in "geometric algebra").
(4) Just another reformulation of complex / quaternion / octonian analysis; for it connects all these purely algebraic objects, and many generalizations thereof, to Felix Klein's Erlangen Programme and Sophus Lie's theory of continuous groups.
(5) The ultimate theory of everything (although it probably will eventually be found to have something to do with it).

Geometric algebra IS a practical and natural (canonical) tool for formulating physical and mathematical problems in homogeneous spaces in a fully covariant fashion. But more importantly, you do not need to understand all those words in order to benefit from it, and this book is an excellent place for physicists of all stripes to start.

Articulate Path to the Future.......2003-07-19

The quality and importance of this book could hardly be overstated. Geometric algebra might casually be considered the "correct" generalization of linear algebra. By considering, for a start, directed line segments, the linear algebra courses presently taught in some high schools and all universities achieve miracles. Although viewed by a few of the slower students as merely unpleasant bookkeeping systems, linear algebra derives its power from allowing algebraic manipulation of sophisticated aggregate objects, namely vectors. The benefits are not just computational, but stem more importantly from a more powerful and more unified, although slightly more abstract point of view than a student had before studying. Geometric algebra is all that and much more. By extending consideration from directed line segments to the inclusion of direct plane segments, directed elements of three space, etc., an extremely flexible and elegant mathematical tool arises. It allows a deeper, quicker, and more concise treatment of essentially all of modern differential geometry. Its applications throughout physics are at once simplifications of ordinary matrix treatments and occasions to allow much greater insight.

Geometric algebra is a great theory, one of highest importance. It will, undoubtedly, find a dominant place in our mathematics curriculum at the highest speed allowed by our educational systems (the highest speed being actually quite slow). This book is an especially good place to begin study. It starts from the most elementary principles, and exposes the material with very thoughtful, clear presentation. The economy and elegance of the geometric algebra itself allows this one substantial but not enormous book to reveal great insights into many branches of study, from differential geometry and its applications to gravity theory to quantum mechanics and classical mechanics.

Book Description

This book provides a careful and detailed algebraic introduction to Grothendieck's local cohomology theory, and illustrates many applications for the theory in commutative algebra and in the geometry of quasi-affine and quasi-projective varieties. Topics covered include Castelnuovo-Mumford regularity, the Fulton-Hansen connectedness theorem for projective varieties, and connections between local cohomology and both reductions of ideals and sheaf cohomology. It is designed for graduate students who have some experience of basic commutative algebra and homological algebra, and also for experts in commutative algebra and algebraic geometry.

Geometric Calculus: According to the Ausdehnungslehre of H. Grassmann

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Geometric Calculus: According to the Ausdehnungslehre of H. Grassmann
Giuseppe Peano
Manufacturer: Birkhäuser Boston
ProductGroup: Book
Binding: Hardcover

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ASIN: 0817641262

Book Description

Calcolo Geometrico, G. Peano's first publication in mathematical logic, is a model of expository writing, with a significant impact on 20th century mathematics. Kannenberg's lucid and crisp translation, Geometric Calculus, will appeal to historians of mathematics, researchers, graduate students, and general readers interested in the foundations of mathematics and the development of a formal logical language.

Despite its uniqueness, Calcolo Geometrico has been strangely neglected by historians of mathematics, and even by scholars of Peano. The book has never been reprinted in its entirety, and only two chapters have ever been translated into English. In part, this neglect has been due to Peano's organization of the work. That is, the section on mathematical logic bears almost no relation to the rest of the book, and the material there was superseded only a year after its publication by Peano's second book. Since all but this first section was generally thought to be expository rather than original work, it was regarded lightly, if noticed at all, and ultimately all but forgotten. Only in very recent years have the book's unique merits begun to be recognized.

Readers of this valuable translation will gain insight into the work of a distinguished mathematician and founder of mathematical logic.

Geometric Algebra for Computer Science: An Object-Oriented Approach to Geometry (The Morgan Kaufmann Series in Computer Graphics)

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A reader from Los Alamos, NM

Geometric Algebra for Computer Science: An Object-Oriented Approach to Geometry (The Morgan Kaufmann Series in Computer Graphics)
Leo Dorst , Daniel Fontijne , and Stephen Mann
Manufacturer: Morgan Kaufmann
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Binding: Hardcover

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Geometric Data Structures for Computer Graphics
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Geometric Algebra for Physicists

ASIN: 0123694655

Book Description

Within the last decade, Geometric Algebra (GA) has emerged as a powerful alternative to classical matrix algebra as a comprehensive conceptual language and computational system for computer science. This book will serve as a standard introduction and reference to the subject for students and experts alike. As a textbook, it provides a thorough grounding in the fundamentals of GA, with many illustrations, exercises and applications. Experts will delight in the refreshing perspective GA gives to every topic, large and small.
-David Hestenes, Distinguished research Professor, Department of Physics, Arizona State University

Geometric Algebra is becoming increasingly important in computer science. This book is a comprehensive introduction to Geometric Algebra with detailed descriptions of important applications. While requiring serious study, it has deep and powerful insights into GAs usage. It has excellent discussions of how to actually implement GA on the computer.
-Dr. Alyn Rockwood, CTO, FreeDesign, Inc. Longmont, Colorado

Until recently, almost all of the interactions between objects in virtual 3D worlds have been based on calculations performed using linear algebra. Linear algebra relies heavily on coordinates, however, which can make many geometric programming tasks very specific and complex-often a lot of effort is required to bring about even modest performance enhancements. Although linear algebra is an efficient way to specify low-level computations, it is not a suitable high-level language for geometric programming.

Geometric Algebra for Computer Science presents a compelling alternative to the limitations of linear algebra. Geometric algebra, or GA, is a compact, time-effective, and performance-enhancing way to represent the geometry of 3D objects in computer programs. In this book you will find an introduction to GA that will give you a strong grasp of its relationship to linear algebra and its significance for your work. You will learn how to use GA to represent objects and perform geometric operations on them. And you will begin mastering proven techniques for making GA an integral part of your applications in a way that simplifies your code without slowing it down.

Features

Explains GA as a natural extension of linear algebra and conveys its significance for 3D programming of geometry in graphics, vision, and robotics.
Systematically explores the concepts and techniques that are key to representing elementary objects and geometric operators using GA.
Covers in detail the conformal model, a convenient way to implement 3D geometry using a 5D representation space.
Presents effective approaches to making GA an integral part of your programming.
Includes numerous drills and programming exercises helpful for both students and practitioners.
Companion web site includes links to GAViewer, a program that will allow you to interact with many of the 3D figures in the book, and Gaigen 2, the platform for the instructive programming exercises that conclude each chapter.

About the Authors

Leo Dorst is Assistant Professor of Computer Science at the University of Amsterdam, where his research focuses on geometrical issues in robotics and computer vision. He earned M.Sc. and Ph.D. degrees from Delft University of Technology and received a NYIPLA Inventor of the Year award in 2005 for his work in robot path planning.

Daniel Fontijne holds a Masters degree in artificial Intelligence and is a Ph.D. candidate in Computer Science at the University of Amsterdam. His main professional interests are computer graphics, motion capture, and computer vision.

Stephen Mann is Associate Professor in the David R. Cheriton School of Computer Science at the University of Waterloo, where his research focuses on geometric modeling and computer graphics. He has a B.A. in Computer Science and Pure Mathematics from the University of California, Berkeley, and a Ph.D. in Computer Science and Engineering from the University of Washington.

* The first book on Geometric Algebra for programmers in computer graphics and entertainment computing

* Written by leaders in the field providing essential information on this new technique for 3D graphics

* This full colour book includes a website with GAViewer, a program to experiment with GA

Customer Reviews:

A reader from Los Alamos, NM.......2007-08-17

Geometric Algebra (GA) is a unifying mathematical language that should be taught instead of or at least in combination with traditional vector analysis. Most other books on GA are aimed at Physicists. This book is a better match for Engineers and Programmers. The authors are all active researchers in applications of GA. They have done a comprehensive and up to date job of collecting, organizing and presenting the material for both beginners and those who follow the development of GA on the web. The examples and problems use GAViewer, an easy to learn programming language with an Open GL view window that can be downloaded for free from the book website. Using GAViewer with the book is very good way to learn GA, especially the 5D Conformal model of 3D space. The authors hold nothing back. Between the book, the code and the website everything is there to make learning GA fun and useful. I highly recommend this book.

Geometric Algebra and Applications to Physics

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Geometric Algebra and Applications to Physics
Venzo de Sabbata , and Bidyut Kumar Datta
Manufacturer: Taylor & Francis
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Binding: Hardcover

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Geometric Algebra for Computer Science: An Object-Oriented Approach to Geometry (The Morgan Kaufmann Series in Computer Graphics)

ASIN: 1584887729

Book Description

Bringing geometric algebra to the mainstream of physics pedagogy, Geometric Algebra and Applications to Physics not only presents geometric algebra as a discipline within mathematical physics, but the book also shows how geometric algebra can be applied to numerous fundamental problems in physics, especially in experimental situations. This reference begins with several chapters that present the mathematical fundamentals of geometric algebra. It introduces the essential features of postulates and their underlying framework; bivectors, multivectors, and their operators; spinor and Lorentz rotations; and Clifford algebra. The book also extends some of these topics into three dimensions. Subsequent chapters apply these fundamentals to various common physical scenarios. The authors show how Maxwell's equations can be expressed and manipulated via space-time algebra and how geometric algebra reveals electromagnetic waves' states of polarization. In addition, they connect geometric algebra and quantum theory, discussing the Dirac equation, wave functions, and fiber bundles. The final chapter focuses on the application of geometric algebra to problems of the quantization of gravity. By covering the powerful methodology of applying geometric algebra to all branches of physics, this book provides a pioneering text for undergraduate and graduate students as well as a useful reference for researchers in the field.

Geometric Computing with Clifford Algebras

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Geometric Computing with Clifford Algebras

Manufacturer: Springer
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Binding: Hardcover

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Geometric Algebra for Computer Science: An Object-Oriented Approach to Geometry (The Morgan Kaufmann Series in Computer Graphics)

ASIN: 3540411984

Book Description

Clifford algebra, then called geometric algebra, was introduced more than a cenetury ago by William K. Clifford, building on work by Grassmann and Hamilton. Clifford or geometric algebra shows strong unifying aspects and turned out in the 1960s to be a most adequate formalism for describing different geometry-related algebraic systems as specializations of one "mother algebra" in various subfields of physics and engineering. Recent work outlines that Clifford algebra provides a universal and powerfull algebraic framework for an elegant and coherent representation of various problems occuring in computer science, signal processing, neural computing, image processing, pattern recognition, computer vision, and robotics. This monograph-like anthology introduces the concepts and framework of Clifford algebra and provides computer scientists, engineers, physicists, and mathematicians with a rich source of examples of how to work with this formalism.

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Some annoyances keep it from greatness
unusual and challenging geometry problems
A Panorama of Geometric Mini-Max Facts

Geometric Problems on Maxima and Minima
Titu Andreescu , Oleg Mushkarov , and Luchezar Stoyanov
Manufacturer: Birkhäuser Boston
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The IMO Compendium: A Collection of Problems Suggested for The International Mathematical Olympiads: 1959-2004 (Problem Books in Mathematics)

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Lie Groups: An Approach through Invariants and Representations (Universitext)
Quaternions, Clifford Algebras and Relativistic Physics
Introduction to Lie Algebras (Springer Undergraduate Mathematics Series)

ASIN: 0817635173

Book Description

Questions of maxima and minima have great practical significance, with applications to physics, engineering, and economics; they have also given rise to theoretical advances, notably in calculus and optimization. Indeed, while most texts view the study of extrema within the context of calculus, this carefully constructed problem book takes a uniquely intuitive approach to the subject: it presents hundreds of extreme value problems, examples, and solutions primarily through Euclidean geometry.

Key features and topics:

* Comprehensive selection of problems, including Greek geometry and optics, Newtonian mechanics, isoperimetric problems, and recently solved problems such as Malfatti’s problem

* Unified approach to the subject, with emphasis on geometric, algebraic, analytic, and combinatorial reasoning

* Presentation and application of classical inequalities, including Cauchy--Schwarz and Minkowski’s Inequality; basic results in calculus, such as the Intermediate Value Theorem; and emphasis on simple but useful geometric concepts, including transformations, convexity, and symmetry

* Clear solutions to the problems, often accompanied by figures

* Hundreds of exercises of varying difficulty, from straightforward to Olympiad-caliber

Written by a team of established mathematicians and professors, this work draws on the authors’ experience in the classroom and as Olympiad coaches. By exposing readers to a wealth of creative problem-solving approaches, the text communicates not only geometry but also algebra, calculus, and topology. Ideal for use at the junior and senior undergraduate level, as well as in enrichment programs and Olympiad training for advanced high school students, this book’s breadth and depth will appeal to a wide audience, from secondary school teachers and pupils to graduate students, professional mathematicians, and puzzle enthusiasts.

Customer Reviews:

Some annoyances keep it from greatness.......2006-12-02

Choice of topics is great. My main annoyance is the lack of suitable references to further explore the important topics that are sketched. The writing is often stilted and so confusing in some parts that you have to read the solution in order to understand the problem. I blame the editors for that. There are some real gems in the problem sets, especially with respect to the tangency principle. This is a good place for people who actually work optimization problems in real life, beyond the math competitions this book is geared to, to understand at a top-level how the methods can be employed. The notation could be more consistent throughout or at least provide a Notations page to facilitate nonlinear reading.

unusual and challenging geometry problems.......2006-10-31

Very interesting and challenging selection of extrema problems - many solved through IMO-level Euclidean geometry. Suitable for high-school students preparing for IMO.

Unfortunately, this Birkhauser book is very expensive for a 264-page paperback; the price pretty much guarantees that it will not be widely read by its intended audience.

A Panorama of Geometric Mini-Max Facts.......2006-02-21

This work as well as all other works of Prof. Andreescu is a math GEM; contains a panorama of minima and maxima problems,facts, and methods in geometry: Malfatti's Problems, Geometric Transformations, Algebraic Inequalities, Calculus Method of Partial Varitation and Tangency Principle, Polygons in a Square, Broken Lines, Distribution of Points, Coverings, and much more.
I like very much particularly the topics and problems in combinatorial geometry.
The text is completely lucid and in a live style.
The works of Prof. Andreescu and his colleagues are so fascinating as I cannot ignore his books, therefore I highly and warmly recommend not only this book, but also all other books of Prof. Andreescu and his colleagues to any math lover.

Clifford (Geometric) Algebras With Applications in Physics, Mathematics, and Engineering

Average customer rating:

Good compilation

Clifford (Geometric) Algebras With Applications in Physics, Mathematics, and Engineering
William E. Baylis
Manufacturer: Birkhäuser Boston
ProductGroup: Book
Binding: Hardcover

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Similar Items:

Lectures on Clifford (Geometric) Algebras and Applications
A Geometric Approach to Differential Forms
Rotations, Quaternions, and Double Groups

ASIN: 0817638687

Customer Reviews:

Good compilation.......2001-12-24

This book, a compilation of 33 articles covering many different aspects and applications of Clifford algebras, can be read profitably by anyone desiring an overview of their history, theory, and applications. I did not read every article, and space also prohibits such a comprehensive review, so I will comment only on the ones that I actually studied.

Chapter introduces Clifford algebras as an extension of the real numbers to include vectors and vector products. The familiar representation in Euclidean space is outlined, with emphasis on the exterior product of two vectors, which, the author points out, is associative (unlike the ordinary cross product). The connection with rotations, reflections, and volume elements is pointed out, and the complex numbers and the Pauli algebra are shown to be Clifford algebras.

A short history of Clifford algebras is given in chapter 2. The reader not familiar with Clifford algebras should have no trouble following the ensuing discussion where some elementary geometric constructions are given of the Clifford algebra on the Euclidean plane. In addition, the operator approach to Weyl, Majorana, and Dirac operators is given, illustrating in detail their connection to physics. Recognizing that the Fierz identities do not by themselves give the Weyl and Majorana spinors, the author introduces what he calls the boomerang method for their construction. The boomerang is essentially a linear combination of bilinear covariants for a spinor, and the author details the conditions under which the spinor can be reconstructed. Interestingly, and unknown to me at the time of reading this chapter, the author constructs a new class of spinors, the "flag-dipole" spinors, that are different from the Weyl, Majorana, and Dirac spinors.

The author of chapter 3 considers the construction of Clifford algebras from a more geometric viewpoint, calling them geometric algebras, which he motivates by the consideration of extending the reals by a unipotent ( a number not equal to +1 or -1 but whose square is 1). The resulting unipodal numbers are isomorphic to the diagonal 2 x 2 matrices. The extension of the unipodal numbers so as to make this isomorphism to the full 2 x 2 matrix algebra leads to Clifford algebras.

In Chapter 9, the spacetime algebra is brought in to study electron physics. The "space-time algebra" or STA is used to characterize the observables associated with Pauli and Dirac spinors. The material presented is standard in physics, wherein the Green's function (propagator) for the Dirac equation is given, along with scattering theory. The typical problem of scattering off a potential barrier of finite width is discussed, along with the Klein paradox.

The space-time algebra is also discussed in the context of the interpretation of quantum mechanics in Chapter 11. The authors really do not add anything new here (in terms of what one might consider "strange" behavior in quantum physics). They interpret Dirac currents as measurable quantities, avoiding seemingly any notion of wave packet collapse and difficulties with defining tunneling time(s), but not answering at all how to measure these currents. In addition, the Pauli principle is interepreted in the context of space-time algebra, without any quantum field theory. Howerver, it is not shown that such an approach satisfies cluster decomposition, casting suspicion on its utility.

In Chapters 21, 22, and 23 the author shows how spinors fit into the framework of the Lorentz group, their relationship to the Clifford algebra, and in general relativity. It is shown how the Dirac spinor can be defined in three different ways, namely as an element of the representation space of the Clifford algebra of spacetime, an element of the representation space of the fundamental representation of the Dirac spinor metric-preserving automorphism group of the Clifford algebra, and as an element of the representation space of the fundamental representation of the covering group of the conformal group.

The most interesting discussion in the book is chapter 28 on extending the Grassmann algebra. Dispensing with any scalar product on a vector space, the author shows how to obtain the relative magnitude between two vectors and this leads to the notion of a multivector. The duals to these are called outer forms, and are the familiar differential forms when depending on spatial position. Many helpful diagrams are used to illustrate the properties of multivectors and pseudomultivectors, the linear span of which is called the extended Grassmann algebra of multivectors. Adding a scalar product reduces the number of directed quantities to four, and electrodynamics can be formulated in a way that is independent of the scalar product.

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