Enhanced descriptions from Syndetics:

Many programmers frequently have limited backgrounds in the mathematics and physics needed for game development or other complex applications. Sooner or later, all programmers run into coding issues that will require an understanding of mathematics or physics concepts like collision detection, 3D vectors, transformations, game theory, or basic calculus. This book provides a simple but thorough grounding in the mathematics and physics topics that programmers need to write these algorithms and programs, using a non-language-specific approach. Applications and examples from game programming are included throughout, and exercise sets follow each chapter for additional practice of the techniques. The CD-ROM provides simulations of the mathematical and physical principles discussed in the book along with the source code.

Table of contents provided by Syndetics

• Acknowledgments (p. xxv)
• Introduction (p. xxvii)
• Part I General Techniques (p. 1)
• 1 Numbers (p. 3)
• Overview (p. 3)
• Writing Numbers (p. 4)
• How Computers Represent Numbers (p. 8)
• Exercises (p. 16)
• Summary (p. 17)
• You Should Now Know (p. 17)
• 2 Arithmetic (p. 19)
• Overview (p. 19)
• Fractions and Remainders (p. 20)
• Proportions, Ratios, and Percentages (p. 29)
• Exponentials (p. 36)
• Logarithms (p. 39)
• Exercises (p. 43)
• Summary (p. 44)
• You Should Now Know (p. 44)
• 3 Algebra (p. 45)
• Overview (p. 45)
• Basic Algebra (p. 46)
• Working with Equations (p. 50)
• Functions and Graphs (p. 65)
• Exercises (p. 74)
• Summary (p. 74)
• You Should Now Know (p. 75)
• 4 Trigonometry and Pythagoras (p. 77)
• Overview (p. 77)
• Angles (p. 78)
• Triangles (p. 82)
• Calculations with Triangles (p. 90)
• Rotations and Reflections (p. 94)
• Exercises (p. 101)
• Summary (p. 101)
• You Should Now Know (p. 101)
• 5 Vectors (p. 103)
• Overview (p. 103)
• Getting from Here to There (p. 104)
• Vector Motion (p. 110)
• Vector Calculations (p. 117)
• Matrices (p. 125)
• Exercises (p. 131)
• Summary (p. 131)
• You Should Now Know (p. 132)
• 6 Calculus (p. 133)
• Overview (p. 133)
• Differentiation and Integration (p. 134)
• Differential Equations (p. 144)
• Approximation Methods (p. 146)
• Exercises (p. 152)
• Summary (p. 152)
• You Should Now Know (p. 152)
• Part II Ballistics and Collisions (p. 153)
• 7 Acceleration, Mass, and Energy (p. 155)
• Overview (p. 155)
• Ballistics (p. 156)
• Mass and Momentum (p. 162)
• Energy (p. 163)
• Exercises (p. 167)
• Summary (p. 168)
• You Should Now Know (p. 169)
• 8 Detecting Collisions Between Simple Shapes (p. 171)
• Overview (p. 171)
• Ground Rules (p. 172)
• When Circles Collide (p. 173)
• When Squares Collide (p. 182)
• When Ovals Collide (p. 190)
• When Things Collide (p. 195)
• Exercises (p. 196)
• Summary (p. 197)
• You Should Now Know (p. 197)
• 9 Resolving Collisions (p. 199)
• Overview (p. 199)
• Resolving a Single Collision (p. 200)
• Multiple Collisions (p. 207)
• Exercises (p. 211)
• Summary (p. 212)
• You Should Now Know (p. 212)
• 10 Detecting Collisions Between Complex Shapes (p. 213)
• Overview (p. 213)
• The Problems of a Complex Shape (p. 214)
• Some Reasonable Problems (p. 225)
• Built-In Solutions (p. 237)
• Exercises (p. 238)
• Summary (p. 239)
• You Should Now Know (p. 239)
• 11 A Simple Pool Game (p. 241)
• Overview (p. 241)
• The Rules of Engagement (p. 242)
• Taking a Shot (p. 248)
• Exercises (p. 256)
• Summary (p. 256)
• You Should Now Know (p. 256)
• Part III More Complex Motion (p. 257)
• 12 Force and Newton's Laws (p. 259)
• Overview (p. 259)
• Force (p. 260)
• Gravity (p. 263)
• Rockets and Satellites (p. 267)
• Exercises (p. 269)
• Summary (p. 269)
• You Should Now Know (p. 269)
• 13 Angular Motion (p. 271)
• Overview (p. 271)
• The Physics of a Lever (p. 272)
• Spin (p. 277)
• Spinning Collisions (p. 279)
• Exercises (p. 294)
• Summary (p. 295)
• You Should Now Know (p. 295)
• 14 Friction (p. 297)
• Overview (p. 297)
• How Friction Works (p. 298)
• Friction and Angular Motion (p. 302)
• Exercises (p. 306)
• Summary (p. 306)
• You Should Now Know (p. 307)
• 15 Strings, Pulleys, and Conveyor Belts (p. 309)
• Overview (p. 309)
• Pulling Things Around (p. 310)
• Continuous Momentum (p. 315)
• Exercises (p. 317)
• Summary (p. 318)
• You Should Now Know (p. 318)
• 16 Oscillations (p. 319)
• Overview (p. 319)
• Springs (p. 320)
• Simple Harmonic Motion (p. 322)
• Damped Harmonic Motion (p. 326)
• Phenomena (p. 331)
• Calculating Spring Motion (p. 332)
• Waves (p. 337)
• Exercises (p. 344)
• Summary (p. 344)
• You Should Now Know (p. 345)
• Part IV 3D Mathematics (p. 347)
• 17 3D Geometry (p. 349)
• Overview (p. 349)
• 3D Vectors (p. 350)
• Rendering (p. 357)
• Casting a Ray (p. 363)
• Exercises (p. 367)
• Summary (p. 367)
• You Should Now Know (p. 368)
• 18 Transforms (p. 369)
• Overview (p. 369)
• Describing Locations in Space (p. 370)
• Applying Transforms (p. 375)
• Exercises (p. 382)
• Summary (p. 382)
• You Should Now Know (p. 383)
• 19 Collision Detection in Three Dimensions (p. 385)
• Overview (p. 385)
• When Worlds Collide (p. 386)
• When Footballs Collide (p. 388)
• When Boxes Collide (p. 391)
• When Cans Collide (p. 395)
• When Stuff Collides (p. 400)
• Resolving Collisions in Three Dimensions (p. 401)
• Exercises (p. 401)
• Summary (p. 401)
• You Should Now Know (p. 402)
• 20 Lighting and Textures (p. 403)
• Overview (p. 403)
• Light (p. 403)
• Materials (p. 407)
• Shading (p. 419)
• Exercises (p. 421)
• Summary (p. 421)
• You Should Now Know (p. 422)
• 21 Modeling Techniques (p. 423)
• Overview (p. 423)
• Mathematical 3D Modeling (p. 424)
• Animated Surfaces (p. 432)
• Bones Animation (p. 435)
• Exercises (p. 441)
• Summary (p. 441)
• You Should Now Know (p. 442)
• Part V Game Algorithms (p. 443)
• 22 Speeding Things Up (p. 445)
• Overview (p. 445)
• Cheap and Expensive (p. 446)
• Pseudo-Physics (p. 452)
• Culling (p. 454)
• Exercises (p. 461)
• Summary (p. 461)
• You Should Now Know (p. 462)
• 23 Tile-Based Games (p. 463)
• Overview (p. 463)
• Generating a Game from Bits (p. 464)
• Advanced Tiling (p. 470)
• Exercises (p. 475)
• Summary (p. 475)
• You Should Now Know (p. 476)
• 24 Mazes (p. 477)
• Overview (p. 477)
• Classifying Mazes (p. 478)
• Creating Mazes (p. 483)
• Navigating Within Mazes (p. 492)
• Exercises (p. 501)
• Summary (p. 501)
• You Should Now Know (p. 502)
• 25 Game Theory and AI (p. 503)
• Overview (p. 503)
• Introduction to Game Theory (p. 504)
• Tactical AI (p. 515)
• Top-Down AI (p. 518)
• Bottom-Up AI (p. 522)
• Exercises (p. 528)
• Summary (p. 528)
• You Should Now Know (p. 528)
• 26 Search Techniques (p. 529)
• Overview (p. 529)
• Problem-Solving (p. 530)
• Case Study (p. 534)
• Genetic Algorithms (p. 538)
• Exercises (p. 545)
• Summary (p. 545)
• You Should Now Know (p. 546)
• Appendix A Glossary of Mathematical Terms (p. 547)
• Appendix B Language References and Pseudocode (p. 567)
• Appendix C About the CD-ROM (p. 575)
• Appendix D Further Reading and Resources (p. 581)
• Appendix E Answers to Exercises (p. 585)
• Index (p. 593)

Reviews provided by Syndetics

CHOICE Review

Kodicek provides an excellent review of the fundamentals of mathematics and physics topics necessary for programmers to write codes. His useful book includes chapter exercises and solutions on topics ranging from foundation concepts of mathematics such as principles of numbers, algebra, and geometry, to more multifaceted areas of mathematics and physics including calculus, 3-D math, and complex physics concepts necessary to solve problems of varying complexity. The book focuses broadly on mathematical techniques, physical principles, applications of math and physics in programming, and related concepts and terminology. Written in a clear plain style, the chapters are well organized and presented in a cumulative sequence, referring to topics covered in earlier chapters. The book delineates extremely well the use of mathematical and physics concepts necessary in writing computer programs. Useful reading for those interested in programming, particularly for games; and a great guide for programmers who want to refresh their knowledge of mathematics and physics fundamentals. ^BSumming Up: Recommended. Upper-division undergraduates through professionals; two-year technical program students. S. Banerjee Buffalo State College