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Power-Up: Unlocking the Hidden Mathematics in Video Games [Kietas viršelis]

3.64/5 (77 ratings by Goodreads)
  • Formatas: Hardback, 264 pages, aukštis x plotis: 235x152 mm, weight: 709 g, 80 halftones. 50 line illus.
  • Išleidimo metai: 23-May-2017
  • Leidėjas: Princeton University Press
  • ISBN-10: 0691161518
  • ISBN-13: 9780691161518
Kitos knygos pagal šią temą:
  • Formatas: Hardback, 264 pages, aukštis x plotis: 235x152 mm, weight: 709 g, 80 halftones. 50 line illus.
  • Išleidimo metai: 23-May-2017
  • Leidėjas: Princeton University Press
  • ISBN-10: 0691161518
  • ISBN-13: 9780691161518
Kitos knygos pagal šią temą:
A fun and lively look at the mathematical ideas concealed in video games Did you know that every time you pick up the controller to your PlayStation or Xbox, you are entering a game world steeped in mathematics? Power-Up reveals the hidden mathematics in many of today's most popular video games and explains why mathematical learning doesn't just happen in the classroom or from books--you're doing it without even realizing it when you play games on your cell phone. In this lively and entertaining book, Matthew Lane discusses how gamers are engaging with the traveling salesman problem when they play Assassin's Creed, why it is mathematically impossible for Mario to jump through the Mushroom Kingdom in Super Mario Bros., and how The Sims teaches us the mathematical costs of maintaining relationships. He looks at mathematical pursuit problems in classic games like Missile Command and Ms. Pac-Man, and how each time you play Tetris, you're grappling with one of the most famous unsolved problems in all of mathematics and computer science. Along the way, Lane discusses why Family Feud and Pictionary make for ho-hum video games, how realism in video games (or the lack of it) influences learning, what video games can teach us about the mathematics of voting, the mathematics of designing video games, and much more. Power-Up shows how the world of video games is an unexpectedly rich medium for learning about the beautiful mathematical ideas that touch all aspects of our lives--including our virtual ones.

Recenzijos

"Lane explores secondary, or hidden, mathematical gems that a player might discover upon mature reflection. . . . Just as most car drivers prefer not to inquire how the internal combustion engine works, most video-type users prefer not to ask how computer magic works. For the few who do ask questions, Lane assures us and as his book testifies, 'there's a lot of mathematics under the surface'."---Andrew James Simoson, MathSciNet "Lane explains some pretty technical concepts in an accessible way. . . . A fun survey of interesting maths related through the lens of video games."---Paul Taylor, Aperiodical "The examples [ in Power-Up] were carefully chosen from very popular games, so even the most casual player will have heard of the vast majority of the games discussed. In general, Lane's writing is easy to digest, and the use of color and high-quality paper gives the book a nice look and feel." * Choice * "Power­Up is a very readable book based on examples taken from popular video games. . . . It is a pity that too many people are deprived of the pleasure of finding things out via the intellectual game of mathematics. Hopefully, the effort of the likes of Matthew Lane will someday solve the severe marketing problem of mathematics." * Computing Reviews * "Overall the book is excellent. Lane has written a high readable text with colorful illustrations. You wont regret reading it and maybe Power-Up will add a new level of insight to your computer gaming." * MAA Reviews * "Matthew Lane explores the mathematical underpinning many popular video games in this well-written and very enjoyable book that is pitched at a very broad audience"---Dominic Thorrington, Mathematics Today

Acknowledgments xi
Introduction 1(6)
1 Let's Get Physical
7(27)
1.1 Platforming Perils
7(3)
1.2 Platforming in Three Dimensions
10(2)
1.3 LittleBigPlanet: Exploring Physics through Gameplay
12(2)
1.4 From 2D to 3D: Bending Laws in Portal
14(4)
1.5 Exploring Reality with A Slower Speed of Light
18(3)
1.6 Exploring Alternative Realities
21(5)
1.7 Beyond Physics: Minecraft or Mine Field?
26(1)
1.8 Closing Remarks
27(2)
1.9 Addendum: Describing Distortion
29(5)
2 Repeat Offenders
34(24)
2.1 Let's Play the Feud!
34(2)
2.2 Game Shows and Birthdays
36(3)
2.3 Beyond the First Duplicate
39(2)
2.4 The Draw Something Debacle
41(5)
2.5 Delayed Repetition: Increasing N
46(2)
2.6 Delayed Repetition: Weight Lifting
48(5)
2.7 The Completionist's Dilemma
53(2)
2.8 Closing Remarks
55(1)
2.9 Addendum: In Search of a Minimal k
55(3)
3 Get Out the Voting System
58(28)
3.1 Everybody Votes, but Not for Everything
58(2)
3.2 Plurality Voting: An Example
60(1)
3.3 Ranked-Choice Voting Systems and Arrow's Impossibility Theorem
61(5)
3.4 An Escape from Impossibility?
66(2)
3.5 Is There a "Best" System?
68(3)
3.6 What Game Developers Know that Politicians Don't
71(5)
3.7 The Best of the Rest
76(6)
3.8 Closing Remarks
82(1)
3.9 Addendum: The Wilson Score Confidence Interval
83(3)
4 Knowing the Score
86(36)
4.1 Ranking Players
86(1)
4.2 Orisinal Original
87(4)
4.3 What's in a Score?
91(7)
4.4 Threes! Company
98(2)
4.5 A Mathematical Model of Threes!
100(5)
4.6 Invalid Scores
105(4)
4.7 Lowest of the Low
109(7)
4.8 Highest of the High
116(5)
4.9 Closing Remarks
121(1)
5 The Thrill of the Chase
122(36)
5.1 I'ma Gonna Win!
122(1)
5.2 Shell Games
123(2)
5.3 Green-Shelled Monsters
125(4)
5.4 Generalizations and Limitations
129(2)
5.5 Seeing Red
131(3)
5.6 Apollonius Circle Pursuit
134(2)
5.7 Overview of a Winning Strategy
136(5)
5.8 Pinpointing the Intersections
141(4)
5.9 Blast Radius
145(3)
5.10 The Pursuer and Pursued in Ms. Pac-Man
148(5)
5.11 Concluding Remarks
153(1)
5.12 Addendum: The Pursuit Curve for Red Shells and a Refined Inequality
153(5)
6 Gaming Complexity
158(26)
6.1 From Russia with Fun
158(2)
6.2 P, NP, and Kevin Bacon
160(5)
6.3 Desktop Diversions
165(4)
6.4 Platforming Problems
169(1)
6.5 Fetch Quests: An Overview
170(5)
6.6 Fetch Quests and Traveling Salesmen
175(8)
6.7 Closing Remarks
183(1)
7 The Friendship Realm
184(26)
7.1 Taking It to the Next Level
184(2)
7.2 Friendship as Gameplay: The Sims and Beyond
186(4)
7.3 A Game-Inspired Friendship Model
190(3)
7.4 Approximations to the Model
193(2)
7.5 The Cost of Maintaining a Friendship
195(3)
7.6 From Virtual Friends to Realistic Romance
198(2)
7.7 Modeling Different Personalities
200(3)
7.8 Improving the Model (Again!)
203(6)
7.9 Concluding Remarks
209(1)
8 Order in Chaos
210(17)
8.1 The Essence of Chaos
210(1)
8.2 Love in the Time of Chaos
211(5)
8.3 Shell Games Revisited
216(7)
8.4 How's the Weather?
223(2)
8.5 Concluding Remarks
225(2)
9 The Value of Games
227(17)
9.1 More Important Than Math
227(3)
9.2 Why Games?
230(12)
9.3 What Next?
242(2)
Notes 244(25)
Bibliography 269(4)
Index 273
Matthew Lane is a mathematician and cofounder of Rithm, a school for aspiring web developers. He is also the creator of Math Goes Pop!, a blog that explores the interconnections between mathematics and popular culture. He lives in San Francisco.