Games for Math: Playful Ways to Help Your Child Learn Math, From Kindergarten to Third Grade

 Peggy Kaye

 Pantheon | 1988 | 256 páginas | rar - epub | 14,2 Mb


link (password: matav)


At a time when the poor math performance of American school children has labeled us a "nation of underachievers," what can parents--often themselves daunted by the mysteries of mathematics--do to help their children? In Games for Math,Peggy Kaye--teacher extraordinaire and author of the highly praised Games for Reading--gives parents more than fifty marvelous and effective ways to help their children learn math by doing just what kids love best: playing games.

Contents 
PART ONE
Chapter One: Counting Counts
HOP, SKIP, TOUCH YOUR NOSE
PENNY TOSS
NUMBER COLLAGE
THE HOW-MANY GAME
THREE KINDS OF FANCY NUMBERS
Chapter Two: Thoughts to Grow On
THE ER GAME
KITCHEN CALCULUS
OODLES OF NOODLES
CLAP CLAP BEEP BEEP
WHAT’S NEXT?
Chapter Three: Size and Shape
STRING TIME
RIBBON ME
HOW MUCH DOES IT HOLD?
SHAPE LOTTO
SHAPE COLLAGE
PART TWO
Chapter Four: Fancy Counting
FILL THE SPOON
GRASSHOPPER
COUNTING AND ESTIMATING
CLEANING COUNTS
FIND A PENNY
SECRET NUMBER
Chapter Five: Adding and Subtracting
MAKE TEN
WHAT DID I DO?
TARGET GAME
NUMBER STORIES
NUMBER LADDER
FAST TRACK
DOUBLE IT
MATH CHECKERS
PYRAMID
FIVE CARDS MAKE TEN
Chapter Six: Size and Shape II
IS IT?
TWO SEWING PROJECTS
MATH IN THE KITCHEN
TANGRAMS
ORIGAMI
Chapter Seven: Multiplication and Division
STAR COUNT
VICTOR VAMPIRE’S BIRTHDAY
LOTS OF BOXES
CALCULATING MATH
Chapter Eight: The Number System
A BUNCH OF BEANS
FIFTY WINS
BAG OF CHIPS
THROW A NUMBER
THREE POTS
GROUP TEN
Chapter Nine: The Bigger the Better
BIGGEST AND SMALLEST
NUMBER TRAILS
NUMBER ESP
PART THREE
Chapter Ten: Strategy Games
TAPATAN
YUT
NINE MEN’S MORRIS
KHALA
Chapter Eleven: It’s a Puzzle
NUMBER BUBBLES
WHAT’S IT WORTH?
COLORED BOXES
Appendices
WHAT ABOUT COMPUTERS?
MATH BOOKS TO READ ALOUD
EXPLAINING NUMBER ESP
A NOTE TO TEACHERS
Other Books by This Author

Brain Teasers: 211 Logic Puzzles, Lateral Thinking Games, Mazes, Crosswords, and IQ Tests to Exercise Your Mind and Keep You Sharp 'til You're 100

 

Ian Livingstone e Jamie Thomson

Skyhorse Publishing |  2009 | 256 páginas | rar - epub | 4,8 Mb

link (password: matav)

A great way to have fun and build brain power, Brain Teasersoffers a variety of games to delight and challenge even the most advanced puzzler. Brain Teasers shows off some outrageously fun new mindbenders, like anasearches (a combination of an anagram, a crossword, and a word search), numberlockers (think of a crossword puzzle with numbers instead of words), and alphabetics (a miniature crossword puzzle that uses each letter of the alphabet exactly once). Perfect for anyone who sits down with the New York Times crossword puzzle every morning or works through Sudoku puzzles on the way home, this book is guaranteed to excite your mind and jump-start your brain.

Mathematical Games, Abstract Games

João Pedro Neto e Jorge Nuno Silva

Dover Publications | 2013 | 208 páginas | rar - epub | 11,85 Mb

link (password : matav)

This user-friendly and visually appealing book offers a collection of board games of strategy — some old, most very recent. None involve chance or hidden information. Perfect for anyone who enjoys an intellectual challenge, these are chiefly new diversions that were chosen by the authors for their strategic and tactical qualities.
Contents include sections on games for two and three players, plus a chapter dedicated to mathematical games (including Nim and games on graphs). Additional chapters discuss the theory and history of board games. Numerous diagrams throughout the book clarify the text, and a helpful glossary offers clarifications of rules.

Contents1.The World of Games
2.Games for Two
Aboyne, Amazons, Anchor, Annuvin, Campaign, Dispatch, Epaminondas, Go, Gogol, Gomoku, Gonnect, Havannah, Hex, Hobbes, Intersections, Iqishiqi, Jade, Lines of Action, Nex, Nosferatu, Pawnographic Chess, SanQi, Semaphore, Slimetrail, Stooges, UN, Y
3.Nim Games
White Knight, Wyt Queen, Whitoff, JIL, LIM, Nim, Plainim, Nimble, Turning Turtles, Silver, Dollar, Stairs, Northcott, Nimk, Blocking Nim, Games on Graphs, Sums of Impartial Games, Wyt Queens, Green Hackenbush
4.Games for Three
Triskelion, Iqishiqi for Three, Porus Torus, Hex for Three, Reversi for Three, Triad, Gomoku for Three, Gonnect for Three

Glossary

Games and Mathematics: Subtle Connections

David Wells

 Cambridge University Press |  2012 | 258 páginas | rar - pdf |1 Mb

link (password: matav)

epub - 3 Mb
link
link1

mobi - 3,8 Mb - link

The appeal of games and puzzles is timeless and universal. In this unique book, David Wells explores the fascinating connections between games and mathematics, proving that mathematics is not just about tedious calculation but imagination, insight and intuition. The first part of the book introduces games, puzzles and mathematical recreations, including knight tours on a chessboard. The second part explains how thinking about playing games can mirror the thinking of a mathematician, using scientific investigation, tactics and strategy, and sharp observation. Finally the author considers game-like features found in a wide range of human behaviours, illuminating the role of mathematics and helping to explain why it exists at all. This thought-provoking book is perfect for anyone with a thirst for mathematics and its hidden beauty; a good high school grounding in mathematics is all the background that is required, and the puzzles and games will suit pupils from 14 years.

Contents
PART I: Mathematical recreations and abstract games
Introduction; Everyday puzzles;
1 Recreations from Euler to Lucas;
Euler and the Bridges of Königsberg; Euler and knight tours; Lucas and mathematical recreations; Lucass game of solitaire calculation;
2 Four abstract games;
From Dudeneys puzzle to Golombs Game; Nine Mens Morris; Hex; Chess; Go;
3 Mathematics and games: mysterious connections;
Games and mathematics can be analysed in the head; Can you -look ahead'?; A novel kind of object; They are abstract. They are difficultRules; Hidden structures forced by the rules; Argument and proof; Certainty, error and truth; Players make mistakes; Reasoning, imagination and intuition; The power of analogy; Simplicity, elegance and beauty; Science and games: lets go exploring;
4 Why chess is not mathematics;
Competition; Asking questions about; Metamathematics and game-like mathematics; Changing conceptions of problem solving; Creating new concepts and new objects; Increasing abstraction; Finding common structures; The interaction between mathematics and sciences;
5 Proving versus checking.
The limitations of mathematical recreationsAbstract games and checking solutions; How do you `prove' that 11 is prime?; Is `5 is prime' a coincidence?; Proof versus checking; Structure, pattern and representation; Arbitrariness and un-manageability; Near the boundary;
PART II: Mathematics: game-like, scientific and perceptual
Introduction;
6 Game-like mathematics;
Introduction; Tactics and strategy; Sums of cubes and a hidden connection; A masterpiece by Euler;
7 Euclid and the rules of his geometrical game;
Cevas theorem; Simsons line; The parabola and its geometrical properties. Dandelins spheres
8 New concepts and new objects;
Creating new objects; Does it exist?; The force of circumstance; Infinity and infinite series; Calculus and the idea of a tangent; What is the shape of a parabola?;
9 Convergent and divergent series;
The pioneers; The harmonic series diverges; Weird objects and mysterious situations; A practical use for divergent series;
10 Mathematics becomes game-like; Eulers relation for polyhedra;
The invention-discovery of groups; Atiyah and MacLane disagree; Mathematics and geography;
11 Mathematics as science;
Introduction. Triangle geometry: the Euler line of a triangleModern geometry of the triangle; The Seven-Circle Theorem, and other New Theorems;
12 Numbers and sequences;
The sums of squares; Easy questions, easy answers; The prime numbers; Prime pairs; The limits of conjecture; A Polya conjecture and refutation; The limitations of experiment; Proof versus intuition;
13 Computers and mathematics;
Hofstadter on good problems; Computers and mathematical proof; Computers and 'proof'; Finally: formulae and yet more formulae;
14 Mathematics and the sciences;
Scientists abstract.

Play's the Thing : Mathematical Games for the Classroom and Beyond

 Alan Lipp

Anthem Press | 2011 | 147 páginas | rar - pdf | 238 kb

link (password : matav)

The book presents 18 games and develops the concepts of game analysis and winning strategies. Students are encouraged to play these mathematical games together, collect data developed through their play, and analyze the data to develop a winning strategy. Through the exploration of mathematical games, ‘The Play’s the Thing’ introduces teachers and students to the fun of play and to the mathematics behind the fun.

ContentsAcknowledgments xi
Prologue To the Teacher xiii
Act 0 To the Student xv
Act 1 Blockers 1
Act 1 Exercises 2
Act 2 Nimble 5
Act 2 Exercises 6
Act 3 More Variations 9
Act 3 Exercises 10
Act 4 Take Away 1, 2, 3 13
Looking for a Strategy 13
Act 4 Exercises 14
Act 5 Two Piles: A Hidden Game 17
Act 6 Two Piles 1, 2, 3 21
Act 7 Nim 29
Act 8 Flit 37
Act 8 Exercises 38
Act 9 Mr Flit 41
Act 10 Landis 47
Act 10 Exercises 48
Act 11 Add’em Up 51
Act 11 Exercises 52
Act 12 Connect-the-Dots 55
Act 12 Exercises 55
Act 13 Boxes 59
Act 13 Exercises 60
Act 14 Hold That Line 65
Act 14 Exercises 66
Act 15 The Fifteen Game 69
Act 15 Exercises 70
Act 16 Sliders 73
Act 16 Exercises 75
Act 17 Lynch 76
Act 17 Exercises 78
Act 18 Progression: Down and Up 81
Act 19 Harder Stuff 87
Answers 97

The Mathematics of Games and Gambling

Edward Packel

The Mathematical Association of America | 2006 - 2.ª edição| 190 páginas | rar - pdf | 880 kb

link
password: matav


The first edition of this book was reprinted eight times! This book introduces and develops some of the important and beautiful elementary mathematics needed for rational analysis of various gambling and game activities. Most of the standard casino games (roulette, , blackjack, keno), some social games (backgammon, poker, bridge) and various other activities (state lotteries, horse racing, etc.) are treated in ways that bring out their mathematical aspects. The mathematics developed ranges from the predictable concepts of probability, expectation, and binomial coefficients to some less well-known ideas of elementary game theory. The Second Edition includes new material on: sports betting and the mathematics behind it; Game theory applied to bluffing in poker and related to the “Texas Holdem phenomenon”: The Nash equilibrium concept and its emergence in the popular culture: Internet links to games and to Java applets for practice and classroom use. The only formal mathematics background the reader needs is some facility with high school algebra. Game-related exercises are included at the end of most chapters for readers interested in working with and expanding ideas treated in the text. Solutions to some of the exercises appear at the end of the book.

Contents
Preface to the First Edition ix
Preface to the Second Edition xiii
1 The Phenomenon of Gambling 1
1.1 A selective history . . . 1
1.2 The gambler in fact and fiction . . . 5
2 Finite Probabilities and Great Expectations 13
2.1 The probability concept and its origins . . 13
2.2 Dice, cards, and probabilities  . . 15
2.3 Roulette, probability and odds. . 17
2.4 Compound probabilities: The rules of the game  . . 20
2.5 Mathematical expectation and its application .. . 22
2.6 Exercises  . . 26
3 Backgammon and Other Dice Diversions 29
3.1 Backgammon oversimplified  . . 29
3.2 Rolling spots and hitting blots  . . 32
3.3 Enteringand bearingoff .  . 34
3.4 The doubling cube  . . 36
3.5 Craps  . . 40
3.6 Chuck-a-Luck . . . 45
3.7 Exercises . . 47
4 Permutations, Combinations, and Applications 51
4.1 Careful counting: Is order important? . . 51
4.2 Factorials and other notation  . . 53
4.3 Probabilities in poker  . . 55
4.4 Betting in poker: A simple model  . . 59
4.5 Distributions in bridge  . . 67
4.6 Keno type games . . 71
4.7 Exercises . . 73
5 Play it Again Sam: The Binomial Distribution 79
5.1 Games and repeatedtrials . . 79
5.2 The binomial distribution . . 79
5.3 Beating the odds and the “law” of averages  . . 83
5.4 Betting systems  . . 90
5.5 A brief blackjack breakthrough. . 93
5.6 Exercises  . . 95
6 Elementary Game Theory 99
6.1 What isgame theory?  . . 99
6.2 Games in extensive form . . 100
6.3 Two-persongames in normal form  . . 105
6.4 Zero-sumgames . . 107
6.5 Nonzero-sum games, Nash equilibria and the prisoners’ dilemma  . 113
6.6 Simple n-persongames . . 118
6.7 Power indices. . 120
6.8 Games computers play  . . . 123
6.9 Exercises . . . 129
7 Odds and Ends 135
7.1 The mathematics of bluffing and the Texas Holdem invasion . . 135
7.2 Off to the races  . . 141
7.3 Lotteries and your expectation . . . 147
7.4 The gambler’s ruin  . 158

The Tower of Hanoi – Myths and Maths

Andreas M. Hinz, Sandi Klavzar, Uros Milutinovic e Ciril Petr

Birkhäuser | 2013 | 353 páginas | pdf | 9 Mb

link
link1

This is the first comprehensive monograph on the mathematical theory of the solitaire game “The Tower of Hanoi” which was invented in the 19th century by the French number theorist Édouard Lucas. The book comprises a survey of the historical development from the game’s predecessors up to recent research in mathematics and applications in computer science and psychology. Apart from long-standing myths it contains a thorough, largely self-contained presentation of the essential mathematical facts with complete proofs, including also unpublished material. The main objects of research today are the so-called Hanoi graphs and the related Sierpiński graphs. Acknowledging the great popularity of the topic in computer science, algorithms and their correctness proofs form an essential part of the book. In view of the most important practical applications of the Tower of Hanoi and its variants, namely in physics, network theory, and cognitive (neuro)psychology, other related structures and puzzles like, e.g., the “Tower of London”, are addressed.
Numerous captivating integer sequences arise along the way, but also many open questions impose themselves. Central among these is the famed Frame-Stewart conjecture. Despite many attempts to decide it and large-scale numerical experiments supporting its truth, it remains unsettled after more than 70 years and thus demonstrates the timeliness of the topic.
Enriched with elaborate illustrations, connections to other puzzles and challenges for the reader in the form of (solved) exercises as well as problems for further exploration, this book is enjoyable reading for students, educators, game enthusiasts and researchers alike.

Contents
Foreword by Ian Stewart v
Preface vii
0 The Beginning of the World 1
0.1 The Legend of the Tower of Brahma . . 1
0.2 History of the Chinese Rings . . 3
0.3 History of the Tower of Hanoi. . 6
0.4 Puzzles and Graphs  . . 23
0.5 Quotient Sets. . 36
1 The Chinese Rings 53
1.1 Theory of the Chinese Rings . . 53
1.2 The Gros Sequence. . 60
1.3 Two Applications. . 65
1.4 Exercises  . 68
2 The Classical Tower of Hanoi 71
2.1 Perfect to Perfect . . 71
2.2 Regular to Perfect . . 82
2.3 Hanoi Graphs . . 94
2.4 Regular to Regular . . 105
2.5 Exercises . . 128
3 Lucas’s Second Problem 131
3.1 Irregular to Regular. . 131
3.2 Irregular to Perfect . . 136
3.3 Exercises. . 140
4 Sierpinski Graphs 141
4.1 Sierpinski Graphs With Base 3  . . 141
4.2 General Sierpinski Graphs  . . 149
4.3 Connections to Topology: Sierpinski Curve and Lipscomb Space . . 160
4.4 Exercises  . . 163
5 The Tower of Hanoi with More Pegs 165
5.1 The Reve’s Puzzle and the Frame-Stewart Conjecture. . 165
5.2 Frame-Stewart Numbers . . 170
5.3 Numerical Evidence for The Reve’s Puzzle . . 179
5.4 Even More Pegs. . 184
5.5 Hanoi Graphs. . 190
5.6 Numerical Results and Largest Disc Moves . . 200
5.7 Exercises . . 209
6 Variations of the Puzzle 211
6.1 What is a Tower of Hanoi Variant? . . 211
6.2 The Tower of Antwerpen .. . 218
6.3 The Bottleneck Tower of Hanoi . . 222
6.4 Exercises . . 226
7 The Tower of London 227
7.1 Shallice’s Tower of London . . 227
7.2 More London Towers . . 231
7.3 Exercises  . . 238
8 Tower of Hanoi Variants with Oriented Disc Moves 241
8.1 Solvability . . 241
8.2 An Algorithm for Three Pegs. . 245
8.3 More Than Three Pegs . . 251
8.4 Exponential and Sub-Exponential Variants. . 256
8.5 Exercises  . . 259
9 The End of the World 261
A Hints and Solutions to Exercises 265

Simulation and Gaming for Mathematical Education: Epistemology and Teaching Strategies

Angela Piu

IG I Global | 2010 | 356 páginas | PDF | 4,4 Mb

link

keep2share.cc
uploaded.net

Technologic and virtual development is growing, creating an environment of online gaming that can be used as an effective and motivational instrument for math didactics in education. Simulation and Gaming for Mathematical Education: Epistemology and Teaching Strategies provides leading research on ways for various learning environments to becreated referring to math didactics through redefinition and reassessment of teaching experiences. A defining collection of field advancements, this publication gradually leads readers through the steps of planning innovative strategies in math education.

Practical Poker Math: Basic Odds & Probabilities for Hold'Em and Omaha

Pat Dittmar

ECW Press | 2008 | 256 páginas | PDF | 3,76Mb

link
depositfiles.comt

PDF | 5 Mb

4shared.com

A study in probability, strategy, and game theory, this handy companion explores all the mathematical methods of mastering the game of poker. Using an original concept called "Total Odds," the book presents a complete odds work-up for both Texas Hold'Em and the high and low hands of Omaha. These principles are accessible to any poker player at any skill level, and the calculations are color-coded, making them easy to follow. Serving as a convenient primer for the beginner and a reference text for more experienced players, this guide is a safe bet for anyone looking to win.

More Math Games & Activities from Around the World

Claudia Zaslavsky

Chicago Review Press | 2003 | 176 páginas | PDF | 6,91 Mb

link
uploading.com

Math, history, art, and world cultures come together in this delightful book for kids, even for those who find traditional math lessons boring. More than 70 games, puzzles, and projects encourage kids to hone their math skills as they calculate, measure, and solve problems. The games span the globe, and many have been played for thousands of years, such as three-in-a-row games like Achi from Ghana or the forbidden game of Jirig from Mongolia. Also included are imaginative board games like Lambs and Tigers from India and the Little Goat Game from Sudan, or bead and string puzzles from China, and Möbius strip puzzles from Germany. Through compelling math play, children will gain confidence and have fun as they learn about the different ways people around the world measure, count, and use patterns and symmetry in their everyday lives.

Mathematics Education for a New Era: Video Games as a Medium for Learning

Keith Devlin

A K Peters/C R C | 2011 | 218 páginas | PDF | 3,4 Mb

link

Stanford mathematician and NPR Math Guy Keith Devlin explains why, fun aside, video games are the ideal medium to teach middle-school math. Aimed primarily at teachers and education researchers, but also of interest to game developers who want to produce videogames for mathematics education, Mathematics Education for a New Era: Video Games as a Medium for Learning describes exactly what is involved in designing and producing successful math educational videogames that foster the innovative mathematical thinking skills necessary for success in a global economy. 

Across the Board: The Mathematics of Chessboard Problems

John J. Watkins

Princeton University Press | 2004 | 272 páginas | DJVU | 2,84 Mb

link direto
link

Across the Board is the definitive work on chessboard problems. It is not simply about chess but the chessboard itself--that simple grid of squares so common to games around the world. And, more importantly, the fascinating mathematics behind it. From the Knight's Tour Problem and Queens Domination to their many variations, John Watkins surveys all the well-known problems in this surprisingly fertile area of recreational mathematics. Can a knight follow a path that covers every square once, ending on the starting square? How many queens are needed so that every square is targeted or occupied by one of the queens?

Each main topic is treated in depth from its historical conception through to its status today. Many beautiful solutions have emerged for basic chessboard problems since mathematicians first began working on them in earnest over three centuries ago, but such problems, including those involving polyominoes, have now been extended to three-dimensional chessboards and even chessboards on unusual surfaces such as toruses (the equivalent of playing chess on a doughnut) and cylinders. Using the highly visual language of graph theory, Watkins gently guides the reader to the forefront of current research in mathematics. By solving some of the many exercises sprinkled throughout, the reader can share fully in the excitement of discovery.

Showing that chess puzzles are the starting point for important mathematical ideas that have resonated for centuries, Across the Board will captivate students and instructors, mathematicians, chess enthusiasts, and puzzle devotees.

Outros livros da série Paradoxes, Perplexities &; Mathematical Conundrums
for the Serious Head Scratcher, publicados pela Princeton University Press, disponíveis no blog:

- Chases and Escapes: The Mathematics of Pursuit and Evasion (2007), de Paul J. Nahin

- Duelling Idiots and Other Probability Puzzlers (2000), de Paul J. Nahin
- Slicing Pizzas, Racing Turtles, and Further Adventures in Applied Mathematics
 (2012), de Robert B. Banks

Mathematical Games and Puzzles

Trevor Rice

St. Martin's Press | 1974 | 94 pages |

rar - PDF - 3 Mb - link (password: matav)

DJVU | 3 Mb - link

Math isn't only about numbers - math skills are found in puzzles and games too.

Take a look at this collection by Trevor Rice

Presents in text and diagrams more than forty games and puzzles that demonstrate mathematical principles.

Games of no Chance 3

(Mathematical Sciences Research Institute Publications)
By Michael H. Albert, Richard J. Nowakowski

Cambridge University Press | 2009 | 576 páginas |  pdf

f3.tiera.ru
uploading.com
lib.freescienceengineering.org

online (em capítulos): library.msri.org

Descrição: his fascinating look at combinatorial games, that is, games not involving chance or hidden information, offers updates on standard games such as Go and Hex, on impartial games such as Chomp and Wythoff's Nim, and on aspects of games with infinitesimal values, plus analyses of the complexity of some games and puzzles and surveys on algorithmic game theory, on playing to lose, and on coping with cycles. The volume is rounded out with an up-to-date bibliography by Fraenkel and, for readers eager to get their hands dirty, a list of unsolved problems by Guy and Nowakowski. Highlights include some of Siegel's groundbreaking work on loopy games, the unveiling by Friedman and Landsberg of the use of renormalization to give very intriguing results about Chomp, and Nakamura's "Counting Liberties in Capturing Races of Go." Like its predecessors, this book should be on the shelf of all serious games enthusiasts.

Win-Win Math Games

Win-Win Math Games
Marilyn Burns

instructor March/april 2009

On-line: icpd.pbworks.com

The 15 Puzzle book

Jerry Slocum, Dic Sonneveld

Slocum Puzzle Foundation | 2006 | 144 páginas | 6 Mb

djvu - link; link1

Descrição: This book contains the definitive, illustrated history of one of the most popular and important mechanical puzzles of all time. It can be argued that the Fifteen Puzzle in 1880 had the greatest impact on American and European society during of any mechanical puzzle the world has ever known. Books by famous mathematicians tell that a deaf mute invented the 15 puzzle, but encyclopedias, other books and web sites say it was invented by Sam Loyd who Martin Gardner called "America’s greatest puzzle designer". Or has Sam Loyd, who said he invented the puzzle, continued to fool the world for more than 100 years? The true story of the puzzle is told here for the first time.
• The real inventor and his patent application records were found.
• The story of how the puzzle came to be manufactured.
• Proof that the 15 puzzle is mathematically impossible to solve.
• How a young New Yorker solved it.
• The worldwide puzzle craze that it created

Games of no Chance

(Mathematical Sciences Research Institute Publications)
Richard J. Nowakowski

Cambridge University Press | 1998 | 549 páginas  pdf | 3 Mb

on-line: msri.org (em capítulos)
link direto

djvu - link


Descrição: Is Nine-Men's Morris, in the hands of perfect players, a win for white or for black--or a draw? Can king, rook, and knight always defeat king and two knights in chess? What can Go players learn from economists? What are nimbers, tinies, switches, minies? This book deals with combinatorial games, that is, games not involving chance or hidden information. Their study is at once old and young: though some games, such as chess, have been analyzed for centuries, the first full analysis of a nontrivial combinatorial game (Nim) only appeared in 1902. This book deals with combinatorial games, that is, games not involving chance or hidden information. Their study is at once old and young: though some games, such as chess, have been analyzed for centuries, the first full anlaysis of a nontrivial combinatorial game (Nim) only appeared in 1902. The first part of this book will be accessible to anyone, regardless of background: it contains introductory expositions, reports of unusual contest between an angel and a devil. For those who want to delve more deeply, the book also contains combinatorial studies of chess and Go; reports on computer advances such as the solution of Nine-Men's Morris and Pentominoes; and new theoretical approaches to such problems as games with many players. If you have read and enjoyed Martin Gardner, or if you like to learn and analyze new games, this book is for you.
More Games of no Chance
(Mathematical Sciences Research Institute Publications)
Richard J. Nowakowski

Cambridge University Press | 2002| 544 páginas

on-line: msri.org (pdf - em capítulos)
link direto

Descrição: This book is a state-of-the-art look at combinatorial games, that is, games not involving chance or hidden information. It contains a fascinating collection of articles by some of the top names in the field, such as Elwyn Berlekamp and John Conway, plus other researchers in mathematics and computer science, together with some top game players. The articles run the gamut from new theoretical approaches (infinite games, generalizations of game values, 2-player cellular automata, Alpha-Beta pruning under partial orders) to the very latest in some of the hottest games (Amazons, Chomp, Dot-and-Boxes, Go, Chess, Hex). Many of these advances reflect the interplay of the computer science and the mathematics. The book ends with an updated bibliography by A. Fraenkel and an updated and annotated list of combinatorial game theory problems by R. K. Guy.

The Mathematics of Games and Gambling

(New Mathematical Library)

Edward Packel

The Mathematical Association of America | 1996| 151 páginas |


pdf -3,4 Mb - link

 Djvu | 1,5 Mb
link direto
link
depositfiles.com
uploading.com
depositfiles.com



Descrição: You can't lose with this MAA Book Prize winner if you want to see how mathematics can be used to analyze games of chance and skill. Roulette, craps, blackjack, backgammon, poker, bridge, lotteries and horse races are considered here in a way that reveals their mathematical aspects. The tools used include probability, expectation, and game theory. No prerequisites are needed beyond high school algebra. No book can guarantee good luck, but this book will show you what determines the best bet in a game of chance or the optimal strategy in a strategic game. Besides being an excellent supplement to a course on probability and good bed-side reading, this book's treatment of lotteries should save the reader some money.

Luck, Logic, and White Lies: The Mathematics of Games

Jorg Bewersdorff

AK Peters | 2004 | 486 páginas | pdf | 29 Mb

link
scribd.com

Descrição: The mathematical underpinnings of games, whether they are strategic or games of chance, have been known for centuries, but are usually only understood by players and aficionados who have a background in mathematics. The author has succeeded in making that knowledge accessible, entertaining, and useful to everyone who likes to play and win. The information applies to such diverse and popular games as Roulette, Monopoly™, Chess, Go, numerous card games, and many more. He reviews the mathematical foundations, probability, combinatorics, and mathematical game theory, the field that won John Nash of A Beautiful Mind the Nobel Prize, and emphasizes the implementation of these techniques so that players can put them to work immediately. An extensive bibliography and sections describing the historical developments are welcome features to put the subject in a broader context

Learning and Mathematics Games

(Journal for Research in Mathematics Education. Monograph, No. 1)
George W. Bright, John G. Harvey, Margariere Wheeler

National Council of Teachers of Mathematics |1985 | 189 páginas | rar - pdf | 1,5 Mb

link
password: matav

Descrição: This monograph presents research findings from a series of 11 studies conducted in grades 5 through 10 on the role of games in learning mathematics. The first chapter considers "What is learning from a game?" and includes two examples of mathematical instructional games, with a definition of such games, cognitive effects, game-related variables, and taxonomic level. The second chapter reviews previous research on the cognitive effects of mathematics instructional games, with tables summarizing information. Chapter 3 presents the research design and procedures of the 11 studies conducted by the authors, which varied in instructional and taxonomic levels in order to describe the conditions under which cognitive effects can be expected. The fourth chapter contains a synthesis of results and effects across all 11 studies. Finally, the fifth chapter presents discussion and conclusions, with sections on instructional level and taxonomic level, interaction patterns, sex-related effects, and implications for teaching. A list of over 130 references is provided, and appendices contain descriptions of individual studies and games, including materials and directions.