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1.

図書

図書
John H. Conway, Derek A. Smith
出版情報: Natick, Mass. : A K Peters, c2003  xii, 159 p. ; 24 cm
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2.

図書

図書
John H. Conway, Heidi Burgiel, Chaim Goodman-Strauss
出版情報: Wellesley, Mass. : AK Peters, c2008  xviii, 426 p. ; 25 cm
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3.

図書

図書
J. H. コンウェイ, R. K. ガイ著 ; 根上生也訳
出版情報: 東京 : シュプリンガー・フェアラーク東京, 2001.11  xii, 323p ; 22cm
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4.

図書

図書
J.H. Conway
出版情報: Natick, Mass. : A K Peters, c2001  xi, 242 p. ; 24 cm
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目次情報: 続きを見る
Prologue
Preface
... On Numbers / Part 0:
All Numbers Great and Small / Chapter 0:
The Class No is a Field / Chapter 1:
The Real and Ordinal Numbers / Chapter 2:
The Structure of the Genral Surreal Number / Chapter 3:
Algebra and Analysis of Numbers / Chapter 4:
Number Theory in the Land of Oz / Chapter 5:
The Curious Field On[subscript 2] / Chapter 6:
Appendix to Part Zero
... and Games / Part 1:
Playing Several Games at Once / Chapter 7:
Some Games are Already Numbers / Chapter 8:
On Games and Numbers / Chapter 9:
Simplifying Games / Chapter 10:
Impartial Games and the Game of Nim / Chapter 11:
How to Lose when you Must / Chapter 12:
Animating Functions, Welter's Game and Hackenbush Unrestrained / Chapter 13:
How to Play Several Games at Once in a Dozen Different Ways / Chapter 14:
Ups, Downs and Bynumbers / Chapter 15:
The Long and the Short and the Small / Chapter 16:
Epilogue
Appendix
Index
Prologue
Preface
... On Numbers / Part 0:
5.

図書

図書
Elwyn R. Berlekamp, John H. Conway, Richard K. Guy
出版情報: Natick, Mass. : A K Peters, c2001-c2004  v. ; 24 cm
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目次情報: 続きを見る
Preface to Second Edition
Preface
Spade-Work!
Whose Game? / 1:
Blue-Red Hackenbush
The Tweedledum and Tweedledee Argument
How Can You Have Half a Move?
... And Quarter Moves?
Ski-Jumps for Beginners
Don't Just Take the Average!
What Is a Jump Worth?
Toads-and-Frogs
Do Our Methods Work?
What is a Game?
When Is a Move Good?
Figure 8(d) Is Worth 3/4
References and Further Reading
Finding the Correct Number is Simplicity Itself / 2:
Which Numbers Are Which?
Simplicity's the Answer!
Simplest Forms for Numbers
Cutcake
Maundy Cake
A Few More Applications of the Simplicty Rule
Positive, Negative, Zero, and Fuzzy Positions
Hackenbush Hotchpotch
Sums of Arbitrary Games
The Outcome of a Sum
The Negative of a Game
Cancelling a Game with its Negative
Comparing Two Games
Comparing Hackenbush Positions
The Game of Col
A Star is Born!
Col Contains Such Values
Game Trees
Green Hackenbush, The Game of Nim, and Nimbers
Get Nimble with Nimbers
Childish Hackenbush
Seating Couples
Winning Strategies
The Sum of Two Finite Games Can Last Forever
A Theorem about Col
Col-lections and Col-lapsings
Another Cutcake Variant
How Childish Can You Get?
Some Harder Games and How to Make Them Easier / 3:
Poker-Nim
Northcott's Game
Bogus Nim-Heaps and the Mex Rule
The Sprague-Grundy Theory for Impartial Games
The White Knight
Adding Nimbers
Wyt Queens
Reversible Moves in General Games
Deleting Dominated Options
Toads-and-Frogs with Ups and Downs
Game Tracking and Identification
What Are Flowers Worth?
A Gallimaufry of Games
Who Wins Sums of Ups, Downs, Stars, and Numbers?
A Closer Look at the Stars
The Values {[up arrow] | [up arrow]} and {0 | [up arrow]}
The Upstart Equality
Gift Horses
The Nim-Addition Rule in Several Variations
Wyt Queens and Wythoff's Game
Answers to Figures 8, 9, and 11
Toad Versus Frog
Two Theorems on Simplifying Games
Berlekamp's Rule for Hackenbush Strings
Taking and Breaking / 4:
Kayles
Games With Heaps
P-Positions and N-Positions
Subtraction Games
Ferguson's Pairing Property
Grundy Scales
Other Take-Away Games
Dawson's Chess
The Periodicity of Kayles
Other Take-and-Break Games
Dawson's Kayles
Variations
Guiles
Treblecross
Officers
Grundy's Game
Prim and Dim
Replication of Nim-Values
Double and Quadruple Kayles
Lasker's Nim
Some Remarks on Periodicity
Standard Form
A Compendium of Octal Games
Additional Remarks
Sparse Spaces and Common Cosets
Will Grundy's Game Be Ultimately Periodic?
Sparse Space Spells Speed
Games Displaying Arithmetic Periodicity
A Non-Arithmetic-Periodicity Theorem
Some Hexadecimal Games
Further References and Reading
Numbers, Nimbers and Numberless Wonders / 5:
Domineering
Switch Games
Cashing Cheques
Some Simple Hot Games
The Tiniest Games
Modern Management of Cash Flow
Tiny Toads-and-Frogs
The Opening Dissection of Toads-and-Frogs
Seating Boys and Girls
Toads-and-Frogs Completely Dissected
Toads-and-Frogs with Two Spaces
More Domineering Values
References
The Heat of Battle / 6:
Snort
A Graphic Picture of Farm Life
Don't Move In A Number Unless There's Nothing Else To Do!
What's in it for Me?
The Left and Right Stops
Cooling--and the Thermograph
Cooling Settles the Mean Value
How to Draw Thermographs
When A Player Has Several Options
Foundations for Thermographs
Examples of Thermographs
Who Is To Move From The Final Stop?
A Four-Stop Example
The Cheque-Market Exchange
Equitable Games
Excitable Games
The Extended Thermograph
Getting the Right Slant
The Thermostatic Strategy
Thermostrat's Not Often Wrong!
Heating
Does The Excitement Show?
Selling Infinitesimal Values To Your Profit-Conscious Friends
Nim, Remoteness and Suspense in Hot Games
Overheating
Cooling the Children's Party
But How Do You Cool A Party By One Degree?
Three Snort Lemmas
A Snort Dictionary
Proof of the Number Avoidance Theorem
Why Thermostrat Works
Blockbusting
... An On We Go!
Hotstrat, Thermostrat and Sentestrat
Hackenbush / 7:
Green Hackenbush
Green Trees
Fusion
Proving The Fusion Principle
A More Complicated Picture
Impartial Maundy Cake
Flower Gardens
The Blue Flower Ploy
Atomic Weights
Atomic Weights of Jungles
Making Tracks in the Jungle
Tracking Down an Animal
Amazing Jungle
Smart Game in the Jungle
Unparted Jungles
Blue-Red Hackenbush Can Be Hard, Too!
Redwood Furniture
Redwood Beds
How Big Is A Redwood Bed?
What's The Bottle
Ordinal Addition, The Colon Principle, and Norton's Lemma
Both Ways of Adding Impartial Games
Many-Way Maundy Cake
Solution to Figure 15
Tracks Cleared Through the Amazing Jungle
How Hard Was The Bed?
NP-Hardness
The Bottle at the End of Chapter 7
It's a Small Small Small Small World / 8:
Uppitiness and Uncertainty
Computing Atomic Weights
Eatcake
Splitting The Atom
Turn-and-Eatcake
All You Need To Know About Atomic Weights But Were Afraid To Ask
Childish Hackenbush Hotchpotch
Atomic Weights of Lollipops
Proving Things About Atomic Weights
Playing Among the Flowers
When is g as uppity as h?
Go Fly A Kite!
All Remote Stars Agree
Large and Small Flowerbeds
Playing Under a Lucky Star
General Multiples of Up
Proof of the Remote Star Rules
Proof That Atomic Weight = Uppitiness
The Wholeness of Hackenbush Hotchpotch
Proper Care of the Eccentric
Galvinized Games
Trading Triangles
Multiples of Positive Games
Multiples Work!
First for the "With" Rule
Now for the "Without" Rule
Shifting Multiples Of Up By Stars
A Theorem on Incentives
Seating Families of Five
Index
Preface to Second Edition
Preface
Spade-Work!
6.

図書

東工大
目次DB

図書
東工大
目次DB
J.H.コンウェイ著 ; 細川尋史訳
出版情報: 東京 : シュプリンガー・フェアラーク東京, 2006.7  vi, 175p ; 21cm
シリーズ名: シュプリンガー数学リーディングス ; 第10巻
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目次情報: 続きを見る
注 : 3x[2]+6xy-5y[2]の[2]は上つき文字
注 : PSL[2]の[2]は下つき文字
注 : Q[p]の[p]は下つき文字
   
第1講 3x[2]+6xy-5y[2]が見えますか? 1
   はじめに 1
   2次形式とは何か? 1
   2つの整数性 3
   同値 5
   素ベクトル,基底と超基底,細分と包括 6
   基底と超基底の関係 7
   基底と超基底のトポグラフ 7
   トポグラフのどこに素ベクトルはあるか? 8
   ベクトルのノルム 10
   等差数列の規則 10
   基底に依存した2次形式の表示式 11
   樹状性 12
   正定値2次形式の湧き出し口 15
   トポグラフは連結である 17
   コノルム,ヴォノルム,単純湧き出し口と2重湧き出し口 18
   符号による2次形式の分類 20
   0を表現しない不定値2次形式-川 21
   整数値2次形式は周期的な川をもつ 23
   半定値2次形式 26
   0を表現する不定値2次形式 27
   講義のまとめ 28
補講1 PSL[2](Z)とファレイ分数 31
   はじめに 31
第2項 格子の形がきこえますか? 39
   はじめに 39
   等スペクトル格子 40
   ミルナーの反例 42
   16次元格子 43
   12次元と8次元の反例 45
   6次元の立方体格子と斜体格子 45
   5次元の反例 48
   速報-ついに発見,4次元の反例! 48
   緊急速報!2次元あるいは3次元に反例はあるのか? 51
   太鼓の形はきこえない! 52
   格子の何をきくことが「できる」のか? 55
   ガウス平均 56
補講2 クヌーザーの糊付けの方法 -ユニモジュラ格子 61
   はじめに 61
   糊付けの例 62
   ルート格子 63
   格子を糊付けする 64
   ニーマイヤーの格子 65
   ルート格子についてのウィットの補題 66
   低次元では立方体であることがききとれる 69
第3講 …そして,その形を感じることができますか? 71
   幾何学それとも算術? 71
   ヴォロノイ細胞 72
   2次元のヴォロノイ細胞 74
   ヴォノルム 75
   指標とコノルム 76
   ヴォノルム空間とコノルム空間 77
   ファノ平面-3次元の場合に対する準備 78
   3次元格子のヴォノルムとコノルム 80
   鈍角の超基底 81
   3次元の鈍角の超基底 83
   実例 85
   コノルムとゼリング変数 88
   ヴォロノイ細胞の5つの形 89
   球詰め型の格子 92
   ミンコフスキの簡約 93
   小マシューセラ2次形式 94
   講義のまとめ 96
補講3 4次元格子の形を感じる 99
   コノルムとゼリング変数 99
   4次元グラフ格子 100
   残りの4次元格子 102
第4講 素数の香り 105
   はじめに 105
   有理数体Q上の同値-対角化 106
   不変量の問題 108
   2次形式の符号 109
   ハッセ-ミンコフスキの定理と大域的関係 111
   不変量が自明な場合への簡約 113
   ウィットの消去法則の証明 114
   p-項の置き換え 115
   止めの一撃 117
   ハッセ-ミンコフスキの不変量の別バージョン 118
   整数係数2次形式の不変量 120
   p-進整数対角化とp-進記号 120
   2-進ジョルダン分解と2-進記号 122
   種 124
   p-進ガウス平均 125
   p-進記号をききとる 127
   p=2の場合 128
   種をきく-かくれんぼごっこ 130
   高次元では種はききとれない 132
補講4 不変量再考-p-進数 135
   p-符号の不変性 135
   p-進数 136
   Q[p]上の2元2次形式 138
   不変量によって規定される有理数係数の2次形式 138
   不変員によって規定される整数係数の2次形式 141
   分母が非本質的な同値 142
   スピノール種 143
付録 数論の風味 147
   3つの有名な定理 147
   ゾロタレフによるヤコビ記号の定義 147
   5つの補題 148
   ヤコビ記号の相互法則 151
   ルジャンドル記号と線型ヤコビ記号 152
   大域的関係 153
   強い意味のハッセ-ミンコフスキの原理 155
   偶ユニモジュラ形式についての定理 156
   偶ユニモジュラ格子の歴史 157
   3平方数の定理 158
   3つの整数の平方による表現 159
   ルジャンドルの定理から導かれる結果 160
   15の定理 163
   普遍的な3変数定値2次形式は存在しない 164
参考文献 165
訳者あとがき 169
索引 171
注 : 3x[2]+6xy-5y[2]の[2]は上つき文字
注 : PSL[2]の[2]は下つき文字
注 : Q[p]の[p]は下つき文字
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