October 2002 | Hardback | 544 pages 100 line
diagrams | ISBN: 0-521-80832-4
This is a state-of-the-art look at combinatorial games - 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. Like its predecessor, Games of No Chance, this
should be on the shelf of all serious combinatorial games
enthusiasts.
Contents
1. The game of hex: the hierarchical approach Vadim V.
Anshelevich; 2. The 4g4g4g4g4 problems and solutions Elwyn
Berlekamp; 3. Idempotents among partisan games Elwyn Berlekamp; 4.
Forcing your opponent to stay in control of a loony DotsAndBoxes
endgame Elwyn Berlekamp and Katherine Scott; 5. The complexity of
clickomania Therese C. Biedl, Erik D. Demaine, Martin L. Demaine,
Rudolf Fleischer, Lars Jacobsen and J. Ian Munro; 6. 1xn konane:
a summary of results Alice Chan and Alice Tsai; 7. More infinite
games J. H. Conway; 8. Phutball endgames are hard Erik D.
Demaine, Martin L. Demaine and David Eppstein; 9. Coin-moving
puzzles Erik D. Demaine, Martin L. Demaine and Helena A. Verrill;
10. Higher numbers in pawn endgames on large chessboards Noam D.
Elkies; 11. Searching for spaceships David Eppstein; 12. Two
player games on cellular automata Aviezri S. Fraenkel; 13.
AlphaBeta pruning under partial orders M. Ginsberg; 14. One
dimensional phutball J. P. Grossman and R. J. Nowakowski; 15.
Hypercube tic-tac-toe Solomon W. Golomb and Alfred W. Hales; 16.
Transfinite chomp Scott Huddleston and Jerry Shurman; 17. Who
wins domineering on rectangular boards? Michael Lachmann,
Cristopher Moore and Ivan Rapaport; 18. Vines Jacob Lurie; 19.
The abstract structure of the group of games David Moews; 20. One-dimensional
peg solitaire, and duotaire Cristopher Moore and David Eppstein;
21. Exhaustive search in Amazons Raymond Georg Snatzke; 22. Go
thermography - the 4/21/98 jiang-rui endgame Bill Spight; 23. An
application of mathematical game theory to Go endgames - some
width-two-entrance rooms with and without kos Takenobu Takizawa;
24. Go endgames are hard David Wolfe; 25. Restoring fairness to
Dukego Greg Martin; 26. Bibliography of combinatorial games -
updated A. Fraenkel; 27. Problems in combinatorial game theory -
updated R. K. Guy; 28. Global threats in combinatorial games: a
computation model with applications to chess endgames Fabian
Maeser; 29. A symmetric strategy in graph avoidance games Frank
Harary, Wolfgang Slany and Oleg Verbitsky.
Series: MATHEMATICAL SCIENCES RESEARCH INSTITUTE PUBLICATIONS VOL.42.
October 2002 | Hardback | 368 pages 80 line
diagrams | ISBN: 0-521-01678-9
Grab a pencil. Relax. Then take off on a mind-boggling journey to
the ultimate frontier of math, mind, and meaning as acclaimed
author Dr Clifford Pickover, Dorothy, and Dr Oz explore some of
the oddest and quirkiest highways and byways of the numerically
obsessed. Prepare yourself for a shattering odyssey as The
Mathematics of Oz unlocks the doors of your imagination. The
thought-provoking mysteries, puzzles, and problems range from
zebra numbers and circular primes to Legion’s number - a number
so big that it makes a trillion pale in comparison. The strange
mazes, bizarre consequences, and dizzying arrays of logic
problems will entertain people at all levels of mathematical
sophistication. The tests devised by enigmatic Dr Oz to assess
human intelligence will tease the brain of even the most avid
puzzle fan. Test your wits on a host of mathematical topics:
geometry and mazes, sequences, series, sets, arrangements,
probability and misdirection, number theory, arithmetic, and even
several problems dealing with the physical world. With numerous
illustrations, this is an original, fun-filled, and thoroughly
unique introduction to numbers and their role in creativity,
computers, games, practical research, and absurd adventures that
teeter on the edge of logic and insanity. The Mathematics of Oz
will have you squirming in frustration and begging for more.
Reviews
‘… the material in the book is not duplicated in other
collections, and some of it is even new, a real rarity in
recreational mathematics.’ Underwood Dudley, author of
Mathematical Cranks
‘A perpetual idea machine, Clifford Pickover is one of the most
creative, original thinkers in the world today.’ Journal of
Recreational Mathematics
‘Run, leap, scurry and scoot to your nearest bookstore and get
his books.’ BYTE
‘Pickover inspires a new generation of da Vincis to build
unknown flying machines and create new Mona Lisas.’ Christian
Science Monitor
‘Pickover is van Leeuwenhoek’s twentieth century equivalent.’
OMNI
October| Hardback | 272 pages 19 line diagrams
9 tables 150 exercises | ISBN: 0521814294
This unique book on the basics of option pricing is
mathematically accurate and yet accessible to readers with
limited mathematical training. It will appeal to professional
traders as well as undergraduates studying the basics of finance.
The author assumes no prior knowledge of probability, and offers
clear, simple explanations of arbitrage, the Black-Scholes option
pricing formula, and other topics such as utility functions,
optimal portfolio selections, and the capital assets pricing
model. Among the many new features of this second edition are: a
new chapter on optimization methods in finance; a new section on
Value at Risk and Conditional Value at Risk; a new and simplified
derivation of the Black-Scholes equation, together with
derivations of the partial derivatives of the Black-Scholes
option cost function and of the computational Black-Scholes
formula; three different models of European call options with
dividends; a new, easily implemented method for estimating the
volatility parameter.
Contents
1. Probability; 2. Normal random variables; 3. Geometric Brownian
motion; 4. Interest rates and present value analysis; 5. Pricing
contracts via Arbitrage; 6. The Arbitrage Theorem; 7. The Black-Scholes
formula; 8. Valuing by expected utility; 9. Exotic options; 10.
Beyond geometric Brownian motion models; 11. Autoregressive
models and mean reversion; 12. Optimization methods in finance.
ctober 2002 | Hardback | 448 pages | ISBN: 0-521-40068-6
Melding together ideas from algebra, topology and analysis, this
book studies the geometric theory of polynomials and rational
functions in the plane. Any theory in the plane should make full
use of the complex numbers and thus the early chapters build the
foundations of complex variable theory. In fact, throughout the
book, the author introduces a variety of ideas and constructs
theories around them, incorporating much of the classical theory
of polynomials as he proceeds. These ideas are used to study a
number of unsolved problems, bearing in mind that such problems
indicate the current limitations of our knowledge and present
challenges for the future. However, theories also lead to
solutions of some problems and several such solutions are given
including a comprehensive account of the geometric convolution
theory. This is an ideal reference for graduate students and
researchers working in this area.
Contents
1. The algebra of polynomials; 2. The degree principle and the
fundamental theorem of algebra; 3. The Jacobian problem; 4.
Analytic and harmonic functions in the unit disc; 5. Circular
regions and Grace’s theorem; 6. The Ilieff-Sendoff conjecture;
7. Self-inversive polynomials; 8. Duality and an extension of
Grace’s theorem to rational functions; 9. Real polynomials; 10.
Level curves; 11. Miscellaneous topics.
Series: CAMBRIDGE STUDIES IN ADVANCED MATHEMATICS VOL.75
October 2002 | Hardback | 372 pages 1 line
diagram 3 tables | ISBN: 0-521-80799-9
Alan Baker’s 60th birthday in August 1999 offered an ideal
opportunity to organize a conference at ETH Zurich with the goal
of presenting the state of the art in number theory and geometry.
Many of the leaders in the subject were brought together to
present an account of research in the last century as well as
speculations for possible further research. The papers in this
volume cover a broad spectrum of number theory including
geometric, algebrao-geometric and analytic aspects. This volume
will appeal to number theorists, algebraic geometers, and
geometers with a number-theoretic background. However, it will
also be valuable for mathematicians (in particular research
students) who would like to be informed of the state of number
theory at the start of the 21st century and in possible
developments for the future.
Contents
Introduction; 1. One century of logarithmic forms G. Wustholz; 2.
Report on p-adic logarithmic forms Kunrun Yui; 3. Recent progress
on linear forms in elliptic logarithms Sinnou David and Noriko
Hirata-Kohno; 4. Solving Diophantine equations by Baker’s
theory Kalman Gyory; 5. Baker’s method and modular curves Yuri
F. Bilu; 6. Application of the Andre?Oort conjecture Paula B.
Cohen and Gisbert Wustholz; 7. Regular dessins Jurgen Wolfart; 8.
Maass cusp forms with integer coefficients Peter Sarnak; 9.
Modular forms, elliptic curves and the ABC-conjecture Dorian
Goldfeld; 10. On the algebraic independence of numbers Yu. V.
Nesterenko; 11. Ideal lattices Eva Bayer-Fluckiger; 12. Integral
points and Mordell?Weil lattices Tetsuji Shioda; 13. Forty years
of effective results in Diophantine theory Enrico Bombieri; 14.
Points on subvarieties of tori Jan-Hendrik Evertse; 15. A new
application of Diophantine approximations G. Faltings; 16. Search
bounds for Diophantine equations D. W. Masser; 17. Regular
systems and ubiquity V. V. Beresnevich, V. I. Bernik and M. M.
Dodson; 18. Diophantine approximation, lattices and flows Gregory
Margulis; 19. Baker's constant and Vinogradov’s bound Ming-Chit
Liu and Tianze Wang; 20. Powers in arithmetic progression T. N.
Shorey; 21. Greatest common divisor A. Schinzel; 22. Heilbronn's
exponential sum and transcendence theory D. R. Heath-Brown.