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Notices of the American Mathematical Society
ISSN 0002-9920 of the American Mathematical Society February 2006 Volume 53, Number 2 Math Circles and Olympiads MSRI Asks: Is the U.S. Coming of Age? page 200 A System of Axioms of Set Theory for the Rationalists page 206 Durham Meeting page 299 San Francisco Meeting page 302 ICM Madrid 2006 (see page 213) > To mak• an antmat•d tub• plot Animated Tube Plot 1 Type an expression in one or :;)~~~G~~~t;~~i~~~~~~~~~~~~~:rtwo ' 2 Wrth the insertion point in the 3 Open the Plot Properties dialog the same variables Tl'le next animation shows • knot Plot 30 Animated + Tube Scientific Word ... version 5.5 Scientific Word"' offers the same features as Scientific WorkPlace, without the computer algebra system. Editors INTERNATIONAL Morris Weisfeld Editor-in-Chief Enrico Arbarello MATHEMATICS Joseph Bernstein Enrico Bombieri Richard E. Borcherds Alexei Borodin RESEARCH PAPERS Jean Bourgain Marc Burger James W. Cogdell http://www.hindawi.com/journals/imrp/ Tobias Colding Corrado De Concini IMRP provides very fast publication of lengthy research articles of high current interest in Percy Deift all areas of mathematics. All articles are fully refereed and are judged by their contribution Robbert Dijkgraaf to the advancement of the state of the science of mathematics. Issues are published as S. K. Donaldson frequently as necessary. Each issue will contain only one article. IMRP is expected to publish 400± pages in 2006. Yakov Eliashberg Edward Frenkel Articles of at least 50 pages are welcome and all articles are refereed and judged for Emmanuel Hebey correctness, interest, originality, depth, and applicability. Submissions are made by e-mail to Dennis Hejhal [email protected]. -
CS599: Algorithm Design in Strategic Settings Fall 2012 Lecture 2: Game Theory Preliminaries
CS599: Algorithm Design in Strategic Settings Fall 2012 Lecture 2: Game Theory Preliminaries Instructor: Shaddin Dughmi Administrivia Website: http://www-bcf.usc.edu/~shaddin/cs599fa12 Or go to www.cs.usc.edu/people/shaddin and follow link Emails? Registration Outline 1 Games of Complete Information 2 Games of Incomplete Information Prior-free Games Bayesian Games Outline 1 Games of Complete Information 2 Games of Incomplete Information Prior-free Games Bayesian Games Example: Rock, Paper, Scissors Figure: Rock, Paper, Scissors Games of Complete Information 2/23 Rock, Paper, Scissors is an example of the most basic type of game. Simultaneous move, complete information games Players act simultaneously Each player incurs a utility, determined only by the players’ (joint) actions. Equivalently, player actions determine “state of the world” or “outcome of the game”. The payoff structure of the game, i.e. the map from action vectors to utility vectors, is common knowledge Games of Complete Information 3/23 Typically thought of as an n-dimensional matrix, indexed by a 2 A, with entry (u1(a); : : : ; un(a)). Also useful for representing more general games, like sequential and incomplete information games, but is less natural there. Figure: Generic Normal Form Matrix Standard mathematical representation of such games: Normal Form A game in normal form is a tuple (N; A; u), where N is a finite set of players. Denote n = jNj and N = f1; : : : ; ng. A = A1 × :::An, where Ai is the set of actions of player i. Each ~a = (a1; : : : ; an) 2 A is called an action profile. u = (u1; : : : un), where ui : A ! R is the utility function of player i. -
Strength in Numbers: the Rising of Academic Statistics Departments In
Agresti · Meng Agresti Eds. Alan Agresti · Xiao-Li Meng Editors Strength in Numbers: The Rising of Academic Statistics DepartmentsStatistics in the U.S. Rising of Academic The in Numbers: Strength Statistics Departments in the U.S. Strength in Numbers: The Rising of Academic Statistics Departments in the U.S. Alan Agresti • Xiao-Li Meng Editors Strength in Numbers: The Rising of Academic Statistics Departments in the U.S. 123 Editors Alan Agresti Xiao-Li Meng Department of Statistics Department of Statistics University of Florida Harvard University Gainesville, FL Cambridge, MA USA USA ISBN 978-1-4614-3648-5 ISBN 978-1-4614-3649-2 (eBook) DOI 10.1007/978-1-4614-3649-2 Springer New York Heidelberg Dordrecht London Library of Congress Control Number: 2012942702 Ó Springer Science+Business Media New York 2013 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. Exempted from this legal reservation are brief excerpts in connection with reviews or scholarly analysis or material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Duplication of this publication or parts thereof is permitted only under the provisions of the Copyright Law of the Publisher’s location, in its current version, and permission for use must always be obtained from Springer. -
Chapter 16 Oligopoly and Game Theory Oligopoly Oligopoly
Chapter 16 “Game theory is the study of how people Oligopoly behave in strategic situations. By ‘strategic’ we mean a situation in which each person, when deciding what actions to take, must and consider how others might respond to that action.” Game Theory Oligopoly Oligopoly • “Oligopoly is a market structure in which only a few • “Figuring out the environment” when there are sellers offer similar or identical products.” rival firms in your market, means guessing (or • As we saw last time, oligopoly differs from the two ‘ideal’ inferring) what the rivals are doing and then cases, perfect competition and monopoly. choosing a “best response” • In the ‘ideal’ cases, the firm just has to figure out the environment (prices for the perfectly competitive firm, • This means that firms in oligopoly markets are demand curve for the monopolist) and select output to playing a ‘game’ against each other. maximize profits • To understand how they might act, we need to • An oligopolist, on the other hand, also has to figure out the understand how players play games. environment before computing the best output. • This is the role of Game Theory. Some Concepts We Will Use Strategies • Strategies • Strategies are the choices that a player is allowed • Payoffs to make. • Sequential Games •Examples: • Simultaneous Games – In game trees (sequential games), the players choose paths or branches from roots or nodes. • Best Responses – In matrix games players choose rows or columns • Equilibrium – In market games, players choose prices, or quantities, • Dominated strategies or R and D levels. • Dominant Strategies. – In Blackjack, players choose whether to stay or draw. -
Generalization of Pinching Operation to Binary Matroids
J. Algebra Comb. Discrete Appl. Received: 14 April 2020 7(3) • 247–258 Accepted: 1 May 2020 Journal of Algebra Combinatorics Discrete Structures and Applications Generalization of pinching operation to binary matroids Research Article Vahid Ghorbani, Ghodratollah Azadi, Habib Azanchiler Abstract: In this paper, we generalize the pinching operation on two edges of graphs to binary matroids and investigate some of its basic properties. For n ≥ 2, the matroid that is obtained from an n-connected matroid by this operation is a k-connected matroid with k 2 f2; 3; 4g or is a disconnected matroid. We find conditions to guarantee this k. Moreover, we show that Eulerian binary matroids are char- acterized by this operation and we also provide some interesting applications of this operation. 2010 MSC: 05B35 Keywords: Binary matroid, Connectivity, Pinching, Splitting, Splitting off, Element splitting 1. Introduction The matroid and graph notations and terminology used here will follow [4] and [7]. Let G be a graph p and S be a subset of the edge set E(G). We denote by GS the graph that is obtained from G by adding p a new vertex w and replacing any edge uv 2 S with two edges uw and wv. The transition from G to GS is called the k-pinching operation [2] where k = jSj. If S is the empty set, then 0-pinching means adding a new single vertex w. If jSj = 1, then applying the pinching operation is equivalent to the subdivision p of uv where S = fuvg. If S = E(G), then we have the parallel classes on the new vertex w on GS such that the sequence of the cardinality of them is equal to the degree sequence of the vertices of G. -
Prizes and Awards Session
PRIZES AND AWARDS SESSION Wednesday, July 12, 2021 9:00 AM EDT 2021 SIAM Annual Meeting July 19 – 23, 2021 Held in Virtual Format 1 Table of Contents AWM-SIAM Sonia Kovalevsky Lecture ................................................................................................... 3 George B. Dantzig Prize ............................................................................................................................. 5 George Pólya Prize for Mathematical Exposition .................................................................................... 7 George Pólya Prize in Applied Combinatorics ......................................................................................... 8 I.E. Block Community Lecture .................................................................................................................. 9 John von Neumann Prize ......................................................................................................................... 11 Lagrange Prize in Continuous Optimization .......................................................................................... 13 Ralph E. Kleinman Prize .......................................................................................................................... 15 SIAM Prize for Distinguished Service to the Profession ....................................................................... 17 SIAM Student Paper Prizes .................................................................................................................... -
Sok: Tools for Game Theoretic Models of Security for Cryptocurrencies
SoK: Tools for Game Theoretic Models of Security for Cryptocurrencies Sarah Azouvi Alexander Hicks Protocol Labs University College London University College London Abstract form of mining rewards, suggesting that they could be prop- erly aligned and avoid traditional failures. Unfortunately, Cryptocurrencies have garnered much attention in recent many attacks related to incentives have nonetheless been years, both from the academic community and industry. One found for many cryptocurrencies [45, 46, 103], due to the interesting aspect of cryptocurrencies is their explicit consid- use of lacking models. While many papers aim to consider eration of incentives at the protocol level, which has motivated both standard security and game theoretic guarantees, the vast a large body of work, yet many open problems still exist and majority end up considering them separately despite their current systems rarely deal with incentive related problems relation in practice. well. This issue arises due to the gap between Cryptography Here, we consider the ways in which models in Cryptog- and Distributed Systems security, which deals with traditional raphy and Distributed Systems (DS) can explicitly consider security problems that ignore the explicit consideration of in- game theoretic properties and incorporated into a system, centives, and Game Theory, which deals best with situations looking at requirements based on existing cryptocurrencies. involving incentives. With this work, we offer a systemati- zation of the work that relates to this problem, considering papers that blend Game Theory with Cryptography or Dis- Methodology tributed systems. This gives an overview of the available tools, and we look at their (potential) use in practice, in the context As we are covering a topic that incorporates many different of existing blockchain based systems that have been proposed fields coming up with an extensive list of papers would have or implemented. -
Guiding Mathematical Discovery How We Started a Math Circle
Guiding Mathematical Discovery How We Started a Math Circle Jackie Chan, Tenzin Kunsang, Elisa Loy, Fares Soufan, Taylor Yeracaris Advised by Professor Deanna Haunsperger Illustrations by Elisa Loy Carleton College, Mathematics and Statistics Department 2 Table of Contents About the Authors 4 Acknowledgments 6 Preface 7 Designing Circles 9 Leading Circles 11 Logistics & Classroom Management 14 The Circles 18 Shapes and Patterns 20 Penny Shapes 21 Polydrons 23 Knots and What-Not 25 Fractals 28 Tilings and Tessellations 31 Graphs and Trees 35 The Four Islands Problem (Königsberg Bridge Problem) 36 Human Graphs 39 Map Coloring 42 Trees: Dots and Lines 45 Boards and Spatial Reasoning 49 Filing Grids 50 Gerrymandering Marcellusville 53 Pieces on a Chessboard 58 Games and Strategy 63 Game Strategies (Rock/Paper/Scissors) 64 Game Strategies for Nim 67 Tic-Tac-Torus 70 SET 74 KenKen Puzzles 77 3 Logic and Probability 81 The Monty Hall Problem 82 Knights and Knaves 85 Sorting Algorithms 87 Counting and Combinations 90 The Handshake/High Five Problem 91 Anagrams 96 Ciphers 98 Counting Trains 99 But How Many Are There? 103 Numbers and Factors 105 Piles of Triangular Numbers 106 Cup Flips 108 Counting with Cups — The Josephus Problem 111 Water Cups 114 Guess What? 116 Additional Circle Ideas 118 Further Reading 120 Keyword Index 121 4 About the Authors Jackie Chan Jackie is a senior computer science and mathematics major at Carleton College who has had an interest in teaching mathematics since an early age. Jackie’s interest in mathematics education stems from his enjoyment of revealing the intuition behind mathematical concepts. -
Prizes and Awards
DENVER • JAN 15–18, 2020 January 2020 Prizes and Awards 4:25 PM, Thursday, January 16, 2020 PROGRAM OPENING REMARKS Michael Dorff, Mathematical Association of America AWARD FOR DISTINGUISHED PUBLIC SERVICE American Mathematical Society BÔCHER MEMORIAL PRIZE American Mathematical Society CHEVALLEY PRIZE IN LIE THEORY American Mathematical Society FRANK NELSON COLE PRIZE IN NUMBER THEORY American Mathematical Society LEONARD EISENBUD PRIZE FOR MATHEMATICS AND PHYSICS American Mathematical Society LEVI L. CONANT PRIZE American Mathematical Society JOSEPH L. DOOB PRIZE American Mathematical Society LEROY P. S TEELE PRIZE FOR MATHEMATICAL EXPOSITION American Mathematical Society LEROY P. S TEELE PRIZE FOR SEMINAL CONTRIBUTION TO RESEARCH American Mathematical Society LEROY P. S TEELE PRIZE FOR LIFETIME ACHIEVEMENT American Mathematical Society LOUISE HAY AWARD FOR CONTRIBUTION TO MATHEMATICS EDUCATION Association for Women in Mathematics M. GWENETH HUMPHREYS AWARD FOR MENTORSHIP OF UNDERGRADUATE WOMEN IN MATHEMATICS Association for Women in Mathematics MICROSOFT RESEARCH PRIZE IN ALGEBRA AND NUMBER THEORY Association for Women in Mathematics SADOSKY RESEARCH PRIZE IN ANALYSIS Association for Women in Mathematics FRANK AND BRENNIE MORGAN PRIZE FOR OUTSTANDING RESEARCH IN MATHEMATICS BY AN UNDERGRADUATE STUDENT American Mathematical Society Mathematical Association of America Society for Industrial and Applied Mathematics COMMUNICATIONS AWARD Joint Policy Board for Mathematics CHAUVENET PRIZE Mathematical Association of America DAVID P. R OBBINS PRIZE Mathematical Association of America EULER BOOK PRIZE Mathematical Association of America DEBORAH AND FRANKLIN TEPPER HAIMO AWARDS FOR DISTINGUISHED COLLEGE OR UNIVERSITY TEACHING OF MATHEMATICS Mathematical Association of America YUEH-GIN GUNG AND DR.CHARLES Y. HU AWARD FOR DISTINGUISHED SERVICE TO MATHEMATICS Mathematical Association of America CLOSING REMARKS Jill C. -
Chicago Journal of Theoretical Computer Science the MIT Press
Chicago Journal of Theoretical Computer Science The MIT Press Volume 1997, Article 2 3 June 1997 ISSN 1073–0486. MIT Press Journals, Five Cambridge Center, Cambridge, MA 02142-1493 USA; (617)253-2889; [email protected], [email protected]. Published one article at a time in LATEX source form on the Internet. Pag- ination varies from copy to copy. For more information and other articles see: http://www-mitpress.mit.edu/jrnls-catalog/chicago.html • http://www.cs.uchicago.edu/publications/cjtcs/ • ftp://mitpress.mit.edu/pub/CJTCS • ftp://cs.uchicago.edu/pub/publications/cjtcs • Kann et al. Hardness of Approximating Max k-Cut (Info) The Chicago Journal of Theoretical Computer Science is abstracted or in- R R R dexed in Research Alert, SciSearch, Current Contents /Engineering Com- R puting & Technology, and CompuMath Citation Index. c 1997 The Massachusetts Institute of Technology. Subscribers are licensed to use journal articles in a variety of ways, limited only as required to insure fair attribution to authors and the journal, and to prohibit use in a competing commercial product. See the journal’s World Wide Web site for further details. Address inquiries to the Subsidiary Rights Manager, MIT Press Journals; (617)253-2864; [email protected]. The Chicago Journal of Theoretical Computer Science is a peer-reviewed scholarly journal in theoretical computer science. The journal is committed to providing a forum for significant results on theoretical aspects of all topics in computer science. Editor in chief: Janos Simon Consulting -
Deborah and Franklin Tepper Haimo Awards for Distinguished College Or University Teaching of Mathematics
MATHEMATICAL ASSOCIATION OF AMERICA DEBORAH AND FRANKLIN TEPPER HAIMO AWARDS FOR DISTINGUISHED COLLEGE OR UNIVERSITY TEACHING OF MATHEMATICS In 1991, the Mathematical Association of America instituted the Deborah and Franklin Tepper Haimo Awards for Distinguished College or University Teaching of Mathematics in order to honor college or university teachers who have been widely recognized as extraordinarily successful and whose teaching effectiveness has been shown to have had influence beyond their own institutions. Deborah Tepper Haimo was President of the Association, 1991–1992. Citation Jacqueline Dewar In her 32 years at Loyola Marymount University, Jackie Dewar’s enthusiasm, extraordinary energy, and clarity of thought have left a deep imprint on students, colleagues, her campus, and a much larger mathematical community. A student testifies, “Dr. Dewar has engaged the curious nature and imaginations of students from all disciplines by continuously providing them with problems (and props!), whose solutions require steady devotion and creativity….” A colleague who worked closely with her on the Los Angeles Collaborative for Teacher Excellence (LACTE) describes her many “watch and learn” experiences with Jackie, and says, “I continue to hear Jackie’s words, ‘Is this your best work?’—both in the classroom and in all professional endeavors. ...[she] will always listen to my ideas, ask insightful and pertinent questions, and offer constructive and honest advice to improve my work.” As a 2003–2004 CASTL (Carnegie Academy for the Scholarship -
Final Program and Abstracts
Final Program and Abstracts Sponsored by the SIAM Activity Group on Discrete Mathematics The SIAG on Discrete Mathematics focuses on combinatorics, graph theory, cryptography, discrete optimization, mathematical programming, coding theory, information theory, game theory, and theoretical computer science, including algorithms, complexity, circuit design, robotics, and parallel processing. This activity group provides an opportunity to unify pure discrete mathematics and areas of applied research such as computer science, operations research, combinatorics, and the social sciences. It organizes the SIAM Conference on Discrete Mathematics; co-sponsors, with ACM SIGACT, the annual Symposium on Discrete Algorithms; and sponsors minisymposia at SIAM meetings and conferences. The activity group also runs DM-Net, an electronic forum; publishes an electronic newsletter; and maintains a website and a member directory. Every two years, the activity group also awards the Dénes König Prize to a young researcher for outstanding research in the area of discrete mathematics. Society for Industrial and Applied Mathematics 3600 Market Street, 6th Floor Philadelphia, PA 19104-2688 USA Telephone: +1-215-382-9800 Fax: +1-215-386-7999 Conference Email: [email protected] Conference Web: www.siam.org/meetings/ Membership and Customer Service: (800) 447-7426 (US& Canada) or +1-215-382-9800 (worldwide) www.siam.org/meetings/dm16 2 2016 SIAM Conference on Discrete Mathematics Table of Contents Local Organizing Committee Corporate Members and Affiliates Program-At-A-Glance ..Separate handout Albert Bush SIAM corporate members provide General Information ............................. 2 Georgia State University, USA their employees with knowledge about, Get-togethers ........................................ 4 Yi Zhao access to, and contacts in the applied Invited Plenary Presentations ..............