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LINEAR ALGEBRA METHODS in COMBINATORICS László Babai
LINEAR ALGEBRA METHODS IN COMBINATORICS L´aszl´oBabai and P´eterFrankl Version 2.1∗ March 2020 ||||| ∗ Slight update of Version 2, 1992. ||||||||||||||||||||||| 1 c L´aszl´oBabai and P´eterFrankl. 1988, 1992, 2020. Preface Due perhaps to a recognition of the wide applicability of their elementary concepts and techniques, both combinatorics and linear algebra have gained increased representation in college mathematics curricula in recent decades. The combinatorial nature of the determinant expansion (and the related difficulty in teaching it) may hint at the plausibility of some link between the two areas. A more profound connection, the use of determinants in combinatorial enumeration goes back at least to the work of Kirchhoff in the middle of the 19th century on counting spanning trees in an electrical network. It is much less known, however, that quite apart from the theory of determinants, the elements of the theory of linear spaces has found striking applications to the theory of families of finite sets. With a mere knowledge of the concept of linear independence, unexpected connections can be made between algebra and combinatorics, thus greatly enhancing the impact of each subject on the student's perception of beauty and sense of coherence in mathematics. If these adjectives seem inflated, the reader is kindly invited to open the first chapter of the book, read the first page to the point where the first result is stated (\No more than 32 clubs can be formed in Oddtown"), and try to prove it before reading on. (The effect would, of course, be magnified if the title of this volume did not give away where to look for clues.) What we have said so far may suggest that the best place to present this material is a mathematics enhancement program for motivated high school students. -
CARPET CLEANING SPECIAL K N O W ? Throughout History, I Dogs Have Been the on OU> 211 Most Obvious Agents in 5 MILES SO
remain young and beautiful only by bathing in and in the story of Lauren Elder’s grueling 36-hour or S a t u r d a y drinking the blood of young innocent girls — includ deal following the crash of a light aiplane that killed ing her daughter’s. 12:30 a.m. on WQAD. her two companions. The two-hour drama is based "Tarzan’s New Adventure” —- Bruce Bennett and "Sweet, Sweet Rachel” — An ESP expert is pit on the book by Lauren Elder and Shirley Ula Holt star in the 1936 release. 1 p.m. on WMT. ted against an unseen presence that is trying to drive Streshinsky. 8 p.m. on NBC. "Harlow” — The sultry screen star of the 1930s is a beautiful woman crazy. The 1971 TV movie stars "Walk, Don’t Run” — A young woman (Saman the subject of the 1965 film biography with- Carroll Alex Dreier, Stefanie Powers, Pat Hingle and Steve tha Eggar) unwittingly agrees to share her apart Baker, Peter Lawford, Red Buttons, Michael Con Ihnat. 12:30 a.m. on KCRG. ment with a businessman (Cary Grant) and an athe- nors and Raf Vallone 1 p.m. on WOC lete (Jim Hutton) during the Tokyo Olympics (1966). "The Left-Handed Gun” — Paul Newman, Lita 11 p.m. on WMT Milan and Hurd Hatfield are the stars of the 1958 S u n d a y western detailing Billy the Kid’s career 1 p.m. on "The Flying Deuces” — Stan Laurel and Oliver KWWL. Hardy join the Foreign Legion so Ollie can forget an T u e s d a y "The Swimmer” — John Cheever’s story about unhappy romance (1939). -
Executive Summary
Communicating the Benefits of Transit Oriented Development The Hudson Bergen Light Rail Transit System and the City of Evanston’s Transit-Oriented Redevelopment Executive Summary, January 2005 Prepared for the Development, Community and Environment Division, EPA By Gloria Ohland and Cali Gorewitz, Reconnecting America’s Center for Transit Oriented Development This is a tale of three cities -- Jersey City and neighboring Hoboken in New Jersey, and Evanston, Illinois – that have experienced an enormous amount of development since the late 1980s, reversing three decades of decline brought on by the great suburban exodus of the 1950s. The result is that in North & Visitors Bureau Convention Shore 2006 all three cities are prospering, posting significant increases in property values and sales taxes and other revenues due to the building boom and resulting increases in business activity. The amount of high-density development that has occurred could never have occurred this quickly if these cities did not have rich transit networks providing very high-quality connections to the abundant jobs, culture and destinations in their big city neighbors: Manhattan is across the Hudson from Hoboken and Jersey City; Chicago and Evanston share a border. Not every project that has been built in these cities is truly transit-oriented, Evanston, IL pedestrian-friendly or human-scaled – station areas in and expensive TOD components like structured parking. But Jersey City lack a good mix of retail, and a number of whereas Evanston’s extensive multimodal transit system Evanston’s commuter and urban rail stations, ironically, was already in place, New Jersey built a new 20-mile light are located along a very wide thoroughfare that used to be rail line through brownfields and abandoned industrial Auto Row. -
A Case Study for Accounting Information Systems
Review of Business Information Systems – June 2014 Volume 18, Number 1 A Case Study For Accounting Information Systems – A Business Continuity Plan For Protecting Critical Financial Information In The NYC Financial Services Industry Mark D. Law, Bloomsburg University, USA Gary Robson, Bloomsburg University, USA ABSTRACT This case study outlines a project launched by the Wall Street West organization, a data redundancy system in Northeastern Pennsylvania which provides backdrop for financial institutions located in New York City. The purpose of this study is threefold. First, the history on the importance of business continuity plans in a post 9/11 world is explored. Second, the Federal Reserve Board, the Office of the Comptroller of the Currency, and the Securities and Exchange Commission recommendations regarding Disaster Recover, in addition to the requirements of The Sarbanes-Oxley Act, are reviewed. Lastly, an overview of Wall Street West’s effort is provided, looking at some of the strategic advantages to locate in Northeastern Pennsylvania and demonstrating the important resources provided by Wall Street West to protect the nation’s national security. Conclusions and case use recommendations are presented as this case is ideally suited for use in an Accounting Information Systems course at either the undergraduate or graduate level creating an awareness of the importance of business continuity planning. Keywords: Backup Plans; Disaster Recovery; Accounting Information Systems INTRODUCTION he United States’ financial services industry has and will continue to face many challenges over the prior and next decades. One of the most important challenges to be confronted will be planning for T and responding to terrorism and natural disasters. -
Perspective the PNAS Way Back Then
Proc. Natl. Acad. Sci. USA Vol. 94, pp. 5983–5985, June 1997 Perspective The PNAS way back then Saunders Mac Lane, Chairman Proceedings Editorial Board, 1960–1968 Department of Mathematics, University of Chicago, Chicago, IL 60637 Contributed by Saunders Mac Lane, March 27, 1997 This essay is to describe my experience with the Proceedings of ings. Bronk knew that the Proceedings then carried lots of math. the National Academy of Sciences up until 1970. Mathemati- The Council met. Detlev was not a man to put off till to cians and other scientists who were National Academy of tomorrow what might be done today. So he looked about the Science (NAS) members encouraged younger colleagues by table in that splendid Board Room, spotted the only mathe- communicating their research announcements to the Proceed- matician there, and proposed to the Council that I be made ings. For example, I can perhaps cite my own experiences. S. Chairman of the Editorial Board. Then and now the Council Eilenberg and I benefited as follows (communicated, I think, did not often disagree with the President. Probably nobody by M. H. Stone): ‘‘Natural isomorphisms in group theory’’ then knew that I had been on the editorial board of the (1942) Proc. Natl. Acad. Sci. USA 28, 537–543; and “Relations Transactions, then the flagship journal of the American Math- between homology and homotopy groups” (1943) Proc. Natl. ematical Society. Acad. Sci. USA 29, 155–158. Soon after this, the Treasurer of the Academy, concerned The second of these papers was the first introduction of a about costs, requested the introduction of page charges for geometrical object topologists now call an “Eilenberg–Mac papers published in the Proceedings. -
Humanizing Mathematics and Its Philosophy a Review by Joseph Auslander
BOOK REVIEW Humanizing Mathematics and its Philosophy A Review by Joseph Auslander Communicated by Cesar E. Silva Humanizing Mathematics and its Philosophy: he wrote and coauthored with Philip Davis and Vera John- Essays Celebrating the 90th Birthday of Reuben Hersh Steiner several books and developed what he terms a Bharath Sriraman, editor Humanist philosophy of mathematics. He has also been a Birkhäuser, 2017 frequent book reviewer for Notices.1 Hardcover, 363 pages ISBN: 978-3-319-61230-0 Although he was not trained as a philosopher, Reuben Hersh has emerged as a major figure in the philosophy of mathematics. His Humanist view is probably the most cogent expression contrasting the dominant philosophies of Platonism and Formalism. Hersh has had a remarkable career. He was born in the Bronx, to immigrant working class parents. He graduated from Harvard at age nineteen with a major in English and worked for some time as a journalist, followed by a period of working as a machinist. He then attended the Courant Institute from which he obtained a PhD in 1962, under the supervision of Peter Lax. Hersh settled into a conventional academic career as a professor at The University of New Mexico, pursuing research mostly in partial differential equations. But beginning in the 1970s he wrote a number of expository articles, in Scientific American, Mathematical Reuben Hersh with co-author Vera John-Steiner Intelligencer, and Advances in Mathematics. Subsequently, signing copies of their book Loving and Hating Mathematics: Challenging the Myths of Mathematical Life Joseph Auslander is Professor Emeritus of Mathematics at the at the Princeton University Press Exhibit, JMM 2011. -
Moab Area Movie Locations Auto Tours – Discovermoab.Com - 8/21/01 Page 1
Moab Area Movie Locations Auto Tours – discovermoab.com - 8/21/01 Page 1 Moab Area Movie Locations Auto Tours Discovermoab.com Internet Brochure Series Moab Area Travel Council The Moab area has been a filming location since 1949. Enjoy this guide as a glimpse of Moab's movie past as you tour some of the most spectacular scenery in the world. All movie locations are accessible with a two-wheel drive vehicle. Locations are marked with numbered posts except for locations at Dead Horse Point State Park and Canyonlands and Arches National Parks. Movie locations on private lands are included with the landowner’s permission. Please respect the land and location sites by staying on existing roads. MOVIE LOCATIONS FEATURED IN THIS GUIDE Movie Description Map ID 1949 Wagon Master - Argosy Pictures The story of the Hole-in-the-Rock pioneers who Director: John Ford hire Johnson and Carey as wagonmasters to lead 2-F, 2-G, 2-I, Starring: Ben Johnson, Joanne Dru, Harry Carey, Jr., them to the San Juan River country 2-J, 2-K Ward Bond. 1950 Rio Grande - Republic Reunion of a family 15 years after the Civil War. Directors: John Ford & Merian C. Cooper Ridding the Fort from Indian threats involves 2-B, 2-C, 2- Starring: John Wayne, Maureen O'Hara, Ben Johnson, fighting with Indians and recovery of cavalry L Harry Carey, Jr. children from a Mexican Pueblo. 1953 Taza, Son of Cochise - Universal International 3-E Starring: Rock Hudson, Barbara Rush 1958 Warlock - 20th Century Fox The city of Warlock is terrorized by a group of Starring: Richard Widmark, Henry Fonda, Anthony cowboys. -
Remembering Paul Cohen (1934–2007) Peter Sarnak, Coordinating Editor
Remembering Paul Cohen (1934–2007) Peter Sarnak, Coordinating Editor Paul Joseph Cohen, one of the stars some classic texts. There he got his first exposure of twentieth-century mathematics, to modern mathematics, and it molded him as a passed away in March 2007 at the mathematician. He tried working with André Weil age of seventy-two. Blessed with a in number theory, but that didn’t pan out, and unique mathematical gift for solving instead he studied with Antoni Zygmund, writing difficult and central problems, he a thesis in Fourier series on the topic of sets of made fundamental breakthroughs uniqueness. In Chicago he formed many long- in a number of fields, the most spec- lasting friendships with some of his fellow stu- tacular being his resolution of Hil- dents (for example, John Thompson, who re- bert’s first problem—the continuum mained a lifelong close friend). hypothesis. The period after he graduated with a Ph.D. Like many of the mathematical gi- was very productive, and he enjoyed a series of Paul Cohen ants of the past, Paul did not restrict successes in his research. He solved a problem his attention to any one specialty. of Walter Rudin in group algebras, and soon To him mathematics was a unified subject that after that he obtained his first breakthrough on one could master broadly. He had a deep under- what was considered to be a very difficult prob- standing of most areas, and he taught advanced lem—the Littlewood conjecture. He gave the first courses in logic, analysis, differential equations, nontrivial lower bound for the L1 norm of trigo- algebra, topology, Lie theory, and number theory nometric polynomials on the circle whose Fourier on a regular basis. -
150 Bay Street 150 Bay Street ™ 150 Bay Street
™ 150 BAY STREET 150 BAY STREET ™ 150 BAY STREET 150 BAY STREET In the Powerhouse Arts District, 150 Bay Street, a landmark loft building listed on the Federal Register of Historic Places, embodies the true artist/luxury loft experience and is the ideal place to work, live and play. Built in 1908 as a warehouse by the architect Howard Chapman, the property was converted to residential, commercial and retail spaces in the 21st century. Interiors feature open floor plans, 14' high ceilings, over-sized windows offering abundant natural light, and historic, architectural detail that all distinguish 150 Bay Street as a premiere luxury loft community to work or live. Further amenities include polished concrete floors and fully equipped kitchens with granite counter tops and brand new appliances to complement spaces that are ideal for entertaining. Conveniently located just minutes from Manhattan via the PATH train or NY Waterway Ferry, and surrounded by burgeoning restaurants, bars and retailers, Jersey City has become a desirable alternative to Manhattan with 150 Bay Street offering all that is needed for a truly modern, luxurious and convenient lifestyle. www.150baystreet.com ™ 150 BAY STREET THE BUILDING Location Bay Street between Provost Road and Marin Boulevard Year Built 1908 Renovations Residential Conversion - 2005; Ground Floor Retail Conversion - 2009 Building Size 203,000 SF Floors 9 plus penthouse, mezzanine, 1 below-grade ™ 150 BAY STREET BUILDING SPECIFICATIONS Location Bay Street between Provost Road Windows Double-insulated, -
Desenho E Cinema
Faculdade de Belas Artes da Universidade do Porto Mestrado em Desenho e Técnicas de Impressão Dissertação de: Elisa Almeida Trindade Orientado por: Doutora Cristina Mateus 2013 Desenho e Cinema Agradecimentos: À minha orientadora Doutora Cristina Mateus, à minha família, aos meus amigos e a todos que tornaram possível este trabalho. Índice Resumo/Abstract 9 3.1. Storyboards 93 Introdução: Breve enquadramento histórico. 3.2. Cenários 99 Projeto e método 11 O gabinete do Dr. Caligari 103 Capítulo 1 Metropolis 104 Realizadores desenhadores 17 A Casa Encantada 106 George Méliès 19 Ken Adam 107 Alfred Hitchcock 21 Fritz Lang 25 3.2.1. Desenhos técnicos e Sergei Eisenstein 28 desenhos concetuais 109 Akira Kurosawa 31 Orson Welles 36 3.2.2. Desenhos de Artefactos 115 Saul Bass 37 Federico Fellini 41 3.3. Desenho de Guarda-roupa 119 Satyajit Ray 45 Collen Atwood 122 Roman Polanski 47 Ngila Dickson 124 Ridley Scott 49 Sandy Powell 125 Martin Scorsese 52 Jacqueline Durran 127 Peter Greenaway 55 Eiko Ishiola 128 Tim Burton 56 3.3.1. Outros Figurinos 129 1.1. Storyboards e outros realizadores 59 F.W. Murnau 61 Jonh Huston 62 3.3.2. Desenhos de outros personagens 133 Terry Gillian 63 Jane Campion 65 Capítulo 4 Told Haynes 66 Outros processos 137 Capítulo 2 Carlos Saura 139 O desenho como parte integrante do filme 67 Pedro Costa 141 Voyage dans la Lune 69 Peter Greenaway 142 A invenção de Hugo 70 Sang d’un poète 71 Capítulo 5 O contrato do desenhador 72 Do Cinema ao Desenho 143 A walk through H 72 Gustav Deutsch 145 O sol do marmeleiro 74 William Kentridge 147 American Splendor 74 Quentin Tarantino 148 Quem tramou Roger Rabbit? 75 Kill Bill 75 Harry Potter e os Talismãs da Morte 76 Detachment 76 Reflexões finais 149 Tabu 77 Argo 78 Bibliografia 153 Culpados por suspeita 80 Capítulo 3 Índice de imagens 158 Função do desenhador de produção e do diretor artístico 81 Henry Bumstead 85 Dante Ferretti 87 Stuart Craig 90 7 8 Resumo: Esta dissertação dá uma pequena contribuição para a análise da utilidade do desenho na arte do cinema, em algumas das suas vertentes. -
University of Oklahoma Graduate College
UNIVERSITY OF OKLAHOMA GRADUATE COLLEGE COMMUNITY, POVERTY, POWER: THE POLITICS OF TRIBAL SELF-DETERMINATION, 1960-1968 A Dissertation SUBMITTED TO THE GRADUATE FACULTY in partial fulfillment of the requirements for the degree of Doctor of Philosophy By Daniel M. Cobb Norman, Oklahoma 2003 UMI Number: 3102433 UMI UMI Microform 3102433 Copyright 2003 by ProQuest Information and Learning Company. All rights reserved. This microform edition is protected against unauthorized copying under Title 17, United States Code. ProQuest Information and Learning Company 300 North Zeeb Road P.O. Box 1346 Ann Arbor, Ml 48106-1346 Copyright by Daniel M. Cobb 2003 AH Rights Reserved. COMMUNITY, POVERTY, POWER: THE POLITICS OF TRIBAL SELF-DETERMINATION, 1960-1968 A Dissertation APPROVED FOR THE DEPARTMENT OF HISTORY BY Acknowledgments This project began seven years ago as a master's thesis at the University of Wyoming. There I had the good fortune of working with Brian C. Hosmer, a skilled historian and constant friend. At the University of Oklahoma, R. Warren Metcalf served as the chair of my committee, and I have benefitted from his constructive criticism as well as his counsel. Professors Loretta Fowler, Albert Hurtado, David Levy, and Donald Fisani contributed generously by reading and critiquing the dissertation in what ultimately proved to be a rather compressed period of time. Although he did not serve on the dissertation committee. Dr. Robert E. Shalhope taught me the importance of “tightening and sharpening” my prose, and his seminars very nearly convinced me to specialize in the nineteenth century. I also extend my appreciation to the Department of History and particularly Department Chair Robert L. -
Mountain Men on Film Kenneth Estes Hall East Tennessee State University, [email protected]
East Tennessee State University Digital Commons @ East Tennessee State University ETSU Faculty Works Faculty Works 1-1-2016 Mountain Men on Film Kenneth Estes Hall East Tennessee State University, [email protected] Follow this and additional works at: https://dc.etsu.edu/etsu-works Part of the American Film Studies Commons, and the Film and Media Studies Commons Citation Information Hall, Kenneth Estes. 2016. Mountain Men on Film. Studies in the Western. Vol.24 97-119. http://www.westernforschungszentrum.de/ This Article is brought to you for free and open access by the Faculty Works at Digital Commons @ East Tennessee State University. It has been accepted for inclusion in ETSU Faculty Works by an authorized administrator of Digital Commons @ East Tennessee State University. For more information, please contact [email protected]. Mountain Men on Film Copyright Statement This document was published with permission from the journal. It was originally published in the Studies in the Western. This article is available at Digital Commons @ East Tennessee State University: https://dc.etsu.edu/etsu-works/596 Peter Bischoff 53 Warshow, Robert. "Movie Chronicle: The Western." Partisan Re- view, 21 (1954), 190-203. (Quoted from reference number 33) Mountain Men on Film 54 Webb, Walter Prescott. The Great Plains. Boston: Ginn and Kenneth E. Hall Company, 1931. 55 West, Ray B. , Jr., ed. Rocky Mountain Reader. New York: E.P. Dutton, 1946. 56 Westbrook, Max. "The Authentic Western." Western American Literatu,e, 13 (Fall 1978), 213-25. 57 The Western Literature Association (sponsored by). A Literary History of the American West. Fort Worth: Texas Christian University Press, 1987.