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Noncommutative Localization in Algebra and Topology
Noncommutative localization in algebra and topology ICMS Edinburgh 2002 Edited by Andrew Ranicki Electronic version of London Mathematical Society Lecture Note Series 330 Cambridge University Press (2006) Contents Dedication . vii Preface . ix Historical Perspective . x Conference Participants . xi Conference Photo . .xii Conference Timetable . xiii On atness and the Ore condition J. A. Beachy ......................................................1 Localization in general rings, a historical survey P. M. Cohn .......................................................5 Noncommutative localization in homotopy theory W. G. Dwyer . 24 Noncommutative localization in group rings P. A. Linnell . 40 A non-commutative generalisation of Thomason's localisation theorem A. Neeman . 60 Noncommutative localization in topology A. A. Ranicki . 81 v L2-Betti numbers, Isomorphism Conjectures and Noncommutative Lo- calization H. Reich . 103 Invariants of boundary link cobordism II. The Blanch¯eld-Duval form D. Sheiham . 143 Noncommutative localization in noncommutative geometry Z. Skoda· ........................................................220 vi Dedicated to the memory of Desmond Sheiham (13th November 1974 ¡ 25th March 2005) ² Cambridge University (Trinity College), 1993{1997 B.A. Hons. Mathematics 1st Class, 1996 Part III Mathematics, Passed with Distinction, 1997 ² University of Edinburgh, 1997{2001 Ph.D. Invariants of Boundary Link Cobordism, 2001 ² Visiting Assistant Professor, Mathematics Department, University of California at Riverside, 2001{2003 ² Research Instructor, International University Bremen (IUB), 2003{2005 vii Publications: 1. Non-commutative Characteristic Polynomials and Cohn Localization Journal of the London Mathematical Society (2) Vol. 64, 13{28 (2001) http://arXiv.org/abs/math.RA/0104158 2. Invariants of Boundary Link Cobordism Memoirs of the American Mathematical Society, Vol. 165 (2003) http://arXiv.org/abs/math.AT/0110249 3. Whitehead Groups of Localizations and the Endomorphism Class Group Journal of Algebra, Vol. -
Remarkable Physicists: from Galileo to Yukawa
Remarkable Physicists From Galileo to Yukawa The 250 years from the second half of the seventeenth century saw the birth of modern physics and its growth into one of the most successful of the sciences.The reader will find here the lives of fifty of the most remarkable physicists from that era described in brief biographies.All the characters profiled have made important contributions to physics, through their ideas, through their teaching, or in other ways.The emphasis is on their varied life-stories, not on the details of their achievements, but, when read in sequence, the biographies, which are organized chronologically, convey in human terms something of the way in which physics was created.Scientific and mathematical detail is kept to a minimum, so the reader who is interested in physics, but perhaps lacks the background to follow technical accounts, will find this collection an inviting and easy path through the subject’s modern development. Remarkable Physicists From Galileo to Yukawa Ioan James Mathematical Institute, Oxford cambridge university press Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, São Paulo Cambridge University Press The Edinburgh Building, Cambridge cb2 2ru, UK Published in the United States of America by Cambridge University Press, New York www.cambridge.org Information on this title: www.cambridge.org/9780521816878 © Ioan James 2004 This publication is in copyright. Subject to statutory exception and to the provision of relevant collective licensing agreements, no reproduction of any part may take -
The Role of GH Hardy and the London Mathematical Society
View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by Elsevier - Publisher Connector Historia Mathematica 30 (2003) 173–194 www.elsevier.com/locate/hm The rise of British analysis in the early 20th century: the role of G.H. Hardy and the London Mathematical Society Adrian C. Rice a and Robin J. Wilson b,∗ a Department of Mathematics, Randolph-Macon College, Ashland, VA 23005-5505, USA b Department of Pure Mathematics, The Open University, Milton Keynes MK7 6AA, UK Abstract It has often been observed that the early years of the 20th century witnessed a significant and noticeable rise in both the quantity and quality of British analysis. Invariably in these accounts, the name of G.H. Hardy (1877–1947) features most prominently as the driving force behind this development. But how accurate is this interpretation? This paper attempts to reevaluate Hardy’s influence on the British mathematical research community and its analysis during the early 20th century, with particular reference to his relationship with the London Mathematical Society. 2003 Elsevier Inc. All rights reserved. Résumé On a souvent remarqué que les premières années du 20ème siècle ont été témoins d’une augmentation significative et perceptible dans la quantité et aussi la qualité des travaux d’analyse en Grande-Bretagne. Dans ce contexte, le nom de G.H. Hardy (1877–1947) est toujours indiqué comme celui de l’instigateur principal qui était derrière ce développement. Mais, est-ce-que cette interprétation est exacte ? Cet article se propose d’analyser à nouveau l’influence d’Hardy sur la communauté britannique sur la communauté des mathématiciens et des analystes britanniques au début du 20ème siècle, en tenant compte en particulier de son rapport avec la Société Mathématique de Londres. -
Alan Turing 1 Alan Turing
Alan Turing 1 Alan Turing Alan Turing Turing at the time of his election to Fellowship of the Royal Society. Born Alan Mathison Turing 23 June 1912 Maida Vale, London, England, United Kingdom Died 7 June 1954 (aged 41) Wilmslow, Cheshire, England, United Kingdom Residence United Kingdom Nationality British Fields Mathematics, Cryptanalysis, Computer science Institutions University of Cambridge Government Code and Cypher School National Physical Laboratory University of Manchester Alma mater King's College, Cambridge Princeton University Doctoral advisor Alonzo Church Doctoral students Robin Gandy Known for Halting problem Turing machine Cryptanalysis of the Enigma Automatic Computing Engine Turing Award Turing test Turing patterns Notable awards Officer of the Order of the British Empire Fellow of the Royal Society Alan Mathison Turing, OBE, FRS ( /ˈtjʊərɪŋ/ TEWR-ing; 23 June 1912 – 7 June 1954), was a British mathematician, logician, cryptanalyst, and computer scientist. He was highly influential in the development of computer science, giving a formalisation of the concepts of "algorithm" and "computation" with the Turing machine, which can be considered a model of a general purpose computer.[1][2][3] Turing is widely considered to be the father of computer science and artificial intelligence.[4] During World War II, Turing worked for the Government Code and Cypher School (GC&CS) at Bletchley Park, Britain's codebreaking centre. For a time he was head of Hut 8, the section responsible for German naval cryptanalysis. He devised a number of techniques for breaking German ciphers, including the method of the bombe, an electromechanical machine that could find settings for the Enigma machine. -
Fitzgerald M., James I. the Mind of the Mathematician (Johns Hopkins
The Mind of the Mathematician THE JOHNS HOPKINS UNIVERSITY PRESS } BALTIMORE Michael Fitzgerald and Ioan James T H E M I N D O F T H E M A N AT H E M AT I C I ∫ 2007 Michael Fitzgerald and Ioan James All rights reserved. Published 2007 Printed in the United States of America on acid-free paper 987654321 The Johns Hopkins University Press 2715 North Charles Street Baltimore, Maryland 21218-4363 www.press.jhu.edu Library of Congress Cataloging-in-Publication Data Fitzgerald, Michael, 1946– The mind of the mathematician / Michael Fitzgerald and Ioan James. p. cm. Includes bibliographical references and index. isbn-13: 978-0-8018-8587-7 (hardcover : acid-free paper) isbn-10: 0-8018-8587-6 (hardcover : acid-free paper) 1. Mathematicians—Psychology. 2. Mathematics—Psychological aspects. 3. Mathematical ability. 4. Mathematical ability—Sex di√erences. I. James, I. M. (Ioan Mackenzie), 1928– II. Title. bf456.n7f58 2007 510.1%9—dc22 2006025988 A catalog record for this book is available from the British Library. Contents Preface vii Introduction ix PART I } TOUR OF THE LITERATURE Chapter 1. Mathematicians and Their World 3 Chapter 2. Mathematical Ability 24 Chapter 3. The Dynamics of Mathematical Creation 42 PART II } TWENTY MATHEMATICAL PERSONALITIES Chapter 4. Lagrange, Gauss, Cauchy, and Dirichlet 67 Chapter 5. Hamilton, Galois, Byron, and Riemann 88 Chapter 6. Cantor, Kovalevskaya, Poincaré, and Hilbert 105 Chapter 7. Hadamard, Hardy, Noether, and Ramanujan 131 Chapter 8. Fisher, Wiener, Dirac, and Gödel 149 References 163 Index 175 This page intentionally left blank Preface Psychologists have long been fascinated by mathematicians and their world. -
Mathematics of Random Systems Filming Student Lectures Meet The
The Oxford Mathematics Annual Newsletter 2020 Meet the Outreach Team Minimal Lagrangians Mathematics of Random Systems Filming Student Lectures 1 The Oxford Mathematics Annual Newsletter 2020 Head of Contents Department’s letter Meet the Outreach Team 3 Minimal Lagrangians and where 4 Mike Giles to find them Nick Woodhouse awarded CBE 5 Oxford Presidents of the London Mathematical Society In December we went through our annual undergraduate admissions process. As usual, we had a huge number of Mathematics of Random Systems 6 very talented applicants, with about 2,700 applicants for PROMYS Europe celebrates its 7 250 places in Mathematics and our various joint degrees, 5th birthday and we very much look forward to seeing this fresh set Appointments and Achievements 8 of students next October. Obituaries 9 Admissions statistics are available from the University’s main website at What’s on in Oxford Mathematics? 10 ox.ac.uk/about/facts-and-figures/admissions-statistics, with the latest data being for those who started their studies in 2018. Approximately Oxford Mathematics Music Events 40% of our students in Maths come from abroad, primarily from China and the EU. Of the UK students, about 75% come from state schools, Roger Penrose’s scientific drawings and 30% are women, reflecting the proportion of girls versus boys taking Oxford Mathematics FRSs A-level Further Mathematics. Almost 20% of our UK students are from an ethnic minority heritage, which is just a little lower than the national Oxford Maths Festival 11 average but includes some variation between different ethnic groups. Thank goodness it’s Friday An area in which we hope to make improvements is in admitting UK 400 years of Savilian professors students from less advantaged backgrounds. -
Introduction to Ring Theory
springer.com Mathematics : Algebra Cohn, Paul M. Introduction to Ring Theory Paul Cohn is a well-known expositor and expert in the field This book follows on from the SUMS book "Groups, Rings and Fields" by David Wallace Most parts of algebra have undergone great changes and advances in recent years, perhaps none more so than ring theory. In this volume, Paul Cohn provides a clear and structured introduction to the subject. After a chapter on the definition of rings and modules there are brief accounts of Artinian rings, commutative Noetherian rings and ring constructions, such as the direct product. Tensor product and rings of fractions, followed by a description of free rings. The reader is assumed to have a basic understanding of set theory, group theory and vector spaces. Over two hundred carefully selected exercises are included, most with outline Springer solutions. 2000, X, 229 p. 1st Order online at springer.com/booksellers edition Springer Nature Customer Service Center LLC 233 Spring Street New York, NY 10013 Printed book USA Softcover T: +1-800-SPRINGER NATURE (777-4643) or 212-460-1500 Printed book [email protected] Softcover ISBN 978-1-85233-206-8 $ 44,99 Available Discount group Professional Books (2) Product category Undergraduate textbook Series Springer Undergraduate Mathematics Series Other renditions Softcover ISBN 978-1-4471-0476-6 Prices and other details are subject to change without notice. All errors and omissions excepted. Americas: Tax will be added where applicable. Canadian residents please add PST, QST or GST. Please add $5.00 for shipping one book and $ 1.00 for each additional book. -
400 Years of Savilian Professors of Geometry
The Oxford Mathematics Newsletter • Spring 2019 Mathematics and music Latest research Oxford Maths Festival 400 years of Savilian Professors of Geometry 1 Round up • Oxford Mathematics • Spring 2019 Head of Contents Departmental News Department’s letter Departmental News 3 Obituary: Sir Michael Atiyah Mike Giles was granted to Oxford’s Mathematical and the world around us. We are 400 years of Savilian Professors 4 Institute as part of the Queen’s 90th immensely proud to have Andrew as a of Geometry birthday celebrations. It is the first Regius colleague at the Mathematical Institute Professorship awarded to Oxford since in Oxford. Comings and goings 5 1842, and one of only three Regius Chairs in mathematics in the UK (the others being In 2016 Andrew was awarded the On 1 September, Mike Giles, Professor of Scientific Research: Hooke and Titchmarsh Fellows 6 at Warwick and St Andrews). Abel Prize, the highest honour in Computing and Professorial Fellow of St Hugh’s mathematics, for his stunning proof of Mathematics and music 7 Professor Martin Bridson, former Head of Fermat’s Last Theorem, a challenge that College, took over from Martin Bridson as Head of Oxford’s Mathematical Institute, writes: stumped mathematicians for 350 years. Appointments and achievements 8 The award of the Regius Professorship In recognition of this transformative work, the Mathematical Institute. Mike writes: to Oxford recognised both our pre- he was also awarded the Copley Medal, OMMS – 9 eminence in fundamental research and the Royal Society’s oldest and most In preparing to write these few words, I looked back at the introductory first cohort for the new MSc degree the enormous benefits that flow to society prestigious award. -
Notices of the American Mathematical Society
AMS PRICES WILL INCREASE SEPTEMBER 1, 1981 CALL 800-556-7774 TO ORDER BOOKS z 0 WITH VISA OR MASTER CARDS (SEE PAGES 349 AND 352) -1 (1 IT1 '.Jl > 3: IT1 ;:;o 3: > -1 :I: '.Jl 0 (1 Notices of the American Mathematical Society < 2.. c: 3 (1) -~ z c: 3 r::1' ...(1) June 1981, Issue 210 ... Volume 28, Number 4, Pages 297-384 10 Providence, Rhode Island USA ...00 JSSN 0002-9920 CALENDAR OF AMS MEETINGS THIS CALENDAR lists all meetings which have been approved by the Council prior to the date this issue of the Notices was sent to press. The summer and annual meetings are joint meetings of the Mathematical Association of America and the Ameri· can Mathematical Society. The meeting dates which fall rather far in the future are subject to change; this is particularly true of meetings to which no numbers have yet been assigned. Programs of the meetings will appear in the issues indicated below. First and second announcements of the meetings will have appeared in earlier issues. ABSTRACTS OF PAPERS presented at a meeting of the Society are published in the journal Abstracts of papers presented to the American Mathematical Society in the issue corresponding to that of the Notices which contains the program of the meet· ing. Abstracts should be submitted on special forms which are available in many departments of mathematics and from the office of the Society in Providence. Abstracts of papers to be presented at the meeting must be received at the headquarters of the Society in Providence, Rhode Island, on or before the deadline given below for the meeting. -
Special Priced Indian Edition Mathematics and Statistics
springer.com Special Priced Indian Edition Mathematics and Statistics * (To be sold in India, Pakistan, Bangaldesh, Sri Lanka and Nepal) Catalogue 2014 Contents Highlights Algebra 1 Analysis 6 Application of Mathematics 14 Graph Theory 21 Geometry 23 Statistics 25 Order Form Algebra 31 Algebraic Geometry 31 Analysis 32 Applications of Mathematics 34 Applied Statistics 35 Calculus 36 Combinatorics 36 Cryptography 37 Difference and Functional Equations 37 General Mathematics 37 Geometry 38 Graph Theory 39 Group Theory 39 Linear and Multilinear Algebras 39 Logic 40 Mathematical Biology 40 Number Theory 40 Numerical Analysis 41 Ordinary Differential Equations 41 Partial Differential Equations 41 Probability Theory 42 Quantitative Finance 42 Ring Theory 43 Set Theory 43 Statistical Theory and Methods 43 Topology 44 Distributor’s Code 47 Distributor’s Addresses 49 South Asian Retailer’s Addresses 59 springer.com Highlights (Algebra) 1 103 Trigonometry Problems: From the Training of the USA IMO Team Titu Andreescu, The University of Texas at Dallas, Richardson, TX, USA Zuming Feng, Phillips Exeter Academy, Exeter, USA About the Book 103 Trigonometry Problems contains highly-selected problems and solutions used in the training and testing of the USA International Mathematical Olympiad (IMO) team. Though many problems may initially appear impenetrable to the novice, most can be solved using only elementary high school mathematics techniques. Key features: - Problem-solving tactics and strategies, along with practical test-taking techniques, provide -
Cambridge E-Books Title Author Collection Name Volume Edition
Cambridge E-Books Title Author Collection name Volume Edition The 2005 Hague Convention on Choice of Court Agreements Ronald A. Brand, Paul Herrup 1 Edited by Evencio Mediavilla, Santiago Arribas, Martin Roth, Jordi 3D Spectroscopy in Astronomy Cepa-Nogué, Francisco Sánchez 1 A. W. H. Phillips: Collected Works in Contemporary Perspective Edited by Robert Leeson 1 Edited by Vincenzo Antonuccio- AGN Feedback in Galaxy Formation Delogu, Joseph Silk 1 The Abolition of the African Slave-Trade by the British Parliament Thomas Clarkson 2 1 The Abolition of the Death Penalty in International Law William A. Schabas 3 Herbert Cole Coombs, Foreword by Aboriginal Autonomy Mick Dodson 1 Absolutism and Society in Seventeenth-Century France William Beik 1 An Account of Some Recent Discoveries in Hieroglyphical Literature and Egyptian Antiquities Thomas Young 1 Account of the Harvard Greek Play Henry Norman 1 An Account of the Present State of the Island of Puerto Rico George D. Flinter 1 Accountability of Armed Opposition Groups in International Law Liesbeth Zegveld 1 Accounting Principles for Lawyers Peter Holgate 1 Achieving Industrialization in East Asia Edited by Helen Hughes 1 Acquiring Phonology Neil Smith 1 Across Australia Baldwin Spencer, F. J. Gillen 2 1 Archibald John Little, Edited by Across Yunnan Alicia Little 1 Across the Jordan Gottlieb Schumacher 1 Across the Plains Robert Louis Stevenson 1 Acta Mythologica Apostolorum in Arabic Edited by Agnes Smith Lewis 1 Acts of Activism D. Soyini Madison 1 Fenton John Anthony Hort, Edited by Brooke Foss Westcott, Thomas The Acts of the Apostles Ethelbert Page 1 Acute Medicine J. -
Free Ideal Rings and Localization in General Rings P
Cambridge University Press 978-0-521-85337-8 — Free Ideal Rings and Localization in General Rings P. M. Cohn Frontmatter More Information Free Ideal Rings and Localization in General Rings Proving that a polynomial ring in one variable over a field is a principal ideal domain can be done by means of the Euclidean algorithm, but this does not extend to more variables. However, if the variables are not allowed to commute, giving a free associative algebra, then there is a generalization, the weak algorithm, which can be used to prove that all one-sided ideals are free. This book presents the theory of free ideal rings (firs) in detail. Particular emphasis is placed on rings with a weak algorithm, exemplified by free associative algebras. There is also a full account of localization, which is treated for general rings, but the features arising in firs are given special attention. Each section has a number of exercises, including some open problems, and each chapter ends in a historical note. paul cohn is Emeritus Professor of Mathematics at the University of London and Honorary Research Fellow at University College London. © in this web service Cambridge University Press www.cambridge.org Cambridge University Press 978-0-521-85337-8 — Free Ideal Rings and Localization in General Rings P. M. Cohn Frontmatter More Information NEW MATHEMATICAL MONOGRAPHS Editorial Board B´ela Bollob´as William Fulton Frances Kirwan Peter Sarnak Barry Simon For information about Cambridge University Press mathematics publications visit http://publishing.cambridge.org/stm/mathematics Already published in New Mathematical Monographs: Representation Theory of Finite Reductive Groups Marc Cabanes, Michel Enguehard Harmonic Measure John B.