From Mathematics to Generic Programming
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Meetings & Conferences of The
Meetings & Conferences of the AMS IMPORTANT INFORMATION REGARDING MEETINGS PROGRAMS: AMS Sectional Meeting programs do not appear in the print version of the Notices. However, comprehensive and continually updated meeting and program information with links to the abstract for each talk can be found on the AMS website. See http://www.ams.org/ meetings/. Final programs for Sectional Meetings will be archived on the AMS website accessible from the stated URL and in an electronic issue of the Notices as noted below for each meeting. Tamar Zeigler, Technion, Israel Institute of Technology, Tel Aviv, Israel Patterns in primes and dynamics on nilmanifolds. Bar-Ilan University, Ramat-Gan and Special Sessions Tel-Aviv University, Ramat-Aviv Additive Number Theory, Melvyn B. Nathanson, City University of New York, and Yonutz V. Stanchescu, Afeka June 16–19, 2014 Tel Aviv Academic College of Engineering. Monday – Thursday Algebraic Groups, Division Algebras and Galois Co- homology, Andrei Rapinchuk, University of Virginia, and Meeting #1101 Louis H. Rowen and Uzi Vishne, Bar Ilan University. The Second Joint International Meeting between the AMS Applications of Algebra to Cryptography, David Garber, and the Israel Mathematical Union. Holon Institute of Technology, and Delaram Kahrobaei, Associate secretary: Michel L. Lapidus City University of New York Graduate Center. Announcement issue of Notices: January 2014 Asymptotic Geometric Analysis, Shiri Artstein and Boaz Program first available on AMS website: To be announced Klar’tag, Tel Aviv University, and Sasha Sodin, Princeton Program issue of electronic Notices: To be announced University. Issue of Abstracts: Not applicable Combinatorial Games, Aviezri Fraenkel, Weizmann University, Richard Nowakowski, Dalhousie University, Deadlines Canada, Thane Plambeck, Counterwave Inc., and Aaron For organizers: To be announced Siegel, Twitter. -
Mathematisches Forschungsinstitut Oberwolfach Emigration Of
Mathematisches Forschungsinstitut Oberwolfach Report No. 51/2011 DOI: 10.4171/OWR/2011/51 Emigration of Mathematicians and Transmission of Mathematics: Historical Lessons and Consequences of the Third Reich Organised by June Barrow-Green, Milton-Keynes Della Fenster, Richmond Joachim Schwermer, Wien Reinhard Siegmund-Schultze, Kristiansand October 30th – November 5th, 2011 Abstract. This conference provided a focused venue to explore the intellec- tual migration of mathematicians and mathematics spurred by the Nazis and still influential today. The week of talks and discussions (both formal and informal) created a rich opportunity for the cross-fertilization of ideas among almost 50 mathematicians, historians of mathematics, general historians, and curators. Mathematics Subject Classification (2000): 01A60. Introduction by the Organisers The talks at this conference tended to fall into the two categories of lists of sources and historical arguments built from collections of sources. This combi- nation yielded an unexpected richness as new archival materials and new angles of investigation of those archival materials came together to forge a deeper un- derstanding of the migration of mathematicians and mathematics during the Nazi era. The idea of measurement, for example, emerged as a critical idea of the confer- ence. The conference called attention to and, in fact, relied on, the seemingly stan- dard approach to measuring emigration and immigration by counting emigrants and/or immigrants and their host or departing countries. Looking further than this numerical approach, however, the conference participants learned the value of measuring emigration/immigration via other less obvious forms of measurement. 2892 Oberwolfach Report 51/2011 Forms completed by individuals on religious beliefs and other personal attributes provided an interesting cartography of Italian society in the 1930s and early 1940s. -
September 2014
LONDONLONDON MATHEMATICALMATHEMATICAL SOCIETYSOCIETY NEWSLETTER No. 439 September 2014 Society Meetings HIGHEST HONOUR FOR UK and Events MATHEMATICAN Professor Martin Hairer, FRS, 2014 University of Warwick, has become the ninth UK based Saturday mathematician to win the 6 September prestigious Fields Medal over Mathematics and the its 80 year history. The medal First World War recipients were announced Meeting, London on Wednesday 13 August in page 15 a ceremony at the four-year- ly International Congress for 1 Wednesday Mathematicians, which on this 24 September occasion was held in Seoul, South Korea. LMS Popular Lectures See page 4 for the full report. Birmingham page 12 Friday LMS ANNOUNCES SIMON TAVARÉ 14 November AS PRESIDENT-DESIGNATE LMS AGM © The University of Cambridge take over from the London current President, Professor Terry Wednesday Lyons, FRS, in 17 December November 2015. SW & South Wales Professor Tavaré is Meeting a versatile math- Plymouth ematician who has established a distinguished in- ternational career culminating in his current role as The London Mathematical Director of the Cancer Research Society is pleased to announce UK Cambridge Institute and Professor Simon Tavaré, Professor in DAMTP, where he NEWSLETTER FRS, FMedSci, University of brings his understanding of sto- ONLINE: Cambridge, as President-Des- chastic processes and expertise newsletter.lms.ac.uk ignate. Professor Tavaré will in the data science of DNA se- (Cont'd on page 3) LMS NEWSLETTER http://newsletter.lms.ac.uk Contents No. 439 September 2014 15 44 Awards Partial Differential Equations..........................37 Collingwood Memorial Prize..........................11 Valediction to Jeremy Gray..............................33 Calendar of Events.......................................50 News LMS Items European News.................................................16 HEA STEM Strategic Project........................... -
Programming Exam 1 on the Assignments Page
COS 126 Midterm 1 Programming Exam Spring 2015 This part of your midterm exam is like a mini-programming assignment. You will create four programs, compile them, and run them on your laptop. Debug your code as needed. This exam is open book, open browser—but only our course website and booksite! Of course, no internal or external communication is permitted (e.g., talking, email, IM, texting, cell phones) during the exam. You may use code from your assignments or code found on the COS126 website. When you are done, submit your program via the course website using the submit link for Programming Exam 1 on the Assignments page. Grading. Your program will be graded on correctness, clarity (including comments), design, and efficiency. You will lose a substantial number of points if your program does not compile or does not have the proper API, or if it crashes on typical inputs. Even though you will electronically submit your code, you must turn in this paper so that we have a record that you took the exam and signed the Honor Code. Print your name, login ID, and precept number on this page (now), and write out and sign the Honor Code pledge before turning in this paper. Note: It is a violation of the Honor Code to discuss this midterm exam question with anyone until after everyone in the class has taken the exam. You have 90 minutes to complete the test. “I pledge my honor that I have not violated the Honor Code during this examination.” ___________________________________________________________________ ___________________________________________________________________ [copy the pledge onto these lines] _____________________________ [signature] NAME: ______________________ Part 0 /12 Part 1 /8 LOGIN: ______________________ Part 2 /5 Part 3 /5 PRECEPT: ______________________ TOTAL /30 !1 The aliquot sum of a positive integer is the sum of its positive divisors other than itself (these divisors are called its proper divisors). -
Richard Von Mises's Philosophy of Probability and Mathematics
“A terrible piece of bad metaphysics”? Towards a history of abstraction in nineteenth- and early twentieth-century probability theory, mathematics and logic Lukas M. Verburgt If the true is what is grounded, then the ground is neither true nor false LUDWIG WITTGENSTEIN Whether all grow black, or all grow bright, or all remain grey, it is grey we need, to begin with, because of what it is, and of what it can do, made of bright and black, able to shed the former , or the latter, and be the latter or the former alone. But perhaps I am the prey, on the subject of grey, in the grey, to delusions SAMUEL BECKETT “A terrible piece of bad metaphysics”? Towards a history of abstraction in nineteenth- and early twentieth-century probability theory, mathematics and logic ACADEMISCH PROEFSCHRIFT ter verkrijging van de graad van doctor aan de Universiteit van Amsterdam op gezag van de Rector Magnificus prof. dr. D.C. van den Boom ten overstaan van een door het College voor Promoties ingestelde commissie in het openbaar te verdedigen in de Agnietenkapel op donderdag 1 oktober 2015, te 10:00 uur door Lukas Mauve Verburgt geboren te Amersfoort Promotiecommissie Promotor: Prof. dr. ir. G.H. de Vries Universiteit van Amsterdam Overige leden: Prof. dr. M. Fisch Universitat Tel Aviv Dr. C.L. Kwa Universiteit van Amsterdam Dr. F. Russo Universiteit van Amsterdam Prof. dr. M.J.B. Stokhof Universiteit van Amsterdam Prof. dr. A. Vogt Humboldt-Universität zu Berlin Faculteit der Geesteswetenschappen © 2015 Lukas M. Verburgt Graphic design Aad van Dommelen (Witvorm) -
November 2014
LONDONLONDON MATHEMATICALMATHEMATICAL SOCIETYSOCIETY NEWSLETTER No. 441 November 2014 Society Meetings ELECTIONS TO COUNCIL AND and Events NOMINATING COMMITTEE 2014 Members should now have for the election can be found on 2014 received a communication from the LMS website at www.lms. Friday the Electoral Reform Society (ERS) ac.uk/about/council/lms-elections. 14 November for both e-voting and paper ballot. For both electronic and postal LMS AGM For online voting, members may voting the deadline for receipt Naylor Lecture cast a vote by going to www. of votes is Thursday 6 November. London votebyinternet.com/LMS2014 and Members may still cast a vote in page 7 using the two part security code person at the AGM, although an Wednesday on the email sent by the ERS and in-person vote must be cast via a 17 December also on their ballot paper. paper ballot. 1 SW & South Wales All members are asked to look Members may like to note that Regional Meeting out for communication from an LMS Election blog, moderated Plymouth page 27 the ERS. We hope that as many by the Scrutineers, can be members as possible will cast their found at http://discussions.lms. 2015 vote. If you have not received ac.uk/elections2014. ballot material, please contact Friday 16 January [email protected], con- Future Elections 150th Anniversary firming the address (post or email) Members are invited to make sug- Launch, London page 9 to which you would like material gestions for nominees for future sent. election to Council. These should Friday 27 February With respect to the election itself, be addressed to the Nominat- Mary Cartwright there are ten candidates proposed ing Committee (nominations@ Lecture, London for six vacancies for Member-at- lms.ac.uk). -
POWERFUL AMICABLE NUMBERS 1. Introduction Let S(N) := ∑ D Be the Sum of the Proper Divisors of the Natural Number N. Two Disti
POWERFUL AMICABLE NUMBERS PAUL POLLACK P Abstract. Let s(n) := djn; d<n d denote the sum of the proper di- visors of the natural number n. Two distinct positive integers n and m are said to form an amicable pair if s(n) = m and s(m) = n; in this case, both n and m are called amicable numbers. The first example of an amicable pair, known already to the ancients, is f220; 284g. We do not know if there are infinitely many amicable pairs. In the opposite direction, Erd}osshowed in 1955 that the set of amicable numbers has asymptotic density zero. Let ` ≥ 1. A natural number n is said to be `-full (or `-powerful) if p` divides n whenever the prime p divides n. As shown by Erd}osand 1=` Szekeres in 1935, the number of `-full n ≤ x is asymptotically c`x , as x ! 1. Here c` is a positive constant depending on `. We show that for each fixed `, the set of amicable `-full numbers has relative density zero within the set of `-full numbers. 1. Introduction P Let s(n) := djn; d<n d be the sum of the proper divisors of the natural number n. Two distinct natural numbers n and m are said to form an ami- cable pair if s(n) = m and s(m) = n; in this case, both n and m are called amicable numbers. The first amicable pair, 220 and 284, was known already to the Pythagorean school. Despite their long history, we still know very little about such pairs. -
The Catalan Mathematical Society EMS June 2000 3 EDITORIAL
CONTENTS EDITORIAL TEAM EUROPEAN MATHEMATICAL SOCIETY EDITOR-IN-CHIEF ROBIN WILSON Department of Pure Mathematics The Open University Milton Keynes MK7 6AA, UK e-mail: [email protected] ASSOCIATE EDITORS STEEN MARKVORSEN Department of Mathematics Technical University of Denmark Building 303 NEWSLETTER No. 36 DK-2800 Kgs. Lyngby, Denmark e-mail: [email protected] KRZYSZTOF CIESIELSKI June 2000 Mathematics Institute Jagiellonian University Reymonta 4 30-059 Kraków, Poland EMS News : Agenda, Editorial, 3ecm, Bedlewo Meeting, Limes Project ........... 2 e-mail: [email protected] KATHLEEN QUINN Open University [address as above] Catalan Mathematical Society ........................................................................... 3 e-mail: [email protected] SPECIALIST EDITORS The Hilbert Problems ....................................................................................... 10 INTERVIEWS Steen Markvorsen [address as above] SOCIETIES Interview with Peter Deuflhard ....................................................................... 14 Krzysztof Ciesielski [address as above] EDUCATION Vinicio Villani Interview with Jaroslav Kurzweil ..................................................................... 16 Dipartimento di Matematica Via Bounarotti, 2 56127 Pisa, Italy A Major Challenge for Mathematicians ........................................................... 20 e-mail: [email protected] MATHEMATICAL PROBLEMS Paul Jainta EMS Position Paper: Towards a European Research Area ............................. 24 -
Mathematical Constants and Sequences
Mathematical Constants and Sequences a selection compiled by Stanislav Sýkora, Extra Byte, Castano Primo, Italy. Stan's Library, ISSN 2421-1230, Vol.II. First release March 31, 2008. Permalink via DOI: 10.3247/SL2Math08.001 This page is dedicated to my late math teacher Jaroslav Bayer who, back in 1955-8, kindled my passion for Mathematics. Math BOOKS | SI Units | SI Dimensions PHYSICS Constants (on a separate page) Mathematics LINKS | Stan's Library | Stan's HUB This is a constant-at-a-glance list. You can also download a PDF version for off-line use. But keep coming back, the list is growing! When a value is followed by #t, it should be a proven transcendental number (but I only did my best to find out, which need not suffice). Bold dots after a value are a link to the ••• OEIS ••• database. This website does not use any cookies, nor does it collect any information about its visitors (not even anonymous statistics). However, we decline any legal liability for typos, editing errors, and for the content of linked-to external web pages. Basic math constants Binary sequences Constants of number-theory functions More constants useful in Sciences Derived from the basic ones Combinatorial numbers, including Riemann zeta ζ(s) Planck's radiation law ... from 0 and 1 Binomial coefficients Dirichlet eta η(s) Functions sinc(z) and hsinc(z) ... from i Lah numbers Dedekind eta η(τ) Functions sinc(n,x) ... from 1 and i Stirling numbers Constants related to functions in C Ideal gas statistics ... from π Enumerations on sets Exponential exp Peak functions (spectral) .. -
Leo Corry HILBERT's 6TH PROBLEM: BETWEEN THE
Leo Corry HILBERT’S 6TH PROBLEM: BETWEEN THE FOUNDATIONS OF GEOMETRY AND THE AXIOMATIZATION OF PHYSICS LEO CORRY1 Abstract. The sixth of Hilbert’s famous 1900 list of twenty-three problems was a programmatic call for the axiomatization of the physical sciences. It was naturally and organically rooted at the core of Hilbert’s conception of what axiomatization is all about. In fact, the axiomatic method which he applied at the turn of the twentieth-century in his famous work on the foundations of geometry originated in a preoccupation with foundational questions related with empirical science in general. Indeed, far from a purely formal conception, Hilbert counted geometry among the sciences with strong empirical content, closely related to other branches of physics and deserving a treatment similar to that reserved for the latter. In this treatment, the axiomatization project was meant to play, in his view, a crucial role. Curiously, and contrary to a once-prevalent view, from all the problems in the list, the sixth is the only one that continually engaged Hilbet’s efforts over a very long period of time, at least between 1894 and 1932. (TO APPEAR IN: Philosophical Transactions of the Royal Society (A) - DOI: 10.1098/rsta.2017.0221) 1. Introduction Of the many important and brilliant talks delivered in International Congresses of Mathematicians (ICM) ever since the inception of this institution in 1897 in Zurich, none has so frequently been quoted and, arguably, none has had the kind of pervasive influence, that had the one delivered by David Hilbert in 1900 at the second ICM in Paris, under the title of “Mathematical Problems”. -
Fermat Meets SWAC: Vandiver, the Lehmers, Computers, and Number Theory
Fermat Meets SWAC: Vandiver, the Lehmers, Computers, and Number Theory Leo Corry Tel Aviv University This article describes the work of Harry Schultz Vandiver, Derrick Henry Lehmer, and Emma Lehmer on calculations related with proofs of Fermat’s last theorem. This story sheds light on ideological and institutional aspects of activity in number theory in the US during the 20th century, and on the incursion of computer-assisted methods into pure fields of mathematical research. The advent of the electronic digital computer than 100. Extending this result beyond 100 opened a new era of unprecedented possibil- involved, above all, straightforward (if tedious) ities for large-scale number crunching. Begin- computations. Yet, little work was devoted to ning in the late 1940s, these gradually increas- such computations before 1920, and even ing possibilities were duly pursued in many then, this remained an essentially marginal branches of science. Some of them, like trend within number theory. meteorology, geophysics, or engineering sci- Thus, when electronic computers started to ence, underwent deep and quick transforma- became available in the late 1940s, few tions. Pure mathematical disciplines such as mathematicians working in the core, ‘‘pure’’ number theory can be counted among the less fields of the discipline incorporated them in receptive audiences for these newly opened their research agendas. Even fewer did so for possibilities. One way to account for this Fermat’s last theorem. Harry Schultz Vandiver somewhat ironic situation is to examine the (1882–1973) was one of the few to do so. He main research trends that shaped progress in joined forces with the couple Derrick Henry the algebraic theory of numbers from the Lehmer (1905–1991), and Emma Lehmer second half of the 19th century on. -
On the Origins of Hilbert's Sixth Problem: Physics and the Empiricist Approach to Axiomatization
On the origins of Hilbert’s sixth problem: physics and the empiricist approach to axiomatization Leo Corry Abstract. The sixth of Hilbert’s famous 1900 list of twenty-three problems is a programmatic call for the axiomatization of physical sciences. Contrary to a prevalent view this problem was naturally rooted at the core of Hilbert’s conception of what axiomatization is all about. The axiomatic method embodied in his work on geometry at the turn of the twentieth-century orig- inated in a preoccupation with foundational questions related with empirical science, including geometry and other physical disciplines at a similar level. From all the problems in the list, the sixth is the only one that continually engaged his efforts over a very long period, at least between 1894 and 1932. Mathematics Subject Classification (2000). Primary 01A60; Secondary 03-03, 70-03, 83-03. Keywords. David Hilbert, axiomatization, physics. 1. Introduction Of the many important and brilliant plenary talks delivered in ICMs ever since the inception of this institution in 1897 in Zurich, none has so frequently been quoted and, possibly, none has had the kind of pervasive influence, as the one delivered by David Hilbert in 1900 at the second ICM in Paris, under the title of “Mathematical Problems”. Rather than summarizing the state of the art in a central branch of mathematics, Hilbert attempted to “lift the veil” and peer into the development of mathematics in the century that was about to begin. He chose to present a list of twenty-three problems that in his opinion would and should occupy the efforts of mathematicians in the years to come.