Brochure on Careers in Applied Mathematics
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A MATHEMATICIAN's SURVIVAL GUIDE 1. an Algebra Teacher I
A MATHEMATICIAN’S SURVIVAL GUIDE PETER G. CASAZZA 1. An Algebra Teacher I could Understand Emmy award-winning journalist and bestselling author Cokie Roberts once said: As long as algebra is taught in school, there will be prayer in school. 1.1. An Object of Pride. Mathematician’s relationship with the general public most closely resembles “bipolar” disorder - at the same time they admire us and hate us. Almost everyone has had at least one bad experience with mathematics during some part of their education. Get into any taxi and tell the driver you are a mathematician and the response is predictable. First, there is silence while the driver relives his greatest nightmare - taking algebra. Next, you will hear the immortal words: “I was never any good at mathematics.” My response is: “I was never any good at being a taxi driver so I went into mathematics.” You can learn a lot from taxi drivers if you just don’t tell them you are a mathematician. Why get started on the wrong foot? The mathematician David Mumford put it: “I am accustomed, as a professional mathematician, to living in a sort of vacuum, surrounded by people who declare with an odd sort of pride that they are mathematically illiterate.” 1.2. A Balancing Act. The other most common response we get from the public is: “I can’t even balance my checkbook.” This reflects the fact that the public thinks that mathematics is basically just adding numbers. They have no idea what we really do. Because of the textbooks they studied, they think that all needed mathematics has already been discovered. -
Social Choice Theory Christian List
1 Social Choice Theory Christian List Social choice theory is the study of collective decision procedures. It is not a single theory, but a cluster of models and results concerning the aggregation of individual inputs (e.g., votes, preferences, judgments, welfare) into collective outputs (e.g., collective decisions, preferences, judgments, welfare). Central questions are: How can a group of individuals choose a winning outcome (e.g., policy, electoral candidate) from a given set of options? What are the properties of different voting systems? When is a voting system democratic? How can a collective (e.g., electorate, legislature, collegial court, expert panel, or committee) arrive at coherent collective preferences or judgments on some issues, on the basis of its members’ individual preferences or judgments? How can we rank different social alternatives in an order of social welfare? Social choice theorists study these questions not just by looking at examples, but by developing general models and proving theorems. Pioneered in the 18th century by Nicolas de Condorcet and Jean-Charles de Borda and in the 19th century by Charles Dodgson (also known as Lewis Carroll), social choice theory took off in the 20th century with the works of Kenneth Arrow, Amartya Sen, and Duncan Black. Its influence extends across economics, political science, philosophy, mathematics, and recently computer science and biology. Apart from contributing to our understanding of collective decision procedures, social choice theory has applications in the areas of institutional design, welfare economics, and social epistemology. 1. History of social choice theory 1.1 Condorcet The two scholars most often associated with the development of social choice theory are the Frenchman Nicolas de Condorcet (1743-1794) and the American Kenneth Arrow (born 1921). -
The "Greatest European Mathematician of the Middle Ages"
Who was Fibonacci? The "greatest European mathematician of the middle ages", his full name was Leonardo of Pisa, or Leonardo Pisano in Italian since he was born in Pisa (Italy), the city with the famous Leaning Tower, about 1175 AD. Pisa was an important commercial town in its day and had links with many Mediterranean ports. Leonardo's father, Guglielmo Bonacci, was a kind of customs officer in the North African town of Bugia now called Bougie where wax candles were exported to France. They are still called "bougies" in French, but the town is a ruin today says D E Smith (see below). So Leonardo grew up with a North African education under the Moors and later travelled extensively around the Mediterranean coast. He would have met with many merchants and learned of their systems of doing arithmetic. He soon realised the many advantages of the "Hindu-Arabic" system over all the others. D E Smith points out that another famous Italian - St Francis of Assisi (a nearby Italian town) - was also alive at the same time as Fibonacci: St Francis was born about 1182 (after Fibonacci's around 1175) and died in 1226 (before Fibonacci's death commonly assumed to be around 1250). By the way, don't confuse Leonardo of Pisa with Leonardo da Vinci! Vinci was just a few miles from Pisa on the way to Florence, but Leonardo da Vinci was born in Vinci in 1452, about 200 years after the death of Leonardo of Pisa (Fibonacci). His names Fibonacci Leonardo of Pisa is now known as Fibonacci [pronounced fib-on-arch-ee] short for filius Bonacci. -
The Astronomers Tycho Brahe and Johannes Kepler
Ice Core Records – From Volcanoes to Supernovas The Astronomers Tycho Brahe and Johannes Kepler Tycho Brahe (1546-1601, shown at left) was a nobleman from Denmark who made astronomy his life's work because he was so impressed when, as a boy, he saw an eclipse of the Sun take place at exactly the time it was predicted. Tycho's life's work in astronomy consisted of measuring the positions of the stars, planets, Moon, and Sun, every night and day possible, and carefully recording these measurements, year after year. Johannes Kepler (1571-1630, below right) came from a poor German family. He did not have it easy growing Tycho Brahe up. His father was a soldier, who was killed in a war, and his mother (who was once accused of witchcraft) did not treat him well. Kepler was taken out of school when he was a boy so that he could make money for the family by working as a waiter in an inn. As a young man Kepler studied theology and science, and discovered that he liked science better. He became an accomplished mathematician and a persistent and determined calculator. He was driven to find an explanation for order in the universe. He was convinced that the order of the planets and their movement through the sky could be explained through mathematical calculation and careful thinking. Johannes Kepler Tycho wanted to study science so that he could learn how to predict eclipses. He studied mathematics and astronomy in Germany. Then, in 1571, when he was 25, Tycho built his own observatory on an island (the King of Denmark gave him the island and some additional money just for that purpose). -
Mathematics and Materials
IAS/PARK CITY MATHEMATICS SERIES Volume 23 Mathematics and Materials Mark J. Bowick David Kinderlehrer Govind Menon Charles Radin Editors American Mathematical Society Institute for Advanced Study Society for Industrial and Applied Mathematics 10.1090/pcms/023 Mathematics and Materials IAS/PARK CITY MATHEMATICS SERIES Volume 23 Mathematics and Materials Mark J. Bowick David Kinderlehrer Govind Menon Charles Radin Editors American Mathematical Society Institute for Advanced Study Society for Industrial and Applied Mathematics Rafe Mazzeo, Series Editor Mark J. Bowick, David Kinderlehrer, Govind Menon, and Charles Radin, Volume Editors. IAS/Park City Mathematics Institute runs mathematics education programs that bring together high school mathematics teachers, researchers in mathematics and mathematics education, undergraduate mathematics faculty, graduate students, and undergraduates to participate in distinct but overlapping programs of research and education. This volume contains the lecture notes from the Graduate Summer School program 2010 Mathematics Subject Classification. Primary 82B05, 35Q70, 82B26, 74N05, 51P05, 52C17, 52C23. Library of Congress Cataloging-in-Publication Data Names: Bowick, Mark J., editor. | Kinderlehrer, David, editor. | Menon, Govind, 1973– editor. | Radin, Charles, 1945– editor. | Institute for Advanced Study (Princeton, N.J.) | Society for Industrial and Applied Mathematics. Title: Mathematics and materials / Mark J. Bowick, David Kinderlehrer, Govind Menon, Charles Radin, editors. Description: [Providence] : American Mathematical Society, [2017] | Series: IAS/Park City math- ematics series ; volume 23 | “Institute for Advanced Study.” | “Society for Industrial and Applied Mathematics.” | “This volume contains lectures presented at the Park City summer school on Mathematics and Materials in July 2014.” – Introduction. | Includes bibliographical references. Identifiers: LCCN 2016030010 | ISBN 9781470429195 (alk. paper) Subjects: LCSH: Statistical mechanics–Congresses. -
Msc in Applied Mathematics
MSc in Applied Mathematics Title: Past, Present and Challenges in Yang-Mills Theory Author: José Luis Tejedor Advisor: Sebastià Xambó Descamps Department: Departament de Matemàtica Aplicada II Academic year: 2011-2012 PAST, PRESENT AND CHALLENGES IN YANG-MILLS THEORY Jos´eLuis Tejedor June 11, 2012 Abstract In electrodynamics the potentials are not uniquely defined. The electromagnetic field is un- changed by gauge transformations of the potential. The electromagnestism is a gauge theory with U(1) as gauge group. C. N. Yang and R. Mills extended in 1954 the concept of gauge theory for abelian groups to non-abelian groups to provide an explanation for strong interactions. The idea of Yang-Mills was criticized by Pauli, as the quanta of the Yang-Mills field must be massless in order to maintain gauge invariance. The idea was set aside until 1960, when the concept of particles acquiring mass through symmetry breaking in massless theories was put forward. This prompted a significant restart of Yang-Mills theory studies that proved succesful in the formula- tion of both electroweak unification and quantum electrodynamics (QCD). The Standard Model combines the strong interaction with the unified electroweak interaction through the symmetry group SU(3) ⊗ SU(2) ⊗ U(1). Modern gauge theory includes lattice gauge theory, supersymme- try, magnetic monopoles, supergravity, instantons, etc. Concerning the mathematics, the field of Yang-Mills theories was included in the Clay Mathematics Institute's list of \Millenium Prize Problems". This prize-problem focuses, especially, on a proof of the conjecture that the lowest excitations of a pure four-dimensional Yang-Mills theory (i.e. -
Newton.Indd | Sander Pinkse Boekproductie | 16-11-12 / 14:45 | Pag
omslag Newton.indd | Sander Pinkse Boekproductie | 16-11-12 / 14:45 | Pag. 1 e Dutch Republic proved ‘A new light on several to be extremely receptive to major gures involved in the groundbreaking ideas of Newton Isaac Newton (–). the reception of Newton’s Dutch scholars such as Willem work.’ and the Netherlands Jacob ’s Gravesande and Petrus Prof. Bert Theunissen, Newton the Netherlands and van Musschenbroek played a Utrecht University crucial role in the adaption and How Isaac Newton was Fashioned dissemination of Newton’s work, ‘is book provides an in the Dutch Republic not only in the Netherlands important contribution to but also in the rest of Europe. EDITED BY ERIC JORINK In the course of the eighteenth the study of the European AND AD MAAS century, Newton’s ideas (in Enlightenment with new dierent guises and interpre- insights in the circulation tations) became a veritable hype in Dutch society. In Newton of knowledge.’ and the Netherlands Newton’s Prof. Frans van Lunteren, sudden success is analyzed in Leiden University great depth and put into a new perspective. Ad Maas is curator at the Museum Boerhaave, Leiden, the Netherlands. Eric Jorink is researcher at the Huygens Institute for Netherlands History (Royal Dutch Academy of Arts and Sciences). / www.lup.nl LUP Newton and the Netherlands.indd | Sander Pinkse Boekproductie | 16-11-12 / 16:47 | Pag. 1 Newton and the Netherlands Newton and the Netherlands.indd | Sander Pinkse Boekproductie | 16-11-12 / 16:47 | Pag. 2 Newton and the Netherlands.indd | Sander Pinkse Boekproductie | 16-11-12 / 16:47 | Pag. -
Mathematical Economics - B.S
College of Mathematical Economics - B.S. Arts and Sciences The mathematical economics major offers students a degree program that combines College Requirements mathematics, statistics, and economics. In today’s increasingly complicated international I. Foreign Language (placement exam recommended) ........................................... 0-14 business world, a strong preparation in the fundamentals of both economics and II. Disciplinary Requirements mathematics is crucial to success. This degree program is designed to prepare a student a. Natural Science .............................................................................................3 to go directly into the business world with skills that are in high demand, or to go on b. Social Science (completed by Major Requirements) to graduate study in economics or finance. A degree in mathematical economics would, c. Humanities ....................................................................................................3 for example, prepare a student for the beginning of a career in operations research or III. Laboratory or Field Work........................................................................................1 actuarial science. IV. Electives ..................................................................................................................6 120 hours (minimum) College Requirement hours: ..........................................................13-27 Any student earning a Bachelor of Science (BS) degree must complete a minimum of 60 hours in natural, -
Famous Mathematicians Key
Infinite Secrets AIRING SEPTEMBER 30, 2003 Learning More Dzielska, Maria. Famous Mathematicians Hypatia of Alexandria. Cambridge, MA: Harvard University The history of mathematics spans thousands of years and touches all parts of the Press, 1996. world. Likewise, the notable mathematicians of the past and present are equally Provides a biography of Hypatia based diverse.The following are brief biographies of three mathematicians who stand out on several sources,including the letters for their contributions to the fields of geometry and calculus. of Hypatia’s student Synesius. Hypatia of Alexandria Bhaskara wrote numerous papers and Biographies of Women Mathematicians books on such topics as plane and spherical (c. A.D. 370–415 ) www.agnesscott.edu/lriddle/women/ Born in Alexandria, trigonometry, algebra, and the mathematics women.htm of planetary motion. His most famous work, Contains biographical essays and Egypt, around A.D. 370, Siddhanta Siromani, was written in A.D. comments on woman mathematicians, Hypatia was the first 1150. It is divided into four parts: “Lilavati” including Hypatia. Also includes documented female (arithmetic), “Bijaganita” (algebra), resources for further study. mathematician. She was ✷ ✷ ✷ the daughter of Theon, “Goladhyaya” (celestial globe), and a mathematician who “Grahaganita” (mathematics of the planets). Patwardhan, K. S., S. A. Naimpally, taught at the school at the Alexandrine Like Archimedes, Bhaskara discovered and S. L. Singh. Library. She studied astronomy, astrology, several principles of what is now calculus Lilavati of Bhaskaracharya. centuries before it was invented. Also like Delhi, India:Motilal Banarsidass, 2001. and mathematics under the guidance of her Archimedes, Bhaskara was fascinated by the Explains the definitions, formulae, father.She became head of the Platonist concepts of infinity and square roots. -
Priorities for the National Science Foundation
December 2020 Priorities for the National Science Foundation Founded in 1888, the American Mathematical Society (AMS) is dedicated to advancing the interests of mathematical research and scholarship and connecting the diverse global mathematical community. We do this through our book and journal publications, meetings and conferences, database of research publications1 that goes back to the early 1800s, professional services, advocacy, and awareness programs. The AMS has 30,000 individual members worldwide and supports mathemat- ical scientists at every career stage. The AMS advocates for increased and sustained funding for the National Science Foundation (NSF). The applications The NSF supports more fundamental research in the of advances in mathematical sciences—and done at colleges and theoretical science, 2 universities—than any other federal agency. A signif- including theory of icant increase in Congressional appropriations would mathe matics, occur help address the effects of years of high-quality grant on a time scale that proposals that go unfunded due to limited funding. means the investment Those unmet needs continue. A 2019 National Science Board report3 stated that in fiscal year 2018, “approxi- is often hard to justify mately $3.4 billion was requested for declined proposals in the short run. that were rated Very Good or higher in the merit review process.” This accounts for about 5440 declined proposals at the NSF. The U.S. is leaving potentially transformative scientific research unfunded, while other countries are making significant investments. In the next section we give an overview of our two priorities. The second, and final section offers a discussion of existing funding mechanisms for mathematicians. -
Professor Shiing Shen CHERN Citation
~~____~__~~Doctor_~______ of Science honoris cau5a _-___ ____ Professor Shiing Shen CHERN Citation “Not willing to yield to the saints of ancient mathematics. In his own words, his objective is and modem times / He alone ascends the towering to bring about a situation in which “Chinese height.” This verse, written by Professor Wu-zhi mathematics is placed on a par with Western Yang, the father of Nobel Laureate in Physics mathematics and is independent of the latter. That Professor Chen-Ning Yang, to Professor Shiing Shen is, Chinese mathematics must be on the same level CHERN, fully reflects the high achievements as its Western counterpart, though not necessarily attained by Professor Chern during a career that bending its efforts in the same direction.” has spanned over 70 years. Professor Chern was born in Jiaxing, Zhejiang Professor Chern has dedicated his life to the Province in 1911, and displayed considerable study of mathematics. In his early thirties, he mathematical talent even as a child. In 1930, after realized the importance of fiber bundle structure. graduating from the Department of Mathematics From an entirely new perspective, he provided a at Nankai University, he was admitted to the simple intrinsic proof of the Gauss-Bonnet Formula graduate school of Tsinghua University. In 1934, 24 and constructed the “Chern Characteristic Classes”, he received funding to study in Hamburg under thus laying a solid foundation for the study of global the great master of geometry Professor W Blaschke, differential geometry as a whole. and completed his doctoral dissertation in less than a year. -
An Outstanding Mathematician Sergei Ivanovich Adian Passed Away on May 5, 2020 in Moscow at the Age of 89
An outstanding mathematician Sergei Ivanovich Adian passed away on May 5, 2020 in Moscow at the age of 89. He was the head of the Department of Mathematical Logic at Steklov Mathematical Institute of the Russian Academy of Sciences (since 1975) and Professor of the Department of Mathematical Logic and Theory of Algorithms at the Mathematics and Mechanics Faculty of Moscow M.V. Lomonosov State University (since 1965). Sergei Adian is famous for his work in the area of computational problems in algebra and mathematical logic. Among his numerous contributions two major results stand out. The first one is the Adian—Rabin Theorem (1955) on algorithmic unrecognizability of a wide class of group-theoretic properties when the group is given by finitely many generators and relators. Natural properties covered by this theorem include those of a group being trivial, finite, periodic, and many others. A simpler proof of the same result was obtained by Michael Rabin in 1958. Another seminal contribution of Sergei Adian is his solution, together with his teacher Petr Novikov, of the famous Burnside problem on periodic groups posed in 1902. The deluding simplicity of its formulation fascinated and attracted minds of mathematicians for decades. Is every finitely generated periodic group of a fixed exponent n necessarily finite? Novikov—Adian Theorem (1968) states that for sufficiently large odd numbers n this is not the case. By a heroic effort, in 1968 Sergei Adian finished the solution of Burnside problem initiated by his teacher Novikov, having overcome in its course exceptional technical difficulties. Their proof was arguably one of the most difficult proofs in the whole history of Mathematics.