Part III of the Mathematical Tripos
Part III of the Mathematical Tripos is a one-year Masters-level taught course in mathematics offered at the Faculty of Mathematics, University of Cambridge. It is regarded as one of the hardest and most intensive mathematics courses in the world and is taken by 200 students each year. One third of the students take the course as a fourth year of mathematical study at Cambridge, whilst the remaining two thirds take the course as a one-year course; the Smith's Prize Examination was founded by bequest of Robert Smith upon his death in 1768 to encourage the study of more advanced mathematics than that found in the undergraduate course. T. W. Körner notes Only a small handful of students took the Smith's prize examination in the nineteenth century; when Karl Pearson took the examination in 1879, the examiners were Stokes, Maxwell and Todhunter and the examinees went on each occasion to the examiner's house, did a morning paper, had lunch there, continued their work on the paper in the afternoon.
In 1883 this was replaced by an exam called Part III and the Smith's Prize awarded for an essay rather than examination. In 1886 this exam was renamed Part II, in 1909 Part II, Schedule B. In 1934 it was again renamed Part III. In the 1980s the Certificate of Advanced Study in Mathematics was introduced. All who have passed the course since 1962 are entitled to these new degrees; the first retrospective M. Math and M. A. St. Degrees were conferred as part of a celebration of the University's 800th anniversary; the course is still referred to as Part III. Students who have completed their undergraduate degree at Cambridge will be awarded both a Bachelor of Arts and the Master of Mathematics degree for four years of study, provided they have not graduated with a B. A; this allows. Progression from Part II of the Mathematical Tripos to Part III requires either a first in Part II or good performances in Parts IB and Part II. Students who complete Part III of the Mathematical Tripos, but did not complete undergraduate studies at Cambridge will be awarded the Master of Advanced Study in Mathematics degree for the one-year course.
The program resulted in a Certificate of Advanced Study in Mathematics instead of a Master's degree. The course lasts one year, divided into three eight-week terms. There are a wide variety of lectures on both pure and applied maths concentrated in the first two terms; the third term is for examinations which, together with the option of writing a part III essay, determine one's final grade entirely. The grades available are Fail, Pass and Distinction. Cambridge recognises that in Part III of the mathematical tripos a merit is equivalent to a First Class in the other parts of the Tripos; the level of achievement required for a distinction is yet higher. Traditionally, results are announced in the University's Senate House. Standing on the balcony, the examiner reads out the class results for each student, printed copies of the results are thrown to the audience below; the students' exact rankings are no longer announced, but highest-ranked student is still identified, nowadays by the tipping of the examiner's academic hat when the relevant name is read out.
In addition to the grades, there are five associated prizes. Four of these may be awarded at the discretion of the examiners: the Mayhew Prize for Applied Mathematics, the Tyson Medal for mathematics and astronomy, the Bartlett Prize for applied probability and the Wishart Prize for statistics. Several notable astronomers and astrophysicists have been awarded the Tyson Medal in the history of Part III maths, including Jayant Narlikar, Ray Lyttleton and Edmund Whittaker. In addition, the Thomas Bond Sprague Prize is awarded by the Rollo Davidson Trust for distinguished performance in actuarial science, insurance, mathematics of operational research, probability and statistics
Université de Montréal
The Université de Montréal is a French-language public research university in Montreal, Canada. The university's main campus is located on the northern slope of Mount Royal in the Outremont and Côte-des-Neiges boroughs; the institution comprises thirteen faculties, more than sixty departments and two affiliated schools: the Polytechnique Montréal and HEC Montréal. It offers more than 650 undergraduate programmes and graduate programmes, including 71 doctoral programmes; the university was founded as a satellite campus of the Université Laval in 1878. It became a independent institution after it was issued a papal charter in 1919, a provincial charter in 1920. Université de Montréal moved from Montreal's Quartier Latin to its present location at Mount Royal in 1942, it was made a secular institution with the passing of another provincial charter in 1967. The school is co-educational, has over 34,335 undergraduate and over 11,925 post-graduate students. Alumni and former students reside across Canada and around the world, with notable alumni serving as government officials and business leaders.
The Université de Montréal was founded in 1878 as a new branch of Université Laval in Quebec City. It was known as the Université de Laval à Montréal; the move went against the wishes of Montréal's prelate, who advocated an independent university in his city. Certain parts of the institution's educational facilities, such as those of the Séminaire de Québec and the Faculty of Medicine, founded as the Montreal School of Medicine and Surgery, had been established in Montréal in 1876 and 1843, respectively; the Vatican granted the university some administrative autonomy in 1889, thus allowing it to choose its own professors and license its own diplomas. However, it was not until 8 May 1919 that a papal charter from Pope Benedict XV granted full autonomy to the university, it thus adopted Université de Montréal as its name. Université de Montréal was granted its first provincial charter on 14 February 1920. At the time of its creation, less than a hundred students were admitted to the university's three faculties, which at that time were located in Old Montreal.
These were the Faculty of Theology, the Faculty of Law, the Faculty of Medicine. Graduate training based on German-inspired American models of specialized coursework and completion of a research thesis was introduced and adopted. Most of Québec's secondary education establishments employed classic course methods of varying quality; this forced the university to open a preparatory school in 1887 to harmonize the education level of its students. Named the "Faculty of Arts", this school would remain in use until 1972 and was the predecessor of Québec's current CEGEP system. Two distinct schools became affiliated to the university; the first was the École Polytechnique, a school of engineering, founded in 1873 and became affiliated in 1887. The second was the École des Hautes Études Commerciales, or HEC, founded in 1907 and became part of the university in 1915. In 1907, Université de Montréal opened the first francophone school of architecture in Canada at the École Polytechnique. Between 1920 and 1925, seven new faculties were added: Philosophy, Sciences, Veterinary Medicine, Dental Surgery and Social Sciences.
Notably, the Faculty of Social Sciences was founded in 1920 by Édouard Montpetit, the first laic to lead a faculty. He thereafter was named secretary-general, a role he fulfilled until 1950. From 1876 to 1895, most classes took place in the Grand séminaire de Montréal. From 1895 to 1942, the school was housed in a building at the intersection of Saint-Denis and Sainte-Catherine streets in Montreal's eastern downtown Quartier Latin. Unlike English-language universities in Montréal, such as McGill University, Université de Montréal suffered a lack of funding for two major reasons: the relative poverty of the French Canadian population and the complications ensuing from its being managed remotely, from Quebec City; the downtown campus was hit by three different fires between 1919 and 1921, further complicating the university's precarious finances and forcing it to spend much of its resources on repairing its own infrastructure. By 1930, enough funds had been accumulated to start the construction of a new campus on the northwest slope of Mount Royal, adopting new plans designed by Ernest Cormier.
However, the financial crisis of the 1930s suspended all ongoing construction. Many speculated that the university would have to sell off its unfinished building projects in order to ensure its own survival. Not until 1939 did the provincial government directly intervene by injecting public funds; the campus's construction subsequently resumed and the mountain campus was inaugurated on 3 June 1943. The Cote-des-Neiges site includes property expropriated from a residential development along Decelles Avenue, known as Northmount Heights; the university's former downtown facilities would serve Montreal's second francophone university, the Université du Québec à Montréal. In 1943, the university assisted the Western Allies by providing laboratory accommodations on its campus. Scientists there worked to develop a nuclear reactor, notably by conducting various heavy water experiments; the research was part of the larger Manhattan Project. Scientists working on the school's campus produced the first atomic batte
Paulo Ribenboim is a Brazilian-Canadian mathematician who specializes in number theory. A native of Recife of Jewish origin, Paulo Ribenboim married in the year of 1951 with the young Catholic Huguette Demangelle, in the French city of Nancy, they have five grandchildren. And has lived in Canada since 1962, he has authored 246 publications including 13 books. Ribenboim has been a professor of mathematics at Queen's University in Kingston, is now a professor emeritus. Jean Dieudonné was one of his doctoral advisors. Andrew Granville has been a doctoral student of Ribenboim; the Ribenboim Prize of the Canadian Number Theory Association is named after him. Paulo Ribenboim Rings and Modules, Interscience Publishers. Paulo Ribenboim.. The Book of Prime Number Records. Springer. ISBN 978-0-387-97042-4. Paulo Ribenboim.. 13 Lectures on Fermat's Last Theorem. Springer-Verlag. ISBN 978-0-387-90432-0. Paulo Ribenboim.. The New Book of Prime Number Records. Springer-Verlag. ISBN 978-0-387-94457-9. Collected Papers of Paulo Ribenboim.
Queens Univ Campus. 1997. ISBN 978-0-88911-735-8. Paulo Ribenboim.. The Little Book of Big Primes. Springer-Verlag. ISBN 978-0-387-97508-5. Paulo Ribenboim.. The Theory of Classical Valuations. Springer-Verlag. ISBN 978-0-387-98525-1. Paulo Ribenboim.. My Numbers, My Friends: Popular Lectures on Number Theory. Springer-Verlag. ISBN 978-0-387-98911-2. Paulo Ribenboim.. Fermat's Last Theorem for Amateurs. Springer-Verlag. ISBN 978-0-387-98508-4. Paulo Ribenboim.. Classical Theory of Algebraic Numbers. Springer-Verlag. ISBN 978-0-387-95070-9. Paulo Ribenboim.. The Little Book of Bigger Primes. Springer-Verlag. ISBN 978-0-387-20169-6. Paulo Ribenboim.. Prime Numbers, Friends Who Give Problems: A Trialogue with Papa Paulo. World-Scientific. ISBN 978-9-814-72581-1. Paulo Ribenboim at the Mathematics Genealogy Project The Canadian Number Theory Association Ribenboim Prize
Peter David Lax is a Hungarian-born American mathematician working in the areas of pure and applied mathematics. Lax has made important contributions to integrable systems, fluid dynamics and shock waves, solitonic physics, hyperbolic conservation laws, mathematical and scientific computing, among other fields. Lax is listed as an ISI cited researcher. According to György Marx he was one of The Martians. In a 1958 paper Lax stated a conjecture about matrix representations for third order hyperbolic polynomials which remained unproven for over four decades. Interest in the "Lax conjecture" grew as mathematicians working in several different areas recognized the importance of its implications in their field, until it was proven to be true in 2003. Lax was born in Hungary to a Jewish family. Lax began displaying an interest in mathematics at age twelve, soon his parents hired Rózsa Péter as a tutor for him, his parents Klara Kornfield and Henry Lax were both physicians and his uncle Albert Kornfeld was a mathematician, as well as a friend of Leó Szilárd.
The family left Hungary on November 15, 1941, traveled via Lisbon to the United States. As a high school student at Stuyvesant High School, Lax took no math classes but did compete on the school math team. During this time, he met with John von Neumann, Richard Courant, Paul Erdős, who introduced him to Albert Einstein; as he was still 17 when he finished high school, he could avoid military service, was able to study for three semesters at New York University. He attended a complex analysis class in the role of a student, but ended up taking over as instructor, he met Anneli Cahn in this class. Before being able to complete his studies, Lax was drafted into the U. S. Army. After basic training, the Army sent him to Texas A&M University for more studies, he was sent to Oak Ridge National Laboratory, soon afterwards to the Manhattan Project at Los Alamos, New Mexico. At Los Alamos, he began working as a calculator operator, but moved on to higher-level mathematics. After the war ended, he remained with the Army at Los Alamos for another year, while taking courses at the University of New Mexico studied at Stanford University for a semester with Gábor Szegő and George Pólya.
Lax returned to NYU for the 1946–1947 academic year, by pooling credits from the four universities at which he had studied, he graduated that year. He stayed at NYU for his graduate studies, marrying Anneli in 1948 and earning a Ph. D. in 1949 under the supervision of Kurt O. Friedrichs. Lax holds a faculty position in the Department of Mathematics, Courant Institute of Mathematical Sciences, New York University, he is a member of the Norwegian Academy of Science and Letters and the National Academy of Sciences, USA. He won a Lester R. Ford Award in 1966 and again in 1973, he was awarded the National Medal of Science in 1986, the Wolf Prize in 1987, the Abel Prize in 2005 and the Lomonosov Gold Medal in 2013. The American Mathematical Society selected him as its Gibbs Lecturer for 2007. In 2012 he became a fellow of the American Mathematical Society. Lax received an Honorary Doctorate from Heriot-Watt University in 1990 In 1970, the Transcendental Students took a CDC 6600 super computer hostage at NYU's Courant Institute which Lax had been instrumental in acquiring.
Some of the students present members of the Weathermen, threatened to destroy the computer with incendiary devices, but Lax managed to disable the devices and save the machine. Complex Proofs of Real Theorems, with Lawrence Zalcman, University Lecture Series, 2012. Linear Algebra and Its Applications, 2nd ed. Wiley-Interscience, New York. Hyperbolic Partial Differential Equations, American Mathematical Society/Courant Institute of Mathematical Sciences. Scattering Theory, with R. S. Phillips, Academic Press, ISBN 0-12-440051-5. Hyperbolic Systems of Conservation Laws and the Mathematical Theory of Shock Waves, Society for Industrial Mathematics. Decay of Solutions of Systems of Nonlinear Hyperbolic Conservation Laws, with J. Glimm, American Mathematical Society. Recent Mathematical Methods in Nonlinear Wave Propagation, with G. Boillat, C. M. Dafermos, T.-P. Liu, T. Ruggeri, Springer. Scattering Theory for Automorphic Functions with R. S. Phillips, Princeton Univ. Press. Calculus with Applications and Computing, with S. Burstein and A. Lax, Springer-Verlag, New York.
Recent Advances in Partial Differential Equations Mathematical Aspects of Production and Distribution of Energy Nonlinear Partial Differential Equations in Applied Science Lax, Peter D.. Selected papers. Vol. I. Berlin, New York: Springer-Verlag. ISBN 978-0-387-22925-6. MR 2164867 Lax, Peter D.. Selected papers. Vol. II. Berlin, New York: Springer-Verlag. ISBN 978-0-387-22926-3. MR 2164868 Lax pair Lax–Milgram theorem Lax–Friedrichs method Lax–Wendroff method Lax–Richtmyer theorem called Lax equivalence theorem Babuška–Lax–Milgram theorem Undercompressive shock wave The Martians 2016 Video Interview with Peter Lax by Atomic Heritage Foundation Voices of the Manhattan Project Peter Lax at the Mathematics Genealogy Project O'Connor, John J.. Elements from his contributions to mathematics. Popularised presentation of Peter Lax by Helge Holden, published on the Abel Prize website. Abel Prize press release and biography Dreifus, C.. "A Conversation with Peter Lax: From Budapest to Los Alamos, a Life in Mathematics".
New York Times. Raussen, M
German National Library of Science and Technology
The German National Library of Science and Technology, abbreviated TIB, is the national library of the Federal Republic of Germany for all fields of engineering and the natural sciences. It is jointly funded by the Federal Ministry of the 16 German states. Founded in 1959, the library operates in conjunction with the Leibniz Universität Hannover. In addition to acquiring scientific literature, it conducts applied research in such areas as the archiving of non-textual materials, data visualization and the future Internet; the library is involved in a number of open access initiatives. With a collection of over 9 million items in 2017, the TIB is the largest science and technology library in the world; the TIB acquires literature in all engineering fields as well as architecture, information technology, mathematics and other basic sciences. It is a particular specialist in the acquisition of "gray literature", difficult to obtain and not available via the standard book or journal trade, it holds a large number of standards, patents, source data, scientific conference proceedings, government research papers and dissertations.
Special collections include the "Albrecht Haupt Collection" of digitally rendered architectural drawings and a regional focus on technical literature from East Asia and Eastern Europe. The film and audiovisual material held by IWF Wissen und Medien is now by TIB. In 2011 its holdings were: 8,900,000 books, journal titles, digital items5.500.000 books 3.400.000 micro-materials 78.000 individual digital documents 46.000 E-journals 17.000 specialized journals 3.500 specialized databases 15,750,000 patent documents and standardsThe physical collection occupies 125 kilometers of shelving. In 2005 the TIB became the world's first Digital Object Identifier registration agency for research data sets in the fields of technology, natural sciences and medicine. Today it offers registration for the results of any publicly funded research conducted in Europe; the TIB is a legal deposit library for research projects sponsored by various agencies of the German Federal Government, in particular: Federal Ministry of Education and Research Federal Ministry of Economics and Technology in the areas of energy and aerospace research Federal Ministry for the Environment, Nature Conservation and Nuclear Safety in energy research and energy technologies Agency for Renewable Resources on behalf of the Federal Ministry of Food and Consumer Protection The TIB is a member of the Leibniz Association, a consortium of 87 non-university research institutes in Germany.
In support of the Association's open access goals, the TIB operates the LeibnizOpen repository in cooperation with Leibniz Institute for Information Infrastructure Fachinformationszentrum Karlsruhe. The TIB advises the Leibniz Association's various member organizations and staff on depositing publications in the repository according to open access guidelines; the amount and importance of non-textual materials such as 3D models, AV media and research data is continually increasing and only a small proportion can be searched at the present time. The goal of the TIB Competence Centre for Non-Textual Materials is to fundamentally improve access to, the use of, such non-textual materials; the TIB develops new multimedia analysis methods such as morphology, speech or structure recognition to create indexing and metadata to help researchers and educators make better use of these complex materials. In addition, the competence center is dedicated to the preservation of multimedia objects, the assignment of DOI and knowledge transfer.
TIB operates the GetInfo portal for science and technology with interdisciplinary search capabilities for the other German National Libraries as well as access to more than 150 million data sets from other specialized databases and library catalogs. The TIB makes scientific videos of lectures, computer animations and experiments available via GetInfo; these video items can be downloaded via Flash Player. The TIB partners with a variety of national and international libraries and associations; the TIB is one of three partners in the Leibniz Library Network for Research Information consortium Goportis, the others being the German National Library of Economics and German National Library of Medicine. This initiative develops and operates online search services, online full-text delivery services, licensing agreements, non-textual materials, document preservation efforts, data storage, open access; the TIB is the scientific information provider for researchers in the newly independent states of the former USSR, including Azerbaijan, Kazakhstan, Kyrgyzstan and the Ukraine.
It collaborates with numerous organizations in China and Eastern Europe. Notable institutional partnerships include: Chinese Academy of Beijing DataCite e. V. German Physical Society Library of the Delft University of Technology, Netherlands National Library of Science and Technology, Ukraine Online Computer Library Center, United States Russian Academy of Natural Sciences, Russia Russian National Public Library for Science and Technology, Russia Swiss Federal Institute of Technology Zurich, Zürich, Switzerland International Association of Technological University Libraries As part of the German national research infrastructure, the TIB conducts its own applied resea
Mark Kac was a Polish American mathematician. He was born to a Polish-Jewish family, his main interest was probability theory. His question, "Can one hear the shape of a drum?" set off research into spectral theory, with the idea of understanding the extent to which the spectrum allows one to read back the geometry. Kac completed his Ph. D. in mathematics at the Polish University of Lwów in 1937 under the direction of Hugo Steinhaus. While there, he was a member of the Lwów School of Mathematics. After receiving his degree he began to look for a position abroad, in 1938 was granted a scholarship from the Parnas Foundation which enabled him to go work in the United States, he arrived in New York City in November, 1938. With the onset of World War II, Kac was able to stay in America, while his parents and brother who remained in Western Ukraine were murdered by the Germans in the mass executions in Krzemieniec in August 1942. From 1939-61 he was at Cornell University, first as an instructor from 1943 as assistant professor and from 1947 as full professor.
While there, he became a naturalized US citizen in 1943. In the academic year 1951–1952 Kac was on sabbatical at the Institute for Advanced Study. In 1952, with Theodore H. Berlin, introduced the spherical model of a ferromagnet and, with J. C. Ward, found an exact solution of the Ising model using a combinatorial method. In 1961 he went to The Rockefeller University in New York City. In the early 1960s he worked with George Uhlenbeck and P. C. Hemmer on the mathematics of a van der Waals gas. After twenty years at Rockefeller, he moved to the University of Southern California where he spent the rest of his career. In his 1966 article with the title "Can one hear the shape of the drum" Kac asked the question whether two resonators of different geometrical shapes can have the same set of frequencies; the answer was positive, meaning that the eigenfrequency set does not uniquely characterize the shape of a resonator. His definition of a profound truth. "A truth is a statement. A profound truth is a truth whose negation is a profound truth."
He preferred to work on results that were robust, meaning that they were true under many different assumptions and not the accidental consequence of a set of axioms. Kac's "proofs" consisted of a series of worked examples that illustrated the important cases; when Kac and Richard Feynman were both Cornell faculty, Kac attended a lecture of Feynman's and remarked that the two of them were working on the same thing from different directions. The Feynman-Kac formula resulted; the complex case, which occurs when a particle's spin is included, is still unproven. Kac had learned Wiener processes by reading Norbert Wiener's original papers, which were "the most difficult papers I have read." Brownian motion is a Wiener process. Feynman's path integrals are another example. Kac's distinction between an "ordinary genius" like Hans Bethe and a "magician" like Richard Feynman has been quoted. Kac became interested in the occurrence of statistical independence without randomness; as an example of this, he gave a lecture on the average number of factors.
This wasn't random in the strictest sense of the word, because it refers to the average number of prime divisors of the integers up to N as N goes to infinity, predetermined. He could see that the answer was c log log N, if you assumed that the number of prime divisors of two numbers x and y were independent, but he was unable to provide a complete proof of independence. Paul Erdős was in the audience and soon finished the proof using sieve theory, the result became known as the Erdős–Kac theorem, they more or less created the subject of probabilistic number theory. Kac sent Erdős a list of his publications, one of his papers contained the word "capacitor" in the title. Erdős wrote back to him "I pray for your soul." 1950 — Chauvenet Prize for 1947 expository article 1959 – member of the American Academy of Arts and Sciences 1965 – member of the National Academy of Sciences 1968 – Chauvenet Prize for 1966 expository article 1971 – Solvay Lecturer at Brussels 1980 – Fermi Lecturer at the Scuola Normale, Pisa Mark Kac and Stanislaw Ulam: Mathematics and Logic: Retrospect and Prospects, New York Dover paperback reprint.
Mark Kac, Statistical Independence in Probability and Number Theory, Carus Mathematical Monographs, Mathematical Association of America, 1959. Mark Kac and related topics in the physical sciences. 1959. Mark Kac, Enigmas of Chance: An Autobiography and Row, New York, 1985. Sloan Foundation Series. Published posthumously with a memoriam note by Gian-Carlo Rota. Feynman–Kac formula Erdős–Kac theorem O'Connor, John J.. Mark Kac at the Mathematics Genealogy Project National Academy of Sciences Biographical Memoir