The Rise of Projective Geometry
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Mathematical Tripos 2020/2021 Guide to Courses in Part Ia
MATHEMATICAL TRIPOS 2021/2022 GUIDE TO COURSES IN PART IA This booklet provides an introduction for new students, giving an outline of the first year with informal and non-technical descriptions of the courses. It is intended to supplement the more formal descriptions contained in the booklet Schedules of Lecture Courses and Form of Examinations. These and other Faculty documents for students taking the Mathematical Tripos are available from http://www.maths.cam.ac.uk/undergrad/ Revised 6th September 2021 1 Introduction The Mathematical Tripos consists of Parts IA, IB and II, taken in successive years, with an optional fourth year, Part III, taken by students who do sufficiently well. Those who successfully complete three years are eligible to graduate with a BA honours degree, while those who go on to complete the additional fourth year graduate with both BA honours and MMath degrees. Unlike many degree courses, the Mathematical Tripos is not modular (at least in its first three years). It is tightly structured, with no choice in the first year, some choice in the second year, and a very wide choice in the third year. The examinations (especially in the second and third years) are cross-sectional, meaning that instead of each lecture course having a dedicated examination paper, each examination paper has questions on many lecture courses. The flexibility that this allows students is considered by the Faculty to be one of the great strengths of the Tripos. This booklet provides an introduction for new students, with an outline of Part IA and informal descrip- tions of the courses. -
James Clerk Maxwell
James Clerk Maxwell JAMES CLERK MAXWELL Perspectives on his Life and Work Edited by raymond flood mark mccartney and andrew whitaker 3 3 Great Clarendon Street, Oxford, OX2 6DP, United Kingdom Oxford University Press is a department of the University of Oxford. It furthers the University’s objective of excellence in research, scholarship, and education by publishing worldwide. Oxford is a registered trade mark of Oxford University Press in the UK and in certain other countries c Oxford University Press 2014 The moral rights of the authors have been asserted First Edition published in 2014 Impression: 1 All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, without the prior permission in writing of Oxford University Press, or as expressly permitted by law, by licence or under terms agreed with the appropriate reprographics rights organization. Enquiries concerning reproduction outside the scope of the above should be sent to the Rights Department, Oxford University Press, at the address above You must not circulate this work in any other form and you must impose this same condition on any acquirer Published in the United States of America by Oxford University Press 198 Madison Avenue, New York, NY 10016, United States of America British Library Cataloguing in Publication Data Data available Library of Congress Control Number: 2013942195 ISBN 978–0–19–966437–5 Printed and bound by CPI Group (UK) Ltd, Croydon, CR0 4YY Links to third party websites are provided by Oxford in good faith and for information only. -
The Cambridge Mathematical Journal and Its Descendants: the Linchpin of a Research Community in the Early and Mid-Victorian Age ✩
View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by Elsevier - Publisher Connector Historia Mathematica 31 (2004) 455–497 www.elsevier.com/locate/hm The Cambridge Mathematical Journal and its descendants: the linchpin of a research community in the early and mid-Victorian Age ✩ Tony Crilly ∗ Middlesex University Business School, Hendon, London NW4 4BT, UK Received 29 October 2002; revised 12 November 2003; accepted 8 March 2004 Abstract The Cambridge Mathematical Journal and its successors, the Cambridge and Dublin Mathematical Journal,and the Quarterly Journal of Pure and Applied Mathematics, were a vital link in the establishment of a research ethos in British mathematics in the period 1837–1870. From the beginning, the tension between academic objectives and economic viability shaped the often precarious existence of this line of communication between practitioners. Utilizing archival material, this paper presents episodes in the setting up and maintenance of these journals during their formative years. 2004 Elsevier Inc. All rights reserved. Résumé Dans la période 1837–1870, le Cambridge Mathematical Journal et les revues qui lui ont succédé, le Cambridge and Dublin Mathematical Journal et le Quarterly Journal of Pure and Applied Mathematics, ont joué un rôle essentiel pour promouvoir une culture de recherche dans les mathématiques britanniques. Dès le début, la tension entre les objectifs intellectuels et la rentabilité économique marqua l’existence, souvent précaire, de ce moyen de communication entre professionnels. Sur la base de documents d’archives, cet article présente les épisodes importants dans la création et l’existence de ces revues. 2004 Elsevier Inc. -
James Joseph Sylvester1
Chapter 8 JAMES JOSEPH SYLVESTER1 (1814-1897) James Joseph Sylvester was born in London, on the 3d of September, 1814. He was by descent a Jew. His father was Abraham Joseph Sylvester, and the future mathematician was the youngest but one of seven children. He received his elementary education at two private schools in London, and his secondary education at the Royal Institution in Liverpool. At the age of twenty he entered St. John’s College, Cambridge; and in the tripos examination he came out sec- ond wrangler. The senior wrangler of the year did not rise to any eminence; the fourth wrangler was George Green, celebrated for his contributions to mathe- matical physics; the fifth wrangler was Duncan F. Gregory, who subsequently wrote on the foundations of algebra. On account of his religion Sylvester could not sign the thirty-nine articles of the Church of England; and as a consequence he could neither receive the degree of Bachelor of Arts nor compete for the Smith’s prizes, and as a further consequence he was not eligible for a fellowship. To obtain a degree he turned to the University of Dublin. After the theological tests for degrees had been abolished at the Universities of Oxford and Cam- bridge in 1872, the University of Cambridge granted him his well-earned degree of Bachelor of Arts and also that of Master of Arts. On leaving Cambridge he at once commenced to write papers, and these were at first on applied mathematics. His first paper was entitled “An analytical development of Fresnel’s optical theory of crystals,” which was published in the Philosophical Magazine. -
Open Research Online Oro.Open.Ac.Uk
Open Research Online The Open University’s repository of research publications and other research outputs The Gender Gap in Mathematical and Natural Sciences from a Historical Perspective Conference or Workshop Item How to cite: Barrow-Green, June; Ponce Dawson, Silvina and Roy, Marie-Françoise (2019). The Gender Gap in Mathematical and Natural Sciences from a Historical Perspective. In: Proceedings of the International Congress of Mathematicians - 2018 (Sirakov, Boyan; Ney de Souza, Paulo and Viana, Marcelo eds.), World Scientific, pp. 1073–1092. For guidance on citations see FAQs. c [not recorded] https://creativecommons.org/licenses/by-nc-nd/4.0/ Version: Accepted Manuscript Link(s) to article on publisher’s website: http://dx.doi.org/doi:10.1142/11060 Copyright and Moral Rights for the articles on this site are retained by the individual authors and/or other copyright owners. For more information on Open Research Online’s data policy on reuse of materials please consult the policies page. oro.open.ac.uk P. I. C. M. – 2018 Rio de Janeiro, Vol. (1073–1068) 1 THE GENDER GAP IN MATHEMATICAL AND NATURAL 2 SCIENCES FROM A HISTORICAL PERSPECTIVE 3 J B-G, S P D M-F R 4 5 Abstract 6 The panel organised by the Committee for Women in Mathematics (CWM) 7 of the International Mathematical Union (IMU) took place at the International nd 8 Congress of Mathematicians (ICM) on August 2 , 2018. It was attended by about 9 190 people, with a reasonable gender balance (1/4 men, 3/4 women). The panel was 10 moderated by Caroline Series, President of the London Mathematical Society and 11 Vice-Chair of CWM. -
Courses in Part Ib of the Mathematical Tripos
UNIVERSITY OF CAMBRIDGE Faculty of Mathematics COURSES IN PART IB OF THE MATHEMATICAL TRIPOS This document contains a list of all the courses which are examinable in Part IB of the Mathematical Tripos together with an informal description of each course and suggestions for preliminary reading. A formal syllabus is given in the booklet Schedules for the Mathematical Tripos. which can be obtained from the Faculty Office, Centre for Mathematical Sciences, Wilberforce Road, Cambridge CB3 0WA (telephone: 01223 337968; e-mail: [email protected]). All the documentation (including Schedules for the Mathematical Tripos) is available on the WWW (http://www.maths.cam.ac.uk/). June 2, 2004 READ ME Five changes have been implemented for 2004/05. They are as follows. There are two new courses, • { Complex Analysis, which will be lectured in the Lent Term and examined in Part IB, May/June 2005. This will run in parallel to Complex Methods, and it is expected that students with mainly pure mathematical interests will take Complex Analysis and students with mainly ap- plied mathematical interests will take Complex Methods. However, the courses are timetabled so that you could attend both courses. A total of four questions will be set in the examination on the two courses, two of which will be on material common to both courses. { The Geometry course has been replaced by a 16-lecture Geometry course given in the Lent term. Topological and Metric Spaces, which was lectured in the Easter term 2004, will be examined for • the first time in Part IB, May/June 2005. -
UTO in Biological Physics
University of Cambridge Department of Applied Mathematics and Theoretical Physics University Lectureship in Biological Physics Applications are invited for a University Lectureship in Biological Physics to be held in the Department of Applied Mathematics and Theoretical Physics (DAMTP). Candidates should have an outstanding record of theoretical research in biological physics or related areas. The successful candidate will be expected to carry forward a programme of research in biological physics, involving the application of physical principles and mathematical techniques to the understanding of living systems and ideally, have a strong interaction with experimental research. We welcome applications from those working in areas such as biological fluid dynamics and biomechanics, as well as, for example, physical aspects of development, evolution and ecology. The post is part of an on-going cross-departmental effort in Cambridge to promote connections between the physical, mathematical and life sciences. The successful applicant will join a substantial and growing research effort within DAMTP in biological physics and mathematical biology. For more information about this research see: http://www.damtp.cam.ac.uk/research The position University Lecturer is one of four grades of academic post at the University of Cambridge, the others being Senior Lecturer, Reader and Professor. Rapid promotion through the grades is possible for candidates whose achievements merit this. A University Lectureship in Cambridge is roughly equivalent to an Associate Professorship in the US. The person appointed will be required to contribute to teaching, examining and administration and to research, including the supervision of graduate students and generation of research funding. So far as formal lecturing is concerned, the average load in DAMTP is some 40 hours per year, typically one undergraduate course and one graduate-level course. -
Mathematical Tripos: IA Vector Calculus Contents
Mathematical Tripos: IA Vector Calculus Contents 0 Introduction i 0.1 Schedule . i 0.2 Lectures . i 0.3 Printed Notes . ii 0.4 Examples Sheets . iii 0.5 Previous Comments, Comments on Comments and Style of Lectures. iii 0.6 Books ................................................... iv 0.7 Revision . iv 0.7.1 Vectors . iv 3 0.7.2 Cylindrical polar co-ordinates (ρ, φ, z) in R . ......................... vi 3 0.7.3 Spherical polar co-ordinates (r, θ, φ) in R ............................ vi 0.7.4 Determinants. vi 1 Partial Differentiation 1 1.1 Scalar Functions of One Variable . 1 1.1.1 Limits . 1 1.1.2 Continuity . 1 1.1.3 Differentiability . 1 1.1.4 Taylor’s Theorem . 2 1.2 Functions of Several Variables . 2 1.2.1 Limits . 3 1.2.2 Continuity . 3 1.3 Derivatives of Vector Functions of One Variable . 4 1.3.1 Example . 4 1.4 Partial Derivatives . 4 1.4.1 Definition . 5 1.4.2 Examples . 5 1.4.3 Directional Derivatives . 7 1.5 Differentiability . 7 1.5.1 Scalar Functions of Two Variables . 7 1.5.2 Functions of Several Variables . 8 1.5.3 Properties of Differentiable Functions . 9 1.6 The Chain Rule and Change of Variables . 9 m m 1.6.1 The Chain Rule for x : R → R and f : R → R ....................... 9 ` m m 1.6.2 The Chain Rule for x : R → R and f : R → R ...................... 11 ` m m n 1.6.3 The Chain Rule for x : R → R and f : R → R ..................... -
Advanced Probability University of Cambridge, Part III of the Mathematical Tripos Michaelmas Term 2006
Advanced Probability University of Cambridge, Part III of the Mathematical Tripos Michaelmas Term 2006 Gr´egory Miermont1 1CNRS & Laboratoire de Math´ematique, Equipe Probabilit´es, Statistique et Mod´elisation, Bt. 425, Universit´eParis-Sud, 91405 Orsay, France Contents 1 Conditional expectation 5 1.1 The discrete case ................................ 5 1.2 Conditioning with respect to a σ-algebra ................... 6 1.2.1 The L2 case ............................... 7 1.2.2 General case ............................... 7 1.2.3 Non-negative case ............................ 8 1.3 Specific properties of conditional expectation ................. 10 1.4 Computing a conditional expectation ..................... 11 1.4.1 Conditional density functions ..................... 11 1.4.2 The Gaussian case ........................... 11 2 Discrete-time martingales 13 2.1 Basic notions .................................. 13 2.1.1 Stochastic processes, filtrations .................... 13 2.1.2 Martingales ............................... 14 2.1.3 Doob’s stopping times ......................... 14 2.2 Optional stopping ................................ 15 2.3 The convergence theorem ............................ 17 2.4 Lp convergence, p > 1 .............................. 18 2.4.1 A maximal inequality .......................... 18 2.5 L1 convergence ................................. 20 2.6 Optional stopping in the UI case ....................... 20 2.7 Backwards martingales ............................. 21 3 Examples of applications of discrete-time martingales -
Forming the Analytical Society at Cambridge University
Forming the Analytical Society at Cambridge University Richard Stout Gordon College Wenham, MA The Analytical Society, an organization begun by students at Cambridge, was founded in 1812. Even though it was entirely student-led, the society was responsible for significant changes in the Cambridge mathematics curriculum and in the way mathematics was perceived in Britain throughout the nineteenth century. Its success was likely due to the outstanding students who formed the group, some of whom went on to become leaders in British science and mathematics for the next fifty years. In this paper we will briefly look at several of those who played important roles in forming and leading the society and we will consider the circumstances leading to its formation. In the fall of 1809, John Frederick William Herschel (1792 – 1871) matriculated at St. John’s College, one of the two largest colleges at Cambridge University. A serious student of mathematics, Herschel came from a privileged, upper-class family. When it didn’t work out for Herschel to be away at school, his family was able to hire a private tutor and allow Herschel to finish his education at home. Because his father, William Herschel, was a world-renowned astronomer--he discovered the planet Uranus--John Herschel likely grew up accustomed to scientific talk and held to high expectations. At Cambridge Herschel would distinguish himself as a superior student, finishing as the senior wrangler in 1813. After graduating from Cambridge Herschel was elected to the Royal Society and became a fellow of St. John’s. Although he continued to do mathematics for several years, primarily as an avocation, Herschel eventually followed in his father’s footsteps and became a distinguished astronomer. -
Early Indian Mathematical Pilgrims to Cambridge
Early Indian Mathematical Pilgrims to Cambridge K. Razi Naqvi Department of Physics, Norwegian University of Science and Technology N-7491 Trondheim, Norway During the nineteenth and the early part of the next century, the University of Cambridge (UoC) was the Mecca of Mathematcis for students from the British Isles and other parts of the British Empire. UoC concentrated on undergraduate teaching; its examination system, particularly the Mathematical Sciences Tripos (hereafter abbreviated as MathTrip), served as a launch pad for re- munerative and influential careers in law, church, politics, even medicine, and various adminis- trative organs of the British Raj. Most examiners were not engaged in research, and few examinees dreamt of qualifying as a high wrangler, or of becoming a creative mathematician. The purpose of this article is to scrutinise the performance of the few Indian students who completed one or both parts of MathTrip, the career choices they made after returning to India, and their efforts, if any, towards the diffusion of modern mathematics in Indian schools and colleges. Almost all of the returnees became functionaries of the colossal British bureaucracy. Rejuvenation of Indian math- ematics was carried out mostly by other enthusiasts, among whom Muslims are conspicuous by their scarcity. “Whether good mathematicians, when women and a handful of men from other they die, go to Cambridge, I do not parts of the British Empire were two mi- know. But it is well known that a large nority groups, whose members performed [?] number of men go there when they equally well. I am concerned here essen- are young for the purpose of being con- tially with those who came from the In- verted into senior wranglers and Smith’s dian subcontinent, and even out of this prizemen.” I would have been happier to small group, I will only speak of those who quote this remark if its author, the eccen- passed MathTrip during the period 1898– tric Oliver Heaviside, had used small in- 1909. -
Arthur Cayley1
Chapter 5 ARTHUR CAYLEY1 (1821-1895) Arthur Cayley was born at Richmond in Surrey, England, on August 16, 1821. His father, Henry Cayley, was descended from an ancient Yorkshire family, but had settled in St. Petersburg, Russia, as a merchant. His mother was Maria Antonia Doughty, a daughter of William Doughty; who, according to some writers, was a Russian; but her father’s name indicates an English origin. Arthur spent the first eight years of his life in St. Petersburg. In 1829 his parents took up their permanent abode at Blackheath, near London; and Arthur was sent to a private school. He early showed great liking for, and aptitude in, numerical calculations. At the age of 14 he was sent to King’s College School, London; the master of which, having observed indications of mathematical genius, advised the father to educate his son, not for his own business, as he had at first intended, but to enter the University of Cambridge. At the unusually early age of 17 Cayley began residence at Trinity College, Cambridge. As an undergraduate he had generally the reputation of being a mere mathematician; his chief diversion was novel-reading. He was also fond of travelling and mountain climbing, and was a member of the Alpine Club. The cause of the Analytical Society had now triumphed, and the Cambridge Mathematical Journal had been instituted by Gregory and Leslie Ellis. To this journal, at the age of twenty, Cayley contributed three papers, on subjects which had been suggested by reading the M´ecanique analytique of Lagrange and some of the works of Laplace.