The Development of Algebraic Structures During the Nineteenth Century
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Duncan F. Gregory, William Walton and the Development of British Algebra: ‘Algebraical Geometry’, ‘Geometrical Algebra’, Abstraction
UvA-DARE (Digital Academic Repository) "A terrible piece of bad metaphysics"? Towards a history of abstraction in nineteenth- and early twentieth-century probability theory, mathematics and logic Verburgt, L.M. Publication date 2015 Document Version Final published version Link to publication Citation for published version (APA): Verburgt, L. M. (2015). "A terrible piece of bad metaphysics"? Towards a history of abstraction in nineteenth- and early twentieth-century probability theory, mathematics and logic. General rights It is not permitted to download or to forward/distribute the text or part of it without the consent of the author(s) and/or copyright holder(s), other than for strictly personal, individual use, unless the work is under an open content license (like Creative Commons). Disclaimer/Complaints regulations If you believe that digital publication of certain material infringes any of your rights or (privacy) interests, please let the Library know, stating your reasons. In case of a legitimate complaint, the Library will make the material inaccessible and/or remove it from the website. Please Ask the Library: https://uba.uva.nl/en/contact, or a letter to: Library of the University of Amsterdam, Secretariat, Singel 425, 1012 WP Amsterdam, The Netherlands. You will be contacted as soon as possible. UvA-DARE is a service provided by the library of the University of Amsterdam (https://dare.uva.nl) Download date:29 Sep 2021 chapter 9 Duncan F. Gregory, William Walton and the development of British algebra: ‘algebraical geometry’, ‘geometrical algebra’, abstraction 1. The complex history of nineteenth-century British algebra: algebra, geometry and abstractness It is now well established that there were two major factors that contributed to the revitalization and reorientation of British mathematics in the early- and mid-nineteenth-century.1 Firstly, there was the external influence consisting of the dedication of the members of the anti-establishment Analytical Society to the ‘Principle of pure D-ism in opposition to the Dot-age of the University’. -
Autobiography of Sir George Biddell Airy by George Biddell Airy 1
Autobiography of Sir George Biddell Airy by George Biddell Airy 1 CHAPTER I. CHAPTER II. CHAPTER III. CHAPTER IV. CHAPTER V. CHAPTER VI. CHAPTER VII. CHAPTER VIII. CHAPTER IX. CHAPTER X. CHAPTER I. CHAPTER II. CHAPTER III. CHAPTER IV. CHAPTER V. CHAPTER VI. CHAPTER VII. CHAPTER VIII. CHAPTER IX. CHAPTER X. Autobiography of Sir George Biddell Airy by George Biddell Airy The Project Gutenberg EBook of Autobiography of Sir George Biddell Airy by George Biddell Airy This eBook is for the use of anyone anywhere at no cost and with almost no restrictions whatsoever. You may copy it, give it away or re-use it under the terms of the Project Gutenberg Autobiography of Sir George Biddell Airy by George Biddell Airy 2 License included with this eBook or online at www.gutenberg.net Title: Autobiography of Sir George Biddell Airy Author: George Biddell Airy Release Date: January 9, 2004 [EBook #10655] Language: English Character set encoding: ISO-8859-1 *** START OF THIS PROJECT GUTENBERG EBOOK SIR GEORGE AIRY *** Produced by Joseph Myers and PG Distributed Proofreaders AUTOBIOGRAPHY OF SIR GEORGE BIDDELL AIRY, K.C.B., M.A., LL.D., D.C.L., F.R.S., F.R.A.S., HONORARY FELLOW OF TRINITY COLLEGE, CAMBRIDGE, ASTRONOMER ROYAL FROM 1836 TO 1881. EDITED BY WILFRID AIRY, B.A., M.Inst.C.E. 1896 PREFACE. The life of Airy was essentially that of a hard-working, business man, and differed from that of other hard-working people only in the quality and variety of his work. It was not an exciting life, but it was full of interest, and his work brought him into close relations with many scientific men, and with many men high in the State. -
GEORGE PEACOCK (1791-1858) George Peacock Was Born on April
GEORGE PEACOCK1 (1791-1858) George Peacock was born on April 9, 1791, at Denton in the north of England, 14 miles from Richmond in Yorkshire. His father, the Rev. Thomas Peacock, was a clergyman of the Church of England, incumbent and for 50 years curate of the parish of Denton, where he also kept a school. In early life Peacock did not show any precocity of genius, and was more remarkable for daring feats of climbing than for any special attachment to study. He received his elementary education from his father, and at 17 years of age, was sent to Richmond, to a school taught by a graduate of Cambridge University to receive instruction preparatory to entering that University. At this school he distinguished himself greatly both in classics and in the rather elementary mathematics then required for entrance at Cambridge. In 1809 he became a student of Trinity College, Cambridge. Here it may be well to give a brief account of that University, as it was the alma mater of four out of the six mathematicians discussed in this course of lectures2. At that time the University of Cambridge consisted of seventeen colleges, each of which had an independent endowment, buildings, master, fellows and scholars. The endowments, generally in the shape of lands, have come down from ancient times; for example, Trinity College was founded by Henry VIII in 1546, and at the beginning of the 19th century it consisted of a master, 60 fellows and 72 scholars. Each college was provided with residence halls, a dining hall, and a chapel. -
The Use and Abuse of Cambridge University's Ten-Year Divinity Statute
Ambition, Anxiety and Aspiration: the use and abuse of Cambridge University’s Ten-Year Divinity Statute. This paper examines the market for and motivation of those who made use of a little-known Cambridge University statute which, in effect, offered a low-cost distance learning degree until 1858. It shows how non-graduates, both clerical and lay, attempted to use its provisions to enhance their status, facilitate career advancement and insulate themselves against status slippage, a problem that became acute in the second decade of the nineteenth century as the reinvigorated universities reasserted their role as educators of the clergy and as the bishops increasingly denied ordination to those educated outside their sphere. In doing so we can observe how the desires of non-graduate clergy to take degrees, and the attempts of liberally-educated non-graduates to enter the pulpits of the established Church, were responded to both by the university which received them and more broadly by the print discourse which critiqued their ambitions. The tensions revealed are relevant not just for understanding something of how the clergy were developing as an occupational group, and the tensions caused by the changing supplies of graduates, but also reflect more generally the status anxieties of the elites and middling sorts as they faced down fears of competition for cultural and economic privilege appendant to educational opportunities. The ten-year divinity statute: interpretation and reputation. Distance learning has a long pedigree at Cambridge University. A papal dispensation allowing monks and friars to proceed to the degree of bachelor of divinity, without first taking a degree in the arts was, in spirit, to survive the reformation. -
The Book and Printed Culture of Mathematics in England and Canada, 1830-1930
Paper Index of the Mind: The Book and Printed Culture of Mathematics in England and Canada, 1830-1930 by Sylvia M. Nickerson A thesis submitted in conformity with the requirements for the degree of Doctor of Philosophy Institute for the History and Philosophy of Science and Technology University of Toronto © Copyright by Sylvia M. Nickerson 2014 Paper Index of the Mind: The Book and Printed Culture of Mathematics in England and Canada, 1830-1930 Sylvia M. Nickerson Doctor of Philosophy Institute for the History and Philosophy of Science and Technology University of Toronto 2014 Abstract This thesis demonstrates how the book industry shaped knowledge formation by mediating the selection, expression, marketing, distribution and commercialization of mathematical knowledge. It examines how the medium of print and the practices of book production affected the development of mathematical culture in England and Canada during the nineteenth and early twentieth century. Chapter one introduces the field of book history, and discusses how questions and methods arising from this inquiry might be applied to the history of mathematics. Chapter two looks at how nineteenth century printing technologies were used to reproduce mathematics. Mathematical expressions were more difficult and expensive to produce using moveable type than other forms of content; engraved diagrams required close collaboration between author, publisher and engraver. Chapter three examines how editorial decision-making differed at book publishers compared to mathematical journals and general science journals. Each medium followed different editorial processes and applied distinct criteria in decision-making about what to publish. ii Daniel MacAlister, Macmillan and Company’s reader of science, reviewed mathematical manuscripts submitted to the company and influenced which ones would be published as books. -
Appendix a Historical Notes
Appendix A Historical notes A.I Determining all permutation groups of a given degree For this section only, we adopt the following conventions. 1. The early researchers in this area adopted the convention that the degree of a permutation group is the number of points in the set on which it acts minus the number of orbits of length 1. For example, the copy of S3 in S4 (a point stabiliser) was counted as a group of degree 3, not 4. 2. When we say. 'all' permutation groups, we mean up to permutational isomorphism, with the definition of degree as given above. 3. We use the word 'group' to mean 'permutation group'. 4. Whenever a range of degrees is given, it is an inclusive one. 5. We make no claims on the accuracy of others' results unless explicitly stated. How ever, we adopt four benchmarks with which to compare all other results: (a) for all groups up to degree 7 we take the enumeration produced by the CAYLEY function lattice; (b) for the imprimitive groups up to degree 11 we take the list of Butler and McKay (1983); (c) for the imprimitive groups of degree 12 we take the list of Royle (1987); (d) for the primitive groups up to degree 50 we take the list of Sims, which first appeared in full in version 3.5 of CAYLEY, released in 1987. Tables containing these figures appear at the end of the section. 122 Appendix A. Historical notes The first work in this area is probably due to Ruffini (1799), who gives the possible orders of the groups of degree 5. -
Regular Permutation Groups and Cayley Graphs Cheryl E Praeger University of Western Australia
Regular permutation groups and Cayley graphs Cheryl E Praeger University of Western Australia 1 What are Cayley graphs? Group : G with generating set S = s, t, u, . 1 { } Group elements: ‘words in S’ stu− s etc vertices: group elements Cayley graph: Cay(G, S) edges: multiplication from S 2 What are Cayley graphs? If S inverse closed: s S s 1 S ∈ ⇐⇒ − ∈ Cayley graph Cay(G, S): may use undirected edges 3 Some reasonable questions Where: do they arise in mathematics today? Where: did they originate? What: kinds of groups G give interesting Cayley graphs Cay(G, S)? Which graphs: arise as Cayley graphs? Does it matter: what S we choose? Are: Cayley graphs important and why? And: what about regular permutation groups? Let’s see how I go with answers! 4 In Topology: Embedding maps in surfaces Thanks to Ethan Hein: flickr.com 5 Computer networks; experimental layouts (statistics) Thanks to Ethan Hein: flickr.com and Jason Twamley 6 Random walks on Cayley graphs Applications: from percolation theory to group computation How large n: g ‘approximately random’ in G? Independence? Method: for random selection in groups – underpins randomised algorithms for group computation (Babai, 1991) 7 Fundamental importance for group actions in combinatorics and geometry Iwilldescribe: Regular permutation groups Origins of Cayley graphs Links with group theory Some recent work and open problems on primitive Cayley graphs 8 Permutation groups Permutation : of set Ω, bijection g :Ω Ω Symmetric group of all permutations→ of Ω group Sym (Ω): under composition, for -
REPORTER S P E C I a L N O 1 T U E S D Ay 1 O C to B E R 2013 Vol Cxliv
CAMBRIDGE UNIVERSITY REPORTER S PECIAL N O 1 T UE S D AY 1 O C TOBER 2013 VOL CXLIV Deputy Vice-Chancellors appointed 2 Chairs of Syndicates, Boards, Committees, and other bodies appointed 2 Appointments Committees: Chairs appointed 3 Other appointment 4 Roll of the Regent House: Vice-Chancellor’s Notice 4 Preliminary list of members of the Faculties: Registrary’s Notice 5 Architecture and History of Art 5 Engineering 24 Asian and Middle Eastern Studies 5 English 26 Biology 6 History 28 Business and Management 11 Human, Social, and Political Science 30 Classics 12 Law 33 Clinical Medicine 13 Mathematics 35 Computer Science and Technology 18 Modern and Medieval Languages 37 Divinity 19 Music 39 Earth Sciences and Geography 20 Philosophy 40 Economics 22 Physics and Chemistry 40 Education 23 Veterinary Medicine 44 Proposed Roll of the Regent House: Registrary’s Notice 45 PUBLISHED BY AUTHORITY 2 CAMBRIDGE UNIVERSITY REPORTER [S PECIAL N O . 1 Deputy Vice-Chancellors appointed THE OLD SCHOOLS. 1 October 2013 The Vice-Chancellor gives notice that he has appointed the following, in accordance with Statute D, III, 7(a), as Deputy Vice-Chancellors for the academical year 2013–14: Dr Jennifer Chase Barnes, MUR, Pro-Vice-Chancellor Professor Lynn Faith Gladden, T, Pro-Vice-Chancellor Professor John Martin Rallison, T, Pro-Vice-Chancellor Professor Jeremy Keith Morris Sanders, SE, Pro-Vice-Chancellor Professor Stephen John Young, EM, Pro-Vice-Chancellor Professor Anthony John Badger, Master of Clare College Professor Dame Athene Margaret Donald, R Professor Dame Ann Patricia Dowling, SID Lord (John Leonard) Eatwell, President of Queens’ College Mr Stuart Laing, Master of Corpus Christi College Mrs Sarah Squire, President of Hughes Hall Professor Dame Jean Olwen Thomas, Master of St Catharine’s College Professor Ian Hugh White, Master of Jesus College Chairs of Syndicates, Boards, Committees, and other bodies appointed THE OLD SCHOOLS. -
Regular Permutation Groups and Cayley Graphs Cheryl E Praeger University of Western Australia
Regular permutation groups and Cayley graphs Cheryl E Praeger University of Western Australia 1 Permutation groups Permutation : of set Ω, bijection g :Ω ! Ω Symmetric group of all permutations of Ω group Sym (Ω): under composition, for example g = (1; 2) followed by h = (2; 3) yields gh = (1; 3; 2) g = (1; 2; 3) has inverse g−1 = (3; 2; 1) = (1; 3; 2) Permutation G ≤ Sym (Ω), that is, subset group on Ω: closed under inverses and products (compositions) Example: G = h(0; 1; 2; 3; 4)i < Sym (Ω) on Ω = f0; 1; 2; 3; 4g 2 Interesting permutation groups occur in: Graph Theory: Automorphism groups (edge-preserving perm's) Geometry: Collineations (line-preserving permutations) Number Theory and Cryptography: Galois groups, elliptic curves Differential equations: Measure symmetry - affects nature of so- lutions Many applications: basic measure of symmetry 3 Regular permutation groups Permutation group: G ≤ Sym (Ω) G transitive: all points of Ω equivalent under elements of G G regular: `smallest possible transitive' that is only the identity element of G fixes a point Example: G = h(0; 1; 2; 3; 4)i on Ω = f0; 1; 2; 3; 4g Alternative view: G = Z5 on Ω = f0; 1; 2; 3; 4g by addition 0 4 1 3 2 4 View of regular permutation groups Take any: group G, set Ω := G Define action: ρg : x ! xg for g 2 G; x 2 Ω(ρg is bijection) Form permutation group: GR = fρgjg 2 Gg ≤ Sym (Ω) ∼ GR = G and GR is regular 5 Visualise regular permutation groups as graphs Given generating set S: G = hSi with s 2 S () s−1 2 S Define graph: vertex set Ω = G, edges fg; sgg for g 2 G; s 2 S Example: G = Z5, S = f1; 4g, obtain Γ = C5, Aut (Γ) = D10. -
View This Volume's Front and Back Matter
Titles in This Series Volume 8 Kare n Hunger Parshall and David £. Rowe The emergenc e o f th e America n mathematica l researc h community , 1876-1900: J . J. Sylvester, Felix Klein, and E. H. Moore 1994 7 Hen k J. M. Bos Lectures in the history of mathematic s 1993 6 Smilk a Zdravkovska and Peter L. Duren, Editors Golden years of Moscow mathematic s 1993 5 Georg e W. Mackey The scop e an d histor y o f commutativ e an d noncommutativ e harmoni c analysis 1992 4 Charle s W. McArthur Operations analysis in the U.S. Army Eighth Air Force in World War II 1990 3 Pete r L. Duren, editor, et al. A century of mathematics in America, part III 1989 2 Pete r L. Duren, editor, et al. A century of mathematics in America, part II 1989 1 Pete r L. Duren, editor, et al. A century of mathematics in America, part I 1988 This page intentionally left blank https://doi.org/10.1090/hmath/008 History of Mathematics Volume 8 The Emergence o f the American Mathematical Research Community, 1876-1900: J . J. Sylvester, Felix Klein, and E. H. Moor e Karen Hunger Parshall David E. Rowe American Mathematical Societ y London Mathematical Societ y 1991 Mathematics Subject Classification. Primary 01A55 , 01A72, 01A73; Secondary 01A60 , 01A74, 01A80. Photographs o n th e cove r ar e (clockwis e fro m right ) th e Gottinge n Mathematisch e Ges - selschafft, Feli x Klein, J. J. Sylvester, and E. H. Moore. -
William Wallace and the Introduction of Continental Calculus to Britain: a Letter to George Peacock
View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by Elsevier - Publisher Connector HISTORIA MATHEMATICA 14 (1987), 119-132 William Wallace and the Introduction of Continental Calculus to Britain: A Letter to George Peacock M. PANTEKI Middlesex Polytechnic, Queensway, EnJield, Middlesex EN3 4SF, United Kingdom Little is known about William Wallace’ work and even less about his attempts to intro- duce Continental calculus to Britain in the early 19th century. A letter written by him to George Peacock in 1833 reveals many interesting facts concerning his role in the reform of British mathematics. This paper presents a brief account of his life and work and the full text of the letter, and proposes that Wallace’ contributions deserve to be acknowledged. o 1987 Academic Press, Inc. Wenig ist tiber das Werk von William Wallace bekannt und noch weniger tiber seine Versuche, den kontinentalen Infinitesimalkalktil im frtihen 19. Jahrhundert nach Britannien einzuRihren. Ein Brief, den er 1833 an George Peacock schrieb, deckt viele interessante Tatsachen auf, die seine Rolle bei der Reform der britischen Mathematik betreffen. Dieser Aufsatz gibt eine kurze Darstelhmg seines Lebens und Werks und den vollstandigen Text des Briefes und bitt daftir ein, daO die Beitrage von Wallace verdienen anerkannt zu werden. 0 1987 Academic Press, Inc. On ne sait qu’un peu sur l’oeuvre de William Wallace et encore moins sur ses essais d’introduire le calcul infinitesimal continental dans les Iles britanniques au debut du 1P”’ siecle. Une lettre qu’il avait &rite a George Peacock en 1833 revtle beaucoup de faits interessantes concemant son r81e dans la reforme des mathematiques britanniques. -
Referees, Publisher's Readers and the Image Of
REFEREES, PUBLISHER’S READERS AND THE IMAGE OF MATHEMATICS IN NINETEENTH CENTURY ENGLAND by SYLVIA NICKERSON In the realm of publishing history it is well known that many of London’s largest nineteenth century publishers hired publisher’s readers to advise them about which literary manuscripts they should publish. Moreover, it has been recognized that these readers often acted as tastemakers and had a hand in shaping the development of literature. Publisher’s readers had a similar effect in relation to the genres of science and mathematics. At Macmillan and Company, publisher’s readers and close advisors to the publisher influenced decisions about which books were published on scientific and mathematical topics. In 1880, Macmillan and Company hired a publisher’s reader to specifically handle the science genre. The chosen reader, Donald MacAlister, also reviewed manuscripts in mathematics, and between 1880 and 1896 MacAlister wrote more than sixty reviews about prospective mathematical books that were being considered for publication. During this time he also wrote reviews evaluating manuscripts in other areas of science. While some observations about his work as a science reader are included, the purpose here is to focus specifically on MacAlister’s influence on Macmillan’s mathematical publishing program. The current article demonstrates that, when publishing on mathematical subjects, the decision-making of book publishers differed from that of mathematical journals. The values that underpinned the decision-making process were different at mathematics journals, general science journals and the book publishers that published mathematics. Each set of values affected the image of mathematics that was cultivated. The article examines the processes of refereeing, and the role of the editor, at nineteenth century mathematical journals by looking at the Cambridge Mathematical Journal and Acta Mathematica.