DOCSLIB.ORG

ACMS 18Th Biennial Conference Proceedings, Westmont College, 2011 Page 1 Friday, June 3 7:45 – 8:45 A.M

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
ACMS 18Th Biennial Conference Proceedings, Westmont College, 2011 Page 1 Friday, June 3 7:45 – 8:45 A.M Association of Christians in the Mathematical Sciences Eighteenth Biennial Conference Proceedings, June 1{4, 2011 Westmont College, Santa Barbara, CA Edited by Russell W. Howell Table of Contents Introduction.......................................... ii Conference Schedule.....................................1 Abstracts of Presentations..................................4 Brian D. Beasley, Where, Oh Waring? The Classic Problem and its Extensions .... 15 Ryan Botts, Lori Carter, Lesson's Learned: A Journey in Computational Science ... 22 Robert L. Brabenec, Thinking Philosophically about Mathematics ............ 29 Jeremy Case, PK Mathematicians ............................. 35 Loredana Ciurdariu, Pascal's Thoughts Seen in the Light of Scripture ......... 53 Eric Gossett, The Search for Hamilton ........................... 66 Nathan Gossett, The Need for a Graphics Programming Course in CS ......... 74 Wayne Iba, Real Simulations and Simulated Reality .................... 81 Stephen Lovett, Bringing Undergraduate Research into the Classroom ......... 90 Nathan Moyer, Connecting Mathematics Students to Philosophy and Faith ....... 95 Judith Palagallo, Calculus Communication Circle ..................... 103 Doug Phillippy, The Study of Mathematics: A Text from a Christian Perspective ... 107 Donna Pierce, Math History Study Abroad Program .................... 120 Michael Rempe, Google and the Mathematics of Web Search ............... 131 Gordon A. Swain, The History of the Area between a Line and a Parabola ....... 138 Mary Walkins, History of Mathematics: An Exercise in Strengths ............ 154 Samuel P. Wilcox, A Bayesian Secondary Analysis in an Asthma Study ........ 158 Josh Wilkerson, What we can Learn from Process Theology ............... 166 Nicholas J. Willis, Two Faith Integration Projects for Freshman Majors ........ 184 Maria Zack, Using Original Historical Mathematics Texts in the Classroom ...... 189 Nicholas C. Zoller, The Mathematics of Cubic Sudoku .................. 199 Participant List........................................ 207 Conference Photos...................................... 210 { i { Introduction Ninety participants, eight spouses, and three children came to Westmont College for the eigh- teenth biennial conference of the Association of Christians in the Mathematical Sciences. They enjoyed superb weather during the conference dates of June 1{4, 2011. Unfortunately, those who chose to spend some extra time in Santa Barbara and stayed through June 5 experienced a rare day of rain. Coincidentally, the last time ACMS convened at Westmont (1993) there was another rare rain event. It might be helpful to California if ACMS could schedule yet another meeting at Westmont when the state is in the midst of its next drought! Among those attending, about ten were at their very first ACMS meeting. All participants enjoyed two presentations given by each of the the three invited speakers: Art Benjamin (Harvey Mudd College), Fred Brooks (University of North Carolina), and Glen Van Brummelen (Quest University). As the conference schedule indicates (page1), there were thirty-three contributed papers in parallel sessions dealing with a variety of topics in mathematics and computer science. Abstracts for the invited addresses and the contributed the papers can be found beginning on page4. Twenty of the contributed papers, which begin on page 15, are part of these Proceedings. There were also two panel discussions relating to the interaction between mathematics and computer science: within institutions, and within ACMS. A final panel session gave an an overview of a recently-completed ACMS book project: Mathematics Through the Eyes of Faith. This project involved eleven ACMS members and was published by HarperOne, San Francisco. Several informal activities complemented the scheduled sessions. On Thursday evening about fifty delegates enjoyed viewing the skies from Westmont's observatory, which houses the largest telescope between Los Angeles and San Francisco. Early on Friday morning twenty-one hikers make a trek up the foothills to Montecito Overlook.A picture of their venture can be found in the conference photos section, which begins on page 210. The traditional conference banquet took place on Friday evening. After Saturday morning parallel sessions dealing with faith integration issues the conference concluded with a worship service. We at Westmont considered it a privilege to host this event. We wish you every blessing in your respective vocations and look forward to seeing many of you again in 2013 at the nineteenth biennial ACMS conference. Bethel University (St. Paul, Minnesota) has agreed to be the host site. In 2015 the conference is planned to convene in Canada for the first time, hosted by Redeemer University College (Ancaster, Ontario). Russell Howell Conference Coordinator { ii { ACMS 18th Biennial Conference Schedule Westmont College, June 1{4, 2011 Wednesday, June 1 5:30 { 6:30 p.m. Dinner 7:00 { 8:30 p.m. Opening Session (Winter Hall, Room 210) Introduction of first-time participants Invited Address: Art Benjamin, Harvey Mudd College Mathemagics! 8:30 { 9:30 p.m. Refreshments Thursday, June 2 7:45 { 8:45 a.m. Breakfast 9:00 { 9:30 a.m. Welcome from Gayle Beebe (President of Westmont); Devotional (Room 210) 9:30 { 10:30 a.m. Invited Address: Art Benjamin, Harvey Mudd College (Room 210) Combinatorial Trigonometry (and a method to DIE for)! 10:30 { 11:00 a.m. Break 11:00 { 12:00 p.m. Invited Address: Fred Brooks, University of North Carolina (Room 210) The Computer Scientist as Toolsmith 12:00 { 1:00 p.m. Lunch (ACMS board meets during this time) 1:30 { 2:30 p.m. Contributed Papers: Assorted Mathematical Topics, I (Room 106) Nicholas Zoller: \The Mathematics of Cubic Sudoku" Brian Beasley: \Waring's Problem and Extensions" Bryant Mathews: \Tropical Mathematics" Contributed Papers: Assorted Computer Science Topics (Room 216) Nathan Gossett: \The Need for Graphics in Computer Science" Gene Rohrbaugh: \The Moral Status of Intelligent Machines" Wayne Iba: \Real Simulations and Simulated Reality" 2:30 { 3:30 p.m. Break 3:30 { 4:30 p.m. Contributed Papers: Faith and the Mathematical Sciences, I (Room 106) Jason Wilson: \Natural Law in the Secular vs. Biblical Mind" Jeremy Case: \Preacher-Kid Mathematicians" Loredana Ciurdariu: \Pascal's Thoughts and the Scriptures" Contributed Papers: Mathematics and Pedagogy, I (Room 216) Kristen Camenga: “Reflections on a Capstone Course" Rebekah Yates: \Linear Algebra as a Discussion Class" Steve Lovett: \Bringing REU into the Classroom" 4:30 { 5:30 p.m. Discussion with Fred Brooks (Room 210) 5:30 { 6:30 p.m. Dinner 7:00 { 8:00 p.m. \Divide and Conquer or Merge and Maximize?" (Panel/Discussion, Room 106) Joint vs. separate Mathematics and Computer Science Programs Phillip Lestmann, Michael Stob, David Stucki, Maria Zack 8:00 { 9:00 p.m. \Computer Science and ACMS" (Discussion, Room 106) Led by Matt DeLong and the ACMS board 9:00 { 10:00 p.m. Observatory Viewing ACMS 18th Biennial Conference Proceedings, Westmont College, 2011 Page 1 Friday, June 3 7:45 { 8:45 a.m. Breakfast 9:00 { 9:30 a.m. Devotional and Announcements (Room 210) 9:30 { 10:30 a.m. Invited Address: Glen Van Brummelen, Quest University (Room 210) Mathematics Across Cultures: How Can Worldview Affect Mathematics? 10:30 { 11:00 a.m. Conference Photo (Winter Hall Lawn) and Break 11:00 { 12:00 p.m. Contributed Papers: Mathematics and Statistics (Room 106) Mike Stob: \R on the Cloud" Sam Wilcock: \A Bayesian Secondary Analysis in an Asthma Study" Talithia Williams: \The Misapplication of Statistics in American Life" Contributed Papers: Computer Science in the Liberal Arts (Room 216) Gene Rohrbaugh: \The Place of Computing in the Liberal Arts" Ryan Botts: \Lessons Learned: A Journey in Computational Science" Lori Carter: \Lessons Learned: A Journey in Computational Science" Open Discussion: \Computer Science in the Liberal Arts" 12:00 { 1:00 p.m. Lunch 1:30 { 2:30 p.m. Invited Address: Glen Van Brummelen, Quest University (Room 210) Trigonometry, Ancient Astronomy, and the Birth of Applied Mathematics 2:30 { 3:30 p.m. Break 3:30 { 4:30 p.m. Contributed Papers: Assorted Mathematical Topics, II (Room 106) Michael Rempe: \The 25 Billion Dollar Linear Algebra Problem" Justin Marks: \Pattern Recognition in Large Data Sets" Jonathan Leech: \Skew Lattices in Algebra and Computer Science" Contributed Papers: Philosophical/Historical Topics, I (Room 216) Gordon Swain: \History of the Area Between a Line and a Parabola" Robert Brabenec: \Thinking Philosophically about Mathematics" Maria Zack: \Using Original Historical Texts in the Classroom" 4:30 { 5:30 p.m. Contributed Papers: Faith and the Mathematical Sciences, II (Room 106) Mark Colgan: \Connecting Calculus with Biblical Ideas" David Stucki: \Teaching Infinity, and Beyond!" Josh Wilkerson: \Faith, Mathematics, and Process Theology" Contributed Papers: Mathematics and Pedagogy, II (Room 216) Mary Walkins: \History of Mathematics: An Exercise in Strengths" Judy Palagallo: \Calculus Communication Circles" Nicholas Willis: \Two Integrative Projects for Freshman Majors" 6:00 { 7:30 p.m. Conference Banquet (Founders' Room in the Dining Commons) ACMS 18th Biennial Conference Proceedings, Westmont College, 2011 Page 2 Saturday, June 4 7:45 { 8:45 a.m. Breakfast 9:00 { 10:00 a.m. Contributed Papers: Book Projects Relating Faith and Mathematics (Room 106) Doug Phillippy: \A Text with a Christian Perspective" Panel: \ACMS Project: Mathematics Through the Eyes of Faith" Jim Bradley,
Load more

Recommended publications
  • “A Valuable Monument of Mathematical Genius”\Thanksmark T1: the Ladies' Diary (1704–1840)
    Historia Mathematica 36 (2009) 10–47 www.elsevier.com/locate/yhmat “A valuable monument of mathematical genius” ✩: The Ladies’ Diary (1704–1840) Joe Albree ∗, Scott H. Brown Auburn University, Montgomery, USA Available online 24 December 2008 Abstract Our purpose is to view the mathematical contribution of The Ladies’ Diary as a whole. We shall range from the state of mathe- matics in England at the beginning of the 18th century to the transformations of the mathematics that was published in The Diary over 134 years, including the leading role The Ladies’ Diary played in the early development of British mathematics periodicals, to finally an account of how progress in mathematics and its journals began to overtake The Diary in Victorian Britain. © 2008 Published by Elsevier Inc. Résumé Notre but est de voir la contribution mathématique du Journal de Lady en masse. Nous varierons de l’état de mathématiques en Angleterre au début du dix-huitième siècle aux transformations des mathématiques qui a été publié dans le Journal plus de 134 ans, en incluant le principal rôle le Journal de Lady joué dans le premier développement de périodiques de mathématiques britanniques, à finalement un compte de comment le progrès dans les mathématiques et ses journaux a commencé à dépasser le Journal dans l’Homme de l’époque victorienne la Grande-Bretagne. © 2008 Published by Elsevier Inc. Keywords: 18th century; 19th century; Other institutions and academies; Bibliographic studies 1. Introduction Arithmetical Questions are as entertaining and delightful as any other Subject whatever, they are no other than Enigmas, to be solved by Numbers; .
    [Show full text]
  • Mathematical Genealogy of the Wellesley College Department Of
    Nilos Kabasilas Mathematical Genealogy of the Wellesley College Department of Mathematics Elissaeus Judaeus Demetrios Kydones The Mathematics Genealogy Project is a service of North Dakota State University and the American Mathematical Society. http://www.genealogy.math.ndsu.nodak.edu/ Georgios Plethon Gemistos Manuel Chrysoloras 1380, 1393 Basilios Bessarion 1436 Mystras Johannes Argyropoulos Guarino da Verona 1444 Università di Padova 1408 Cristoforo Landino Marsilio Ficino Vittorino da Feltre 1462 Università di Firenze 1416 Università di Padova Angelo Poliziano Theodoros Gazes Ognibene (Omnibonus Leonicenus) Bonisoli da Lonigo 1477 Università di Firenze 1433 Constantinople / Università di Mantova Università di Mantova Leo Outers Moses Perez Scipione Fortiguerra Demetrios Chalcocondyles Jacob ben Jehiel Loans Thomas à Kempis Rudolf Agricola Alessandro Sermoneta Gaetano da Thiene Heinrich von Langenstein 1485 Université Catholique de Louvain 1493 Università di Firenze 1452 Mystras / Accademia Romana 1478 Università degli Studi di Ferrara 1363, 1375 Université de Paris Maarten (Martinus Dorpius) van Dorp Girolamo (Hieronymus Aleander) Aleandro François Dubois Jean Tagault Janus Lascaris Matthaeus Adrianus Pelope Johann (Johannes Kapnion) Reuchlin Jan Standonck Alexander Hegius Pietro Roccabonella Nicoletto Vernia Johannes von Gmunden 1504, 1515 Université Catholique de Louvain 1499, 1508 Università di Padova 1516 Université de Paris 1472 Università di Padova 1477, 1481 Universität Basel / Université de Poitiers 1474, 1490 Collège Sainte-Barbe
    [Show full text]
  • Philosophical Transactions (A)
    INDEX TO THE PHILOSOPHICAL TRANSACTIONS (A) FOR THE YEAR 1889. A. A bney (W. de W.). Total Eclipse of the San observed at Caroline Island, on 6th May, 1883, 119. A bney (W. de W.) and T horpe (T. E.). On the Determination of the Photometric Intensity of the Coronal Light during the Solar Eclipse of August 28-29, 1886, 363. Alcohol, a study of the thermal properties of propyl, 137 (see R amsay and Y oung). Archer (R. H.). Observations made by Newcomb’s Method on the Visibility of Extension of the Coronal Streamers at Hog Island, Grenada, Eclipse of August 28-29, 1886, 382. Atomic weight of gold, revision of the, 395 (see Mallet). B. B oys (C. V.). The Radio-Micrometer, 159. B ryan (G. H.). The Waves on a Rotating Liquid Spheroid of Finite Ellipticity, 187. C. Conroy (Sir J.). Some Observations on the Amount of Light Reflected and Transmitted by Certain 'Kinds of Glass, 245. Corona, on the photographs of the, obtained at Prickly Point and Carriacou Island, total solar eclipse, August 29, 1886, 347 (see W esley). Coronal light, on the determination of the, during the solar eclipse of August 28-29, 1886, 363 (see Abney and Thorpe). Coronal streamers, observations made by Newcomb’s Method on the Visibility of, Eclipse of August 28-29, 1886, 382 (see A rcher). Cosmogony, on the mechanical conditions of a swarm of meteorites, and on theories of, 1 (see Darwin). Currents induced in a spherical conductor by variation of an external magnetic potential, 513 (see Lamb). 520 INDEX.
    [Show full text]
  • Where, Oh Waring? the Classic Problem and Its Extensions
    Where, Oh Waring? The Classic Problem and its Extensions Brian D. Beasley Presbyterian College, Clinton, SC Brian Beasley (B.S., Emory University; M.S., University of North Carolina; Ph.D., University of South Carolina) has taught at Pres- byterian College since 1988. He became a member of the Mathe- matical Association of America in 1989 and joined ACMS in 2007. Outside the classroom, Brian enjoys family time with his wife and two sons. He is an enthusiastic Scrabble player, a not-so-avid jog- ger, and a very shaky unicyclist. In the 2009-2010 academic year, one of our mathematics majors, Olivia Hightower, became interested in the history of Edward Waring and his famous conjecture about expressing positive integers as the sum of kth powers. Olivia's investigation eventually led to her honors project on Waring's Problem, in which she focused on the history of the conjecture, the eventual proof that all positive integers may be written as the sum of at most nine cubes, and the work of Hardy and Wright in establishing lower bounds in the case of sufficiently large integers. Her research renewed her professor's own interest in Waring, leading to the following article. This paper will sketch brief outlines of Waring's life and the history behind the eventual solution to his problem. In addition, it will present some of the related questions currently being studied, such as expressing sufficiently large integers as sums of powers, sums of powers of primes, and sums of unlike powers. We begin with a short summary of the biography of Edward Waring.
    [Show full text]
  • Magdalene College Magazine 2017-18
    magdalene college magdalene magdalene college magazine magazine No 62 No 62 2017–18 2017 –18 Designed and printed by The Lavenham Press. www.lavenhampress.co.uk MAGDALENE COLLEGE The Fellowship, October 2018 THE GOVERNING BODY 2013 MASTER: The Rt Revd & Rt Hon the Lord Williams of Oystermouth, PC, DD, Hon DCL (Oxford), FBA 1987 PRESIDENT: M E J Hughes, MA, PhD, Pepys Librarian, Director of Studies and University Affiliated Lecturer in English 1981 M A Carpenter, ScD, Professor of Mineralogy and Mineral Physics 1984 H A Chase, ScD, FREng, Director of Studies in Chemical Engineering and Emeritus Professor of Biochemical Engineering 1984 J R Patterson, MA, PhD, Praelector, Director of Studies in Classics and USL in Ancient History 1989 T Spencer, MA, PhD, Director of Studies in Geography and Professor of Coastal Dynamics 1990 B J Burchell, MA, and PhD (Warwick), Tutor, Joint Director of Studies in Human, Social and Political Science and Reader in Sociology 1990 S Martin, MA, PhD, Senior Tutor, Admissions Tutor (Undergraduates), Director of Studies and University Affiliated Lecturer in Mathematics 1992 K Patel, MA, MSc and PhD (Essex), Director of Studies in Economics & in Land Economy and UL in Property Finance 1993 T N Harper, MA, PhD, College Lecturer in History and Professor of Southeast Asian History (1990: Research Fellow) 1994 N G Jones, MA, LLM, PhD, Dean, Director of Studies in Law and Reader in English Legal History 1995 H Babinsky, MA and PhD (Cranfield), College Lecturer in Engineering and Professor of Aerodynamics 1996 P Dupree,
    [Show full text]
  • Waring's Problem
    MATHEMATICS MASTER’STHESIS WARING’SPROBLEM JANNESUOMALAINEN HELSINKI 2016 UNIVERSITYOFHELSINKI HELSINGIN YLIOPISTO — HELSINGFORS UNIVERSITET — UNIVERSITY OF HELSINKI Tiedekunta/Osasto — Fakultet/Sektion — Faculty Laitos — Institution — Department Faculty of Science Department of Mathematics and Statistics Tekijä — Författare — Author Janne Suomalainen Työn nimi — Arbetets titel — Title Waring’s Problem Oppiaine — Läroämne — Subject Mathematics Työn laji — Arbetets art — Level Aika — Datum — Month and year Sivumäärä — Sidoantal — Number of pages Master’s Thesis 9/2016 36 p. Tiivistelmä — Referat — Abstract Waring’s problem is one of the two classical problems in additive number theory, the other being Goldbach’s conjecture. The aims of this thesis are to provide an elementary, purely arithmetic solution of the Waring problem, to survey its vast history and to outline a few variations to it. Additive number theory studies the patterns and properties, which arise when integers or sets of integers are added. The theory saw a new surge after 1770, just before Lagrange’s celebrated proof of the four-square theorem, when a British mathematician, Lucasian professor Edward Waring made the profound statement nowadays dubbed as Waring’s problem: for all integers n greater than one, there exists a finite integer s such that every positive integer is the sum of s nth powers of non- negative integers. Ever since, the problem has been taken up by many mathematicians and state of the art techniques have been developed — to the point that Waring’s problem, in a general sense, can be considered almost completely solved. The first section of the thesis works as an introduction to the problem. We give a profile of Edward Waring, state the problem both in its original form and using present-day language, and take a broad look over the history of the problem.
    [Show full text]
  • {PDF} Charles Darwin, the Copley Medal, and the Rise of Naturalism
    CHARLES DARWIN, THE COPLEY MEDAL, AND THE RISE OF NATURALISM 1862-1864 1ST EDITION PDF, EPUB, EBOOK Marsha Driscoll | 9780205723171 | | | | | Charles Darwin, the Copley Medal, and the Rise of Naturalism 1862-1864 1st edition PDF Book In recognition of his distinguished work in the development of the quantum theory of atomic structure. In recognition of his distinguished studies of tissue transplantation and immunological tolerance. Dunn, Dann Siems, and B. Alessandro Volta. Tomas Lindahl. Thomas Henry Huxley. Andrew Huxley. Adam Sedgwick. Ways and Means, Science and Society Picture Library. John Smeaton. Each year the award alternates between the physical and biological sciences. On account of his curious Experiments and Discoveries concerning the different refrangibility of the Rays of Light, communicated to the Society. David Keilin. For his seminal work on embryonic stem cells in mice, which revolutionised the field of genetics. Derek Barton. This game is set in and involves debates within the Royal Society on whether Darwin should receive the Copley Medal, the equivalent of the Nobel Prize in its day. Frank Fenner. For his Paper communicated this present year, containing his Experiments relating to Fixed Air. Read and download Log in through your school or library. In recognition of his pioneering work on the structure of muscle and on the molecular mechanisms of muscle contraction, providing solutions to one of the great problems in physiology. James Cook. Wilhelm Eduard Weber. For his investigations on the morphology and histology of vertebrate and invertebrate animals, and for his services to biological science in general during many past years. Retrieved John Ellis.
    [Show full text]
  • Waring's Problem and the Circle Method
    GENERAL I ARTICLE Waring's Problem and the Circle Method C S Yogananda In 1770, in his book M editationes Algebraicae, Edward Waring made the statement that every positive integer is a sum of nine cubes, is also a sum of not more than 19 fourth powers, and so on. The so on was taken to mean that given a positive integer k there is a num­ ber depending only on k, say s, such that every positive integer can be expressed as a sum of at most s number C S Yogananda obtained of k -th powers. There is no obvious heuristic reason to his PhD in Mathematics believe the truth or falsity of the statement. There are in 1990 from the Institute examples either way. Lagrange had proved, coinciden­ of Mathematical Sciences, tally in 1770, that every positive integer can be written Chennai. He has been as a sum of not more than four squares. On the other involved in the Math- hand, if one wants to write any positive integer as a sum ematicalOlympiad Programme at different of powers of 2 then it is not too difficult to see that there levels since 1989. is no finite number, say m, such that every positive inte­ His research interests lie ger can be written as a sum of m or fewer powers of 2. in number theory; his (Proof: Suppose on the contrary that there is such a other interests include m 1 classical music and number 171" But then 2 + - 1 can not be written as mountaineering.
    [Show full text]
  • California Fair List 2018
    BERNARD QUARITCH LTD. PASADENA CONVENTION CENTER, FEBRUARY 9 FEBRUARY CENTER, CONVENTION PASADENA - 11, 2018, BOOTH 308 2018,BOOTH 11, CALIFORNIA INTERNATIONALCALIFORNIA ANTIQUARIAN BOOK FAIR st 51 BERNARD QUARITCH LTD 40 SOUTH AUDLEY ST, LONDON W1K 2PR Tel: +44 (0)20-7297 4888 Fax: +44 (0)20-7297 4866 e-mail: [email protected] web site: www.quaritch.com Bankers: Barclays Bank plc, Level 27, 1 Churchill Place, London E14 5HP Sort code: 20-65-90 Acct no: 10511722 Swift code: BARC GB22 Sterling account: IBAN: GB62 BARC 206590 10511722 Euro account: IBAN: GB91 BARC 206590 45447011 U.S. Dollar account: IBAN: GB10 BARC 206590 63992444 VAT number: GB 840 1358 54 Mastercard, Visa, and American Express accepted Recent Catalogues: 1436 Travel, Natural History & Scientific Exploration 1435 Music 1434 Medieval and Renaissance Manuscripts 1433 English Books & Manuscripts 1432 Continental Books Recent Lists: 2018/1 English Books & Manuscripts 2017/14 Politics, Statecraft, Mirrors of Princes 2017/13 Photography – Autumn Miscellany 2017/12 Economics 2017/11 Revolution and Propaganda Cover image and vignette opposite from item 23. © Bernard Quaritch 2018 WINE AND LOVE – WITH TRANSLATIONS BY COWLEY 1// ANACREON done into English out of the original Greek … Oxford, Printed by L. Lichfield … for Anthony Stephens … 1683. 8vo., pp. [20], 72, 79-114; a very good copy in contemporary mottled calf, front joint cracked. $945 First edition. The ‘Anacreontea’, a collection of 60 Greek poems on wine, beauty and erotic love, though long attributed to Anacreon was actually by numerous anonymous imitators. The present collection of fifty-two poems is similarly anonymous and collaborative, and contains translations (or imitations) attributed to Oldham, Cowley, Thomas Wood and Francis Wallis.
    [Show full text]
  • A Forgotten Paper on the Fundamental Theorem of Algebra
    5. Smithies 13/9/00 11:25 AM Page 333 Notes Rec. R. Soc. Lond. 54 (3), 333–341 (2000) © 2000 The Royal Society A FORGOTTEN PAPER ON THE FUNDAMENTAL THEOREM OF ALGEBRA by FRANK SMITHIES 167 Huntingdon Road, Cambridge CB3 0DH, UK SUMMARY In 1798, there appeared in the Philosophical Transactions of the Royal Society a paper by James Wood, purporting to prove the fundamental theorem of algebra, to the effect that every non-constant polynomial with real coefficients has at least one real or complex zero. Since the first generally accepted proof of this result was given by Gauss in 1799, Wood’s paper deserves careful examination. After giving a brief outline of Wood’s career, I describe the argument of his paper. His proof turns out to be incomplete as it stands, but it contains an original idea, which was to be used later, in the same context, by von Staudt, Gordan and others, without knowledge of Wood’s work. After putting Wood’s work in context, I conclude by showing how his idea can be used to prove the complex form of the fundamental theorem of algebra, stating that every non-constant polynomial with complex coefficients has at least one zero in the complex field. INTRODUCTION Professor Peter Goddard, Master of St John’s College, Cambridge, has drawn attention to a paper by James Wood, one of his predecessors, entitled ‘On the roots of equations’, which appeared in Philosophical Transactions volume 88. It was communicated by Nevil Maskelyne, F.R.S., the Astronomer Royal, and was read on 17 May 1798.1 The paper purports to prove what is usually called the fundamental theorem of algebra, stating it in the form ‘Every equation has as many roots of the form a±√(±b2) as it has dimensions’; in more modern language, the author is saying that a non- constant polynomial of degree n≥1, with real coefficients, has n real or complex zeros (some of which may be repeated).
    [Show full text]
  • The Two Substantial Mathematical Essays in the Final Volume Are One by Masani on the Work of Wiener and One by Wermer on Function Algebras
    CORE Metadata, citation and similar papers at core.ac.uk Provided by Elsevier - Publisher Connector HM 18 REVIEWS 85 The two substantial mathematical essays in the final volume are one by Masani on the work of Wiener and one by Wermer on function algebras. Masani claims to survey about “70 percent of Wiener’s mathematical work and 25 percent of his work in the empirical realms” [3, p. 3281. The mathematics treated is remarkable in its range and imagination, particularly for the ideas that arose in his concern with problems of physics and of engineering. For one example of how far he was ahead of his time, we find on p. 312 a 1926 quote from Wiener, followed by a comment by L. Schwartz, showing that Wiener recognized the need in differential equations for the theory that ultimately became the theory of distributions. Wermer sketches a fascinating story of interplay between abstract functional analysis and classical function theory. Finally, there is a treatment of the history of (the history of) mathematics in America-parentheses seem appropriate here, where the associative law may not apply-by Merzbach, one of the assistant editors. Along with sketches of the lives and works of the pioneers, she traces the subject through periods of growth and decay. Fortunately, she sees an upswing in command now, of which these volumes bear witness. She ends with a caution to workers in the history of mathematics “to beware of both its popularity and its methodological champions” [3, p. 6641. No doubt the readers of Historia Mathematics will recognize more immediately than does this mathematician the meaning of the second warning.
    [Show full text]
  • Holy Trinity Coventry - Marriages 1865-1872 Film 1067415 Page 1
    Holy Trinity Coventry - Marriages 1865-1872 Film 1067415 Page 1 Date Groom [ (x) if by mark] Groom info. Groom's address Groom's father to Bride [ (x) if by mark] Bride's info. Bride's address Bride's father Witnesses to marriage [ (x) if by mark] Bn 07.05.1865 Beale, George 24, bac., porter Well Street Richard Beale, Sgt. 60th Regiment to Stokes, Elizabeth 22, spin. Well Street Josiah Stokes, licensed victualler wits Josiah Stokes, Eliza Beale Bn 08.05.1865 Young, James 46, bac., labourer Ct. 1, Cross Cheaping William Young, labourer to Barnes, Ann 26, spin. Cross Cheaping William Barnes, schoolmaster wits Joseph Young, Martha Young Bn 14.05.1865 Hulm, Abel 27, bac., elastic weaver Chauntry Place Abel Hulm, weaver to Sidwell, Emma Eliza 21, spin. Palmer Lane Henry Sidwell, weaver wits Charles Moore, Ann Eliza Hulm Bn 15.05.1865 Whadcock, Charles (x) 37, wid., weaver Silver Street Richard Whadcock, weaver to Gutteridge, Harriett 36, spin. Silver Street John Gutteridge, weaver wits Joseph Ashley (x), Anne Ashley RC 21.05.1865 Riley, John 27, bac., weaver Peel Street, Red Lane James Riley, weaver to Taylor, Ann 27, spin. Charles Street, Hill Fields George Taylor, weaver wits Jeremiah Taylor, Harriett Cook Bn 17.06.1865 Yardley, Thomas 26, wid., watch jeweller Well Street Illegitimate son of Anna Yardley to Turner, Martha 26, spin. Jesson Street Thomas Turner, wheelwright wits David Eaves, Fanny Causebrook (x) Bn 18.06.1865 Smith, Tom 23, bac., watchmaker Well Street Joseph Smith, watchmaker to Corby, Sarah (x) 24, spin. Well Street Frederick Corby, weaver wits Joseph Smith, ?Laneg Fatems Bn 18.06.1865 Hewson, John 21, bac., baker Well Street William Hewson, weaver to Trickett, Harriett (x) 20, spin.
    [Show full text]