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Fabio Tonini –
Fabio Tonini Personal Data Date of Birth May 16, 1984 Citzenship Italy Current Position Since Researcher (RTDA) at University of Florence November 2018 Positions Held October 2018 Scholarship at Scuola Normale Superiore of Pisa October 2015 Post Doc at the Freie University of Berlin - September 2018 April 2013 - Post Doc at the Humboldt University of Berlin September 2015 January 2012 Scholarship at Scuola Normale Superiore of Pisa - January 2013 January 2009 Ph.D. student at Scuola Normale Superiore of Pisa under the supervision of - January Prof. Angelo Vistoli 2012 Italian National Scientific Habilitation (ASN) May 2021 - Professore II fascia May 2030 Education May 2013 Ph.D. at Scuola Normale Superiore of Pisa December Diploma at Scuola Normale Superiore of Pisa 2008 September Master’s Degree in Pure Mathematics, University of Pisa, with honors 2008 July 2006 Bachelor’s Degree in Pure Mathematics, University of Pisa, with honors Universitá degli Studi di Firenze, Dipartimento di Matematica e Informatica ’Ulisse Dini’, Viale Morgagni, 67/a, Firenze, 50134 Italy B fabio.tonini@unifi.it • Í people.dimai.unifi.it/tonini/ PhD’s Thesis Title Stacks of ramified Galois covers defended the 2 May 2013 pdf online link Advisor Angelo Vistoli Master’s Thesis Title Rivestimenti di Gorenstein (Gorenstein covers) pdf online link Advisor Angelo Vistoli Research Interests { Algebraic Geometry { Algebraic stacks, Moduli theory { Action of algebraic groups and Galois covers { Representation theory { Algebraic fundamental groups and gerbes Memberships { GNSAGA, INdAM, Gruppo Nazionale per le Strutture Algebriche, Geomet- riche e le loro Applicazioni Teaching Experience 2020/21 Course Title: Matematica e statistica, First year at “Scienze Farmaceutiche”, University of Florence 2020/21 Course Title: Matematica con elementi di Statistica, First year at “Scienze Naturali”, University of Florence. -
A Historical Outline of the Theorem of Implicit Nctions
Divulgaciones Matem acute-a t icas Vol period 10 No period 2 open parenthesis 2002 closing parenthesis commannoindent pp periodDivulgaciones 171 endash 180 Matem $ nacutefag $ t icas Vol . 10No . 2 ( 2002 ) , pp . 171 −− 180 A .... Historical .... Outline .... of the .... Theorem .... of nnoindentImplicit ..A F-un h nctions f i l l H i s t o r i c a l n h f i l l Outline n h f i l l o f the n h f i l l Theorem n h f i l l o f Un Bosquejo Hist acute-o rico del Teorema de las Funciones Impl dotlessi-acute citas n centerlineGiovanni Mingarif I m pScarpello l i c i t nquad open parenthesis$ F−u $ giovannimingari n c t i o n s g at l ibero period it closing parenthesis Daniele Ritelli dr itelli at e c onomia period unibo period it n centerlineDipartimentofUn di Matematica BosquejoDivulgaciones per Hist Matem le Scienzea´ $ tn icasacute Economiche Vol .f 10og No$ .e 2 Sociali( rico 2002 )delcomma , pp . Teorema 171 { 180 de las Funciones Impl $ nBolognaacutefn ItalyimathgA$ c Historical i t a s g Outline of the Theorem Abstract n centerline f Giovanniof Mingari Scarpello ( giovannimingari $ @ $ l ibero . it ) g In this article a historical outline ofImplicit the implicit functionsF theory− u nctions is presented startingUn from Bosquejo the wiewpoint Hist ofo´ Descartesrico del Teorema algebraic geometry de las Funciones Impl ´{ citas n centerline f Daniele Ritelli dr itelli $@$ e c onomia . unibo . it g open parenthesisGiovanni 1 637 closing Mingari parenthesis Scarpello and Leibniz ( giovannimingari open parenthesis 1 676@ l or ibero 1 677 closing . -
HOMOTECIA Nº 6-15 Junio 2017
HOMOTECIA Nº 6 – Año 15 Martes, 1º de Junio de 2017 1 Entre las expectativas futuras que se tienen sobre un docente en formación, está el considerar como indicativo de que logrará realizarse como tal, cuando evidencia confianza en lo que hace, cuando cree en sí mismo y no deja que su tiempo transcurra sin pro pósitos y sin significado. Estos son los principios que deberán pautar el ejercicio de su magisterio si aspira tener éxito en su labor, lo cual mostrará mediante su afán por dar lo bueno dentro de sí, por hacer lo mejor posible, por comprometerse con el porvenir de quienes confiadamente pondrán en sus manos la misión de enseñarles. Pero la responsabilidad implícita en este proceso lo debería llevar a considerar seriamente algunos GIACINTO MORERA (1856 – 1907 ) aspectos. Obtener una acreditación para enseñar no es un pergamino para exhib ir con petulancia ante familiares y Nació el 18 de julio de 1856 en Novara, y murió el 8 de febrero de 1907, en Turín; amistades. En otras palabras, viviendo en el mundo educativo, es ambas localidades en Italia. asumir que se produjo un cambio significativo en la manera de Matemático que hizo contribuciones a la dinámica. participar en este: pasó de ser guiado para ahora guiar. No es que no necesite que se le orie nte como profesional de la docencia, esto es algo que sucederá obligatoriamente a nivel organizacional, Giacinto Morera , hijo de un acaudalado hombre de pero el hecho es que adquirirá una responsabilidad mucho mayor negocios, se graduó en ingeniería y matemáticas en la porque así como sus preceptores universitarios tuvieron el compromiso de formarlo y const ruirlo cultural y Universidad de Turín, Italia, habiendo asistido a los académicamente, él tendrá el mismo compromiso de hacerlo con cursos por Enrico D'Ovidio, Angelo Genocchi y sus discípulos, sea cual sea el nivel docente donde se desempeñe. -
Continuous Nowhere Differentiable Functions
2003:320 CIV MASTER’S THESIS Continuous Nowhere Differentiable Functions JOHAN THIM MASTER OF SCIENCE PROGRAMME Department of Mathematics 2003:320 CIV • ISSN: 1402 - 1617 • ISRN: LTU - EX - - 03/320 - - SE Continuous Nowhere Differentiable Functions Johan Thim December 2003 Master Thesis Supervisor: Lech Maligranda Department of Mathematics Abstract In the early nineteenth century, most mathematicians believed that a contin- uous function has derivative at a significant set of points. A. M. Amp`ereeven tried to give a theoretical justification for this (within the limitations of the definitions of his time) in his paper from 1806. In a presentation before the Berlin Academy on July 18, 1872 Karl Weierstrass shocked the mathematical community by proving this conjecture to be false. He presented a function which was continuous everywhere but differentiable nowhere. The function in question was defined by ∞ X W (x) = ak cos(bkπx), k=0 where a is a real number with 0 < a < 1, b is an odd integer and ab > 1+3π/2. This example was first published by du Bois-Reymond in 1875. Weierstrass also mentioned Riemann, who apparently had used a similar construction (which was unpublished) in his own lectures as early as 1861. However, neither Weierstrass’ nor Riemann’s function was the first such construction. The earliest known example is due to Czech mathematician Bernard Bolzano, who in the years around 1830 (published in 1922 after being discovered a few years earlier) exhibited a continuous function which was nowhere differen- tiable. Around 1860, the Swiss mathematician Charles Cell´erieralso discov- ered (independently) an example which unfortunately wasn’t published until 1890 (posthumously). -
A New Vision of the Senses in the Work of Galileo Galilei
Perception, 2008, volume 37, pages 1312 ^ 1340 doi:10.1068/p6011 Galileo's eye: A new vision of the senses in the work of Galileo Galilei Marco Piccolino Dipartimento di Biologia, Universita© di Ferrara, I 44100 Ferrara, Italy; e-mail: [email protected] Nicholas J Wade University of Dundee, Dundee DD1 4HN, Scotland, UK Received 4 December 2007 Abstract. Reflections on the senses, and particularly on vision, permeate the writings of Galileo Galilei, one of the main protagonists of the scientific revolution. This aspect of his work has received scant attention by historians, in spite of its importance for his achievements in astron- omy, and also for the significance in the innovative scientific methodology he fostered. Galileo's vision pursued a different path from the main stream of the then contemporary studies in the field; these were concerned with the dioptrics and anatomy of the eye, as elaborated mainly by Johannes Kepler and Christoph Scheiner. Galileo was more concerned with the phenomenology rather than with the mechanisms of the visual process. His general interest in the senses was psychological and philosophical; it reflected the fallacies and limits of the senses and the ways in which scientific knowledge of the world could be gathered from potentially deceptive appearances. Galileo's innovative conception of the relation between the senses and external reality contrasted with the classical tradition dominated by Aristotle; it paved the way for the modern understanding of sensory processing, culminating two centuries later in Johannes Mu« ller's elaboration of the doctrine of specific nerve energies and in Helmholtz's general theory of perception. -
On the Origin and Early History of Functional Analysis
U.U.D.M. Project Report 2008:1 On the origin and early history of functional analysis Jens Lindström Examensarbete i matematik, 30 hp Handledare och examinator: Sten Kaijser Januari 2008 Department of Mathematics Uppsala University Abstract In this report we will study the origins and history of functional analysis up until 1918. We begin by studying ordinary and partial differential equations in the 18th and 19th century to see why there was a need to develop the concepts of functions and limits. We will see how a general theory of infinite systems of equations and determinants by Helge von Koch were used in Ivar Fredholm’s 1900 paper on the integral equation b Z ϕ(s) = f(s) + λ K(s, t)f(t)dt (1) a which resulted in a vast study of integral equations. One of the most enthusiastic followers of Fredholm and integral equation theory was David Hilbert, and we will see how he further developed the theory of integral equations and spectral theory. The concept introduced by Fredholm to study sets of transformations, or operators, made Maurice Fr´echet realize that the focus should be shifted from particular objects to sets of objects and the algebraic properties of these sets. This led him to introduce abstract spaces and we will see how he introduced the axioms that defines them. Finally, we will investigate how the Lebesgue theory of integration were used by Frigyes Riesz who was able to connect all theory of Fredholm, Fr´echet and Lebesgue to form a general theory, and a new discipline of mathematics, now known as functional analysis. -
NSP4 Pragmatist Kant
Nordic NSP Studies in Pragmatism Helsinki — 2019 Giovanni Maddalena “Anti-Kantianism as a Necessary Characteristic of Pragmatism” In: Krzysztof Piotr Skowronski´ and Sami Pihlstrom¨ (Eds.) (2019). Pragmatist Kant—Pragmatism, Kant, and Kantianism in the Twenty-first Century (pp. 43–59). Nordic Studies in Pragmatism 4. Helsinki: Nordic Pragmatism Network. issn-l 1799-3954 issn 1799-3954 isbn 978-952-67497-3-0 Copyright c 2019 The Authors and the Nordic Pragmatism Network. This work is licensed under a Creative Commons Attribution-NonCommercial 3.0 Unported License. CC BY NC For more information, see http://creativecommons.org/licenses/by-nc/3.0/ Nordic Pragmatism Network, NPN Helsinki 2019 www.nordprag.org Anti-Kantianism as a Necessary Characteristic of Pragmatism Giovanni Maddalena Universit`adel Molise 1. Introduction Pragmatists declared their anti-Cartesianism at the first appearance of the movement, in Peirce’s series on cognition written for the Journal of Specu- lative Philosophy (1867–8). As is well known, the brilliant young scientist characterized Cartesian doubt as a “paper doubt”, by opposing it to sci- entists’ true “living doubt” (Peirce 1998 [1868], 115).1 Some readers have not understood the powerful novelty that his opposition to Cartesianism implies. According to Peirce, research does not proceed from skeptical, “paper” doubt. For Peirce, doubt is possible because of a previous cer- tainty, a position which is similar to the one held by Augustine (Augustine 1970). Research moves from one certainty to another; the abandonment of an initial certainty is only reasonable in the presence of a real and surprising phenomenon that alters one of the pillars on which it stands. -
Reflections on Vailati's Pragmatism
Reflections on Vailati's Pragmatism M. CAAMANO AND P. SUPPES Preliminary remarks The pragmatic project of developing a richer notion of experience Classical pragmatists made a sustained effort to develop a new con ception of experience, free from some simplistic assumptions shared by both traditional rationalists and empiricists, like the idea that experi enceresults from a combination of simple sensations. In his main paper on pragmatism, "The origins and the fundamental idea.of pragmatism" (1909b), Giovanni Vailati characterized our experience of permanent, objective existence in terms of a certain kind of conditional expecta tions, in particular, those which are conditioned to certain deliberate actions of ours being performed. His experiential account of objective existence, based on a systematic relation between deliberate actions and expectations, is a permanent contribution to pragmatic thought, which we analyze and assess. We also consider Vailati's revision of the l"eircean pragmatic maxim, the pragmatic evaluation of meaningless assertions, and his vindication of inferential usefulness as a determin ing factor in both formal systems and empirical theories. Our discus sion will as well include a critical analysis of some less satisfactory aspects of Vailati's thought, whose Brentanian conception of mental facts contrasts sharply with James' sophisticated study of the mind in The Principles of Psychology (1890). But let us now make some prelim inary comments to place Vailati's work within the broader pragmatic tradition. Evans' bibliography (1930) of the references to pragmatism Logic and Pragmatism. Selected Essays QY Giovanni Vailati. C. Arrighi, P. Cantu, M. De Zan, and P. Suppes. Copyright © 2009, CSLI Publications. -
Rudi Mathematici
Rudi Mathematici Y2K Rudi Mathematici Gennaio 2000 52 1 S (1803) Guglielmo LIBRI Carucci dalla Somaja Olimpiadi Matematiche (1878) Agner Krarup ERLANG (1894) Satyendranath BOSE P1 (1912) Boris GNEDENKO 2 D (1822) Rudolf Julius Emmanuel CLAUSIUS Due matematici "A" e "B" si sono inventati una (1905) Lev Genrichovich SHNIRELMAN versione particolarmente complessa del "testa o (1938) Anatoly SAMOILENKO croce": viene scritta alla lavagna una matrice 1 3 L (1917) Yuri Alexeievich MITROPOLSHY quadrata con elementi interi casuali; il gioco (1643) Isaac NEWTON consiste poi nel calcolare il determinante: 4 M (1838) Marie Ennemond Camille JORDAN 5 M Se il determinante e` pari, vince "A". (1871) Federigo ENRIQUES (1871) Gino FANO Se il determinante e` dispari, vince "B". (1807) Jozeph Mitza PETZVAL 6 G (1841) Rudolf STURM La probabilita` che un numero sia pari e` 0.5, (1871) Felix Edouard Justin Emile BOREL 7 V ma... Quali sono le probabilita` di vittoria di "A"? (1907) Raymond Edward Alan Christopher PALEY (1888) Richard COURANT P2 8 S (1924) Paul Moritz COHN (1942) Stephen William HAWKING Dimostrare che qualsiasi numero primo (con (1864) Vladimir Adreievich STELKOV l'eccezione di 2 e 5) ha un'infinita` di multipli 9 D nella forma 11....1 2 10 L (1875) Issai SCHUR (1905) Ruth MOUFANG "Die Energie der Welt ist konstant. Die Entroopie 11 M (1545) Guidobaldo DEL MONTE der Welt strebt einem Maximum zu" (1707) Vincenzo RICCATI (1734) Achille Pierre Dionis DU SEJOUR Rudolph CLAUSIUS 12 M (1906) Kurt August HIRSCH " I know not what I appear to the world, -
The Art of the Intelligible
JOHN L. BELL Department of Philosophy, University of Western Ontario THE ART OF THE INTELLIGIBLE An Elementary Survey of Mathematics in its Conceptual Development To my dear wife Mimi The purpose of geometry is to draw us away from the sensible and the perishable to the intelligible and eternal. Plutarch TABLE OF CONTENTS FOREWORD page xi ACKNOWLEDGEMENTS xiii CHAPTER 1 NUMERALS AND NOTATION 1 CHAPTER 2 THE MATHEMATICS OF ANCIENT GREECE 9 CHAPTER 3 THE DEVELOPMENT OF THE NUMBER CONCEPT 28 THE THEORY OF NUMBERS Perfect Numbers. Prime Numbers. Sums of Powers. Fermat’s Last Theorem. The Number π . WHAT ARE NUMBERS? CHAPTER 4 THE EVOLUTION OF ALGEBRA, I 53 Greek Algebra Chinese Algebra Hindu Algebra Arabic Algebra Algebra in Europe The Solution of the General Equation of Degrees 3 and 4 The Algebraic Insolubility of the General Equation of Degree Greater than 4 Early Abstract Algebra 70 CHAPTER 5 THE EVOLUTION OF ALGEBRA, II 72 Hamilton and Quaternions. Grassmann’s “Calculus of Extension”. Finite Dimensional Linear Algebras. Matrices. Lie Algebras. CHAPTER 6 THE EVOLUTION OF ALGEBRA, III 89 Algebraic Numbers and Ideals. ABSTRACT ALGEBRA Groups. Rings and Fields. Ordered Sets. Lattices and Boolean Algebras. Category Theory. CHAPTER 7 THE DEVELOPMENT OF GEOMETRY, I 111 COORDINATE/ALGEBRAIC/ANALYTIC GEOMETRY Algebraic Curves. Cubic Curves. Geometric Construction Problems. Higher Dimensional Spaces. NONEUCLIDEAN GEOMETRY CHAPTER 8 THE DEVELOPMENT OF GEOMETRY, II 129 PROJECTIVE GEOMETRY DIFFERENTIAL GEOMETRY The Theory of Surfaces. Riemann’s Conception of Geometry. TOPOLOGY Combinatorial Topology. Point-set topology. CHAPTER 9 THE CALCULUS AND MATHEMATICAL ANALYSIS 151 THE ORIGINS AND BASIC NOTIONS OF THE CALCULUS MATHEMATICAL ANALYSIS Infinite Series. -
RM Calendar 2017
Rudi Mathematici x3 – 6’135x2 + 12’545’291 x – 8’550’637’845 = 0 www.rudimathematici.com 1 S (1803) Guglielmo Libri Carucci dalla Sommaja RM132 (1878) Agner Krarup Erlang Rudi Mathematici (1894) Satyendranath Bose RM168 (1912) Boris Gnedenko 1 2 M (1822) Rudolf Julius Emmanuel Clausius (1905) Lev Genrichovich Shnirelman (1938) Anatoly Samoilenko 3 T (1917) Yuri Alexeievich Mitropolsky January 4 W (1643) Isaac Newton RM071 5 T (1723) Nicole-Reine Etable de Labrière Lepaute (1838) Marie Ennemond Camille Jordan Putnam 2002, A1 (1871) Federigo Enriques RM084 Let k be a fixed positive integer. The n-th derivative of (1871) Gino Fano k k n+1 1/( x −1) has the form P n(x)/(x −1) where P n(x) is a 6 F (1807) Jozeph Mitza Petzval polynomial. Find P n(1). (1841) Rudolf Sturm 7 S (1871) Felix Edouard Justin Emile Borel A college football coach walked into the locker room (1907) Raymond Edward Alan Christopher Paley before a big game, looked at his star quarterback, and 8 S (1888) Richard Courant RM156 said, “You’re academically ineligible because you failed (1924) Paul Moritz Cohn your math mid-term. But we really need you today. I (1942) Stephen William Hawking talked to your math professor, and he said that if you 2 9 M (1864) Vladimir Adreievich Steklov can answer just one question correctly, then you can (1915) Mollie Orshansky play today. So, pay attention. I really need you to 10 T (1875) Issai Schur concentrate on the question I’m about to ask you.” (1905) Ruth Moufang “Okay, coach,” the player agreed. -
On History of Epsilontics
ANTIQUITATES MATHEMATICAE Vol. 10(1) 2016, p. xx–zz doi: 10.14708/am.v10i0.805 Galina Ivanovna Sinkevich∗ (St. Petersburg) On History of Epsilontics Abstract. This is a review of genesis of − δ language in works of mathematicians of the 19th century. It shows that although the sym- bols and δ were initially introduced in 1823 by Cauchy, no functional relationship for δ as a function of was ever ever specied by Cauchy. It was only in 1861 that the epsilon-delta method manifested itself to the full in Weierstrass denition of a limit. The article gives various interpretations of these issues later provided by mathematicians. This article presents the text [Sinkevich, 2012d] of the same author which is slightly redone and translated into English. 2010 Mathematics Subject Classication: 01A50; 01A55; 01A60. Key words and phrases: History of mathematics, analysis, continu- ity, Lagrange, Ampére, Cauchy, Bolzano, Heine, Cantor, Weierstrass, Lebesgue, Dini.. It is mere feedback-style ahistory to read Cauchy (and contemporaries such as Bernard Bolzano) as if they had read Weierstrass already. On the contrary, their own pre-Weierstrassian muddles need historical reconstruction. [Grattan-Guinness 2004, p. 176]. Since the early antiquity the concept of continuity was described throgh the notions of time, motion, divisibility, contact1 . The ideas about functional accuracy came with the extension of mathematical interpretation to natural-science observations. Physical and geometrical notions of continuity became insucient, ultimately ∗ Galina Ivanovna Sinkeviq 1The 'continuous' is a subdivision of the contiguous: things are called continuous when the touching limits of each become one and the same and are, as the word implies, contained in each other: continuity is impossible if these extremities are two.