Theorems in pure mathematics can be proved right but the models used in applied mathematics, natural and social science, as well as in engineering, can at most be “not yet proved wrong”

2016 ◽  
Vol 53 (11) ◽  
pp. 1440-1442 ◽  
Author(s):  
Kevin Burke
Keyword(s):  
Social Science ◽  
Applied Mathematics ◽  
Pure Mathematics

scholarly journals Fractional Derivatives and Integrals: What Are They Needed For?

Mathematics ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 164 ◽  
Author(s):  
Vasily E. Tarasov ◽  
Svetlana S. Tarasova
Keyword(s):  
Power Law ◽  
Applied Mathematics ◽  
Mathematical Problem ◽  
Frequency Dispersion ◽  
Point Of View ◽  
Fading Memory ◽  
Fractional Operator ◽  
Distributed Lag ◽  
Pure Mathematics ◽  
New Research

The question raised in the title of the article is not philosophical. We do not expect general answers of the form “to describe the reality surrounding us”. The question should actually be formulated as a mathematical problem of applied mathematics, a task for new research. This question should be answered in mathematically rigorous statements about the interrelations between the properties of the operator’s kernels and the types of phenomena. This article is devoted to a discussion of the question of what is fractional operator from the point of view of not pure mathematics, but applied mathematics. The imposed restrictions on the kernel of the fractional operator should actually be divided by types of phenomena, in addition to the principles of self-consistency of mathematical theory. In applications of fractional calculus, we have a fundamental question about conditions of kernels of fractional operator of non-integer orders that allow us to describe a particular type of phenomenon. It is necessary to obtain exact correspondences between sets of properties of kernel and type of phenomena. In this paper, we discuss the properties of kernels of fractional operators to distinguish the following types of phenomena: fading memory (forgetting) and power-law frequency dispersion, spatial non-locality and power-law spatial dispersion, distributed lag (time delay), distributed scaling (dilation), depreciation, and aging.

scholarly journals Horace Lamb and the circumstances of his appointment at Owens College

2012 ◽  
Vol 67 (2) ◽  
pp. 139-158 ◽  
Author(s):  
Brian Launder
Keyword(s):  
Applied Mathematics ◽  
South Australia ◽  
Critical Juncture ◽  
Classical Fluid ◽  
Sequence Of Events ◽  
Pure Mathematics ◽  
Research In Education

This paper examines a succession of incidents at a critical juncture in the life of Professor Horace Lamb FRS, a highly regarded classical fluid mechanicist, who, over a period of some 35 years at Manchester, made notable contributions in research, in education and in wise administration at both national and university levels. Drawing on archived documents from the universities of Manchester and Adelaide, the article presents the unusual sequence of events that led to his removing from Adelaide, South Australia, where he had served for nine years as the Elder Professor of Mathematics, to Manchester. In 1885 he was initially appointed to the vacant Chair of Pure Mathematics at Owens College and then, in 1888, as an outcome of his proposal for rearranging professorial responsibilities, to the Beyer Professorship of Pure and Applied Mathematics.

Berlin Roots – Zionist Incarnation: The Ethos of Pure Mathematics and the Beginnings of the Einstein Institute of Mathematics at the Hebrew University of Jerusalem

2004 ◽  
Vol 17 (1-2) ◽  
pp. 199-234 ◽  
Author(s):  
Shaul Katz
Keyword(s):  
Middle East ◽  
Applied Mathematics ◽  
Jewish People ◽  
Controversial Issue ◽  
Academic Needs ◽  
German Mathematician ◽  
Pure Mathematics ◽  
Hebrew University

Officially inaugurated in 1925, the Hebrew University of Jerusalem was designed to serve the academic needs of the Jewish people and the Zionist enterprise in British Mandatory Palestine, as well as to help fulfill the economic and social requirements of the Middle East. It is intriguing that a university with such practical goals should have as one of its central pillars an institute for pure mathematics that purposely dismissed any of the varied fields of applied mathematics. This paper tells of the preparations for the inauguration of the Hebrew University during the years 1920–1925 and analyzes the founding phase of the Einstein Institute of Mathematics that was established there during the years 1924–1928. Special emphasis is given to the first terms in which this Institute operated, starting from the winter of 1927 with the activities of the director and one of the founders, the German mathematician Edmund Landau, and onward from 1928 when his successors, particularly Adolf Abraham Halevi Fraenkel and Mihály-Michael Fekete, continued Landau's heritage of pure mathematics. The paper shows why and how the Institute succeeded in rejecting applied mathematics from its court and also explores the controversial issue of center and periphery in the development of science, a topic that is briefly analyzed in the concluding section.

Aerial Navigation as Applied Mathematics

1945 ◽  
Vol 38 (7) ◽  
pp. 314-316
Author(s):  
Laura Blank
Keyword(s):  
High School ◽  
Secondary Schools ◽  
Federal Government ◽  
Young Women ◽  
Applied Mathematics ◽  
Young Men ◽  
South Pacific ◽  
Pure Mathematics ◽  
Aerial Navigation ◽  
The Moment

In the fall of 1942 at the urgent request of the federal government, as an incentive to interest in piloting and navigating airplanes, many of the secondary schools of our country set into operation classes in aerial navigation, aerodynamics and meteorology. The navigation courses were in the main, the responsibility of the teachers of mathematics. They have been preparing youth including a few young women now for three years. The motive of these young folk in selecting the course is either the wish to pilot soon or that of understanding a timely subject. Many of the young men of the earlier classes are flying missions now “down under” in the South Pacific.* Some are flying their own planes from England for furloughs and then new assignments. Now the Army Air Corps is closed to admissions, and moreover, many men classified in that branch of the service for months, “on the line,” awaiting anxiously their transfer to preflight have been notified officially that they will not be needed as pilots or navigators or even bombardiers. One wonders what the effect will be on elections to a high school course in navigation. Will it develop that aerial navigation is an emergency subject, incident to the war, in secondary schools, to vanish from the curriculum in a few years, parts of it to be taken over into the courses in so-called pure mathematics? Or will navigation continue as a course optional in high school? At the moment options are holding up well.

scholarly journals Gerald Beresford Whitham. 13 December 1927 — 26 January 2014

2015 ◽  
Vol 61 ◽  
pp. 555-577 ◽  
Author(s):  
A. A. Minzoni ◽  
N. F. Smyth
Keyword(s):  
Wave Propagation ◽  
Academic Career ◽  
Applied Mathematics ◽  
Reaction Diffusion ◽  
Nonlinear Wave Propagation ◽  
Research Areas ◽  
California Institute Of Technology ◽  
Pure Mathematics ◽  
Mathematical Techniques ◽  
Institute Of Technology

Gerald Beresford Whitham was one of the leading applied mathematicians of the twentieth century. His original, deep and insightful research into nonlinear wave propagation formed the foundation of and mathematical techniques for much of the current research in this area. Indeed, many of these ideas and techniques have spread beyond wave propagation research into other areas, such as reaction–diffusion, and has influenced research in pure mathematics. His textbook Linear and nonlinear waves , published in 1974, is still the standard reference for the mathematics of wave motion. Whitham was also instrumental in building from scratch the Department of Applied Mathematics at the California Institute of Technology and, through choosing key people in new, promising research areas, in making it into one of the leading centres of applied mathematics in the world, with an influence far beyond its small size. During his academic career, Whitham received major awards and prizes for his research. He was elected a Fellow of the Royal Society in 1965 and a Fellow of the American Academy of Arts and Sciences in 1959, and was awarded the Norbert Wiener Prize for Applied Mathematics in 1980.

In a Flat Spin

1983 ◽  
Vol 36 (3) ◽  
pp. 496-500
Author(s):  
J. E. D. Williams
Keyword(s):  
Air Force ◽  
Applied Mathematics ◽  
Royal Air Force ◽  
Pure Mathematics ◽  
The Right

An announcement of Wing Commander Anderson's recent death appears on another page. Mr William's spirited criticism of Anderson's ‘Rotations in Navigation’, and by implication his more recent note on Coriolis (May 1983 issue), was of course written before the sad news was known. It is published here without modification (and in spite of the author's offer to withdraw it) as would undoubtedly have been Wing Commander Anderson's wish.At the end of the last war Wing Commander E. W. Anderson was one of the most distinguished practising navigators in the Royal Air Force. ‘Andy’, as he is known to so many, has since become navigation's leading exegete through his work in this Institute, his articles, lectures and books. ‘Rotations in Navigation’, however, has got him in a flat spin. The reason why has wider implications worth examining.Andy starts by suggesting that the difficulty of explaining Coriolis ‘may be due to the intellectual danger of trusting mathematics without making sure that the right circumstances surround the formulae which emerge’. This observation illustrates how well one can write English without saying what one means. Circumstances, right or wrong, cannot surround a formula although the statement a formula makes may be irrelevant to our circumstances. It is precisely because pure mathematics is the language, as Russell put it, ‘in which we do not know what we are talking about or care whether what we say about it is true’, that applied mathematics is the language in which we are obliged to say what we mean or be seen to use the language wrongly.

scholarly journals Sociological game theory: agency, social structures and interaction processes

2021 ◽  
Author(s):  
Tom R. Burns ◽  
Ewa Roszkowska ◽  
Nora Machado ◽  
Ugo Corte
Keyword(s):  
Social Psychology ◽  
Game Theory ◽  
Social Science ◽  
Applied Mathematics ◽  
Social Rules ◽  
Social Games ◽  
Interaction Processes ◽  
The Social ◽  
Classical Game ◽  
Classical Game Theory

This article presents two sociological theories, alternatives to classical game theory. These social science-based game theories discussed here present reformulations of classical game theory in applied mathematics (CGT). These theories offer an important advance to classical game theory, thanks to the application of central concepts in sociology and social psychology, as well as the results of empirical analyses of individual and collective behaviour. These two theories emerging in the social sciences are, the first, based on systems theory, is social science game theory (SGT); the other is Erwing Goffman’s interactionist theory (IGT) based on social psychology. Each of these theories, both focused on the analysis of social games, are presented and contrasted with classical game theory, highlighting the centrality of social rules in structuring and regulating human behaviour, and the need to include them in any analysis.

scholarly journals Teaching mathematics as a way of thinking – not calculating

2021 ◽  
Vol 9 (1) ◽  
Author(s):  
Keith Devlin
Keyword(s):  
Mathematical Thinking ◽  
Applied Mathematics ◽  
Academic Research ◽  
Real Life ◽  
Mechanical Activity ◽  
Private Industry ◽  
Life Problems ◽  
Pure Mathematics ◽  
Wide Range ◽  
Formal Procedures

Important aspects of mathematical thinking are exploring, questioning, working systematically, visualizing, conjecturing, explaining, generalizing, justifying, and proving (but excluding the execution of formal procedures either done by machines or viewed as a “lower-level”, mechanical activity). See, for example, Stacey (2006); Devlin (2012a,b,c); Singh et al. (2018); NRICH (2020).Mathematical thinking is what this essay is about. But before I start, it should be noted that I write from the perspective of a career that spanned both academic research in pure mathematics and the world of applied mathematics, where I worked on a wide range of real-life problems for private industry and government.

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