Open Access. Powered by Scholars. Published by Universities.®
Physical Sciences and Mathematics Commons™
Open Access. Powered by Scholars. Published by Universities.®
Articles 1 - 10 of 10
Full-Text Articles in Physical Sciences and Mathematics
Basel Problem: Historical Perspective And Further Proofs From Stochastic Processes, Uwe Hassler, Mehdi Hosseinkouchack
Basel Problem: Historical Perspective And Further Proofs From Stochastic Processes, Uwe Hassler, Mehdi Hosseinkouchack
Euleriana
In this note, we offer a historical perspective on solutions of the Basel problem. In particular, we have a closer look at some of the less famous results by Euler E41 and provide a review of a selection of the assemblage of earlier proofs. Moreover, we show how to generate further proofs using Karhunen-Lo\`{e}ve expansions of stochastic processes.
Euler Archive Spotlight, Cynthia Huffman Ph.D.
Euler Archive Spotlight, Cynthia Huffman Ph.D.
Euleriana
This issue we spotlight the translations of Jordan Bell, one of the most prolific translators for the Euler Archive.
Learning Mathematics From The Master: A Collection Of Euler-Based Primary Source Projects For Today’S Students, Part Ii, Janet H. Barnett, Dominic Klyve, Dave Ruch
Learning Mathematics From The Master: A Collection Of Euler-Based Primary Source Projects For Today’S Students, Part Ii, Janet H. Barnett, Dominic Klyve, Dave Ruch
Euleriana
This article and its prequel together highlight a set of nine classroom-ready projects that draw on the remarkable writing of Leonhard Euler (1707--1783) as a means to help students develop an understanding of standard topics from today’s undergraduate mathematics curriculum. Part of a larger collection of primary source projects intended for use in a wide range of undergraduate mathematics courses, these projects are freely available to students and their instructors. We provide a general description of the pedagogical design underlying these projects, more detailed descriptions of the individual projects themselves, and instructions for obtaining downloadable copies for classroom use.
Review Of The History Of Mathematics: A Source-Based Approach (Vol. 2), Part I, Erik R. Tou
Review Of The History Of Mathematics: A Source-Based Approach (Vol. 2), Part I, Erik R. Tou
Euleriana
Review of The History of Mathematics: A Source-Based Approach (Vol. 2), Part I, by June Barrow-Green, Jeremy Gray, and Robin Wilson. MAA Press, 2022, 330 + xiv pages.
Variety And Variation, Christopher Goff, Erik R. Tou
Variety And Variation, Christopher Goff, Erik R. Tou
Euleriana
Welcome to Volume 2 of Issue 2 of Euleriana. While we occasionally discover themes that emerge from the articles and translations presented in a given issue, the wide range of Euler’s work more often results in a variety of topics for each issue. This is no less true for Issue 2.
Euler Archive Spotlight, Cynthia Huffman Ph.D.
Euler Archive Spotlight, Cynthia Huffman Ph.D.
Euleriana
A spotlight on the Euler Archive focusing on Euler and the Basel Problem.
Leonhard Euler’S Correspondence Schedule, Dominic Klyve
Leonhard Euler’S Correspondence Schedule, Dominic Klyve
Euleriana
In addition to his large number of published articles and books, Leonhard Euler engaged in a prolific correspondence with scientists, mathematicians, and administrators throughout his career. By compiling the dates of all of his known letters, as described in the Opera Omnia, we can get some understanding of Euler’s weekly schedule. We report here for the first time Euler’s preference, particularly during his Berlin Period, of writing letters on Tuesdays and Saturdays.
Learning Mathematics From The Master: A Collection Of Euler-Based Primary Source Projects For Today’S Students, Part I, Janet Heine Barnett, Dominic Klyve, Kenneth M. Monks, Adam E. Parker
Learning Mathematics From The Master: A Collection Of Euler-Based Primary Source Projects For Today’S Students, Part I, Janet Heine Barnett, Dominic Klyve, Kenneth M. Monks, Adam E. Parker
Euleriana
This article and its sequel will together highlight a set of nine classroom ready projects that draw on the remarkable writing of Leonhard Euler (1707–1783) as a means to help students develop an understanding of standard topics from today’s undergraduate mathematics curriculum. Part of a larger collection of primary source projects intended for use in a wide range of undergraduate mathematics courses, these projects are freely available to students and their instructors. We provide a general description of the pedagogical design underlying these projects, more detailed descriptions of the individual projects themselves, and instructions for obtaining downloadable copies for classroom …
On A New Class Of Oscillations, Sylvio R. Bistafa
On A New Class Of Oscillations, Sylvio R. Bistafa
Euleriana
In this publication, Euler derived for the first time, the differential equation of the (undamped) simple harmonic oscillator under harmonic excitation, namely, the motion of an object subjected to two acting forces, one proportional to the distance travelled, the other one varying sinusoidally with time.
Review Of Change And Variations, Robert E. Bradley
Review Of Change And Variations, Robert E. Bradley
Euleriana
Review of Change and Variations: A History of Differential Equations to 1900, by Jeremy Gray, Springer Undergraduate Mathematics Series, 2021, 419 + xxii pages.