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Articles 1 - 30 of 34
Full-Text Articles in Physical Sciences and Mathematics
Newton, Maclaurin, And The Authority Of Mathematics, Judith V. Grabiner
Newton, Maclaurin, And The Authority Of Mathematics, Judith V. Grabiner
Pitzer Faculty Publications and Research
Sir Isaac Newton revolutionized physics and astronomy in his Principia. How did he do it? Would his method work on any area of inquiry, not only in science, but also about society and religion? We look at how some Newtonians, most notably Colin Maclaurin, combined sophisticated mathematical modeling and empirical data in what has come to be called the "Newtonian Style." We argue that this style was responsible not only for Maclaurin’s scientific success but for his ability to solve problems ranging from taxation to insurance to theology. We show how Maclaurin’s work strengthened the prestige of Newtonianism and …
A (Not So) Complex Solution To A² + B² = Cⁿ, Arnold M. Adelberg, Arthur T. Benjamin, David I. Rudel '99
A (Not So) Complex Solution To A² + B² = Cⁿ, Arnold M. Adelberg, Arthur T. Benjamin, David I. Rudel '99
All HMC Faculty Publications and Research
No abstract provided in this article.
Random Walks On The Torus With Several Generators, Timothy Prescott '02, Francis E. Su
Random Walks On The Torus With Several Generators, Timothy Prescott '02, Francis E. Su
All HMC Faculty Publications and Research
Given n vectors {i} ∈ [0, 1)d, consider a random walk on the d-dimensional torus d = ℝd/ℤd generated by these vectors by successive addition and subtraction. For certain sets of vectors, this walk converges to Haar (uniform) measure on the torus. We show that the discrepancy distance D(Q*k) between the kth step distribution of the walk and Haar measure is bounded below by D(Q*k) ≥ C1k−n/2, where C1 = C(n, d) is …
Heights And Diophantine Problems, Lenny Fukshansky
Heights And Diophantine Problems, Lenny Fukshansky
CMC Faculty Publications and Research
Lecture given at Rice University, September 2004.
Putnam, Pizza & Problem Solving, Andrew J. Bernoff, Francis E. Su
Putnam, Pizza & Problem Solving, Andrew J. Bernoff, Francis E. Su
All HMC Faculty Publications and Research
Ok, here's a difficult question for you.. How can you get roughly 10% of the student body at your college to get up early on a Saturday and spend six hours working on an incredibly difficult exam for which many will get a score of zero?
A Liouville-Gelfand Equation For K-Hessian Operators, Jon T. Jacobsen
A Liouville-Gelfand Equation For K-Hessian Operators, Jon T. Jacobsen
All HMC Faculty Publications and Research
In this paper we establish existence and multiplicity results for a class of fully nonlinear elliptic equations of k-Hessian type with exponential nonlinearity. In particular, we characterize the precise dependence of the multiplicity of solutions with respect to both the space dimension and the value of k. The choice of exponential nonlinearity is motivated by the classical Liouville-Gelfand problem from combustible gas dynamics and prescribed curvature problems.
An Experimental Study Of Micron-Scale Droplet Aerosols Produced Via Ultrasonic Atomization, Thomas D. Donnelly, J. Hogan '03, A. Mugler '04, N. Schommer '04, M. Schubmehl '02, Andrew J. Bernoff, B. Forrest '02
An Experimental Study Of Micron-Scale Droplet Aerosols Produced Via Ultrasonic Atomization, Thomas D. Donnelly, J. Hogan '03, A. Mugler '04, N. Schommer '04, M. Schubmehl '02, Andrew J. Bernoff, B. Forrest '02
All HMC Faculty Publications and Research
In the last 10 years, laser-driven fusion experiments performed on atomic clusters of deuterium have shown a surprisingly high neutron yield per joule of input laser energy. Results indicate that the optimal cluster size for maximizing fusion events should be in the 0.01–μm diameter range, but an appropriate source of droplets of this size does not exist. In an attempt to meet this need, we use ultrasonic atomization to generate micron-scale droplet aerosols of high average density, and we have developed and refined a reliable droplet sizing technique based on Mie scattering. Harmonic excitation of the fluid in …
Magical Miscellany, Francis Su
Magical Miscellany, Francis Su
All HMC Faculty Publications and Research
What is a Math Fun Fact, you ask? A Math Fun Fact is any mathematical tidbit that can be presented or grasped quickly, is surprising or captivating, can be generally enjoyed by friends of mathematics, and is hopefully fun! Of course, part of the fun is thinking about why the Fun Fact is true--so we won't spoil the fun. Though, we may give you some hints and references
However, since there are infinitely many Math Fun Facts (prove this), we can only bring you a few each time... here are a few whose conclusions might be considered "magical".
Is Mathematics Education Taking A Step Backward?, Frances Kuwahara Chinn
Is Mathematics Education Taking A Step Backward?, Frances Kuwahara Chinn
Humanistic Mathematics Network Journal
This paper considers the recent history of mathematics teaching.
Using Humanistic Content And Teaching Methods To Motivate Students And Counteract Negative Perceptions Of Mathematics, Roger Haglund
Using Humanistic Content And Teaching Methods To Motivate Students And Counteract Negative Perceptions Of Mathematics, Roger Haglund
Humanistic Mathematics Network Journal
This paper examines the following questions: How is math commonly taught, why is it taught this way, and what are the outcomes? Who are some of the voices calling for change and what are they saying? Can a humanistic approach produce positive results in students who have learned to dislike math and have not been successful in a traditional classroom?
Taxicab Geometry As A Vehicle For The Journey Toward Enlightenment, Neil Greenspan
Taxicab Geometry As A Vehicle For The Journey Toward Enlightenment, Neil Greenspan
Humanistic Mathematics Network Journal
No abstract provided.
Tesselland: A Mathematical Oddment, Martin Glover
Tesselland: A Mathematical Oddment, Martin Glover
Humanistic Mathematics Network Journal
No abstract provided.
Bridging To Infinity, Mike Pinter
Bridging To Infinity, Mike Pinter
Humanistic Mathematics Network Journal
The author's own experiences as a mathematics student and teacher have influenced how he thinks about the infinite. Author Madeleine L'Engle has also shaped his thinking with her writing. The author offers some thoughts that connect some of L'Engle's writing with his experience.
Man's Cards And God's Dice: A Conceptual Analysis Of Probability For The Advanced Student, Elie Feder
Man's Cards And God's Dice: A Conceptual Analysis Of Probability For The Advanced Student, Elie Feder
Humanistic Mathematics Network Journal
No abstract provided.
Mathematics, The Liberal Arts, And Slavish Devotions, J. D. Phillips
Mathematics, The Liberal Arts, And Slavish Devotions, J. D. Phillips
Humanistic Mathematics Network Journal
No abstract provided.
What Are Mathematical Problems?, Emam Hoosain
What Are Mathematical Problems?, Emam Hoosain
Humanistic Mathematics Network Journal
No abstract provided.
A Linear Perspective To Art, Sarah Littler
A Linear Perspective To Art, Sarah Littler
Humanistic Mathematics Network Journal
No abstract provided.
Humanistic Mathematics As Mathematics For All, Michael N. Fried
Humanistic Mathematics As Mathematics For All, Michael N. Fried
Humanistic Mathematics Network Journal
No abstract provided.
A Brief Look At Mathematics And Theology, Philip J. Davis
A Brief Look At Mathematics And Theology, Philip J. Davis
Humanistic Mathematics Network Journal
No abstract provided.
Humanistic Mathematics: Personal Evaluation And Excavations, Stephen I. Brown
Humanistic Mathematics: Personal Evaluation And Excavations, Stephen I. Brown
Humanistic Mathematics Network Journal
No abstract provided.
Innumeracy And Its Perils, Numeracy And Its Promises, Ramakrishnan Menon
Innumeracy And Its Perils, Numeracy And Its Promises, Ramakrishnan Menon
Humanistic Mathematics Network Journal
No abstract provided.
Book Review: Fermat's Enigma By Simon Singh, Matthew Becker
Book Review: Fermat's Enigma By Simon Singh, Matthew Becker
Humanistic Mathematics Network Journal
No abstract provided.
Base And Subbase In A Number System, Walter S. Sizer
Base And Subbase In A Number System, Walter S. Sizer
Humanistic Mathematics Network Journal
No abstract provided.
Are You A Quantitative Or Qualitative Runner?: 5.13 Miles And Rosemary-Lilac Shampoo, Shelly Sheats Harkness
Are You A Quantitative Or Qualitative Runner?: 5.13 Miles And Rosemary-Lilac Shampoo, Shelly Sheats Harkness
Humanistic Mathematics Network Journal
No abstract provided.
Radon Transforms And The Finite General Linear Groups, Michael E. Orrison
Radon Transforms And The Finite General Linear Groups, Michael E. Orrison
All HMC Faculty Publications and Research
Using a class sum and a collection of related Radon transforms, we present a proof G. James’s Kernel Intersection Theorem for the complex unipotent representations of the finite general linear groups. The approachis analogous to that used by F. Scarabotti for a proof of James’s Kernel Intersection Theorem for the symmetric group. In the process, we also show that a single class sum may be used to distinguish between distinct irreducible unipotent representations.
Random Walks With Badly Approximable Numbers, Doug Hensley, Francis Su
Random Walks With Badly Approximable Numbers, Doug Hensley, Francis Su
All HMC Faculty Publications and Research
Using the discrepancy metric, we analyze the rate of convergence of a random walk on the circle generated by d rotations, and establish sharp rates that show that badly approximable d-tuples in Rd give rise to walks with the fastest convergence.
Mathematical Magic, Arthur T. Benjamin
Mathematical Magic, Arthur T. Benjamin
All HMC Faculty Publications and Research
In this paper, we present simple strategies for performing mathematical calculations that appear magical to most audiences. Specifically, we explain how to square large numbers, memorize pi to 100 places and determine the day of the week of any given date.
Blowup And Dissipation In A Critical-Case Unstable Thin Film Equation, Thomas P. Witelski, Andrew J. Bernoff, Andrea L. Bertozzi
Blowup And Dissipation In A Critical-Case Unstable Thin Film Equation, Thomas P. Witelski, Andrew J. Bernoff, Andrea L. Bertozzi
All HMC Faculty Publications and Research
We study the dynamics of dissipation and blow-up in a critical-case unstable thin film equation. The governing equation is a nonlinear fourth-order degenerate parabolic PDE derived from a generalized model for lubrication flows of thin viscous fluid layers on solid surfaces. There is a critical mass for blow-up and a rich set of dynamics including families of similarity solutions for finite-time blow-up and infinite-time spreading. The structure and stability of the steady-states and the compactly-supported similarity solutions is studied.
Semilinear Equations With Discrete Spectrum, Alfonso Castro
Semilinear Equations With Discrete Spectrum, Alfonso Castro
All HMC Faculty Publications and Research
This is an overview of the solvability of semilinear equations where the linear part has discrete spectrum. Semilinear elliptic and hyperbolic equations, as well as Hammerstein integral equations, are used as motivating examples. The presentation is intended to be accessible to non experts.
An Existence Result For A Class Of Sublinear Semipositone Systems, Alfonso Castro, C. Maya, Ratnasingham Shivaji
An Existence Result For A Class Of Sublinear Semipositone Systems, Alfonso Castro, C. Maya, Ratnasingham Shivaji
All HMC Faculty Publications and Research
We consider the existence of positive solutions for the system
-Δui = λ[fi(u1,u2,...,um) - hi]; Ω
ui = 0; ∂Ω
where λ > 0 is a parameter, Δ is the Laplacian operator, Ω is a bounded domain in Rn; n ≥ 1 with a smooth boundary ∂Ω, fi are C1 functions satisfying f1(0,0,...,0) = 0, lim z→∞ fi(z,z,...,z) = ∞ and lim z→∞ fi(z,z,...,z)/z = 0, and hi are nonnegative continuous functions in Ω for i = 1,2,...,m. …