Physical Sciences and Mathematics Commons^™

Greedy Signal Recovery Review, Deanna Needell, Joel A. Tropp, Roman Vershynin

CMC Faculty Publications and Research

The two major approaches to sparse recovery are L1-minimization and greedy methods. Recently, Needell and Vershynin developed Regularized Orthogonal Matching Pursuit (ROMP) that has bridged the gap between these two approaches. ROMP is the first stable greedy algorithm providing uniform guarantees.

Even more recently, Needell and Tropp developed the stable greedy algorithm Compressive Sampling Matching Pursuit (CoSaMP). CoSaMP provides uniform guarantees and improves upon the stability bounds and RIC requirements of ROMP. CoSaMP offers rigorous bounds on computational cost and storage. In many cases, the running time is just O(NlogN), where N is the ambient dimension of the signal. This …

Biggers, Covella (Houchens), 1921-2022 (Sc 1610), Manuscripts & Folklife Archives

MSS Finding Aids

Finding aid only for Manuscripts Small Collection 1610. Three handwritten sermons by Episcopalian clergyman John Wesley Venable, and one early nineteenth-century ciphering book (unbound) executed by Burrell Adams.

Carman, William, 1790-1841 (Mss 52), Manuscripts & Folklife Archives

MSS Finding Aids

Ciphering books (2) of William Carman, a teacher in Mayfield, Kentucky. One book is dated 1815-1816; the other one is undated, but evidently of the same period. The ciphering used is the British pound system. The title page of one volume is by Gavin G. Craig of WKU's Penmanship Department.

Environmental Limits On The Nonresonant Cosmic-Ray Current-Driven Instability, Brian Reville, John Kirk, Peter Duffy, Stephen O'Sullivan

Articles

We investigate the so-called nonresonant cosmic-ray streaming instability, first discussed by Bell (2004). The extent to which thermal damping and ion-neutral collisions reduce the growth of this instability is calculated. Limits on the growth of the nonresonant mode in SN1006 and RX J1713.7-3946 are presented.

Imagine Math Day: Encouraging Secondary School Students And Teachers To Engage In Authentic Mathematical Discovery, Darryl H. Yong, Michael E. Orrison Jr.

All HMC Faculty Publications and Research

Research mathematicians and school children experience mathematics in profoundly different ways. Ask a group of mathematicians what it means to “do mathematics” and you are likely to get a myriad of responses: mathematics involves analyzing and organizing patterns and relationships, reasoning and drawing conclusions about the world, or creating languages and tools to describe and solve important problems. Students of mathematics often report “doing mathematics” as performing calculations or following rules. It’s natural that they see mathematics as monolithic rather than an evolving, growing, socially constructed body of knowledge, because most mathematical training in primary and secondary schools consists of …

Blair Family - Ciphering Book (Sc 1659), Manuscripts & Folklife Archives

MSS Finding Aids

Finding aid only for Manuscripts Small Collection 1659. Ciphering book created by Blair family member in Fleming County, Kentucky. Although undated, the book contains several mathematical problems with dates ranging from 1792 to 1796. Fleming County, which is noted in one of the problems, was established in 1798.

An Optimal-Order Error Estimate For A Family Of Ellam-Mfem Approximations To Porous Medium Flow, Hong Wang

Faculty Publications

Mathematical models used to describe porous medium flow lead to coupled systems of time-dependent nonlinear partial differential equations, which present serious mathematical and numerical difficulties. Standard methods tend to generate numerical solutions with nonphysical oscillations or numerical dispersion along with spurious grid-orientation effect. The ELLAM-MFEM time-stepping procedure, in which an Eulerian–Lagrangian localized adjoint method (ELLAM) is used to solve the transport equation and a mixed finite element method (MFEM) is used for the pressure equation, simulates porous medium flow accurately even if large spatial grids and time steps are used. In this paper we prove an optimal-order error estimate for …

Σary, Minnesota State University Moorhead, Mathematics Department

Math Department Newsletters

No abstract provided.

A Hike Through The Forest: The Knapsack Problem In Graph Theory, Bridget K. Druken

Senior Honors Projects

Graph theory is a branch of mathematics which studies graphs a collection of a set of edges and vertices used to sometimes model structures. My interest in graph theory began last semester in a math/computer science course entitled “Discrete Structures." One aspect which makes graph theory an appealing area to research is the amount of understanding that comes from a relatively short amount of time spent learning the subject material. The visual appeal of being able to draw a graph along practical applications that surface daily make graph theory a prime candidate for further research. Through research of the history …

Differential Equations: A Universal Language, Bethany Caron

Senior Honors Projects

“Mathematics knows no races or geographic boundaries; for mathematics, the cultural world is one country.” – David Hilbert Differential equations are equations of one or more variables that involve both functions and their derivatives. These equations have many applications to the everyday “non-math” world, including modeling in engineering, physics, biology, chemistry, and economics. Differential equations are used when a situation arises where one needs to study a continuously changing quantity (expressed as a function) and its rate of change (expressed through its derivatives). The solutions to differential equations are functions that make the original equation hold true, and they can …

A Brief Study Of Some Aspects Of Babylonian Mathematics, Tom Zara

Senior Honors Theses

Beginning over 4000 years ago, the Babylonians were discovering how to use mathematics to perform functions of daily life and to evolve as a dominant civilization. Since the beginning of the 1800s, about half a million Babylonian tablets have been discovered, fewer than five hundred of which are mathematical in nature. Scholars translated these texts by the end of the 19th century. It is from these tablets that we gain an appreciation for the Babylonians’ apparent understanding of mathematics and the manner in which they used some key mathematical concepts. Through this thesis, the author will provide background information about …

Dynamic Web Tools For Trigonometry, Steven J. Wilson

Innovations in Math Technology

In the last 20 years, computer technology having mathematical capability has been developed, improved, and become widely available, but textbook presentations are still largely free of any discussion that might require technology. Technology could be used in mathematical instruction for student drill and practice, for instructor demonstrations that promote conceptual understanding, or for the exploration of mathematical ideas, but software is often designed to be pedagogically generic, leaving its use to the creativity of the instructor. Technological solutions for local machines can be quite extensive, but cost and time constraints then limit availability for student use. The internet has the …

Inverse Spectral Results On Even Dimensional Tori, Carolyn Gordon, Pierre Guerini, Thomas Kappeler, David Webb

Dartmouth Scholarship

Given a Hermitian line bundle L over a flat torus M, a connection ∇ on L, and a function Q on M, one associates a Schrödinger operator acting on sections of L; its spectrum is denoted Spec(Q;L,∇). Motivated by work of V. Guillemin in dimension two, we consider line bundles over tori of arbitrary even dimension with “translation invariant” connections ∇, and we address the extent to which the spectrum Spec(Q;L,∇) determines the potential Q. With a genericity condition, we show that if the connection is invariant under the isometry of M defined by the map x→-x, then the spectrum …

Barriers To Using Ict In Mathematics Teaching: Issues In Methodology, Rebecca Hudson, Anne L. Porter, Mark I. Nelson

Faculty of Informatics - Papers (Archive)

In this paper we examine the barriers to using ICT of secondary mathematics teachers in the classroom. The sample contained 114 mathematics teachers from public secondary schools in New South Wales (Australia). The instrument used in this study was a survey questionnaire mailed to secondary schools in the New South Wales Department of Education and Training. The questionnaire design is a closed-response with five open-ended questions. Results of the study showed that lack of access to computer labs is the number one barrier to using ICT in the classroom. But when a second analysis using a logistic regression analysis modeling …

Is Mathematics Created By Humans Or Is It Discovered By Humans? A Catholic Intellectual Perspective, Jason J. Molitierno

Presidential Seminar on the Catholic Intellectual Tradition

In this essay, Dr. Molitierno intends to show that not only is it appropriate to discuss the Catholic Intellectual Tradition in light of mathematics, the CIT can actually be exemplified in mathematics!

The Art Of Teaching Mathematics, Garikai Campbell, Jon T. Jacobsen, Aimee S A Johnson, Michael E. Orrison Jr.

All HMC Faculty Publications and Research

On June 10–12, 2007, Harvey Mudd College hosted A Conference on the Art of Teaching Mathematics. The conference brought together approximately thirty mathematicians from the Claremont Colleges, Denison, DePauw, Furman, Middlebury, Penn State, Swarthmore, and Vassar to explore the topic of teaching as an art. Assuming there is an element of artistic creativity in teaching mathematics, in what ways does it surface and what should we be doing to develop this creativity?

New Classes Of Codes For Cryptologists And Computer Scientists, Florentin Smarandache, W.B. Vasantha Kandasamy

Branch Mathematics and Statistics Faculty and Staff Publications

Historically a code refers to a cryptosystem that deals with linguistic units: words, phrases etc. We do not discuss such codes in this book. Here codes are message carriers or information storages or information transmitters which in time of need should not be decoded or read by an enemy or an intruder. When we use very abstract mathematics in using a specific code, it is difficult for non-mathematicians to make use of it. At the same time, one cannot compromise with the capacity of the codes. So the authors in this book have introduced several classes of codes which are …