Abstract TBD
Abstract TBD
This will be a two-part informational session on Math Department Scholarships and Undergraduate Research in Mathematics. To begin, Professor Childs will give a short overview of the Math Department Scholarship process including how to become eligible and important deadlines. This will be followed by Professor Palsson discussing opportunities for undergraduate research. This will include information about opportunities at VT (both during the semester and outside the semester) as well as ways to be involved in undergraduate research through summer programs such as REUs (Research Experiences for Undergraduates) run at a variety of schools across the country. There will be ample opportunity to ask questions.
From Cryptography to Quantum computing the cloud in essence seeks to solve an incredibly complex problem: how do we use the fewest resources for the most benefit? This goal requires subject matter expertise in several practical and theoretical domains one of the largest being mathematics. Coding and Software development utilizes skills in almost every branch of mathematics from linear algebra to functional analysis which makes a strong foundation in math crucial for proper understanding of the cloud. Math is also used in a variety of physical applications. How much energy are we using for a data center? How much water? How can we strive to be earth’s best employer? In this presentation I will guide you through some of the key examples of clouds use of mathematics and hopefully inspire you to ask questions and learn and be curious.
Mathematics Education Research is a systematic study of the teaching and learning of mathematics. In this talk, I will share methods and results from the NSF funded "Proofs Project," which investigates the persistent challenges that introductory proofs students experience as they transition from calculation-based mathematics to proof-based mathematics. Proof by mathematical induction is one such challenge. Prior research indicates a variety of related factors that contribute to students' difficulties with this proof technique and suggests a promising instructional approach, called quasi-induction, to support more effective learning. However, students still experience difficulty in bridging the gap between quasi-induction and formal induction. To better understand this cognitive gap, The Proofs Project collected video data of research-based instruction on proof by mathematical induction in two Virginia Tech Math 3034 classes. I'll share our methods for qualitatively analyzing this data, findings from the study, and implications for instruction. For more information on The Proofs Project, visit our website: https://math.vt.edu/proofs-project.html.
In calculus we learn about trig functions, integrals and many of the objects that harmonic analysis relies on. In this talk, I will connect to your calculus knowledge to give an idea of what harmonic analysis is about. Further, I will show some successes of the theory and give a glimpse of major open problems, such as the restriction conjecture and the Kakeya conjecture, that harmonic analysts are trying to solve.
What do you mean there is more math to learn??? This session will feature a panel of Math Department faculty and graduate students walking through some of the most commonly asked questions involving graduate school. Some topics include: How and when to apply, courses and activities and experiences to prepare, and letters of recommendation. Graduate school is a big next step in continuing one's math career dependent on many factors, including personal interests, career / academic goals, etc., so please bring any questions you have regarding the process and experience!
Image reconstruction, such as problems from medical imaging, and so-called inverse problems in general are often ill-posed. The main problem is that the solution does not depend continuously on the data, which means that the solution is extremely sensitive to small changes in the data. These problems generally involve reconstructing/computing a (very) large number of parameters, such as absorption of x-rays in tissue, combining a physical model with measurements to estimate the unknown parameters in the model. As measurements always involve noise, the ill-posedness creates serious problems for accurate reconstruction. Moreover, in many cases, we do not have enough data to uniquely determine the parameters. I will explain some of the problems, use mathematical tools like the singular value decomposition (SVD) to demonstrate and analyze these problems, and discuss some solutions and interesting research directions.
Many highly significant decisions—including in college admissions, hiring, insurance, criminal justice and more—are made with the assistance of algorithms and mathematical models. There are, of course, many technical questions about how to design such models. But the use of such models also raises ethical questions concerning fairness, transparency, and accountability. I'll talk about some of these ethical issues, using a variety of recent case studies.
We summarize some recent reduced order model (ROM) developments for the quasi-geostrophic equations (QGE) (also known as the barotropic vorticity equations). The QGE are a simplified model for geophysical flows in which rotation plays a central role, such as wind-driven ocean circulation in mid-latitude ocean basins. Since the QGE represent a practical compromise between efficient numerical simulations of ocean flows and accurate representations of large scale ocean dynamics, these equations have often been used in the testing of new numerical methods for ocean flows. ROMs have also been tested on the QGE for various settings in order to understand their potential in efficient numerical simulations of ocean flows. We survey the ROMs developed for the QGE in order to understand their potential in efficient numerical simulations of more complex ocean flows: We explain how classical numerical methods for the QGE are used to generate the ROM basis functions, we outline the main steps in the construction of projection-based ROMs (with a particular focus on the under-resolved regime, when the closure problem needs to be addressed), we illustrate the ROMs in the numerical simulation of the QGE for various settings, and we present several potential future research avenues in the ROM exploration of the QGE and more complex models of geophysical flows.