Juan Pablo Mejía-Ramos, Rutgers University

Kyeong Hah Roh, Arizona State University

Abstract

Fostering logical thinking is a paramount objective, as it underpins the ability to convey ideas and construct rigorous arguments in mathematics. This presentation delves into the critical landscape of undergraduate students' engagement with logic within mathematical contexts. Drawing upon the outcomes of empirical studies conducted by my research teams, I will illuminate the intricate tapestry of undergraduate students' reasoning about logic. This presentation encompasses three fundamental facets of logical thinking: (1) the idiosyncratic meanings students attribute to quantifiers, (2) students' logical consistency while evaluating mathematical statements and accompanying arguments, and (3) students' learning of logical principles for proof of conditional statements. By sharing key insights and research findings, I aim to offer valuable perspectives to enhance teaching and learning experiences in mathematical logic.

Bio Sketch

Kyeong Hah Roh is an associate professor of mathematics education in the School of Mathematical and Statistical Sciences at Arizona State University in Tempe, Arizona, USA. She earned her Ph.D. in mathematics (differential geometry) from Seoul National University in 2000 and her Ph.D. in mathematics education from the Ohio State University in 2005. She served as Program Chair for SIGMAA on RUME (2012-2013) and a member of the Analysis Course Study Group of the MAA Committee on the Undergraduate Program in Mathematics (CUPM) in 2012. Her research program focuses on undergraduate students' reasoning about logic and its role in learning mathematical concepts and proofs. National Science Foundation has funded her work on designing a research-based real analysis curriculum (DUE-0837443), modeling undergraduate students' reflection and abstraction of proof structures in transition to proofs courses (DUE-1954613), and generating a research-informed transition to a mathematical proof curriculum (DUE-2141925). Kyeong Hah enjoys listening to classical music and playing the piano in her spare time.

Yvonne Lai, University of Nebraska, Lincoln

Daniel Appelö, Virginia Tech

Dr. Roummel Marcia, UC Merced

Abstract

In everyday life, we are constantly inundated with digital signals and, in particular, images, from web browsing and video meetings to movie streaming and video gaming. These signals can carry large volumes of data, but the information they contain are often redundant, meaning they have inherent structures that can be exploited to facilitate storage and transfer. In this talk, I will discuss some of the mathematics underlying image processing techniques (specifically linear algebra and optimization) and describe how they can be used in several important applications.