What does math research really look like? Which subfield is right for me? Do people like me go to graduate school, and succeed? This book provides students a sneak preview of math research in a variety of subfields. Each chapter features the work of a different mathematician along with enough background material for an advanced undergraduate or early graduate student to understand the key ideas and get a sense for the styles of thinking involved in each subfield. Each chapter is prefaced by a short biography of the mathematician who wrote the chapter (all people connected to the Carleton College Summer Math Program for Women), providing advice and examples of paths from undergraduate education, through graduate school and beyond.

This book provides a source of ideas and starting points for in-class projects, independent studies, and student talks as well as supplementary reading in courses. The profiles of early career mathematicians and statisticians at the beginning of each chapter are valuable as an advising resource for students considering graduate school, or to show students a diverse view of modern mathematicians in a Math for Liberal Arts-style course.

Includes a variety of self-contained short chapters that introduce a different topic in research mathematics Chapters provide brief accessible introductions to current research areas Chapters include information about author's particular research contributions, and their career path through math

Autorentext

Dr. Abra Brisbin is a Professor in the Department of Mathematics at the University of Wisconsin-Eau Claire. She earned a bachelor's degree in mathematics from Carleton College and served as a teaching assistant at the Carleton Summer Math Program in 2004 and then went on to complete a Ph.D. in applied math from Cornell University, focusing on applications of statistics to genetics. She did a postdoctoral fellowship in statistical genetics at Mayo Clinic in Rochester, MN before joining the faculty at UW-Eau Claire in 2012. Her research at UW-Eau Claire has included statistical genetics, the scholarship of teaching and learning of statistics, and statistics and machine learning applied to a variety of topics suggested by her undergraduate research student collaborators. Her publication list includes two papers with undergraduate co-authors. In addition to teaching courses on statistics, calculus, and math modeling, she has also co-developed courses on Programming for Data Science and on Data Mining and Machine Learning for the UW-Eau Claire Master's of Data Science program, and developed a course on Data Structures and Algorithms in Bioinformatics for an undergraduate major in Bioinformatics, which she helped create. Since becoming department chair in 2022, she has been applying her penchant for data analysis to facilitate the smooth running of the department, including using linear programming in Python to optimize course schedules.

Dr. Karen Lange is a Professor in the Department of Mathematics at Wellesley College. She attended the Carleton Summer Math Program in 1999 before completing her undergraduate degree at Swarthmore College, her doctoral degree at the University of Chicago, and a National Science Foundation Postdoctoral Fellowship at the University of Notre Dame. Lange is a mathematician who works in computability theory, a branch of mathematical logic that studies theoretical models of computation. Lange's research has encompassed understanding various balance scales that calibrate computational information and applying these tools to measure the difficulty of problems throughout mathematics. Throughout her career, she has been particularly interested in the complexity of algebraic and model-theoretic problems. She is passionate about supporting students on their mathematical journeys, both in the classroom and out, and partners with students and colleagues to make mathematics more inclusive and accessible. As part of these efforts, Lange is a current MAA/AWM Section Lecturer and has collaborated with or advised students on multiple articles for the MAA's undergraduate journal Math Horizons. These articles are usually in connection with her undergraduate capstone writing seminar, Explaining Mathemat*ics,* which is part of the Calderwood Seminars Program in Public Writing.

Dr. Erin McNicholas is a full professor of mathematics at Willamette University. She attended the Carleton Summer Math Program in 1995, its first year. Before receiving her Ph.D. from the University of Arizona in 2006, she worked for the State of Oregon as a Metrologist and for the cryptography group at Sandia National Laboratory. She enjoys exploring problems through an algebraic lens and her publications include research articles and book chapters on algebraic voting theory, dynamical algebraic combinatorics, graph theory, and matroids. She has received teaching awards from Willamette University and the University of Arizona. She develops courses and materials that highlight the contributions of underrepresented communities and integrate multiple mathematical perspectives. As part of this work she co-authored the textbook Explorations in Number Theory: Commuting through the Numberverse. She was co-PI on the Willamette Valley NSF REU Grant from 2015-2018 and has published work with multiple undergraduate coauthors.

Dr. Emilie Purvine is a Senior Data Scientist at Pacific Northwest National Laboratory. Her academic background is in pure mathematics, with a bachelor's degree from University of Wisconsin - Madison, during which time she attended the Carleton Summer Mathematics Program in 2003, and a PhD from Rutgers University where she studied enumerative combinatorics and discrete dynamics. Her research since joining PNNL in 2011 has focused on applications of combinatorics and computational topology together with theoretical advances needed to support the applications. Over her time at PNNL, Emilie has been both principal investigator and technical staff on a number of projects in applications ranging from computational chemistry and biology to cyber security and power grid modeling. Her current research uses complex mathematical models to develop cyber analytics, study machine learning models for interpretability, and enhance digital biosecurity. Emilie has supported numerous interns while at PNNL and enjoys the opportunity to speak to student and faculty audiences about her work and what it is like to be a mathematician at a national laboratory. She was an Mathematical Association of America / Association for Women in Mathematics Section Lecturer for academic years 2023-24 and 2024-25.

Inhalt

Chapter 1: On Partially Ordered Sets and the 1/3-2/3 Conjecture.- Chapter 2: Group Actions and Riemann Surfaces.- Chapter 3: Challenges in Using Data for Public Policy Decisions.- Chapter 4: A Taste of Discretized Differential Geometry: Communicating Mathematics With Conceptual Metaphor.- Chapter 5: The Scholarship of Teaching and Learning.- Chapter 6: My Journey In Geometry.- Chapter 7: Continued Fractions Connecting Number Theory, Dynamical Systems, And Hyperbolic Geometry.- Chapter 8: Stochastic Models in Biology.- Chapter 9: Finding Your Path.