Instructor: Marc Ryser
In modern medicine, mathematical modeling and statistical (big) data analysis are playing an increasingly important role to uncover complex disease mechanisms. In this course, we undertake an excursion into the world of quantitative biomedical research and discover a range of fascinating mathematical principles that govern human health and disease. Based on a series of concrete research topics we will learn how to critically read the biomedical literature, develop our own hypotheses and use the language of mathematics to formalize them.
Math 240: Introduction to Applied Mathematics
Instructor: Ingrid Daubechies
The course will consist of 3 or 4 concrete applications, for which precise mathematical questions will be formulated, and a mathematical framework developed that will make it possible to answer these questions. In doing so, we will encounter and explore portions of real analysis, probability, linear algebra, convex analysis, information theory and maybe others. We will also learn how to construct watertight mathematical arguments, and explore different proof techniques. Prerequisites: none beyond high school calculus
Math 282S: Mathematical and Interdisciplinary Modeling
Instructor: Veronica Ciocanel
Introduction to mathematical techniques and their applications to real world problems. Class meetings will start with an introduction to a mathematical tool (and often its implementation), with the remainder of the class devoted to working in teams on modeling strategies for a given problem. Practice problems will be drawn from the COMAP Mathematical or Interdisciplinary Contest for Modeling, and students may have the opportunity to participate in the contest in February. Students will learn about a range of tools useful for modeling and write reports describing models and results. Prerequisite: Math 111 (or 121) and 112 (or 122). Some programming experience is useful but not required. Half-credit course.
Math 290: History of Mathematics
Instructor: Lillian Pierce
Have you ever wondered where the numerical shapes 0, 1, 2, 3... come from? Who came up with using the symbol pi? Would we think about math differently if we used different symbols? How did people ever start thinking about solving equations? Why are people so interested in triangles, circles, and squares? Why are there infinitely many prime numbers? What does it mean for an infinite set to be countable or uncountable? Why do people sometimes say math is beautiful?
Math 290 will include a mix of lecture/discussions, guest lectures from scholars around the country, student presentations, problem sets, and informational essays written by students. The textbooks will include “Journey through Genius” by William Dunham, which has a European perspective, and “The Crest of the Peacock” by George Gheverghese Joseph, which has a worldwide perspective. Additional readings will be distributed throughout the semester, and chosen by students as they develop independent projects.
Math 466: Mathematics of Machine Learning
Instructor: Elchanan Solomon
The course will explore mathematics underlying the practice and theory of various machine learning concepts and algorithms. Statistical learning theory, optimization theory, neural networks, representation learning, dimensionality reduction, data embeddings, and reinforcement learning will be introduced. The interplay between mathematics and real applications will be a component of the course, and theoretical lectures will be complemented by opportunities to implement ML techniques in code and on real data. Students can take both this course and Mathematics 465 for credit. Recommended prerequisite: Mathematics 230/340 and 218/216/221 and some familiarity with programming, preferably Python.
Math 477S: Math Modeling with Writing
Instructor: Inmaculada Sorribes Rodriguez
Introduction to techniques used in the construction, analysis, and evaluation of mathematical models. During the first half of the course we will study important mathematical models that have been applied in different fields such as biology, chemistry, or physics. We will read scientific papers and present their key concepts. Midpoint through the semester the students will pick individual projects of mathematical modeling to work on, and emphasis will be given to short project reports and presentations. At the end of the semester every student will give a short presentation of their project. Individual modeling projects may be in biology, chemistry, economics, engineering, medicine, or physics. Considerable attention is given to writing in an interdisciplinary context. Not open to student that have taken Math 476S. Prerequisite: Mathematics 353 or 356 or consent of instructor.
Instructor: Gregory Herschlag
This is a new math course involving theory of sampling coupled with real world problems. Students will learn Monte Carlo methods including Importance Sampling, Markov Chain Monte Carlo and extensions. Theoretical concepts will be coupled to physical problems, including gerrymandering, imaging analysis, genetics, and more.
Math 590-02: Algorithmic Trading
Instructor: David Ye
This course explores the complexity of financial data and the challenges in modeling them. Increasing portions of trading and investment activities are now fully automated. Many key decisions are driven by computer algorithms and models built on top of ever-larger financial data sets. Students will learn a variety of financial data sets, perform research and analysis on these data, and develop mathematical and risk management models for profitable trading and investment strategies.