Mathematics

Academic Department Introduction

Mathematics has a fascinating dual nature. Many study it as an object of beauty and intellectual challenge. Others are motivated by its applications to real-world problems. Increasingly, mathematics is an essential tool for modeling phenomena in the physical, biological, and social sciences. Mathematical literacy is the key to surviving and thriving in the world of technology. At its heart, mathematics is the study of patterns: It is a creative art as well as a logical system.

Mathematics has always been a part of the liberal arts core at Wellesley College. Our students often combine a major in mathematics with a minor or a second major in another field. We offer a variety of courses and tracks, with a good representation of pure and applied mathematics. Our faculty are active in research, and we have a wealth of research opportunities for students.

Learning goals

Perform mathematical calculations, implement numerical algorithms, and use computational software or programming language to produce viable solutions.
Draw from existing knowledge and extend it, applying concepts to solve novel problems in new contexts.
Use mathematical and statistical structures to represent real-world phenomena, gain insight, and answer questions.

Programs of Study

Mathematics major and minor

Students will see the role of creativity and appreciate the beauty of deep mathematical ideas and connections.

Major requirements

Minor requirements

Statistics minor

Statistics is the science of drawing inferences from data. The statistics minor is recommended for students who wish to gain experience in both the theoretical foundations of statistics and applied data analysis.

Minor requirements

Course Highlights

Introduction to Bayesian Statistical Methods

STAT320

This course is an introduction to Bayesian theory and applications. Bayesian methods provide a powerful alternative to classical (frequentist) statistical methods. In this course we emphasize the development of Bayesian inference and conduct hands-on data analysis within the Bayesian framework. We begin with a brief overview of essential distinctions between classical and Bayesian methods and progress through the following topics: conjugate families of distributions; posterior simulation and analysis when the posterior is intractable; Bayesian regression and classification; and hierarchical models.

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Calderwood Seminar in Public Writing: Explaining Mathematics

MATH340

In this course, students will leverage their prior mathematical knowledge to communicate complex mathematical ideas to audiences ranging from the general public to other mathematicians. Each week, students will research a new topic and produce a piece of writing explaining this topic in a specific context. Assignments may include research abstracts, book reviews, interviews with mathematicians, newspaper articles, and technical documentation. Class time will be devoted to discussing the mathematical content behind each assignment as well as workshopping students' writing. This course will give students the opportunity to ground (and expand on) the mathematics they have learned and make connections across the discipline. Moreover, this course's unique format will help students develop their research and independent learning skills.
Number Theory

MATH223

Number theory is the study of the most basic mathematical objects: the natural numbers (1, 2, 3, etc.). It begins by investigating simple patterns: for instance, which numbers can be written as sums of two squares? Do the primes go on forever? How can we be sure? The patterns and structures that emerge from studying the properties of numbers are so elegant, complex, and important that number theory has been called "the Queen of Mathematics." Once studied only for its intrinsic beauty, number theory has practical applications in cryptography and computer science. Topics include the Euclidean algorithm, modular arithmetic, Fermat's and Euler's Theorems, public-key cryptography, quadratic reciprocity. MATH 223 has a focus on learning to understand and write mathematical proofs; it can serve as valuable preparation for MATH 305.

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Places and spaces Math Common Room

This popular gathering space fosters community among faculty and students (math majors and beyond). Faculty hold office hours and meet informally with students, and students work together on p-sets or just hang out.

Research highlights

Jia Yuan (Amy) Hu ’25 and Marley DeSimone ’24 conducted research during the 2022–23 academic year, under the supervision of Professor Qing (Wendy) Wang. Their research project concerns mediation analysis models with a large number of candidate mediators that may present some inherent grouping features. They investigated employing different penalization techniques, including methods that incorporate group-wise regularization, to reduce the dimension of the original set of candidate mediators and identify true mediating variables via a multistep algorithm.
Ava Mock ’23 completed her honors thesis under the supervision of Professor Megan Kerr. Her project is a study of the action of the Weyl group (a set of symmetries) on the Cartan subalgebras of affine Kac-Moody algebras. Kac-Moody algebras are infinite-dimensional generalizations of classical Lie algebras. The goal is an understanding of the geometric consequences of expanding to the Kac-Moody setting.
Camille Lorie ’24 and Zixu Wang ’24 did research with Professor Ismar Volić on modeling political structures with hypergraphs. These objects are well suited for capturing the dynamics of coalitions, political decision-making, and conflict. Many standard structures from hypergraphs and related objects, such as simplicial complexes, can be recast in the language of political structures.

Opportunities

Institute for Mathematics and Democracy

Housed at Wellesley, IMD is dedicated to education, research, and outreach in mathematics and politics with the goal of empowering all citizens to become informed participants and impartial agents of change in the democratic process. Students are welcome to get involved in a number of capacities.

Beyond Wellesley

Many mathematics majors work in software and web development, finance, engineering, education, and management consulting. The study of statistics prepares students for graduate study in statistics, biostatistics, or a related field; research in applied science or social science; or work in business, medicine, technology, law, finance, or other fields. The mathematics department graduates about 25 to 30 majors per year. Recent alums have entered mathematics or statistics graduate programs at Boston University, Columbia University, Cornell University, UC Berkeley, Duke University, and Harvard University, among others.