In the University of Chicago’s Department of

Mathematics, undergraduates even at the fi rst-

year level have the opportunity to study with

faculty members who have been recognized as

both outstanding scholars and teachers. Three

current faculty members have won the Quantrell

Award for Excellence in Undergraduate Teaching,

an honor presented annually by the University.

Two current faculty have won the Fields Medal,

which is the highest honor in mathematics and is considered to be the

equivalent of a Nobel Prize.

Ngô Bao Châu, UChicago Professor in Mathematics, received a 2010 Fields Medal, the highest honor in mathematics.

Mathematics

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Sample CoursesHonors Calculus

This sequence emphasizes the theoretical

aspects of one-variable analysis and,

in particular, the consequences of

completeness in the real number system.

The third quarter includes an introduction to

linear algebra. At least one section is off ered

as an inquiry-based learning (IBL) course.

Algebraic Number Theory

Students tackle advanced concepts in

number theory, including factorization in

Dedekind domains, integers in a number

fi eld, prime factorization, basic properties

of ramifi cation, and local degree.

Introduction to Representation Theory

of Finite Groups

Topics in this course include group

algebras and modules, semisimple

algebras, and the theorem of Maschke;

characters, character tables, orthogonality

relations, and calculation; and induced

representations and characters. Students

examine applications to permutation

groups and solvability of groups.

Mathematical Logic I

This course introduces mathematical logic,

including propositional and predicate logic

and the syntactic notion of proof versus the

semantic notion of truth (e.g., soundness,

completeness). Students discuss the Gödel

completeness theorem, the compactness

theorem, and applications of compactness

to algebraic problems.

Introduction to Algebraic Topology

This course includes such topics as the

fundamental group of a space, Van

Kampen’s theorem, covering spaces

and groups of covering transformation,

existence of universal covering spaces

built up out of cells, and theorems of

Gauss, Brouwer, and Borsuk-Ulam.

The mathematics major’s rigorous curriculum prepares students for problem solving in a number of fi elds.

P H YS I C A L S C I E N C E SP H YS I C A L S C I E N C E S

CO L L E G I AT E D I V I S I O NCO L L E G I AT E D I V I S I O N

Th e Department of Mathematics at the University of Chicago is likewise one of the largest in the nation, which not only ensures a wide breadth of research interests but gives unparalleled support for undergraduate interests in the fi eld of mathematics, regardless of their background in the subject. Th e department off ers an honors curriculum for the most advanced students, which may include one or more graduate

sequences. Students can choose programs with a particular emphasis, such as applied mathematics or mathematics with a specialization in economics. Th e department awards both BA and BS degrees, and off ers a minor program and a joint degree option. Additionally, our students have the opportunity to take PhD-level courses in mathematics, as well as pursue a master of science in mathematics.

MAJORS

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Many students double major in mathematics and a related discipline. For example, double majors in mathematics and physics, economics, or computer science have proven to be popular in recent years. In addition, knowledge of mathematics is valuable for students preparing for advanced professional study and for graduate study in other disciplines.

Curriculum Once students complete or receive placement for a yearlong calculus sequence, they are free to explore a broad spectrum of advanced mathematics. Mathematics majors enjoy courses in the following: n Analysis: The basis for all advanced

courses in analysis and topology, the real analysis sequence carefully examines both the theoretical and problem-solving aspects of multivariable calculus and linear algebra, and is designed for students who require a thorough treatment of analysis in several dimensions. The Honors Analysis sequence is a highly theoretical, advanced version, which focuses on the real number system, metric spaces, normed linear spaces, basic functional analysis, operator theory, complex analysis, differential calculus in Euclidean space, Fourier series and Fourier integrals, the Lebesgue integral, and other topics.

n Algebra: A basis for advanced courses in algebra, number theory, and logic, the algebra sequence covers groups, rings, fields, abstract linear algebra, and Galois theory. An honors version of this sequence is available.

n Electives: Advanced courses and sequences are available in topology, number theory, geometry, complex

variables, ordinary and partial differential equations, functional analysis, differential geometry, representation theory, commutative algebra, computability theory, set theory, logic, and more.

In addition, the University of Chicago’s Directed Reading Program, organized by mathematics graduate students, pairs an undergraduate student with a graduate mentor to read and study in an area of mathematics outside the regular curriculum.

Student Achievements

University of Chicago mathematics majors regularly receive the most competitive and prestigious distinctions in the country. In the last five years, these have included Department of Defense Graduate fellowships, Goldwater scholarships, and National Science Foundation fellowships. One of our 2008 graduates won a Fulbright Fellowship Award.

University of Chicago students have a tradition of placing near the top among more than 250 teams that participate in the William Lowell Putnam national undergraduate mathematics competition held each year.

Extracurricular Activities

The study of mathematics is not strictly limited to the classroom. n The student-run Undergraduate

Mathematics Club offers a series through which students give talks on topics of interest.

n Chicago Careers in Science and Technology provides mentoring and internship opportunities around the world for students interested in rapidly changing fields like physics, computer science, and engineering. Areas include

particle physics, national security, search engines, bioinformatics, alternative energies, and entertainment.

n Association for Women in Mathematics brings together women undergraduates, graduates, and members of the faculty in the Department of Mathematics.

After Graduation

Mathematics degree recipients pursue a variety of careers:n About one-fourth of mathematics degree

recipients enter graduate programs in mathematics, economics, statistics, or computer science at the top graduate schools in the country, including the University of Chicago, Harvard, Princeton, MIT, Yale, Columbia, Stanford, Michigan, and the University of California at Berkeley.

n One-half of mathematics majors accept offers of employment immediately after college. Many graduates put their mathematics degrees to work in investment banks and in consulting, actuarial, insurance, and computer firms.

n Other mathematics degree recipients postpone graduate studies and direct their energies to teaching jobs in the Peace Corps, at high schools, or in Math for America. The University of Chicago Urban Teacher Education Program (Chicago UTEP) offers the opportunity for students to earn an MAT degree with a fifth year of study, qualifying them to teach high school mathematics.

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