*Undergraduate degrees: B.A. or B.S.
Undergraduate minor*

## Educating Problem Solvers

The UO offers a mathematics program that emphasizes the subject as part of a broad liberal arts education geared toward the application of math in many careers. Because mathematical study helps develop habits of disciplined and logical thought, it has always been considered an important part of a university education. Mathematics has significant applications to both the physical and social sciences. The UO’s mathematics department has the dual function of teaching mathematics as an intellectual discipline and for purposes of application.

Students majoring in mathematics can choose a focus from three distinct areas: applied mathematics, pure mathematics, and secondary teaching. Students consult with their advisers to construct individual paths of study.

Through the UO Mathematics department, you’ll be prepared for work in fields like engineering, computer programming, information technology, financial planning, data management, business, and education. If you’re interested in pure mathematics, the UO offers a track that will specifically prepare you for the advanced study of mathematics at the graduate level. Mathematics teachers are also in demand, to ensure that future generations are prepared for jobs that value mathematical and analytical skills and technical knowledge.

According to Associate Professor Arkady Vaintrob, Director of Undergraduate Studies for the Mathematics department, the study of math encourages a collective spirit and collaborative effort. Students studying the subject adjust to not being able to solve a problem in a couple of minutes, a process that allows for more advanced abstract thought. "They expect new challenges, and this leads them to thinking outside of the box," he says. “That is how the discipline progresses.”

The hub of the UO’s undergraduate mathematics community is a lounge called Hilbert Space (a clever pun on the abstract mathematical concept of the same name), which features a small kitchen, study tables, and blackboards for mathematical discussions. You will usually find a group of students congregated there working in groups, consulting with peer advisers, and using computers loaded with sophisticated mathematics software. There’s a place here for you, too.

## A Three-Track System

- The undergraduate
**Applied Mathematic track**explores the branches of mathematics involved with the study of the physical, biological, or sociological disciplines. Sample courses include the Introduction to Numerical Analysis, Mathematical Modeling, Differential Equations, and Probability and Statistics - The
**Pure Mathematics track**focuses on the study and development of mathematic principles for their own sake, rather than for their immediate application. This track is designed to prepare students for graduate studies. Courses include, Topology, Abstract Algebra, Mathematical Statistics, and Introduction to Analysis. - The
**Secondary Education track**prepares students to teach math in secondary institutions. Courses include Elementary Analysis, Number Theory, and Fundamentals of Abstract Algebra, and Geometries from an Advanced Viewpoint.

## Points of Interest

- The American Mathematical Society has ranked the University of Oregon’s mathematics department in the top group of U.S. research departments.
- The Hilbert Space provides a unique and comfortable atmosphere where undergraduate math students gather to work in groups, receive guidance from peer advisers, and utilize sophisticated mathematical software.
- Weekly seminars present topics outside the standard curriculum: introducing a research area, solving an interesting problem, or simply revealing the beauty of math.
- As early as sophomore year, students majoring in mathematics have the opportunity to work as teaching assistants in lower-level university math classes.
- The department invites prominent professors and mathematicians from around the globe to present the Moursund Lectures and Niven Lectures aimed at researchers, students, and a general science audience.
- Mathematics students have the opportunity to take part in the Putnam Competition, a national examination that tests originality as well as technical competence. Prizes are awarded to top finishers in the nation.
- The Mathematics department bestows awards on outstanding students at different levels of study within the major.

## Sample Courses

**Number Theory**explores properties of whole numbers such as congruences, unique factorization, Gaussian reciprocity, and basic properties of prime numbers.**Calculus with Theory**(Honors Calculus) covers both applications of calculus and its theoretical background. Throughout a year-long sequence, students will study axiomatic treatment of the real numbers, limits and the least upper bound property, differential and integral calculus, sequences and series, and Taylor’s theorem.**Introduction to Proof**shows how mathematics establishes truth and communicates ideas. This course teaches students to understand and create proofs in the context of interesting mathematical problems.**Introduction to Abstract Algebra**introduces the theory of groups, rings, and fields. Students also study polynomial rings, unique factorization, and Galois theory.**Discrete Mathematics**teaches elements of set theory, mathematical logic, induction, basic combinatorics, graph theory, and their applications.

## Hands-on Learning

As early as sophomore year, exemplary math students can become undergraduate teaching assistants in lower-level mathematics courses for non-majors. The teaching assistants earn an hourly wage, but most importantly they learn to be comfortable in front of a classroom, and how to articulate their knowledge in a way other students can understand. Students majoring in mathematics may study abroad in any country, but two popular and successful programs are Math in Moscow and the Budapest Semesters in Mathematics. Both programs are conducted in English.

## Interdisciplinary Opportunities

The Mathematics department provides basic mathematical and statistical training for students in the social, biological, and physical sciences. Proficiency in mathematics and/or computer science is required for a Bachelor of Science degree at the university.

Several departments—including biology, chemistry, business, economics, physics, and computer and information science—require mathematics and statistics courses as a part of their curricula. Coursework in the anthropology, sociology, and psychology departments often require statistical analysis. Students and scholars working in these fields use math skills to calculate percentages, and to compute and analyze data.

Students majoring in mathematics find their studies highly compatible with physics, economics, and computer science. Majors fulfilling the applied mathematics option are learning how to use math as a tool to comprehend phenomena in other disciplines. Other students compliment their math studies with courses in education and architecture.

## Student Work

Students are routinely surprised by the beauty and breadth of application of the mathematics they learn at the UO. Whether students enroll in math classes to fulfill a requirement, to pursue a major in math, or simply to explore the discipline, many students readily admit that mathematics is not the subject they assumed it to be.

Though he enjoyed his high school math classes, **Alex Miller** says he was first exposed to "real" mathematics in the honors calculus sequence. Miller, who is a junior majoring in mathematics, credits Professor **Jon Brundan** for changing his view about mathematics. "Professor Brundan really knew how to turn the conventional high school conception of mathematics and calculus on its head."

**Andrew Reiser**, a student in the UO's Robert D. Clark Honors College, is majoring in math. "I’ve been interested in figuring out how things work and solving problems" from a young age, he says, "and math is a big part of those experiences." Reiser says that the UO’s mathematics department has presented him "with a deeper and more detailed picture of the subject." That knowledge came in handy when he took part in the annual Putnam Competition, an undergraduate math exam in which he scored in the top 25 percent in the nation.

As early as elementary school, **Hayley Belli** knew she wanted to make math a part of her future. "I love the subject because it is straightforward," she says. "Answers are either right or wrong." Belli has taken full advantage of the research and scholarship opportunities at the UO. She has participated in two mathematical summer Research Experience for Undergraduates (REUs), conducting research at universitites across the nation. She has presented her research at other universities, was selected as the UO nominee for the Goldwater Scholarship, and was awarded a UO Undergraduate Research Fellowship.

**Colin Grundzien**, a senior double majoring in mathematics and history, says that he originally shied away from studying math in college, believing the subject was limited to the study of arithmetic. He now knows that his previous understanding of the subject was a bit shortsighted and lauds mathematics for possessing a unique structure and elegance. Grundzien says that the skill most developed and challenged as a mathematics major is logic.

## Selected Faculty Work

Professor **James Isenberg** works in partial differential equations and differential geometry, with emphasis on applications in physics. He focuses on solutions of Einstein’s equations of general relativity and the relationships (via heat flows) between topology and geometry.

Associate Professor **Hal Sadofsky**, head of the mathematics department, teaches algebraic topology and honors calculus. He does research in algebraic topology, specifically in the study of stable homotopy theory. This is an area which uses tools from abstract algebra to study properties of continuous functions and of topological spaces.

Associate Professor **Dev Sinha**, director of graduate studies, teaches courses including Introduction to Proof, Topology, and advanced calculus. His teaching interests and practices include creating context to facilitate abstract reasoning, presenting outlines to help students organize what they learn, "putting problems first" in teaching proofs, and giving frequent small assignments to foster independence in advanced courses. His research interests lie at the interface of algebraic and geometric topology.

Associate Professor **Arkady Vaintrob**, director of undergraduate studies, teaches courses on abstract algebra and topology and runs the problem-solving seminar for students interested in challenging problems. His research interests are in the areas of algebra and geometry related to physics (such as string theory).

Professor **Marie Vitulli**’s work encompasses areas of algebraic geometry and commutative algebra. She teaches classes in linear and abstract algebra, and in calculus. Vitulli is the director of the Women in Math project, a collection of publications about gender and mathematics.

## Career Opportunities

Mathematics has applications in almost every professional field. You apply your math course work in accounting, computer software, business, and finance. Math skills are exercised in architecture and other fields of design. You might become a much-needed mathematics teacher, passing on valuable knowledge to young students, or decide to explore theoretical and abstract concepts through a master’s or doctoral program.

**Contact Information**

(541) 346-4705

(541) 346-0987 fax