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# Mathematics

Mathematics is the science of quantity and space. As such, mathematics is absolutely essential for engineers, physicists, and other scientists; it is the language by which they express their laws, it suggests relationships, and it helps in testing conjectures. In recent years, mathematics has been used more and more in biology, economics, psychology, sociology, political science, data science, and cyber security. In addition, most mathematical research aims at a deeper understanding of problems that lead inevitably to abstraction, generalization, and theorem proving. Many mathematicians find this “aesthetic” activity of “drawing necessary conclusions” the most attractive feature of their subject.

As an academic discipline, mathematics consists of the science of quantity (e.g. algebra, statistics, and combinatorics) and space (e.g., geometry and topology) and other subjects (e.g. analysis) that are concerned with both quantity and space.

### Recently Offered Courses

For the most part, courses taught by the Department of Mathematics fall into one of three general categories: 1) applied and computational mathematics, 2) pure mathematics, and 3) probability and statistics. Included in the first group would be calculus, differential equations, and courses in numerical methods. Logic, abstract algebra, higher geometry, number theory, and topology would be examples of pure mathematics. Rounding out the undergraduate curriculum are courses in probability, mathematical statistics, and applied statistics. These are taught at both elementary and advanced levels.

### Honors Program

The Department of Mathematics offers three math major tracks: the Standard Track, the Applied Track, and the Honors Track. Students who complete the Honors track, satisfy a minimum GPA requirement in the major, and complete and defend an honors thesis under the supervision of a faculty member will be awarded honors in mathematics.

For the most mathematically talented and motivated first-year students who are qualified, the department offers an intensive two-semester course in multivariate calculus and linear algebra that takes an integrated approach to the subjects that is broader and deeper than the standard courses.

### Undergraduate Research

After building a mathematical coursework foundation, undergraduate students have several options to pursue research. Students who are generally interested in mathematical research are encouraged to attend summer REU experiences away from Vanderbilt in order to broaden their experience. Every summer several students pursue this option and continue their research when they return the following academic year under the supervision of a Vanderbilt mathematics faculty member.

Students whose coursework inspires specific pure or applied research interests pursue research with a faculty member either through independent study or financially supported summer work. Common applied areas include economics, physics, and mathematical biology.

Students with interdisciplinary interests will combine mathematical modeling independent study with scientific, medical, or engineering lab work under the supervision of a mathematics faculty member.

### Other Special Opportunities

By design, Vanderbilt’s mathematics major is flexible. Required courses have been held to a minimum, giving students the opportunity to choose classes and pursue directions that best suit their particular objectives. Independent study is also available.

Each semester, the department appoints a number of highly qualified upperclass mathematics majors as undergraduate teaching assistants. These students conduct weekly discussion sessions for freshman-level calculus and statistics courses taught in a lecture/recitation format. Over the years, these positions have provided many mathematics majors with a truly memorable educational experience. Undergraduates can also take full advantage of our graduate mathematics program. Seniors who have completed all of the relevant undergraduate courses in a given area can enroll in graduate classes if they wish to pursue the topic in even greater depth. The proliferation of advanced placement and pre-college credit is making this opportunity attractive to increasing numbers of students.

### After Vanderbilt

The problem-solving skills and quantitative reasoning that play such prominent roles in mathematics courses prepare undergraduate majors for a wide variety of careers, professional schools, and graduate training. In recent years, probably the single most common objective for our majors has been a business career. Many plan to work a few years after graduation and then return to school for an MBA. There is probably no better undergraduate major for that goal than mathematics. Medical school and law school are also fairly common career paths. Some of our majors go into teaching, and each year several individuals enter a wide range of graduate programs including mathematics, statistics, biostatistics, finance, actuarial science, engineering, computer science, data science, and the natural sciences. Opportunities are also plentiful in industry. Companies needing to fill positions that have a decidedly quantitative orientation—for example, quality control of market research—will invariably seek out mathematics majors. The department has a complete set of courses to prepare students to enter careers in actuarial science and each year several students find jobs as actuaries after passing one or more pre-professional exams.

### Faculty

The Department of Mathematics has a distinguished international faculty of approximately fifty that includes a Fields Medalist, ten Fellows of the American Mathematical Society, and several International Congress of Mathematicians invited speakers. The department has a variety of research groups including: algebraic logic, group theory, approximation theory, noncommutative geometry, operator algebras, mathematical biology, partial differential equations, harmonic analysis, number theory, differential geometry, topology, combinatorics, and graph theory. The stimulating research environment is supported by an ongoing program that attracts visiting scholars from institutions around the world and hosts several major conferences per year.

### Contact

John Rafter

Director of Undergraduate Studies

Department of Mathematics

1326 Stevenson Center

Vanderbilt University

Nashville, TN 37240

Phone: (615) 322-6672

john.rafter@vanderbilt.edu