## Academic Programs

The courses in the Department of Mathematics and Statistics aim to:

- promote rigorous thinking in a systematic, deductive, intellectual discipline.
- help students identify and articulate mathematical and statistical problems that they encounter, both in formal academic work and elsewhere.
- foster technical competence in mathematics and statistics as an aid to the better comprehension of the physical, biological, and social sciences.
- guide and direct majors toward an interest in research in the mathematical and statistical sciences.

### Learning Goals

Students taking courses in the Department of Mathematics and Statistics will think rigorously and systematically both within the context of the discipline and in its applications—and, ideally, throughout the liberal arts curriculum. Students will learn to identify and articulate mathematical problems that they encounter, both in mathematics and in other disciplines. Students will develop skills necessary to engage these problems within a mathematical and/or statistical framework. Finally, students will learn how to communicate their mathematical and statistical findings to a variety of audiences.

### Curriculum

Mathematics majors take a three-year core sequence of courses in calculus, linear algebra, abstract algebra, and analysis, designed to provide a foundation for further study in the major areas of modern mathematics. Students with substantial advanced placement may complete this sequence by the end of their sophomore year. Students who have completed the core sequence may take advanced courses in algebra, analysis, topology, or other special topics.

Mathematics courses for majors fall into six general categories:

**Preliminary Calculus**

This category includes MATH 105, 118, or advanced placement. These are not listed among the requirements, but are of course prerequisites for all subsequent courses in mathematics.

**Intermediate Calculus/Linear Algebra**

This category includes MATH 215, 121 or 216. These courses are taught for the benefit of both majors and non-majors, but are the real “introduction” to math for most majors.

**Core Major Courses**

This category includes MATH 317-318 (Analysis) and MATH 333-334 (Algebra). These courses are the “cornerstone” of the major, introducing many important ideas in which modern mathematics is based, and also sharpening students’ skills in mathematical discourse (i.e., careful statements of definitions, theorems, proofs).

**Intermediate Electives**

- MATH 203 (Statistical Methods and Their Applications)
- MATH 204 (Differential Equations)
- MATH 210 (Linear Optimization and Game Theory)
- MATH 218 (Probability)
- MATH 222 (Introduction to Scientific Computing)
- MATH/CMSC 235 (Information and Coding Theory)
- MATH 286 (Applied Multivariate Statistical Analysis).

These courses are designed for both majors and non-majors, and provide majors an excellent opportunity to explore interests outside the core sequence. Students can expect at least two electives at this level to be offered most semesters. We coordinate with Bryn Mawr so that if a topic is not offered in a given year at Haverford, it may be offered at Bryn Mawr.

**Advanced Electives:**

- MATH 328 (Mathematical Statistics)
- MATH 335-336 (Topology)
- MATH/CMSC 340 (Analysis of Algorithms)
- MATH/CMSC 345 (Theory of Computation)
- MATH 390 (Advanced Topics in Algebra)
- MATH 391 (Advanced Topics in Geometry and Topology)
- MATH 392 (Advanced Topics in Analysis)
- MATH 394 (Advanced Topics in Discrete Math and Computer Science)
- MATH 395 (Advanced Topics in Combinatorics)
- MATH 396 (Advanced Topics in Probability and Statistics)
- MATH 397 (Advanced Topics in Applied Mathematics)

Courses at this level are very important for students planning to go to graduate school in mathematics or related fields. The department typically offers five to six courses at this level per year.

**Other Courses:**

- MATH 399 (Senior Seminar): a required year-long group seminar for seniors that offers advice, support, and practice in preparing the senior paper and oral presentation.
- MATH 400 (Senior Research): a required year-long course for seniors that involves independent work with their senior thesis advisor.
- MATH 460 (Teaching Assistantship in Mathematics): a half-credit course, in which students work closely with a single faculty member in a single course at the 100 or 200 level, offering various kinds of classroom support including problem sessions, review, tutoring, and laboratory assistance. Very good experience for students considering teaching as a career. Open to junior and senior majors by invitation, and may be taken at most twice. Does not count toward the major.

### Major Requirements

- MATH 215, and either MATH 121 or MATH 216.
- MATH 317 and 333, and one of MATH 318 or 334.
- Four additional electives in mathematics or approved related courses at the 200 level or higher. At least one of these must be at the 300 level. (Note: MATH 399, MATH 400, MATH 460, and MATH 480 do not count toward this requirement.)
- The senior seminar, fall and spring.
- A senior paper and oral presentation.

We strongly advise students planning graduate study in mathematics or related fields to take additional courses at the 300 level. Majors may substitute equivalent courses in mathematics at Bryn Mawr College for any requirement, subject to advisor approval.

### Minor Requirements

Mathematics minors take the same core sequence as do the majors, though not necessarily to the same depth, followed by a selection of electives tailored to the student’s interest. Statistics minors take a separate core sequence in probability and statistics, with later flexibility in pursuing either a more applied or a more theoretical track.

**Mathematics Minor Requirements**

- MATH 215 (Linear Algebra) and either MATH 121 (Multivariable calculus) or MATH 216 (Advanced Calculus).
- MATH 317 (Analysis I) and MATH 333 (Algebra I).
- Two additional electives in mathematics at the 200 level or higher.

Minors may substitute equivalent courses in mathematics at Bryn Mawr College for any requirement, subject to advisor approval.

**Statistics Minor Requirements**

- One of the following courses (Introduction to Statistics): STAT 203, ECON 204, PSYC 200, SOCL 215
- STAT 286 (Applied Multivariate Statistical Analysis)
- MATH 218 (Probability)
- MATH 215 (Linear Algebra)
- MATH 121 or MATH 216 (Multivariable Calculus)
- One of the following:
- STAT 328 (Mathematical Statistics)
- STAT 396 (Advanced Topics in Probability and Statistics)
- ECON 304 (Econometrics)
- SOCL 320 (Advanced Quantitative Methods for Sociologists).

#### Options for the Statistics Minor

Information about the Statistics program at Haverford

- A
*math minor*can also be a statistics minor. If a student wants to be a math minor and a statistics minor, the following courses: STAT 203, ECON 204, MATH 218, STAT 286, STAT 328 and STAT 396, cannot be counted to satisfy both the math minor and statistics minor. - A
*math major*can also be a statistics minor. If a student wants to be a math major and a statistics minor, the following apply:- STAT 203, ECON 204 and STAT 286 cannot be counted to satisfy both the math major and statistics minor requirement.
- At most one of the following courses can be counted to satisfy both the math major and statistics minor: MATH 218, STAT 328 and STAT 396.

*Math majors with economics concentration*: If a math major wants to be an econ concentrator and a statistics minor, MATH 218, STAT 286, STAT 328 and STAT 396 cannot be counted toward both the economics concentration and the statistics minor.*Economics majors with math concentration*: If an economics major wants to be a math concentrator and also a statistics minor, the following apply:- MATH 218, STAT 286, STAT 328 and STAT 396 cannot be counted to satisfy both the stat minor and the math concentration requirement.
- ECON 304 cannot be counted toward the statistics minor. (ECON 304 is required by the economics major.)

For further information about the statistics minor, please see the PDF supplement on the mathematics website, or contact the minor coordinator.

### Senior Project

The senior paper is a year-long research project that includes both written thesis and oral presentation. Our students will engage advanced content and techniques in pure mathematics, applied mathematics and statistics. They will gain ownership of the process and material, will write clear, careful and correct mathematics/statistics, and will develop an oral presentation that highlights the central ideas of their thesis work at a level appropriate for an audience in the mathematical/statistical sciences.

A detailed description of the format, goals, and assessment criteria for the senior experience can be found in the complete departmental statement in the Catalog (PDF).

### Concentrations & Interdisciplinary Minors

Mathematics majors can pursue four areas of concentration:

#### Computer Science (more theoretical)

It may come as a surprise to some that many of the fundamental questions in computer science (including the famous P versus NP problem) are in essence mathematical questions. Conversely, some of the deepest foundational questions about the nature of mathematics (such as: what constitutes a proof?) are inherently computational in nature. Computers have also become a powerful tool in mathematical research and its applications, both theoretical and experimental. A full understanding of their capability and potential can only be realized by formal coursework in computer science. The concentration is open to math or physics majors

#### Scientific Computing (more applied)

Many disciplines in the natural and social sciences include a significant sub-discipline that is explicitly computational. Examples include astronomy, biology, chemistry, economics, and physics. In some fields, such as biology, the use of computation has become so widespread that basic literacy in computation is increasingly important and may soon become required. The Concentration in Scientific Computing gives students an opportunity to develop a basic facility with the tools and concepts involved in applying computation to a scientific problem, and to explore the specific computational aspects of their own major disciplines.

#### Concentration in Mathematical Economics

Mathematics and economics are complementary disciplines. Most branches of modern economics use mathematics and statistics extensively, and some important areas of mathematical research have been motivated by economic problems. Economists and mathematicians have made important contributions to each other’s disciplines. Economist Kenneth Arrow, for example, did path-breaking work in the field of mathematical optimization; and in 1994 mathematician John Nash was awarded the Nobel Prize in economics for introducing a theory of equilibrium in non-cooperative games that has become central to contemporary economic theory. Haverford’s Concentration in Mathematical Economics enables students in each of the disciplines not only to gain proficiency in the other, but also to understand the ways in which they are related and complementary.

#### Mathematics Education (for majors interested in teaching mathematics)

The Bryn Mawr-Haverford Education Program invites students to study the discipline of education; explore the interdisciplinary field of educational studies; begin the path of teacher preparation for traditional classrooms; and participate in teaching experiences in a range of classroom and extra-classroom settings. Focused on teaching and learning as social, political, and cultural activities, the Education Program challenges students to explore the relationships among schooling, human development, and society as they gain knowledge and skills of educational theory and practice. Students who complete one of the Education Program options are prepared to become lifelong learners, educators, researchers, leaders and agents of change.

### Affiliated Programs

Many of our graduates have pursued successful and interesting careers in various engineering disciplines. Our 4+1 program with the University of Pennsylvania, 3/2 engineering program with CalTech, and the Master’s degree course exchange agreements with Swarthmore and the University of Pennsylvania offer robust—and unique—opportunities.