## 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.

Haverford’s Institutional Learning Goals are available on the President’s website, at http://hav.to/learninggoals.

### 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, statistics, applied math, or other special topics.

Mathematics courses for majors fall into six general categories:

**Preliminary Calculus**

This category includes MATH H105, MATH H118, 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 H215, MATH H121 or MATH H216. 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 H317-MATH H318 (Analysis) and MATH H333-MATH H334 (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**

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.

Course | Title |
---|---|

MATH H203 | Statistical Methods and Their Applications |

MATH H204 | Differential Equations |

MATH H210 | Linear Optimization and Game Theory |

MATH H218 | Probability |

MATH H222 | Introduction to Scientific Computing |

MATH/CMSC H235 | Information and Coding Theory |

MATH H286 | Applied Multivariate Statistical Analysis |

**Advanced Electives:**

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.

Course | Title |
---|---|

MATH H328 | Mathematical Statistics |

MATH H335 | Topology |

MATH H337 | Differential Geometry |

MATH/CMSC H340 | Analysis of Algorithms |

MATH/CMSC H345 | Theory of Computation |

MATH H390 | Advanced Topics in Algebra |

MATH H391 | Advanced Topics in Geometry and Topology |

MATH H392 | Advanced Topics in Analysis |

MATH H394 | Advanced Topics in Discrete Math and Computer Science |

MATH H395 | Advanced Topics in Combinatorics |

MATH H396 | Advanced Topics in Probability and Statistics |

MATH H397 | Advanced Topics in Applied Mathematics |

**Other Courses:**

- MATH H399 (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 H400 (Senior Research): a required year-long course for seniors that involves independent work with their senior thesis advisor.
- MATH H460 (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 H215, and either MATH H121 or MATH H216.
- MATH H317 and MATH H333, and one of MATH H318 or MATH H334.
- 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 H399, MATH H400, MATH H460, and MATH H480 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.

Majors must take either MATH H317 or MATH H333 at Haverford College; exceptions to this rule are granted only under unusual circumstances, with advance permission of the department chair. Majors may substitute equivalent courses at Bryn Mawr College for any other course requirement for the major, subject to advisor approval. Courses taken at other institutions may be used to satisfy major requirements, provided that the department chair approves these courses in advance.

### 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 H215 (Linear Algebra) and either MATH H121 (Multivariable calculus) or MATH H216 (Advanced Calculus).
- MATH H317 (Analysis I) and MATH H333 (Algebra I).
- Two additional electives in mathematics at the 200 level or higher.

Courses taken at other institutions may be used to satisfy minor requirements, provided that the department chair approves these courses in advance.

**Statistics Minor Requirements**

- One of the following courses (Introduction to Statistics): STAT H203, ECON H204, PSYC H200, SOCL H215
- STAT H286 (Applied Multivariate Statistical Analysis)
- MATH H218 (Probability)
- MATH H215 (Linear Algebra)
- MATH H121 or MATH H216 (Multivariable Calculus)
- One of the following:
- STAT H328 (Mathematical Statistics)
- STAT H396 (Advanced Topics in Probability and Statistics)
- ECON H304 (Econometrics)
- SOCL H320 (Advanced Quantitative Methods for Sociologists).

Courses taken at other institutions may be used to satisfy minor requirements, provided that the department chair approves these courses in advance.

#### 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: cannot be counted to satisfy both the math minor and statistics minor, the following courses: STAT H203, ECON H204, MATH H218, STAT H286, STAT H328 and STAT H396, 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 H203, ECON H204 and STAT H286 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 H218, STAT H328 and STAT H396.

*Math majors with economics concentration*: If a math major wants to be an econ concentrator and a statistics minor, MATH H218, STAT H286, STAT H328 and STAT H396 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 H218, STAT H286, STAT H328 and STAT H396 cannot be counted to satisfy both the stat minor and the math concentration requirement.
- ECON H304 cannot be counted toward the statistics minor. (ECON H304 is required by the economics major.)

### Senior Project

The senior paper is a year-long research project that includes both a written thesis and an oral presentation. Our students will engage with advanced content and techniques in pure mathematics, applied mathematics, and statistics. They will gain ownership of the process and material, write clear, careful, and correct mathematics/statistics, and 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.

### Concentrations & Interdisciplinary Minors

Mathematics majors can pursue four areas of concentration:

#### Computer Science (more theoretical)

t 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.