Department of Mathematics and Statistics
Academic Programs
Department Website:
https://www.haverford.edu/mathematicsandstatistics
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 threeyear 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 nonmajors, but are the real “introduction” to math for most majors.
Core Major Courses
This category includes MATH H317MATH H318 (Analysis) and MATH H333MATH 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 nonmajors, 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 H399I (Senior Seminar): a required yearlong group seminar for seniors that offers advice, support, and practice in preparing the senior paper and oral presentation.
 MATH H400 (Senior Research): a required yearlong course for seniors that involves independent work with their senior thesis advisor.
 MATH H460 (Teaching Assistantship in Mathematics): a halfcredit 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.
Senior Project
Senior Project Learning Goals
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 through understanding the content and the details of the problem they are investigating, constructing illustrative examples, carrying out novel computations or carefully analyzing a data set. Our students will write clear, careful and correct mathematics/statistics, from precise definition or description of a model to rigorous proofs or wellsupported analyses. They 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.
Senior Project Assessment
The grade for the senior thesis is determined by the following:
 Level of engagement with advanced mathematics or statistics.
 Level of ownership of the material and of the writing process.
 Adherence to professional standards of written mathematics and statistics.
The grade for the senior seminar is determined by the following:
 Completing all the assignments in accordance with the assignment description.
 Meeting deadlines for each assignment.
 Quality of intermediate drafts, including whether easily discernible progress has been made from one assignment to another.
 Engaged participation in seminar meetings.
 Quality of the thesis presentation.
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 H324 (Advanced Econometrics)
Options for the Statistics Minor
 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.)

For further information about the statistics minor, please see the PDF supplement on the mathematics website, or contact the minor coordinator.
Concentrations and 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 subdiscipline 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.
Mathematical Economics (for majors interested in applying their skills to economic problems)
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 pathbreaking 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 noncooperative games that has become central to contemporary economic theory. Haverford’s Area of 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 MawrHaverford 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 extraclassroom 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.
For the requirements for these concentrations, see those headings in this catalog or visit the departmental website.
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. For more information on these options, visit the Engineering website: https://www.haverford.edu/engineering/