# Mathematics

Pattern and form surround us—from the branching angles of our blood vessels and the complexity of computer algorithms to inventory scheduling and the four-dimensional geometry of our universe. As the pure expression of pattern and form, mathematics provides the language for science. In the past 75 years, many disciplines have been virtually transformed by the infusion of mathematics, so that alongside the traditional field of mathematical physics, one now finds new disciplines such as mathematical biology, mathematical ecology, mathematical economics, mathematical linguistics and mathematical psychology.

But mathematics is so much more than its applications. As the study of formal structures, mathematics offers a supreme beauty, an abstract forest of pattern and form, at once deep, intricate, logical, and surprising, a forest holding wonders both known and unknown. The search for these wonders is no game, for mathematics bears on eternal truth: Primes—such as 2, 3, 5, 7, 11, 13, ...—cannot be written as the product of two smaller integers. How many primes are there? Infinitely many. This is a well-known wonder proved by Euclid. Twin primes—such as 3 and 5, 5 and 7, 11 and 13, 17 and 19, ... —are “consecutive” primes. How many twin primes are there? No one knows. Mathematicians have unleashed their most sophisticated weapons on this problem, but the question remains unanswered. It is an unknown wonder. Will you be the first to find the answer? Whatever the answer, it is an eternal and universal truth: true for all time, in all places, to every intellect.

To reflect the diversity of modern mathematics and its applications, the department, alone or in conjunction with the economics department, offers three separate majors:

- Mathematics
- Mathematics-computer science
- Mathematics-economics

*The Lawrence Difference*

- Our students actively engage in classroom discussion, regularly work on problems whose solution requires creative thought, and generally develop a keener appreciation of the beauty, power and richness of mathematics.
- Our core sophomore sequence provides majors with a firm foundation in the two pillars of mathematics (Abstract Algebra and Real Analysis), paving the way for exploration of diverse elective offerings at the junior and senior level. We offer courses in many areas of pure and applied mathematics, elementary and advanced statistics, and computer science.
- As they explore the terrain of mathematics, our majors could not ask for better guides than the faculty here at Lawrence, for the Department of Mathematics has won numerous university teaching awards.
- Our students come from all over the U.S. and many foreign countries, but they have an unusual spirit of camaraderie -- from taking classes together, from working in groups on problem sets, and from talking and munching at “Math Tea” on Wednesday afternoons, but also from their natural common bond: a love of mathematics.
- Majors engage in a 1-term independent study during their senior year, working on a topic of their choice under the guidance of a faculty member. This transforming experience demonstrates a student’s ability to learn mathematics with little supervision and to clearly and cogently express this knowledge both verbally and in writing.
- Majors can study abroad through programs such as the Budapest Semesters in Mathematics, Math in Moscow, and the Lawrence University London Centre.
- The mathematics major fits well into the 5-year double degree program, leading to a B.A. from the college and a B.Mus. from the conservatory.

*Senior Experiences*

Our students pursue advanced topics of their choice in Senior Independent Studies. Here are a few recent ones:

- Bayesian Statistics
- Non-Euclidean Geometry
- Machine Learning
- Linear Programming and Economic Analysis
- Group Theory and Physics
- The Four Color Theorem
- Mathematical Logic and Advanced Set Theory

For a full description of Lawrence’s computer facilities and for descriptions of the computer science courses visit the computer science website.