As a general rule, we recommend that students finish MAT211 and MAT229 before study abroad, and then be sure to finish MAT330 and MAT331 or approved substitutes by the end of the junior year. Students should also be aware of what one might call "hemisphere issues": At many institutions, courses are arranged into two-semester sequences, and it is difficult to jump in to such a sequence in the middle. Thus it is often easier for students travelling in the fall semester to find appropriate courses in northern hemisphere programs, and for those in the spring to find matches in the southern hemisphere.
When students have narrowed down the list of study abroad programs they are interested in, they should meet with the mathematics department chairperson to discuss specific course choices and get approval for using these courses to meet specific major requirements. The informal description of the major which follows emphasizes some of the issues students should consider when planning their study abroad. (See also the general course planning information for math majors and the official description of the math major in the College Catalog.)
The math major begins with the following "core" courses:
MAT109/110/111: Three semesters of calculus. Many of our majors place out of part of this sequence. These are very standard courses, easily substituted with courses at other institutions. However, they would usually be completed long before a student plans details of study abroad.
MAT211: Introduction to Higher Mathematics. This course is a "bridge" to more advanced courses, and focuses on finding patterns, making conjectures, formulating proofs, and writing in the discipline of mathematics. Similar courses exist at some other institutions, especially American liberal arts colleges, but one is less likely to find courses with this purpose and philosophy at schools abroad. Since MAT211 is a prerequisite for most of our more advanced "theory" courses, we strongly recommend that students take it before leaving for study abroad. If they wait, they are likely to face problems completing their remaining courses in sequence and on time after they return. Prerequisite: MAT111.
MAT229: Linear Algebra and Differential Equations: The topics treated in this course are standard parts of the mathematics curriculum, and versions of them would be found in almost any math department: systems of linear equations and matrices, vector spaces, linear transformations, determinants, eigenvalues and eigenvectors, nth order linear differential equations, and systems of first-order differential equations. However, F&M is somewhat unusual in placing both topics in a single course. This course is a prerequisite for most of our more advanced applied courses; as such, students would be well advised to take it before going abroad or find some appropriate substitute while abroad. Prerequisite: MAT111.
MAT330: Abstract Algebra. This course is an introduction to abstract algebraic systems such as groups, rings, and fields. The precise selection of topics varies somewhat with the instructor, but we always include substantial exposure to the idea of a group and its properties. As a point of reference, one professor's typical course focuses on groups, and covers definitions, cyclic groups, permutation groups, homomorphisms and isomorphisms, quotient groups, and (ideally) culminates in the classification theorem for finite abelian groups. Other instructors might do less group theory, but either supplement it with rings or fields, or spend more time on participatory student activities. Prerequisite: MAT211. It should be relatively easy to find an appropriate substitute for MAT330 in any college or university with a mathematics major.
MAT331: Introduction to Analysis. The ideas and proof techniques of mathematical analysis, including a rigorous development of the real number system, some topics from calculus, cardinality of infinite sets, and other topics as chosen by the instructor. This course is intended to build the skills students need for the more advanced content in courses like complex analysis and topology. Prerequisite: MAT211. In general, it is probably somewhat easier for students studying elsewhere to find an appropriate match for MAT330 than for MAT331, but both are usually possible.
After this point, the major branches out. Roughly, students are expected to take at least one applied or mathematical modeling course (probably at the 300 level), at least one course at the 400 level, and enough electives to have a total of nine courses beyond calculus 3.