In 1960, Eugene Wigner, a renowned physicist of mid-century, wrote an article entitled "The unreasonable effectiveness of mathematics." Wigner focused on the remarkable interplay between mathematics and the physical sciences, something that was well understood in 1960. His title is even more relevant today because mathematics now contributes to almost every discipline. Mathematics is effective because it finds hidden patterns that unite apparently unrelated phenomena, thereby allowing our intuitions about one thing to illuminate our understanding of others. Mathematics focuses on quantitative relationships, forcing us to isolate the pivotal components of a thing or process, and enables us to explore the 'What if?' questions that are the basis of thoughtful planning. And mathematics is a vehicle for the most precise communication.
This is the most flexible of the three concentrations, allowing the widest choice of electives. Students who are considering graduate study often pursue this concentration, as do some students aiming for pre-college teaching, but the flexible requirements of the concentration are also appropriate for students with other goals.
The major requirements of the Standard Concentration are:
- a core consisting of Math 111 or 131, 112 or 132, 211, 212 or 213, and 214;
- completing the major writing requirement and computer proficiency requirement;
- Math 307 and 311 plus either
- Math 495-6 and three other three-credit 400 level mathematics courses and one three-credit mathematics course at the 300-400 level (for a total of at least eight upper-division courses), or
- (excluding Math 495-6) three three-credit mathematics courses at the 400-level, plus two other three-credit mathematics courses at the 300-400 level (for a total of at least seven upper-division courses).
With permission of the department chair, certain three-credit upper-division mathematical courses from other departments (e.g., Computer Science, Economics, or Physics) may be used as upperdivision elective courses in this requirement.
Experience shows that some students skip part of the freshman/sophomore core described above, without receiving AP credit or credit by examination for the skipped courses. In such cases, each skipped course must be replaced by a three-credit mathematics course numbered 300 or higher.
The program described above is an adequate undergraduate mathematics program by national standards. However, the Committee on the Undergraduate Program of the Mathematical Association of America has recommended that mathematics majors pursue a kind of in-depth study of mathematics that goes beyond the requirements outlined above. Consistent with that recommendation, the department encourages its students to take at least two additional mathematical science courses at the 400-level, in addition to the 38 hour program described above. Ideally these courses should be part of a sequence that builds upon and shows the inter-relations between other courses in the major. Whether the courses are applications-oriented or theoretical is not important. This recommendation is particularly important for students contemplating graduate study in mathematics.
By careful planning, students can build a unifying theme into their study-in-depth option. Four relatively common examples are:
- Algebra in depth: courses chosen from Math 405, 408, 412, 430, and 432
- Analysis in depth: courses chosen from Math 403, 405, 416, and 428
- Applied Mathematics in depth: courses chosen from Math 405, 413, 414, AS 441 and AS 442
- Operations Research/Actuarial Science in depth: courses chosen from Math 401, 402, 413, 424, and 432
Other coherent study-in-depth programs can be designed by students and their advisors.