Advanced Track

Students who choose Mathematics Majors come with various backgrounds. Some of them are ready to study Mathematics on a highly professional, challenging level, and may find classes which emphasize calculations rather than concepts and proofs to be inappropriate.

In order to serve these students better, the Department of Mathematics is developing the Advanced Track option within the Mathematics Major Program

The core of Advanced Track is a system of challenging advanced courses.  In the Advanced Track courses, all the mathematical statements are presented rigorously, discussed from an advanced perspective, and are fully justified with proofs. Within the standard major, this level of maturity does not typically begin until junior- and senior-year courses, and then the material from introductory courses is revisited in more detail.  The Advanced Track students cover this material at the advanced level from the start, saving time and effort. They become better prepared for the challenges of a graduate or professional school
at the finest universities and a career in a variety of fields.

A student may have legitimate concerns about her/his ability to overcome the difficulties related with the Advanced Track. At the beginning of study, we will do our best to make prompt and careful diagnostics. Should issues related with the difficulties arise, a student would be advised to switch to more conventional and easier courses without loss of a semester.

The initial courses of the Advanced Track will also be accepted for majors other than mathematics, as well as the traditional math major. Therefore, a student would not have a problem if she/he would decide later to switch to the traditional math major, or a different major.

The Advanced Track Program is currently under development. It begain in the Fall of 2016.  In Fall 2017, it provides the courses MAT 141 (Analysis I) and MAT 150 (Introduction to Advanced Mathematics). In Spring 2018, the program includes  MAT 142 (Analysis II), MAT 220 (Vector Geometry), and MAT314 (Abstract Algebra II). We expect to offer MAT315 (Advanced Linear Algebra) for the first time in Fall 2018.

The AT Program does not start with Calculus, but with two Analysis courses, MAT 141 and MAT 142, which cover the material of single variable calculus at a much deeper theoretical level, and includes all the proofs. A student who successfully completes both MAT 141 and MAT 142 will receive equivalency for MAT 320 (Foundations of Analysis). A student who already has credits for AP or BC Calculus is very welcome in the AT Program, but these credits do not allow her/him to skip MAT 141 or MAT 142.

MAT 150 (Introduction to Advanced Mathematics) replaces and provides MAT 200 (Logic, Language and Proof). MAT 220 (Vector Geometry) replaces and provides MAT 211 (Introduction to Linear Algebra). MAT314 (Abstract Algebra II) is a continuation of MAT313 (Abstract Algebra). It covers the topics of modules over rings, theory of fields and field extensions, and an introduction to Galois theory.  It is intended for math majors, and in particular majors in the Advanced Track program.