# Preparing For Eventual Entry into a Graduate Program in the Mathematical Sciences

If you are interested in eventually pursuing graduate studies in mathematics, applied mathematics, biomathematics, mathematics education, or statistics, it is imperative that you *speak with your advisor early *in your career as an undergraduate, so that you can plan an appropriate course of study. In most cases, students admitted to graduate study in mathematics receive financial support in the form of a stipend and work as research or teaching assistants, so *do not restrict your consideration of graduate studies because of finances*. Also, keep in mind that you will need letters of recommendation when you apply; see our 6 etiquette tips for requesting letters of recommendation.

If graduate studies are a possibility you want to consider, you should look at the offerings and requirements of a variety of graduate programs, and choose those that best suit your interests. Some schools offer more than one program in mathematical sciences; others have a single program with different specialization tracks. For instance, our department offers a Mathematics graduate program with tracks in “pure” mathematics and mathematics education, but is also involved in two interdisciplinary graduate programs, one in Applied Mathematics and one in Statistics.

It is typical and often recommended to change schools between undergraduate and graduate studies. You should discuss your options with your faculty advisor (in particular, ask for recommendations as well as contact names), and make sure your studies both in and out of the classroom will prepare you to enter the graduate programs in which you are interested. The *comprehensive emphasis* is the most natural choice for those interested in graduate studies in mathematics. It includes courses in real and complex analysis (MATH 425A, MATH 425B, and MATH 424) and a second course in linear algebra (MATH 413), which are required by many programs. Further recommendations are given below.

## Graduate studies in mathematics

If you plan to pursue studies in mathematics, you should choose the *comprehensive emphasis* (for more details, see the list of our undergraduate emphases), and take abstract algebra (MATH 415A and MATH 415B) and if possible topology (MATH 432). Most “pure” mathematics graduate programs have core courses and qualifying exams on the topics of analysis, algebra, and geometry/topology. Your first year of graduate school will be easier if you come in with a solid foundation in these topics.

## Graduate studies in applied mathematics

If you are interested in a PhD in applied mathematics, it is still recommended that you take the *comprehensive emphasis*. You may prefer to select the differential equations sequence (MATH 454 and MATH 456) rather than the abstract algebra sequence. You could also choose some of the other mathematics options, but it is important that you take the analysis courses (at least MATH 425A and MATH 424) and a second course in linear algebra (MATH 413).

## Graduate studies in biomathematics

If you are interested in biomathematics, it is recommended that you take the *comprehensive emphasis*, together with a few courses selected from the following list: biology (MCB 181R, MCB 182, MCB 320,MCB 410, MCB 411, MCB 416), biochemistry (BIOC 460 or BIOC 462A and BIOC 462B, BIOC 471A), ecology (ECOL 335, ECOL 426, ECOL 496N) or computer science (CSC 120, CSC 245, CSC 345). An alternative is to complete the *life sciences emphasis*, but include analysis (at least MATH 425A and MATH 424), as well as linear algebra (MATH 413).

## Graduate studies in mathematics education

If you are interested in mathematics education, be aware that graduate programs in mathematics education are typically offered either by colleges of education or by mathematics departments, and as a consequence admission requirements differ.

If the Ph.D. mathematics education program you are interested in is housed in a college of education, faculty will look more favorably on candidates with K–12 teaching experience. A typical path is to become a licensed K–12 mathematics teacher (with a bachelors degree in mathematics), teach for a few years (and perhaps, although not necessarily, work on a Master's degree in mathematics or in education), and then go back to graduate school full-time. In this instance, you would need to follow the *mathematics education emphasis* and have the desire to teach in a K–12 classroom. Although it is not always absolutely essential to have K–12 experience to be admitted to a college of education program, it would put you at a decided disadvantage not to have had some K–12 experience.

In cases where the Ph.D. program is housed in a mathematics department, K–12 teaching experience will very likely not be critical. In determining admission, the department will typically look for the strength of your mathematical preparation, grades, GRE scores, etc. As an undergraduate, you should take the *comprehensive emphasis* and pursue as much mathematics as possible. You should also couple this with whatever teaching experiences are available — assisting an instructor in some way (for instance through our Undergraduate Teaching Assistantship (UTA) Program or the University Teaching Teams Program), peer-tutoring (see our tutoring page for tutoring services on campus — most of the links listed there also give information on how to apply for tutor positions), working in a local area school (see our Center for Retention and Recruitment of Mathematics Teachers for one such opportunity), working part-time for an education program (K–12 or university level) — anything that would give you experience teaching and/or helping others learn mathematics. An undergraduate research experience related to mathematics education would also be advantageous.

Finally, it is important to note that without at least three years of full-time K–12 teaching experience, it will likely be quite difficult for you, once you finish your Ph.D., to be hired in a college of education. In mathematics departments, this will likely not be a concern.

## Graduate studies in statistics

If you are interested in a PhD statistics, it is recommended you take the *probability and statistics emphasis*, but include linear algebra (MATH 413) and some computer science courses (such as CSC 252, CSC 352). Knowledge of real analysis of several variables (MATH 425B) is also important. MS degrees may not expect students to have as much theoretical background; check with specific programs to determine their expectations.

## General expectations that you should keep in mind

Graduate schools increasingly expect applicants to *have gone beyond the standard undergraduate curriculum*. In particular, you will often be in competition with students who have some sort of research experience and, if you apply to very prestigious schools, with students who have already taken some graduate-level courses. You should discuss the possibility of getting involved in an undergraduate research project (our Undergraduate Research Assistant (URA) Program, the University's Undergraduate Biology Research Program, and the Arizona Space Grant are a few options) or an internship with your advisor. Writing an honors thesis in mathematics as a part of the Honors Program is an additional option. These experiences also provide excellent opportunities for faculty to get to know you well. This is very helpful when you apply to graduate programs since you will need letters of recommendation.

Many graduate programs also require applicants to take the Graduate Record Examination (GRE). Please see our GRE page for more information and links.

**A note on MATH 355 and MATH 254 :** MATH 355 is the differential equations course that all mathematics majors are expected to take. This course emphasizes the ideas of dynamical systems and makes use of a more sophisticated approach to differential equations. MATH 254 is a differential equations course that is aimed at engineering and science majors. It can be substituted for MATH 355 in the case of those pursuing two or more majors (with faculty advisor approval), but for those interested in pursuing graduate studies in mathematics, it is not appropriate.