# Department of Mathematics

## Frequently asked questions: background required for the program.

### What math background is needed for the Master's program in math?

Students in the M.S. program in math should have completed undergraduate course work in mathematics that includes material covered in a year-long advanced calculus course, covering real-valued functions of one real variable as well as vector-valued functions of several variables, as well as a course in linear algebra.

Courses at CCNY satisfying this requirement are Math 32300 and Math 32404 for the advanced calculus sequence, and Math 34600 for linear algebra.

Students with an undergraduate degree in mathematics or a mathematical field who lack this background may be admitted conditionally to the MS program, but the appropriate course work will have to be completed without graduate credit. For students interested in the graduate probability and statistics courses, undergraduate courses in probability and statistics are also required. Please contact the graduate advisor for further information.

### What do you mean exactly by the one-year "Advanced Calculus" course requirement?

"Advanced calculus" is a bit of a misnomer, as really what is required is advanced, theoretical treatment of the foundations of calculus. Such courses are called "Real Analysis," "Introduction to Analysis," "Advanced Calculus", "Functions of one or more real variables" and many other names at different instuitions. Though courses in multivariate calculus, differential equations, Fourier methods, and so on, are continuations of a basic calculus sequence, they are generally not sufficiently theoretical to satisfy the advanced calculus course requirement. Any course which does not have a significant emphasis on students doing proofs will not meet this requirement.

### I'm interested in Master's program in math but I've only had one year of calculus, or some kind of biology- or business-oriented calculus. What should I do?

Students who haven't had much in the way of thorough calculus preparation should take more calculus, as appropriate, generally as second-degree undergraduate status students or in non-matriculated graduate student status. It can take several years to complete such prepartion- three semesters of calculus is required preparation for the undergraduate Advanced Calculus sequence, which is itself a year, and for Linear Algebra, which can be taken concurrently with the first semester of Advanced Calculus. That would give a minimal level of preparation- additional courses in differential equations, proof-based undergraduate courses as well as calculus-based probability and statistics courses may also be appropriate.

### It's clear that I need some more background before beginning my graduate studies. Do I have to take those preparatory courses at CCNY?

No, many of those courses can be taken pretty much anywhere- at CCNY, at another CUNY campus, or at many different institutions. Sometimes different schools have different structure to their calculus, differential equations and linear algebra courses, but generally for multivariate calculus and linear algebra, it doesn't matter too much about where the courses are completed. For the advanced calculus sequence, many campuses offer only one semester of advanced calculus, or cover different topics, so for those it may be good to plan more carefully.

### Can I pursue a PhD in math at CCNY?

The mathematics PhD program at CUNY is located at the CUNY Graduate Center (GC). Many CCNY faculty have joint appointments as GC faculty and may teach at either campus, as well as supervise doctoral dissertations for GC students enrolled in the PhD program. All PhD courses are taught at the GC campus, on 34th Street and 5th Avenue. CCNY Master's program students may apply for admission to the CUNY PhD program. In addition, with permission of the graduate advisor and agreement of the instructor at the GC, CCNY Master's students may obtain permits to take courses at the GC towards their Master's degree requirements. For more information on the CUNY Math doctoral program visit the CUNY Math PhD program.