The department offers specialized programs in applied mathematics. For each of the programs, there is a minimum requirement of 30 credit hours of course work, at least 18 of which must be at the 400 level or higher. Students in the program must complete course work requirements in each of the following groups:

  • At least 15 hours of courses designated MATH
  • At least 6 hours of courses not designated MATH
  • 6 hours of thesis work (see below) or successful completion of a comprehensive exam

Given the great diversity of topics used in applications, there cannot be a large common core of requirements for the MS in applied mathematics.  Still, all students pursuing this degree are strongly advised to take MATH 431 Introduction to Numerical Analysis I and MATH 441 Mathematical Modeling. “In addition, to add breadth to the student’s education, the set of courses designated MATH must include three credit hours of approved coursework in at least three of the following seven breadth areas. (The list includes suitable courses for each area. Please note that a course may be used to satisfy only one breadth area requirement.)


Applied Mathematics Breadth Areas


Analysis and Linear Analysis:
MATH 471
Advanced Engineering Mathematics *
MATH 423
Introduction to Real Analysis I
MATH 405
Advanced Matrix Analysis
Probability and its Applications:
MATH 439
Integrated Numerical and Statistical Computations
MATH 491
Probability I
Numerical Analysis and Scientific Computing:
MATH 431
Introduction to Numerical Analysis I
MATH 432
Numerical Differential Equations
MATH 433
Numerical Solutions of Nonlinear Systems and Optimization
Differential Equations:
MATH 435
Ordinary Differential Equations
MATH 445
Introduction to Partial Differential Equations
MATH 449
Dynamical Models for Biology and Medicine
Inverse Problems and Imaging:
MATH 439
Integrated Numerical and Statistical Computations
MATH 440
Computational Inverse Problems
MATH 475
Mathematics of Imaging in Industry and Medicine
Logic and Discrete Mathematics:
MATH 406
Mathematical Logic and Model Theory
MATH 408
Introduction to Cryptology
Life Science:
MATH 441
Mathematical Modeling
MATH 449
Dynamical Models for Biology and Medicine
MATH 478
Computational Neuroscience
* Not suitable for credit towards the PhD requirements.


Other suitable courses for students in applied mathematics include:

MATH 424 Introduction to Real Analysis II 3
MATH 425 Complex Analysis I 3
MATH 427 Convexity and Optimization 3
MATH 428 Fourier Analysis 3
MATH 444 Mathematics of Data Mining and Pattern Recognition 3
MATH 475 Mathematics of Imaging in Industry and Medicine 3
MATH 492 Probability II 3


The student must pass a comprehensive oral examination on three areas, two of which must be on the list of breadth areas  (although no particular courses are specified). The third area for the examination may be any approved subject.

A student in the MS program in applied mathematics may substitute the comprehensive examination requirement with an expository or original thesis, which will count as 6 credit hours of course work. The thesis will be defended in the course of an oral examination, during which the student will be questioned about the thesis and related topics. These two variants correspond to the graduate school’s plan A and plan B.