The department offers specialized programs in applied mathematics. For each of the programs, there is a minimum requirement of 27 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:
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 taken within the department must include three credit hours of approved course work 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.)
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.