Sample study plans for students with concentrations in scientific computing, imaging, mathematical biology, and stochastics follow. The graduate committee will entertain ideas for other serious study plans or qualifying exam subjects in addition to the most common variants.

#### Scientific Computing Concentration

 MATH 431 Introduction to Numerical Analysis I 3 MATH 432 Numerical Differential Equations 3 MATH 433 Numerical Solutions of Nonlinear Systems and Optimization 3 MATH 439 Integrated Numerical and Statistical Computations 3 or MATH 440 Computational Inverse Problems MATH 441 Mathematical Modeling 3 MATH 445 Introduction to Partial Differential Equations 3 MATH 449 Dynamical Models for Biology and Medicine 3 or MATH 478 Computational Neuroscience Application area 9

#### Imaging Concentration

 MATH 428 Fourier Analysis 3 MATH 431 Introduction to Numerical Analysis I 3 MATH 432 Numerical Differential Equations 3 MATH 433 Numerical Solutions of Nonlinear Systems and Optimization 3 MATH 439 Integrated Numerical and Statistical Computations 3 or MATH 440 Computational Inverse Problems MATH 441 Mathematical Modeling 3 MATH 444 Mathematics of Data Mining and Pattern Recognition 3 MATH 445 Introduction to Partial Differential Equations 3 MATH 475 Mathematics of Imaging in Industry and Medicine 3 EBME 410 Medical Imaging Fundamentals 3 PHYS 431 Physics of Imaging 3 PHYS 460 Advanced Topics in NMR Imaging 3

#### Life Science Concentration

 MATH 431 Introduction to Numerical Analysis I 3 MATH 432 Numerical Differential Equations 3 MATH 433 Numerical Solutions of Nonlinear Systems and Optimization 3 MATH 439 Integrated Numerical and Statistical Computations 3 MATH 440 Computational Inverse Problems 3 MATH 441 Mathematical Modeling 3 MATH 445 Introduction to Partial Differential Equations 3 MATH 449 Dynamical Models for Biology and Medicine 3 MATH 478 Computational Neuroscience 3 Application area 9

#### Stochastics Concentration

 MATH 423 Introduction to Real Analysis I 3 MATH 424 Introduction to Real Analysis II 3 MATH 431 Introduction to Numerical Analysis I 3 MATH 441 Mathematical Modeling 3 MATH 491 Probability I 3 MATH 492 Probability II 3 Application area 9