MS in Computational and Applied Mathematics Curriculum

The MCAM program consists of at least nine graduate level courses related to Computational and Applied Mathematics, as described below, and can be completed in as few as nine months or up to two years. 

Working with your academic advisers, you will develop a course program and select one of the following tracks. Each track includes a sequence of three courses.

Computational Mathematics Track Applied Analysis and Modeling Track
  1. Mathematical Computation I: Matrix Computation (CAAM 30900 or Applied Linear Algebra (CAAM 31430)
  2. Mathematical Computation II: Optimization (CAAM 31020 or CAAM 31015)
  3. Machine Learning (CAAM 37710) or Applied Approximation Theory (CAAM 31050)
  1. Applied Dynamical Systems (CAAM 31410) or Applied Analysis (CAAM 31440)
  2. Applied Functional Analysis (CAAM 31210)
  3. Partial Differential Equations (CAAM 31220)

You will complete three additional courses of your choice, selecting from the track you did not pursue above or from other courses offered as part of the CAM graduate programs. Some courses may have prerequisite requirements or require instructor consent in order to enroll. Recent course offerings have included (but are not limited to) the list below.

  • Scientific Computing with Python
  • Inverse Problems and Data Assimilation
  • Monte Carlo Simulation
  • Modern Applied Optimization
  • Applied Complex Analysis
  • Applied Fourier Analysis
  • Applied Partial Differential Equations
  • Asymptotic Analysis

View selected course descriptions
  • Topics in Random Matrix Theory
  • Stochastic Calculus
  • Mathematical Computation III: Numerical Methods for PDEs
  • Fast Algorithms
  • Variational Methods in Image Processing
  • Foundations of Computational Dynamics
  • Algorithms for Massive Datasets
  • Solving PDEs with Machine Learning
  • Measure Theoretic Probability (sequence)
  • Modern Inference

For the remaining courses, you can select from the above lists or from graduate-level courses related to CAM offered through the Physical Science Division, TTIC, or the Booth Business School.

Thesis Option

Student writes in notebook while looking up at the board

Students interested in pursuing applications to a PhD program are encouraged to take the option of a MS degree with thesis.

To pursue this option, you will be required to:

  1. Complete the requirements above
  2. Write and defend a master’s thesis under the guidance of a CAM faculty advisor.

The program does not have a separate period of study allocated to thesis work, so students continue to take courses while working on their thesis.

Russell Hua - Advisor: Bal

Thesis Title: Existence of Scattering Solutions to Weakly Nonlinear Schrodinger Equations

Lekun Wang - Advisor: Barber

Thesis Title: Distribution-Free Uncertainty Quantifications with Conditional Guarantees for Image-To-Image Regression Models

Ruizhe Chen - Advisor: Xiu

Thesis Title: Forecasting Macroeconomic Variables Using Principle Component Analysis and Supervised Sparse Autoencoders

Matthew Frazier - Advisor: Bal

Thesis Title: Topological Properties of Cold Plasma

Yuelian Li - Advisor: Kondor

Thesis Title: Implementing and Evaluating a P-Tensor-based Framework on Node and Graph Classification Tasks

Jingchun Shao - Advisor: Khoo

Thesis Title: Quantized Tensor Train for Compressed Sensing

Alex Huang - Advisor: Ma

Thesis Title: Scaled Gradient Descent for Low-Rank Adaptation in Language Model Fine-Tuning

Kaiwen Fu - Advisor: Sanz-Alonso

Thesis Title: Through Variational Inference to Data Assimilation

Haoming Wang - Advisor: Lim

Thesis Title: Glivenko-Cantelli for f-divergence
 

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