University of Wisconsin–Madison

MS-ACM Program Requirements

Applied and Computatational Math

The MS in Applied and Computational Mathematics provides students with a rigorous, modern training in applied and computational mathematics and in the mathematics of data. The program is targeted to students with an undergraduate degree in mathematics or other quantitative disciplines such as computer science, statistics, economics and engineering. Through foundational and advanced coursework, students gain a strong combination of quantitative and computational skills as well as data fluency, positioning them for careers in industry or for advanced studies. Students can satisfy the 30-credit requirement in 12 to 24 months, with accelerated paths supported by relevant summer course offerings. Graduates are well-prepared for roles in information technology, finance, engineering, research, and education – particularly within the rapidly growing sectors of machine learning and artificial intelligence – or to pursue a PhD in the mathematical, statistical, and computational sciences.

 

Program Structure

The program has requirements for 30 graduate credits.

The core of 18 credits may be chosen from the three categories of (i) theory and modeling, (ii) computational methods and (iii) mathematical data science. The 12 electives may be chosen from a diverse set of mathematical topics including probability; real, complex and stochastic analysis; ordinary and partial differential equations; programming; optimization; machine learning; mathematical statistics; and high-performance computing.

Below is the run down of the degree requirements:

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Students must complete 18 credits from the following Core categories. At least 6 credits must be completed from each category. At least two courses must be numbered 700 or higher.

Theory and Modeling6
Applied Mathematical Analysis 2: Partial Differential Equations 
Applied Dynamical Systems, Chaos and Modeling 
Introduction to Stochastic Processes 
Methods of Applied Mathematics 1 
Methods of Applied Mathematics-2 
Computational Methods6
Numerical Linear Algebra 
Numerical Analysis 
Methods of Computational Mathematics I 
Methods of Computational Mathematics II 
Stochastic Computational Methods 
Mathematical Data Science6
Graphs and Networks in Data Science 
Mathematical Methods in Data Science 
Data-Driven Dynamical Systems, Stochastic Modeling and Prediction 
Stochastic Computational Methods 
Randomized Linear Algebra and Applications

Students must complete at least 12 additional credits from the lists below. At most 6 credits can be taken from List B. At most one MATH course can be taken in coursework numbered 800-899.

ElectivesRequired to complete 12 credits
MATH/​STAT  431Introduction to the Theory of Probability 
MATH 519Ordinary Differential Equations 
MATH 521Analysis I 
MATH 522Analysis II 
MATH 531Probability Theory 
MATH/​B M I/​BIOCHEM/​BMOLCHEM  609Mathematical Methods for Systems Biology 
MATH 619Analysis of Partial Differential Equations 
MATH 623Complex Analysis 
MATH 627Introduction to Fourier Analysis 
MATH 629Introduction to Measure and Integration 
MATH 635An Introduction to Brownian Motion and Stochastic Calculus 
MATH 705Mathematical Fluid Dynamics 
MATH 716Ordinary Differential Equations 
MATH 719Partial Differential Equations 
MATH 720Partial Differential Equations 
MATH 721A First Course in Real Analysis 
MATH 722Complex Analysis 
MATH 725A Second Course in Real Analysis 
MATH/​STAT  733Theory of Probability I 
MATH/​STAT  734Theory of Probability II 
MATH 735Stochastic Analysis 
MATH 801Topics in Applied Mathematics 
MATH/​E C E/​STAT  888Topics in Mathematical Data Science 
List BCan take no more than 6 from List B
COMP SCI 300 Programming II 
COMP SCI 400Programming III 
COMP SCI/​E C E/​I SY E  524Introduction to Optimization 
COMP SCI/​I SY E/​MATH/​STAT  726Nonlinear Optimization I 
COMP SCI/​I SY E/​MATH  730Nonlinear Optimization II 
COMP SCI/​E C E  760Machine Learning 
COMP SCI/​E C E  761Mathematical Foundations of Machine Learning 
MATH/​COMP SCI/​I SY E/​STAT  525Linear Optimization 
STAT 615Statistical Learning 
STAT/​MATH  709Mathematical Statistics I 
STAT/​MATH  710Mathematical Statistics II 
STAT 771Computational Statistics 
STAT/​ECON/​GEN BUS  775Bayesian Statistics 
STAT 849Advanced Statistical Methods 
L I S 461Data and Algorithms: Ethics and Policy 
E C E 742Computational Methods in Electromagnetics 
E C E/​COMP SCI/​E M A/​E P/​M E  759High Performance Computing for Applications in Engineering