Applied Mathematics and Computational Science (AMCS)

The Applied Mathematics and Computational Sciences (AMCS) program prepares students for success in constructing computational solutions to mathematical problems in a variety of areas.

This preparation emphasizes the fundamentals of modeling, analyzing and computationally solving problems in many disciplines. The program in AMCS offers four tracks, each of which leads to a frontier of computational mathematics. The four track areas are:

  • Partial Differential Equations (PDEs)
  • Operations Research (OR)
  • Information Science (IS)
  • Modeling and Numerical Simulation (MNS)

A student seeking a degree in Applied Mathematics and Computational Sciences must specify one track area as a major. For the M.S. degree, course requirements include four designated Core courses, as well as a minimum of three Immersion courses and one Specialty course from the student’s chosen major area. Additional elective coursework to meet the credit requirements for the degree gives students the flexibility to pursue further breadth and/or depth in their program. Each course carries 3 credit hours.

The M.S. degree requirement is 30 credits (generally comprised of 10 courses). Typically, students will take 12 credits (4 courses) per semester in the program, completing the M.S. program in 3 semesters (1.5 years). .

Students pursuing a Ph.D. must first satisfy the coursework requirements for the M.S. program, take at least 6 additional credits (for a minimum of 12 courses overall), pass qualifying examinations and pursue original research culminating in a doctoral dissertation. Ph.D. coursework in AMCS includes diversity requirements in a particular domain of application and in computer science, ensuring that graduates are equipped to lead multidisciplinary research in which they are required to communicate in the language of and understand the intellectual culture of each contributing discipline— from formulation, to mathematical technique, to computational implementation, to analysis and interpretation of results. Completing the Ph.D. program generally takes 3 additional years beyond the completion of the M.S. program requirements. Further details on degree coursework requirements as well as Ph.D. program qualification and requirements are described in Section 4. .

The Core courses required for all students in the AMCS program include:

  • Numerical Optimization (AMCS 211)
  • Applied Partial Differential Equations (AMCS 231)
  • Probability and Random Processes (AMCS 241)
  • Numerical Linear Algebra (AMCS 251)
.

The Immersion courses in each AMCS track are as follows: Partial Differential Equations

  • Stochastic Differential Equations (AMCS 236)
  • Numerical Analysis of Partial Differential Equations (AMCS 306) )
  • Applied Partial Differential Equations II (AMCS 331)
Geometric Modeling and Scientific Visualization:
  • Scientific Visualization (AMCS 247) )
  • Computer Graphics (AMCS 248) )
  • Geometric Modeling (AMCS 272) )
Operations Research:
  • Linear and Nonlinear Optimization (AMCS 212) )
  • Machine Learning (AMCS 229) )
  • Stochastic Differential Equations (AMCS 236) )
  • Algorithmic Paradigms (AMCS 261) )
Information Science:
  • Machine Learning (AMCS 229) )
  • Information Networks (AMCS 337) )
  • Computational Methods in Data Mining (AMCS 340) )
Modeling and Numerical Simulation:
  • Stochastic Differential Equations (AMCS 236) )
  • Scientific Visualization (AMCS 247) )
  • Stochastic Methods in Engineering (AMCS 308) )
  • Computational Science and Engineering (AMCS 330) )
  • Computational Methods in Data Mining (AMCS 340) )

The Specialty courses in the AMCS program are specified by individual faculty members and may vary from year to year.


Course Descriptions