Ph.D. Degree in Computational and Applied Mathematics

The University of Chicago has recently created a Committee on Computational and Applied Mathematics (CCAM), an inter-departmental program to provide graduate training leading to the Ph.D. in Computational and Applied Mathematics. The Committee is now accepting applications to this exciting new Ph.D. program.

Background

The use of computational, mathematical and statistical modeling in various areas of science has increased dramatically in recent years, triggered by massive increases in computing power and data acquisition. Mechanistic models for physical problems that reflect underlying physical laws are being combined with data-driven approaches in which statistical inference and optimization play key roles. These developments are transforming research agendas throughout statistics and applied mathematics, and are impacting a broad range of scientific disciplines.

A critical need now exists to train the next generation of computational and applied mathematicians to confront data-centric problems in the natural and social sciences. In response to these developments, the Committee on Computational and Applied Mathematics has been formed to provide graduate training in Computational and Applied Mathematics that reflects both the scientific demands and the unique strengths of the University of Chicago faculty across the Division of the Physical Sciences, including the recent hiring of several new faculty under a Computational and Applied Mathematics Initiative (CAMI).

Graduate Program Logistics

Admissions

The program will admit a small number of exceptionally qualified students. Each student will be assigned to a member of the steering committee to plan and approve a course of study.

Thesis committee

By the end of their second year, students will choose a thesis advisor from CCAM and two additional thesis committee members. A student may propose an advisor who is not a member of CCAM, with approval of the steering committee, in which case the additional members of the thesis committee will be from CCAM.

Course Requirements

The course requirements of the Ph.D. in Computational and Applied Mathematics are fairly low, consistent with the goal of involving students in original research early in their graduate careers. Together with an assigned advisor, students will select courses from core sequences and a diverse set of possible electives. Example topics include traditional areas such as partial differential equations, numerical analysis, and dynamical systems, as well as modern signal processing, machine learning, data collection and processing, optimization, stochastic modeling and analysis, and the statistical analysis of high dimensional data. Students will complete preliminary examinations in two chosen areas, typically in their second year of study. The track will be highly interdisciplinary, with many students interacting with at least one scientific domain.

Students are required to take nine quarter courses over the first two years, according to a plan designed in consultation with the advisor. This allows students to take preparatory courses as needed. Courses are chosen from a selected set of courses in computational, statistical, and mathematical foundations. Students are also required to take at least one graduate level course in a scientific domain such as chemistry, genetics, geophysical sciences, molecular biology, neuroscience, and physics. Examples of each group of courses is provided below.

  1. Computational and Statistical Foundations
    1. Computer Science
      • CMSC 37000 Algorithms
      • TTIC 31080 Approximation Algorithms
       
    2. Optimization
      • Stat 30900 Matrix Computation
      • Stat 31015 Convex Optimization
       
    3. Statistics and Machine Learning
      • Stat 37710 Machine Learning
      • Stat 37400 Nonparametric Inference
      • Stat 37500 Pattern Recognition
      • Stat 37750 Compressed Sensing
  2. Mathematical Foundations
    1. Analysis and Differential Equations
      • Math 312 Analysis I
      • Math 313 Analysis II
      • Math PDE Analysis
    2. Mathematical Computation
      • Stat 37760 Modern signal processing
      • Stat 31095 Numerical ODEs
      • Stat 31100 Numerical PDEs
    3. Dynamical Systems
      • Applied dynamical systems I/II
      • Advanced topics in dynamical systems

  3. Applications and Domain Science
    • Stat 35410 Computational Biology
    • Stat 42510 Computational Neuroscience
    • Chem 36800 Advanced Computational Chemistry
    • TTIC 31040 Introduction to Computer Vision

As two example nine-course sequences, a student with a machine learning focus might take

  • Stat 30900 Matrix Computation
  • Stat 31015 Convex Optimization
  • Stat 37710 Machine Learning
  • CMSC 37000 Algorithms
  • Stat 37500 Pattern Recognition
  • Math 312 Analysis I
  • Stat 37760 Modern signal processing
  • Stat 31095 Numerical ODEs
  • TTIC 31040 Introduction to Computer Vision
and a student interested in numerical methods might take
  • Stat 30900 Matrix Computation
  • Stat 31015 Convex Optimization
  • Math 312 Analysis I
  • Math 313 Analysis II
  • Stat 37760 Modern signal processing
  • Math PDE Analysis
  • Stat 31095 Numerical ODEs
  • Stat 31100 Numerical PDEs
  • Chem 36800 Advanced Computational Chemistry

Faculty

The CCAM is made up of faculty from several departments, including Statistics, Computer Science, Mathematics, Neurobiology, Ecology and Evolution, Human Genetics, Chemistry, and Astronomy and Astrophysics. The number and representation of the CCAM faculty is expected to grow in the coming years.

 

Application Requirements

Applicants must use the online application. Applications will be reviewed starting on 12/31/2016; the application deadline is 1/31/2017. The following materials are required:

  • A copy of your transcript from each undergraduate or graduate institution you have attended
  • At least three letters of recommendation
  • GRE test scores (general exam required, subject test strongly recommended)
  • TOEFL or IELTS test scores if needed (see http://internationalaffairs.uchicago.edu/page/english-language-requirements to see if you are required to submit these scores)
  • Candidate statement
  • Resume or CV
  • $90 application fee

Applicants may send questions to ccam-admissions@galton.uchicago.edu.

 

 

NSF RTG Grant

The CCAM is partly supported by an NSF Research Training Groups in the Mathematical Sciences grant from NSF's Division of Mathematical Sciences. This grant recognizes and supports many of the activities of the CCAM. The PIs and senior personnel of the grant include a diverse group of twelve faculty working in statistics, machine learning and applied mathematics, including people at Toyota Technological Institute at Chicago (TTIC) and Argonne National Laboratory. The research activity organized under this RTG includes investigations in chemistry and molecular dynamics, climate science, computational neuroscience, convex and nonlinear optimization, machine learning, and statistical genetics. The RTG is centered around vertically integrated research experiences, and includes innovations in both undergraduate and graduate education. The computational components of the research provide an entryway for undergraduates to engage in advanced research together with faculty, postdocs and graduate students. The RTG supports interactive working groups and mentorship activities, with postdocs assuming leadership roles. Two summer schools on data science will be hosted at TTIC during the RTG, with case studies drawn from research of the group. A series of minicourses and "boot camps" are planned for the RTG participants on topics including modern large scale computational principles and skills that are increasingly important in industry and many scientific disciplines.

 

Last update:12/30/2016