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CSEMoverview.pdf, Exercises of Theory of Computation

Carnegie InstituteTheory of Computation

Oden Institute for Computational Engineering and Sciences and. Department of Mathematics. The University of Texas at Austin. Computational Science ...

Typology: Exercises

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COMPUTATIONAL SCIENCE,
ENGINEERING & MATHEMATICS:
PATH TO DEGREE
Fall 2022
Todd Arbogast
Chair of the Graduate Studies Committee
Center for Subsurface Modeling of the
Oden Institute for Computational Engineering and Sciences
and
Department of Mathematics
The University of Texas at Austin
Computational Science, Engineering, and Mathematics 1 of 43
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COMPUTATIONAL SCIENCE,

ENGINEERING & MATHEMATICS:

PATH TO DEGREE

Fall 2022

Todd Arbogast Chair of the Graduate Studies Committee Center for Subsurface Modeling of the Oden Institute for Computational Engineering and Sciences and Department of Mathematics The University of Texas at Austin

Computational Science & Engineering

Computational science and engineering (CSE) is an exciting and emerging field of rigorous interdisciplinary scientific study. The use of mathematical modeling is growing rapidly and used

  • to understand the dynamics of complex systems, and
  • to make predictions about their behavior.

Traditionally, the pillars of science are theory and experiment. Today, CSE is becoming the third pillar, providing a link between the first two pillars through high performance computing and simulation.

The CSEM Degree Program

CSEM Students, Fall 2018

Computational Science, Engineering, and Mathematics

Overview of CSEM

CSEM is interdisciplinary. To analyze, model, and simulate a system, researchers must develop a broad and deep understanding of the three CSEM Concentration Areas: Area A. Applicable mathematics; Area B. Numerical analysis and scientific computation; Area C. Applications and mathematical modeling of a natural, engineered, social, or other system. A disciplinary view misses the surprisingly complex ways these interact.

Each student must demonstrate breadth and proficiency in each of the three concentration areas. Research for CSEM dissertations must demonstrate an interdisciplinary theme and draw on knowledge from the three CSEM concentration areas.

Computational Science and Engineering

2

What is CS&E?

CS&E – Computational Science and Engineering :

The multidisciplinary field concerned with the study, development,

and use of computational methods and computers to enable

scientific discovery and engineering applications.

Mathematics &

Mathematical Modeling

Science & Engineering Computer Science

Computational Science

and Engineering (CS&E)

CSEM Leadership (2022)

  • Dr. Karen Willcox, Director of the Oden Institute
  • Dr. Todd Arbogast, Chair of the Graduate Studies Committee (GSC)
  • Dr. George Biros, Graduate Advisor
  • Ms. Stephanie Rodriguez, Graduate Coordinator
  • CSEM oversight: The Graduate Studies Subcommittee (GSSC)

Some Statistics of the CSEM program

Current (2021–22)

  • 105 Students Enrolled
  • 90 Students Enrolled in the Ph.D. program
  • 39 Students on Fellowship (approx.)
  • 53.3% US Students
  • 34 CAM Option/56 CSE Option/15 Terminal MS
  • 11 PhD Degrees Awarded 2020–
  • Average 6 Years to Degree Completion (2 yrs for MS, 4 yrs for PhD)
  • About 15-25 new students enrolled each year

Degree Requirements

Computational Science, Engineering, and Mathematics

CSEM Masters Degree

Options. Fulfill one of the following

  1. Thesis and 24 credit hours of coursework plus 6 credit hours of thesis preparation (30 credit hours total);
  2. Report and 30 credit hours of coursework plus 3 credit hours of report preparation (33 credit hours total);
  3. 36 credit hours of coursework. Note: Ph.D. candidates will fulfill this requirement. Be sure to request your degree! This is a two-year program of study. (A full graduate load is 3 courses or 9 credit hours per semester).

Requirements.

  • Course selection must be approved by the Graduate Advisor.
  • At least 24 hours taken for a letter-grade in the 3 CSEM Areas.
  • At least 6 hours in each CSEM Area.
  • All Graduate School requirements must be fulfilled.
  • Overall grade point average 3.0 (B) or better.
  • Reports and Theses require an advisor from the CSEM GSC and a reader to approve the document.

Master’s Report vs. Thesis

No university document distinguishes clearly between a report and a thesis in terms of length or scope.

CSEM policy:

  • A report is a library project, reviewing what scholars have said about a particular topic.
  • A thesis is an original contribution to knowledge in which a novel analysis or argument is offered, a problem is analyzed using a new or previously untried framework, or data about a subject is collected and analyzed.
  • The work required to produce the document is expected to be equivalent to 3 credit hours for a report and 6 for a thesis.

1. Coursework

Computational Science, Engineering, and Mathematics

Ph.D. Degree Options

Two starting points (the two degree options):

  1. Computational and Applied Mathematics (CAM) Option [more math, less applications background]
  2. Computational Science and Engineering (CSE) Option [more applications, less math background]

Upon entering the program, each student must elect an option.

The key question is: Can you handle graduate level mathematics?

The single ending point (a single degree): Doctor of Philosophy with a major in Computational Science, Engineering, and Mathematics

First Semester

Three required courses.

Area A. Functional analysis

  • CAM: CSE 386C/M 383C Methods of Applied Mathematics I
  • CSE: CSE 386M/EM 386M Functional Analysis in Theoretical Mechanics

Area B. Numerical linear algebra

  • CSE 383C/CS 383C Numerical Analysis: Linear Algebra

Area C. Applications and modeling

  • CSE 389C Introduction to Mathematical Modeling in Science and Engineering I

Second Semester

Three required courses.

Area A. Mathematical Methods

  • CAM: CSE 386D/M 383D Methods of Applied Mathematics II
  • CSE: CSE 386L/EM 386L Mathematical Methods in Engineering and Science

Area B. One course chosen from:

  • CSE 383L/M 387D Numerical Treatment of Differential Equations
  • CSE 3832M Foundational Techniques of Machine Learning and Data Sciences

Area C. Applications and modeling

  • CSE 389D Introduction to Mathematical Modeling in Science and Engineering II