Courses - Spring 2023
AMSC420
Mathematical Modeling
Credits:
3
Grad Meth:
Reg, P-F
Prerequisite: 1 course with a minimum grade of C- from (MATH240, MATH461, MATH341); and 1 course with a minimum grade of C- from (MATH241, MATH340); and 1 course with a minimum grade of C- from (MATH246, MATH341); and 1 course with a minimum grade of C- from (STAT400, STAT410); and 1 course with a minimum grade C- from (CMSC106, CMSC131).
Cross-listed with: MATH420.
Credit only granted for: AMSC420 or MATH420.
The course will develop skills in data-driven mathematical modeling through individual and group projects. Emphasis will be placed on both analytical and computational methods, and on effective oral and written presentation of results.
AMSC460
Computational Methods
Credits:
3
Grad Meth:
Reg, P-F, Aud
Prerequisite: 1 course with a minimum grade of C- from (MATH240, MATH341, MATH461); and 1 course with a minimum grade of C- from (MATH241, MATH340); and 1 course with a minimum grade of C- from (CMSC106, CMSC131); and minimum grade of C- in MATH246.
Cross-listed with: CMSC460.
Credit only granted for: AMSC460, AMSC466, CMSC460, or CMSC466.
Basic computational methods for interpolation, least squares, approximation, numerical quadrature, numerical solution of polynomial and transcendental equations, systems of linear equations and initial value problems for ordinary differential equations. Emphasis on methods and their computational properties rather than their analytic aspects. Intended primarily for students in the physical and engineering sciences.
AMSC466
Introduction to Numerical Analysis I
Credits:
3
Grad Meth:
Reg, P-F, Aud
Prerequisite: 1 course with a minimum grade of C- from (MATH240, MATH341, MATH461); and 1 course with a minimum grade of C- from (MATH241, MATH340); and 1 course with a minimum grade of C- from (CMSC106, CMSC131); and minimum grade of C- in MATH410.
Cross-listed with: CMSC466.
Credit only granted for: AMSC460, CMSC460, AMSC466, or CMSC466.
Floating point computations, direct methods for linear systems, interpolation, solution of nonlinear equations.
AMSC498A
Selected Topics in Applied Mathematics
Credits:
1 - 3
Grad Meth:
Reg, P-F, Aud
AMSC661
Scientific Computing II
Credits:
3
Grad Meth:
Reg
Prerequisite: Must have knowledge of Matlab or Python. Must have basic knowledge of ordinary and partial differential equations (MATH246 and MATH462 or equivalent, or permission of instructor).
Cross-listed with: CMSC661.
Credit only granted for: AMSC661 or CMSC661.
Numerical methods for solving ordinary and partial differential equations (elliptic, parabolic, hyperbolic, and dispersive): motivation, analysis, and implementation. Finite difference methods, finite element methods, Fourier and Chebyshev spectral methods, and meshless methods.
AMSC664
Advanced Scientific Computing II
Credits:
3
Grad Meth:
Reg
Prerequisite: AMSC663 or CMSC663.
Restriction: Permission of instructor.
Cross-listed with: CMSC664.
Credit only granted for: AMSC664 or CMSC664.
In the sequence Advanced Scientific Computing I & Advanced Scientific Computing II, (AMSC663/CMSC663 and CMSC664/CMSC664, respectively) students work on a year-long individual project to develop software for a scientific task in a high performance computing environment. Lectures will be given on available computational environments, code development, implementation of parallel algorithms.
AMSC674
Partial Differential Equations II
Credits:
3
Grad Meth:
Reg, Aud
Prerequisite: MATH673 or AMSC673; or permission of instructor.
Cross-listed with: MATH674.
Credit only granted for: AMSC674 or MATH674.
Boundary value problems for elliptic partial differential equations via operator-theoretic methods. Hilbert spaces of functions. Duality, weak convergence. Sobolev spaces. Spectral theory of compact operators. Eigenfunction expansions.
Offered Spring only.
AMSC689
Research Interactions in Applied Mathematics and Scientific Computation
Credits:
1 - 3
Grad Meth:
Reg, Aud
AMSC715
Numerical Methods for Evolution Partial Differential Equations
Credits:
3
Grad Meth:
Reg, Aud
Prerequisite: Permission of instructor; or one graduate level course in partial differential equations or one graduate level course in numerical analysis or scientific computing.
Credit only granted for: AMSC612 or AMSC715.
Formerly: AMSC612.
Additional information: This course continues AMSC 714, but can be taken independently, and is a complement to the graduate courses MATH 673 and MATH 674 in PDEs, AMSC 666 in numerical analysis, and AMSC 660 and AMSC 661 in scientific computing.
Topics include: Heat and wave equations: maximum principle, energy methods and Sobolev spaces, finite difference and finite element methods, von Neumann analysis, stability and error estimates;Linear first order PDEs: upwinding and monotone schemes, finite difference, finite volume, and discontinuous Galerkin methods; Nonlinear conservation laws: weak solutions and entropy conditions,monotone methods.
AMSC760
Applied Statistics Practicum
Credits:
3
Grad Meth:
Reg
Prerequisite: Must have completed one year of graduate study in Applied Statistics.
Restriction: Must have project proposal approved by SAC coordinator.
A semester long applied applied statistical project (a minimum 10 hours per week or 120 hours in total), in an internship of collaborative research-laboratory setting working on a substantive applied quantitative project with significant statistical content.
AMSC762
Data Analysis Project
Credits:
1
Grad Meth:
Reg
Restriction: Permission of CMNS-Applied Mathematics department; and permission of instructor.
This course cannot be used to meet any of the Applied Statistics Area's seminar requirements. Offered yearly, required of and limited to MS non-thesis and doctoral students in Applied Statistics Area, for whom the resulting projects serve as a Qualifying Exam component. After 5-6 lectures or presentations on components of successful data analyses and write-ups, 3-4 sessions will discuss previous student project submissions. The culminating project, to be completed in a two week period between semesters, is an analysis and written report of one of three project choices made available each year to represent a spectrum of realistic applied statistical problems.
AMSC764
Advanced Numerical Optimization
Credits:
3
Grad Meth:
Reg, Aud
Prerequisite: MATH410; or permission of instructor.
Cross-listed with C MSC764.
Credit only granted for: AMSC607, AMSC764 or CMSC764. F ormerly: AMSC607.
Modern numerical methods for solving unconstrained and constrained nonlinear optimization problems in finite dimensions. Design of computational algorithms and the analysis of their properties.
AMSC799
Master's Thesis Research
Credits:
1 - 6
Grad Meth:
S-F
AMSC808A
Advanced Topics in Applied Mathematics
Credits:
1 - 3
Grad Meth:
Reg, Aud
AMSC898
Pre-Candidacy Research
Credits:
1 - 8
Grad Meth:
S-F
AMSC899
Doctoral Dissertation Research
Credits:
6
Grad Meth:
S-F
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