Courses - Spring 2025
AMSC
Applied Mathematics & Scientific Computation
Department Site
Open Seats as of
12/21/2024 at 10:30 PM
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
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
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.
AMSC663
Advanced Scientific Computing I
Credits:
3
Grad Meth:
Reg, S-F
Prerequisite: AMSC660 or CMSC660; and (AMSC661 or CMSC661).
Restriction: Permission of instructor.
Cross-listed with: CMSC663.
Credit only granted for: AMSC663 or CMSC663.
In the sequence Advanced Scientific Computing I & Advanced Scientific Computing II, (CMSC663/CMSC663 and AMSC664/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
AMSC698K
Advanced Topics in Applied Mathematics; Quantum Computation on NISQ devices
Credits:
3
Grad Meth:
Reg, Aud
Conventional computers encode information in binary form, achieving very high precision in deterministic calculations. Quantum computers, on the other hand, encode information in quantum objects, which exhibit probabilistic behavior when measured; thus, one might infer that this approach is more powerful in solving problems in the probabilistic realm. While instrumentation of quantum computers is in its infancy, quantum algorithms are being developed to provide efficient solutions to various probabilistic problems. This course offers a hands-on approach to quantum computing, including implementation and testing of quantum algorithms on real quantum hardware. Example codes and homework assignments will employ python modules to handle the data exchange with quantum computers.
Prerequisites: AMSC698Q (The Mathematics of Quantum Information Science) or CMSC675 (Introduction to Quantum Information Processing) or permission from the instructor.
Prerequisites: AMSC698Q (The Mathematics of Quantum Information Science) or CMSC675 (Introduction to Quantum Information Processing) or permission from the instructor.
AMSC714
Numerical Methods For Stationary PDEs
Credits:
3
Grad Meth:
Reg, Aud, S-F
Prerequisite: One graduate level course in partial differential equations or one graduate level course in numerical analysis or scientific computing; or permission of instructor.
Credit only granted for: AMSC 714 or AMSC 614.
Formerly: AMSC614.
Additional information: This course 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: Maximum principle, finite difference method, upwinding, error analysis; Variational formulation of elliptic problems, inf-sup theory; The finite element method and its implementation; Piecewise polynomial interpolation theory in Sobolev spaces; A priori and a posteriori error analyses, adaptivity; Fast solvers; Variational crimes; Mixed finite element 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
AMSC808X
Advanced Topics in Applied Mathematics; Numerical Methods for Data Science and Machine Learning
Credits:
3
Grad Meth:
Reg, Aud, S-F
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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