Courses - Fall 2022
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
AMSC660
Scientific Computing I
Credits:
3
Grad Meth:
Reg, Aud
Prerequisite: Must have knowledge of Matlab or Python.
Cross-listed with: CMSC660.
Credit only granted for: AMSC660 or CMSC660.
Fundamental techniques in scientific computation with an introduction to theory and software for each topic. Computer numbers and sources of errors, numerical linear algebra, optimization, and Monte Carlo methods.
AMSC663
Advanced Scientific Computing I
Credits:
3
Grad Meth:
Reg
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.
AMSC666
Numerical Analysis I
Credits:
3
Grad Meth:
Reg, Aud
Prerequisite: CMSC466 or AMSC466; and MATH410.
Cross-listed with: CMSC666.
Credit only granted for: AMSC666 or CMSC666.
Approximation theory, numerical solution of initial-value problems, iterative methods for linear systems, optimization.
AMSC673
Partial Differential Equations I
Credits:
3
Grad Meth:
Reg, Aud
Prerequisite: MATH411; or students who have taken courses with comparable content may contact the department.
Cross-listed with: MATH673.
Credit only granted for: AMSC673 or MATH673.
Analysis of boundary value problems for Laplace's equation, initial value problems for the heat and wave equations. Fundamental solutions, maximum principles, energy methods. First order nonlinear PDE, conservation laws. Characteristics, shock formation, weak solutions. Distributions, Fourier transform.
Offered fall only. Cross-listed with MATH673.
AMSC689
Research Interactions in Applied Mathematics and Scientific Computation
Credits:
1 - 3
Grad Meth:
Reg, Aud
AMSC714
Numerical Methods For Stationary PDEs
Credits:
3
Grad Meth:
Reg, Aud
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.
AMSC721
Mathematical Population Biology
Credits:
3
Grad Meth:
Reg, Aud
Cross-listed with: BIOL721.
Credit only granted for: AMSC721 or BIOL721.
The mathematical modeling of real-life phenomena in the natural, engineering, and social sciences often involve having to solve systems of difference or differential equations. These systems are inherently complex, owing to their (typically) high dimensionality and nonlinearity. Hence, their exact solutions are difficult (if at all feasible) to obtain. Consequently, these systems are generally studied using a combination of asymptotic analysis and numerical discretization approaches. This course will cover a broad spectrum of techniques, theories and tools for modeling and analysing real-life phenomena arising in population biology, with emphasis on the study and asymptotic analysis of general classes of unstructured (single species discrete-time and continuous-time models, interacting populations etc.) and structured (spatially-structured, age-structured, sex-structured) population biology models arising in ecology and epidemiology.
AMSC760
Applied Statistics Practicum
Credits:
3
Grad Meth:
Reg, S-F
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, S-F
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.
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
AMSC808N
Advanced Topics in Applied Mathematics; Numerical Methods for Data Science and Machine Learning
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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