Courses - Fall 2024
AMSC
Applied Mathematics & Scientific Computation
Department Site
Open Seats as of
01/20/2025 at 10:30 AM
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
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.
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
AMSC698Q
Advanced Topics in Applied Mathematics; The Mathematics of Quantum Information Science
Credits:
3
Grad Meth:
Reg, Aud
Prerequisites: Linear Algebra, Calculus, Probability, or Permission by the instructor.
This course will provide students with the necessary mathematical tools and background knowledge to understand, model, and conceptualize quantum information science and its building blocks and systems. The course will use elements from calculus, linear algebra, real and complex analysis, and probability.
This course will provide students with the necessary mathematical tools and background knowledge to understand, model, and conceptualize quantum information science and its building blocks and systems. The course will use elements from calculus, linear algebra, real and complex analysis, and probability.
AMSC715
Numerical Methods for Evolution Partial Differential Equations
Credits:
3
Grad Meth:
Reg, Aud, S-F
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.
AMSC721
Mathematical Population Biology
Credits:
3
Grad Meth:
Reg, Aud
Prerequisite: Calculus, differential equations, modeling, linear algebra, familiarity with mathematical software and programming languages (e.g., MATLAB, R, Python etc.); or permission of instructor.
Cross-listed with: BIOL721.
Credit only granted for: AMSC721 or BIOL721.
Additional information: Open to advanced undergraduates by permission of instructor.
Foundational principles for modeling and analysis of real-life phenomena in population biology. Topics include design and analysis of models for general classes of unstructured (single species discrete-time and continuous-time, interacting populations etc.) and structured (spatially-structured, age- structured, sex-structured) population biology models in ecology and epidemiology, dynamics analysis of population biology models (asymptotic stability and bifurcation theory), numerical discretization of continuous-time models, statistical analysis (parameter estimation, uncertainty quantification).
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.
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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