Graduate Courses for Applied Mathematics & Scientific Computation (AMSC)
Schedule of Classes:
Fall |
Winter |
Spring |
Summer
(Only current and next semester available)
AMSC 420 Mathematical Modeling (3 credits)
Prerequisite: MATH241, MATH246, STAT400, MATH240 or MATH461; and
permission of department. Also offered as MATH420. Credit will be
granted for only one of the following: AMSC420, MAPL420, or MATH420.
Formerly MAPL 420.
The course will develop skills in mathematical modeling through
practical experience. Students will work in groups on specific projects
involving real-life problems that are accessible to their existing
mathematical backgrounds. In addition to the development of mathematical
models, emphasis will be placed on the use of computational methods to
investigate these models, and effective oral and written presentation of
the results.
AMSC 452 Introduction to Dynamics and Chaos (3 credits)
Prerequisites: MATH240 and MATH246. Also offered as MATH452. Credit will
be granted for only one of the following: AMSC452, MAPL452, or MATH452.
Formerly MAPL 452.
An introduction to mathematical dynamics and chaos. Orbits,
bifurcations, Cantor sets and horseshoes, symbolic dynamics, fractal
dimension, notions of stability, flows and chaos. Includes motivation
and historical perspectives, as well as examples of fundamental maps
studied in dynamics and applications of dynamics.
AMSC 460 Computational Methods (3 credits)
Prerequisites: MATH240; and MATH241; and CMSC106 or CMSC114 or ENEE114.
Also offered as CMSC460. Credit will be granted for only one of the
following: AMSC/CMSC/MAPL460 or AMSC/CMSC/MAPL466. Formerly MAPL 460.
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.
AMSC 462 Computer Science for Scientific Computing (3 credits)
Prerequisite: CMSC106 or CMSC131; and (AMSC460 or CMSC460); or
permission of department. This course cannot be used toward the
upper-level math requirement for MATH and STAT majors. Students who take
CMSC311 or CMSC330 will not be given credit for this course. Also
offered as CMSC462. Credit will be granted for only one of the
following: AMSC462 or CMSC462.
A survey of computer science for scientists and engineers. The goal is
to enable the student to write efficient, well-organized programs for
today's machines. Topics to be treated include computer organization,
computer arithmetic, processes and operating systems, the memory
hierarchy, comparison of the Fortran and C families of languages,
compilers, the run time environment, memory allocation, preprocessors
and portability, and documentation. Specific topics will vary from
semester to semester.
AMSC 466 Introduction to Numerical Analysis I (3 credits)
Prerequisites: MATH240; and MATH241; and CMSC106 or CMSC114 or ENEE114.
Also offered as CMSC466. Credit will be granted for only one of the
following: AMSC/CMSC/MAPL460 or AMSC/CMSC/MAPL466. Formerly MAPL 466.
Floating point computations, direct methods for linear systems,
interpolation, solution of nonlinear equations.
AMSC 477 Optimization (3 credits)
Prerequisites: (AMSC/CMSC/MAPL460, or AMSC/CMSC/MAPL466 or
AMSC/CMSC/MAPL467) with a grade of C or better. Also offered as CMSC477.
Credit will be granted for only one of the following: AMSC477, CMSC477
or MAPL477. Formerly MAPL 477.
Linear programming including the simplex algorithm and dual linear
programs, convex sets and elements of convex programming, combinatorial
optimization, integer programming.
AMSC 498 Selected Topics in Applied Mathematics (1-3 credits)
Repeatable to 6 credits if content differs. Formerly MAPL 498.
Topics in applied mathematics of special interest to advanced
undergraduate students.
AMSC 600 Advanced Linear Numerical Analysis (3 credits)
Prerequisite: AMSC/CMSC/MAPL 666 or permission of instructor. Also
offered as CMSC 760. Credit will be granted for only one of the
following: AMSC 600, CMSC 760 or MAPL 600. Formerly MAPL 600.
Advanced topics in numerical linear algebra, such as dense eigenvalue
problems, sparse elimination, iterative methods, and other topics.
AMSC 607 Advanced Numerical Optimization (3 credits)
Prerequisite: MATH 410 or permission of instructor. Also offered as
CMSC764. Credit will be granted for only one of the following: AMSC607,
CMSC764, or MAPL607. Formerly MAPL 607.
Modern numerical methods for solving unconstrained and constrained
nonlinear optimization problems in finite dimensions. Design of
computational algorithms and the analysis of their properties.
AMSC 612 Numerical Methods in Partial Differential Equations (3 credits)
Prerequisite: a graduate level one semester course in partial
differential equations or a theoretical graduate level course in applied
field such as fluid mechanics; or permission of instructor. Credit will
be granted for only one of the following: AMSC 612 or MAPL 612. Formerly
MAPL 612.
Finite difference methods for elliptic, parabolic, and hyperbolic
partial differential equations. Additional topics such as spectral
methods, variational methods for elliptic problems, stability theory
for hyperbolic initial-boundary value problems, and solution methods
for conservation laws.
AMSC 614 Mathematics of the Finite Element Method (3 credits)
Prerequisite: one semester graduate level course in partial differential
equations; or permission of instructor. Credit will be granted for only
one of the following: AMSC 614 or MAPL 614. Formerly MAPL 614.
Variational formulations of linear and nonlinear elliptic boundary
value problems; formulation of the finite element method; construction
of finite element subspaces; error estimates; eigenvalue problems; time
dependent problems.
AMSC 660 Scientific Computing I (3 credits)
Prerequisite: AMSC/CMSC/MAPL 460, AMSC/CMSC/MAPL466, or knowledge of
basic numerical analysis (linear equations, nonlinear integration,
interpolation) with permission of instructor. Also offered as CMSC 660.
Credit will be granted for only one of the following: AMSC 660, CMSC 660
or MAPL 660. Formerly MAPL 660.
Monte Carlo simulation, numerical linear algebra, nonlinear systems and
continuation method, optimization, ordinary differential equations.
Fundamental techniques in scientific computation with an introduction to
the theory and software of each topic.
AMSC 661 Scientific Computing II (3 credits)
Prerequisite: AMSC/CMSC/MAPL 460 or AMSC/CMSC/MAPL 466 or knowledge of
basic numerical analysis (linear equations, nonlinear equations,
integration, interpolation) with permission of instructor. Knowlege of C
or Fortran. Also offered as CMSC 661. Credit will be granted for only
one of the following: AMSC 661, CMSC 661 or MAPL 661. Formerly MAPL 661.
Fourier and wavelet transform methods, numerical methods for elliptic
partial differential equations, numerical linear algebra for sparse
matrices. Finite element methods, numerical methods for tiem dependent
partia l differential equations. Techniques for scientific computation
with an introduction to the theory and software for each topic. Course
is part of a two course sequence (660 and 661), but can be taken
independently.
AMSC 662 Computer Organization and Programming for Scientific Computing (3 credits)
Prerequisite: AMSC/CMSC/MAPL 460, AMSC/CMSC/MAPL 466, or knowledge of
basic numerical analysis (linear equations, nonlinear equations,
integration, interpolation) with permission of instructor. Knowledge of
C or Fortran. Also offered as CMSC 662. Credit will be granted for only
one of the following: AMSC 662 or CMSC 662.
This course presents fundamental issues of computer hardware, software,
parallel computing, and scientific data management for programming for
scientific computation.
AMSC 663 Advanced Scientific Computing I (3 credits)
Prerequisite: AMSC/CMSC/MAPL 660, AMSC/CMSC/MAPL 661, and permission of
instructor. Also offered as CMSC 663. Credit will be granted for only
one of the following: AMSC 663 or CMSC 663.
In the sequence MAPL 663, MAPL 664 students work on a year-long
individual project to develop software for a scientific task in a high
perfomance computing environment. Lectures will be given on available
computational environments, code development, implementation of
parallel algorithms.
AMSC 664 Advanced Scientific Computing II (3 credits)
Prerequisite: AMSC 663 and permission of instructor. Also offered as
CMSC 664. Credit will be granted for only one of the following: AMSC 664
or CMSC 664.
In the sequence MAPL 663, MAPL 664 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 code
development and validation, parallel algorithms for partial
differential equations, nonlinear systems, optimization.
AMSC 666 Numerical Analysis I (3 credits)
Prerequisites: AMSC/CMSC/MAPL 466; and MATH 410. Also offered as CMSC
666. Credit will be granted for only one of the following: AMSC 666,
CMSC 666 or MAPL 666. Formerly MAPL 666.
Iterative methods for linear systems, piecewise interpolation,
eigenvalue problems, numerical integration.
AMSC 667 Numerical Analysis II (3 credits)
Prerequisite: AMSC/CMSC/MAPL 666. Also offered as CMSC 667. Credit will
be granted for only one of the following: AMSC 667, CMSC 667 or MAPL
667. Formerly MAPL 667.
Nonlinear systems of equations, ordinary differential equations,
boundary value problems.
AMSC 670 Ordinary Differential Equations I (3 credits)
Prerequisite: MATH 405; and MATH 410 or equivalent. Also offered as MATH
670. Credit will be granted for only one of the following: AMSC 670,
MAPL 670 or MATH 670. Formerly MAPL 670.
Existence and uniqueness, linear systems usually with Floquet theory
for periodic systems, linearization and stability, planar systems
usually with Poincare-Bendixson theorem.
AMSC 671 Ordinary Differential Equations II (3 credits)
Prerequisite: MATH 630; and AMSC/MAPL/MATH 670 or equivalent. Also
offered as MATH 671. Credit will be granted for only one of the
following: AMSC 671, MAPL 671 or MATH 671. Formerly MAPL 671.
The content of this course varies with the interests of the instructor
and the class. Stability theory, control, time delay systems,
Hamiltonian systems, bifurcation theory, and boundary value problems.
AMSC 673 Partial Differential Equations I (3 credits)
Prerequisite: MATH 411 or equivalent. Also offered as MATH 673. Credit
will be granted for only one of the following: AMSC 673, MAPL 673 or
MATH 673. Formerly MAPL 673.
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.
AMSC 674 Partial Differential Equations II (3 credits)
Prerequisite: AMSC/MAPL/MATH 673 or permission of instructor. Also
offered as MATH 674. Credit will be granted for only one of the
following: AMSC 674, MAPL 674 or MATH 674. Formerly MAPL 674.
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.
AMSC 687 Minicourse Series in the Mathematical Sciences (1 credits)
Also offered as MATH 687 and STAT 687. Credit will be granted for only
one of the following: AMSC 687, MATH 687 or STAT 687.
This series will consist of up to sixteen 3-lecture presentations
covering a broad range of topics in the mathematical sciences. Each
minicourse is intended to be self-contained and accessible to first year
graduate students and advanced undergraduates. The goal of each
minicourse is to present an active research area or significant result
and the necessary vocabulary and perspective for students to appreciate
it. The goal of the Minicourse Series is to broaden a student's
awareness of the mathematical sciences and to inform them of research
directions.
AMSC 689 Research Interactions in Applied Mathematics and Scientific Computation (1-3 credits)
Prerequisite: consent of instructor. Repeatable to 06 credits if content
differs.
The students participate in a vertically integrated (undergraduate,
graduate and/or postdoctoral, faculty) research group. Format varies,
but includes regular meetings, readings and presentations of material.
See graduate program's online syllabus or contact the graduate program
director for more information.
AMSC 698 Advanced Topics in Applied Mathematics (1-4 credits)
Repeatable if content differs. Formerly MAPL 698.
AMSC 699 Applied Mathematics Seminar (1-3 credits)
Repeatable if content differs. Formerly MAPL 699.
Seminar to acquaint students with a variety of applications of
mathematics and to develop skills in presentation techniques.
AMSC 701 Introduction to Continuum Mechanics (3 credits)
Background from algebra and geometry, kinematics of deformation. Stress
equations of motion, thermodynamics of deforming continua. Theory of
constitutive relations. Materials with memory. Initial boundary value
problems of nonlinear solid and fluid thermomechanics. Boundary value
problems of linear theories of solids and fluids.
AMSC 799 Master's Thesis Research (1-6 credits)
AMSC 898 Pre-Candidacy Research (1-8 credits)
AMSC 899 Doctoral Dissertation Research (1-8 credits)
