• Two Math Faculty to Speak at ICM

    Congratulations to faculty members Pierre-Emmanuel Jabin and Xuhua He who have been selected as invited speakers at the International Congress of Mathematics in Rio de Read More
  • Promotions and New Faculty

    We are delighted to announce that faculty members Jacob Bedrossian, Maria Cameron, Amin Gholampour, and Christian Zickert have been promoted to the rank of Associate Read More
  • William E. Kirwan Distinguished Undergraduate Lectures

    Mathematics for Art Investigation: Mathematical tools for image analysis increasingly play a role in helping art historians and art conservators assess the state of conversation Read More
  • Upcoming Conferences

    We would like to draw your attention to several exciting conferences coming up in the Mathematics Department: The Spring Dynamics Conference, Friday, March 31 - Sunday, Read More
  • Putnam Exam

    We would like to congratulate the University Maryland team on their excellent performance on this year's William Lowell Putnam Mathematical Competition, the premier undergraduate math Read More
  • 1
  • 2
  • 3
  • 4
  • 5

Description

Basic computational methods for interpolation, least squares, approximation, numerical quadrature, numerical solution of nonlinear equations, systems of linear equations, and initial value problems for ordinary differential equations. Emphasis on the methods and their computational properties rather on their analytic aspects.

Prerequisites

(MATH 240 and MATH 241) or (MATH 340 and MATH 341); and (CMSC 106 or CMSC131)

Note: Also listed as CMSC 460.

Topics

Computer Arithmetic and Errors

Machine arithmetic
Error analysis
Stability and conditioning

Solving linear systems of equations

Gaussian elimination
well-conditioning vs. ill-conditioning, matrix and vector norms

Software for Gaussian elimination

Interpolation

Polynomial interpolation
Piecewise polynomial interpolation
Spline interpolation
Software for interpolation

Numerical Integration

Elementary integration formulas (midpoint, trapezoidal rules, etc.)
Gaussian quadrature
Adaptive quadrature
Software for adaptive integration

Solution of nonlinear systems of equations

Bisection method, secant method, Newton's method
Methods for systems of equations
Software for solving nonlinear equations

Numerical solution of ordinary differential equations

Stability and stiffness
Basic numerical methods
Stepsize control
Methods for stiff systems
Software for solving initial value problems

Linear least squares problems

Data fitting and least squares
QR factorization
Software for least squares problems

  • William E. Kirwan Hall, home of the Mathematics Department

    William E. Kirwan Hall, home of the Mathematics Department

  • The Experimental Geometry Lab explores the structure of low dimensional space

    The Experimental Geometry Lab explores the structure of low dimensional space

  • Maryland mathematicians help to investigate the inner workings of E_8

    Maryland mathematicians help to investigate the inner workings of E_8

  • Hyperbolic Space Tiled with Dodecahedra

    Hyperbolic Space Tiled with Dodecahedra

  • Isotropoic Gaussian random field with Matern correlation

    Isotropoic Gaussian random field with Matern correlation

  • Part of the proof of the Peter-Weyl theorem

    Part of the proof of the Peter-Weyl theorem