• The Canadian Journal of Statistics Award 2018, to Victor de Oliveira and Benjamin Kedem

    The Canadian Journal of Statistics Award is presented each year by the Statistical Society of Canada to the author(s) of an article published in the journal, in recognition of the outstanding quality of the methodological innovation and presentation. This year’s winner is the article entitled “Bayesian analysis of a density ratio Read More
  • Outstanding Director of Graduate Studies Award

    Professor Konstantina Trivisa has been selected for the Outstanding Director of Graduate Studies (DGS) Award for 2018.  Directors of Graduate Studies are critical partners of the Graduate School in shaping graduate education and ensuring the success of graduate students.  The Outstanding Director of Graduate Studies Award recognizes exceptional contributions made Read More
  • Congratulations to Putnam Exam Participants

    Congratulations to our Putnam Exam participants. The University of Maryland Putnam Team was ranked 15th among the 575 competing institutions in the highly competitive Putnam mathematics exam on December 2, 2017. Congratulations to Aaron George, who ranked 39th and Erik Metz who ranked 81st, and to Jason Zou, Justin Hontz Read More
  • Girls Talk Math

    Girls Talk Math is a two-week summer day camp hosted by the Department of Mathematics at the University of Maryland. The camp will occur weekdays July 9-20, 2018 from 9:00 am - 4:00 pm. Rising-9th to rising-12th grade students who attend high school within driving distance of the University can apply. Read More
  • James Owings and Adam Kleppner

    The mathematics department mourns the recent passing of two of our Professors Emerti: Jim Owings and Adam Kleppner. James Claggett Owings, Jr. received his PhD in recursion theory at Cornell in 1966, under the direction of Gerald Sacks.  For many years, Jim was one of the leaders of the Maryland Read More
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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