• Moving Mathematics Forward: Twenty Years Since the Historic Graduation of Drs. Inniss, Scott, and Weems

    A significant milestone for the mathematical community took place on December 21, 2000, when Tasha R. Inniss, Sherry E. Scott, and Kimberly S. Weems received their PhDs from the University of Maryland College Park.Join us twenty years later for a celebratory conversation with Dr. Inniss, Dr. Scott, and Dr. Weems Read More
  • Results of SCUDEM V 2020 Challenge

    Congratulations to the three UMD teams and their mentor, Radu Balan, for the outstanding results at the SCUDEM V 2020 challenge. Mathematical modeling is such an important component of what science and applied mathematics is all about these days, and it is fantastic to see that Maryland is a major Read More
  • Sergei Novikov wins the 2020 Russian Academy of Sciences Gold Medal

    Congratulations to our colleague Sergei Novikov for receiving the 2020 Russian Academy of Sciences Gold Medal.Sergei and John Milnor will be sharing the award. For more details about the award, follow this link: https://nauka.tass.ru/nauka/10085945 congratulate our colleague Sergey Novikov for receiving the 2020 Russian Academy of Sciences Gold Medal.Sergey and Read More
  • 2020 Alexander Prize Recipients

    Xue Ke and Patrick Daniels won the 2020 James C. Alexander Prize for Graduate Research in Mathematics.Xue Ke PhD dissertation title is “Affine Pavings of Hessenberg Ideal Fibers”. The dissertation was directed by Patrick Brosnan.Patrick Daniels PhD dissertation title is “A Tannakian Framework for G-Displays and Rapoport-Zink Spaces”. The dissertation Read More
  • Adjunct Professor, Gail Letzer named AWM Fellow

    Our Adjunct Professor, Gail Letzter, was named a Fellow of the Association for Women in Mathematics.   The AWM Fellows Program recognizes individuals who have demonstrated a sustained commitment to the support and advancement of women in the mathematical sciences, consistent with the AWM mission: “to encourage women and girls 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

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