• Four Science Terps Awarded 2025 Goldwater Scholarships

    Four undergraduates in the University of Maryland’s College of Computer, Mathematical, and Natural Sciences (CMNS) have been awarded 2025 scholarships by the Barry Goldwater Scholarship and Excellence in Education Foundation, which encourages students to pursue advanced study and research careers in the sciences, engineering and mathematics.  Over the last 16 years, UMD’s nominations… Read More
  • Announcing the Winners of the Frontiers of Science Awards

    Congratulations to our colleagues who won the 2025 Frontiers of Science Award: - Dan Cristofaro-Gardiner, for his join paper with Humbler and Seyfaddini: “Proof of the simplicity conjecture”, Annals of Mathematics 2024. - Dima Dolgopyat & Adam Kanigowski, for their joint paper with Federico Rodriguez Hertz: “Exponential mixing implies Bernoulli”, Annals of Mathematics… Read More
  • 2024 Putnam Results

    We are very excited to report that our MAryland Putnam team ranked 7th among 477 institutions that participated in the 2024 Putnam math competition. Our team members this year were Daniel Yuan, Isaac Mammel, and Clarence Lam. Daniel Yuan ranked 26th among 3,988 participants. Clarence Lam and Isaac Mammel were recognized for… Read More
  • From Math Olympiads to Diplomacy: Meet Visiting Math Professor Qendrim Gashi

    Maryland Global, published a great interview with our visiting professor (and diplomat), Qendrim Gashi. The interview is available at https://marylandglobal.umd.edu/about/news/math-olympiads-diplomacy-meet-visiting-math-professor-qendrim-gashi Read More
  • Eugenia Brin, Longtime Supporter of Science and Performing Arts at UMD, Dies

    Eugenia Brin, a Russian immigrant and retired NASA scientist who, with her family of accomplished Terps, became an important benefactor of the University of Maryland, died on Dec. 3, 2024. She was 76 years old. The rest of the article can be read here: https://cmns.umd.edu/news-events/news/eugenia-brin-1948-2024 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. Will use MATLAB.

Prerequisites

1 course with a minimum grade of C- from (MATH240, MATH461, MATH341); and 1 course with a minimum grade of C- from (MATH340, MATH241); and 1 course with a minimum grade of C- from (CMSC106, CMSC131); and minimum grade of C- in MATH246.

Level of Rigor

Standard

Sample Textbooks

  • Numerical Analysis by R. Burden, J. Faires, A. Burden
  • Numerical Computing with Matlab, by Cleve B. Moler

Applications

Computer Science, Economics, Business, Engineering, Physics, Astronomy

If you like this course, you might also consider the following courses:

Math 420, Math 416, Stat 430.

Additional Notes

  • Duplicate credit with AMSC466 and CMSC466; cross-listed with CMSC460
  • Students interested in grad school in Applied Math should consider this course
  • Students interested in grad school in Statistics should consider this course

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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