Course Information

Prof. Martin Weinberg

LGRT 530/545-3821/weinberg@astro.umass.edu

References:

Numerical Methods That Work	Acton
Introduction to Numerical Analysis	Stoer & Bulirsch
Mathematics of Scientific Computing, 3rd ed	Kincaid & Cheney
Data Analysis, 3rd ed	Brandt
The Art of Computer Programming	D. Knuth, Addison & Wesley, 3 vols
Numerical Recipes	Press et al.
Other refs and journal articles as needed	TBA

Requirements:

1. Approximately 8-10 problem sets
2. Final exam

Notes:

We will be discussing algorithms and approaches to numerical problem solving. This is NOT a course in scientific programming although we will discuss approaches to numerical project design, if there is interest.

Suggested syllabus

Subject to modification by students' interests and experience

1. Machine computation/error analysis
2. Polynomials/approximation
   • Interpolation
   • Quadrature
   • Differentiation
   • Extrapolation
   • Rational functions
3. ODEs
4. Linear algebra
   • Basic
   • Pseudo inverse (SVD)
5. Extremization
   • Newton's method (1 and n dimensional)
   • Simplex method
   • Downhill techniques
   • Simulated annealing
6. Root finding
7. Sorting
8. Functional approximation/filtering/smoothing
   • Least squares (LSQ)
   • Non-linear least squares (NLSQ)
   • Orthogonal functions
   • Fourier analysis and friends
9. Statistics
   • Parameter estimation
     • LSQ
     • Chi-squared
     • General maximum likelihood
   • Hypothesis testing
     • Distribution based
     • Correlations
     • Non-parametric (e.g. KS)
     • Bayesian approaches
   • Monte Carlo and (pseudo) random numbers
10. Special advanced topics, for example:
    • Visualization tools
    • Parallel program design
    • Markov Chain Monte Carlo
    • Particle simulation/chaotic dynamics