Math 584 A/BCourse Notes (posted in D2L)

Math 581A/B:Course Notes 2022-23

Math 589 A/B:Course Notes (2019-20)

Fall Semester:

Textbooks for Math 589A: "Numerical Linear Algebra" by Lloyd N. Trefethen and David Bau, III, SIAM 1997; "Analysis of Numerical Methods" by Eugene Isaccson and Herbert Keller; and "Computer Methods for Ordinary Differential Equations and Differential-Algebraic equations", Uri Ascher and Linda Petzold, SIAM 1998Note: To refresh the required background in linear algebra, it is highly recommended to read the first several chapters of "Linear Algebra Done Right" by Axler Sheldon. As a programming language we will use either Python or Matlab, at the student's choice. Last semester students almost unanimously chose Python; however, there were some who later regretted their choice. I recommend Python to those with at least medium level programming skills and Matlab to people with little programming experience.

Spring Semester:

Optimization:

- Convex Optimization
byStephen Boyd and Lieven Vandenberghe, Cambridge University Press- Planning Algorithm, S. LaValle
- Calculus of Variations, I. M. Gelfand, S.V. Fomin, Calculus of Variations, Dover
- Optimization Algorithms in Physics, A. K. Hartmann, H. Rieger, Wiley-VCH, 2002
- Introduction to Optimization, B. Polyak. Optimization Software, New York (1987)

Probability, Statistics, Stochastic Processes and Data Science:

- Stochastic Processes in Physics andChemistry, N. van Kampen, third edition ed. Amsterdam: Elsevier, 2007
- Information theory,inference, and learning algorithms, D. J. C. Mackay, Cambridge University Press, 2003.
- The Nature of Computation, C. Moore and S. Mertens, New York, NY, USA: Oxford University Press, Inc., 2011.
H. E. Taylor and S. Karlin, 3rd ed. Academic Press, Feb. 1998.

- Handbook of stochasticmethods for physics, chemistry and the natural sciences, C. W. Gardiner, Berlin: Springer-Verlag, 2004, vol. 13.
- Stochastic Processes: Theory for applications, R.G. Gallager, Cambridge University Press, 2013.

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