- Computer numbers
- Floating point arithmetic
- Sources of errors
- Stability and Conditioning

- [1] Bindel and Goodman, Principles of scientific computing http://math.nyu.edu/faculty/shelley/Classes/SciComp/BindelGoodman.pdf (Chapter 2)
- [2] G.W. Stewart, Afternotes on numerical analysis, SIAM 1996 (Lecture 7)

- Matrix Norms
- Eigenvalues and eigenvectors
- Singular Value Decomposition
- Condition numbers
- LU decomposition
- Cholesky factorization
- Least Squares and QR factorization

- [1] Bindel and Goodman, Principles of scientific computing http://math.nyu.edu/faculty/shelley/Classes/SciComp/BindelGoodman.pdf, Chapter 4 and 5
- [2] J. Demmel "Applied Numerical Linear Algebra"

- Newton's method and variants
- Continuation
- Globally Convergent Methods

- [1] Randall J. LeVeque, Finite Difference Methods for Ordinary and Partial Differential Equations, SIAM 2007, ( freely available online via the UMD library), Chapter 9, Chapter 10, Appendix E
- [2] J. Nocedal and S. Wright, "Numerical Optimization" (Chapter 11)
- [3] G.W. Stewart, Afternotes on numerical analysis, SIAM 1996 (Lecture 5, Hybrid Method)

- Line search methods (steepest descend, Newton's, BFGS, SR1)
- Trust region methods (Newton's, BFGS, SR1)
- Nonlinear conjugate gradient methods (Fletcher - Reeves, Polak - Ribiere)

- [1] J. Nocedal and S. Wright, "Numerical Optimization" (Chapters 2, 3, 4, 5)

- Consistency, Stability Convergence
- Linear Stability Theory
- Runge-Kutta Methods
- Multistep Methods (Adams, BDF)
- Symplectic Methods for Integrating Hamiltonian systems

- [1] John Strain, Lectures on Numerical solutions of ODE (Consistency, Stability, Convergence, Runge-Kutta methods and multistep methods, linear stability theory,stiff problems)
- [2] E. Hairer, S.~P. Norsett, G. Wanner, Solving Ordinary Differential Equations I. Nonstiff Problems. 2nd Revised Edition, Springer, 2000
- [3] Symplectic methods: Erns Hairer, Geometric Numerical Integration. Lecture 1, Lecture 2, Lecture 3, Lecture 4, Lecture 5.
- [4] M. P. Allen's talk in the workshop "Computational methods for statistical mechanics - at the interface between mathematical statistics and molecular simulation", June 2 - 6, 2014, Edinburgh, Scotland
- [5] Lecture notes on symplecticmethods: SymplecticMethods.pdf

- Basic statistics: random numbers, pseudo-random numbers
- Mean, variance, central limit theorem
- Monte-Carlo Integration, convergience (Codes: MCint.m, MCnsphere.m)
- Variance reduction, importance smapling
- Metropolis and Metropolis-Hastings algorithms
- Simulated annealing

- [1] Lecture notes: MonteCarlo.pdf (updated 12/8/2015 at 10:58 AM)
- [2] Bindel and Goodman, Principles of scientific computing http://math.nyu.edu/faculty/shelley/Classes/SciComp/BindelGoodman.pdf (Chapter 9)
- [3] A. Chorin, O. Hald, Stochastic Tools in Mathematics and Science, Third Edition, Springer, 2013 (2nd edition is also fine, it is available via UMD library: http://link.springer.com.proxy-um.researchport.umd.edu/book/10.1007%2F978-1-4419-1002-8)
- [4] S. Kirkpatrick; C. D. Gelatt; M. P. Vecchi, Optimization by Simulated Annealing, Science, New Series, Vol. 220, No. 4598. (May 13, 1983), pp. 671-680
- [5] David J. Wales, Jonathan P. K. Doye, Global Optimization by Basin-Hopping and the Lowest Energy Structures of Lennard-Jones Clusters Containing up to 110 Atoms, J. Phys. Chem. A 1997, 101, 5111-5116