Numerical Methods I

The course covers the standard techniques of numerical computation from a theoretical as well as a practical perspective with a particular emphasis on large-scale high-performance computation, and provides the foundation for more specialized third year courses in computation and modeling.

It is assumed that participants have the mathematical background equivalent to two semesters of Engineering and Science Mathematics - attendance of the first year B track (Multivariable Calculus, ODE; Linear Algebra, Fourier Methods, Probability) is highly recommended but not formally required - or Analysis I/II and Linear Algebra I.

The course is appropriate as a home school elective for students of all majors with a particular interest in computation. It is recommended that students commit to this course for the full year. Students interested in a more compact introduction to methods of numerical computation are advised to take the one-semester Engineering and Science Mathematics 4A (Numerical Methods) instead.

Topics covered throughout the year are: computer arithmetic, condition of algorithms, systems of linear equations including iterative methods, computation of eigenvalues, interpolation and least square methods, numerical quadrature, numerical solution of ordinary differential equations, linear and nonlinear optimization, expectation-maximization algorithms, Monte-Carlo methods, introduction to parallelization and visualization.

Collaborative project work in groups of two or three is permissible provided:

• Each member of the group maintains and submits their own runnable version of the code.
• You state who you collaborated with (e.g. as comments in the source files).
• Each member of the group is able to explain the code without help from others.

You may consult books and internet resources, provided you always quote the source.