Essay (for graduate credit only)

The essay deadline for graduate credit is Tuesday December 7th.

Your essay should either address some issue (such as sensitivity of polynomial roots) that complements a lecture topic, branch out to an advanced topic not covered in the lectures, or discuss the applications of a learned topic. The essay will require approximately 20 hours of self-study and writing together and make up 10% of the total graduate grade. Certain level of understanding should be demonstrated.

The essay should have at least 6 pages.

You have the freedom of choosing any related topic to write about. Below are just some suggestions:

• Application(s) of FFT
• Application(s) of quaternions
• Applications of linear programming (in transportation, scheduling, network flows, etc.)
• Duality in linear programming
• Variational problems in parametric form
• Variational problems involving higher-order derivatives
• The Ritz method in the calculus of variations
• Bézier curves
• Boundary value problems in ODEs
• B-splines
• Curve and surface fitting
• Curve implicitization and parametrization
• Applications of Geodesics
• Asymptotic curves
• Minimal surfaces
• Ruled surfaces
• Deformable modeling
• Shape registration and recognition
• Fast polynomial interpolation
• Householder transform and eigenvalue computation
• Laguerre's method on polynomial root finding
• Monte Carlo simulation
• Filter-based applications
• Multivariate resultants
• Partial differential equations
• Random number generation
• Rational interpolation
• Scattered data interpolation
• Sensitivity of polynomial roots
• Simulated annealing
• SVD algorithm

Homework Policy

The homework must be submitted at the beginning of the lecture on the due date. Any homework turned in after this time will be considered late. Late homework will be accepted until 5pm on the due date for a penalty of 30%. Homework will not be accepted beyond that time.