For this class, I want students to complete a smallish project, which should involve some mathematics and some computation.
Ideally, this is done in pairs.
Each group will make a presentation to the rest of us of their project DATE TBD.
This will be about 30 minutes and would include a brief discussion of the mathematics, as
well as a brief demonstration of some software that was written for the project.
You would also hand in a short typed (LaTeX) description of your work.
It is not intended to be onerous, but to stimulate each of you to go a little further than
the lectures.
Different topics may have different emphasis on how much to write up and how much to code.
Location:
We have Blocker Room 302 for Tuesday, April 28 2:30--5:30 PM and Wednesday, April 29 1:00--4:00 PM
If needed, we will also have some in Blocker 121 1:00--3:00 PM on Monday, May 4.
Presentations:
Aaishah Ale-Rasool and Pooja Joshi, The Hilbert Polynomial and the Dimension of a Variety.
We can use the Hilbert Polynomial to define the dimension of a variety.
In this presentation, we will talk about this relation and compute a few examples for affine and projective varieties.
Daniel Dale and Somak Dutta, Certified Homotopy Continuation using interval arithmetic.
Homotopy continuation is a standard method for numerically solving systems of polynomials, however in some applications
such as for monodromy actions, standard implementations are poorly suited.
We describe such a method for certifying path calculations using interval arithmetic and Moore’s criterion as implemented
in the package Algpath.
John Ajayi and Kai Neshat Truncated Gröbne Bases for Integer Programming.
We will discuss what is Integer Programming, the Buchberger Algorithm for Integer Programming, multivariate grading of
the Toric ideal associated with the integer programming problem, and a truncated Buchberger Algorithm to solve the
problem.
