Short Projects
These short projects are ideal candidates for Master of
Engineering projects and could also be used as way to get
involved in the Simlab activities. Each of them requires about a
semester's work.
This set of projects is divided into three groups. The first
two groups are aimed at our goal of creating active models
of physical objects. These active models are software objects
that contain the behavior descriptions of physical objects, and
can be used to create accurate simulations of objects. They will
form the basis of collaborative engineering design. The simulation generation
projects improve our ability to generate these accurate
simulations, while the Support for
Collaboration projects focus on embedding active models in
the World Wide Web and providing Java and C++ tools for
manipulating these objects.
Finally there are a few projects related to verifying some fundamental
conjectures in computer science. These projects involve
implementing a programs that perform a large body of experiments
(possibly using a network of workstations) and then refining this
data to determine if the conjecture still makes sense.
- Coupling MathBus and Einstein
Working with our colleagues at Beam Technologies,
develop mechanisms for coupling our mathematical
representations to the Einstein simulation generation
tools developed by Beam. There are several subprojects in
project, including implementing differentiation (of
mathematical expressions and of programs) in using the
MathBus term structure and C++,
See Richard Zippel
or Rick Palmer for
further information.
- Graphical Editors for Equations
This project will create a two dimensional, WYSIWYG (what
you see is what you get) editor for mathematical
expressions that will be integrated into a World Wide Web
browser using Java Applets and/or ActiveX. This tool is
to be able to cut and paste equations between Web
browsers and commercial applications like Matlab, Maple
and Mathematica using the MathBus term structure and OLE
automation.
See Richard Zippel
for further information.
- Graphical Editors for Geometric Models
This project will create a two dimensional, WYSIWYG
editor for two and three dimensional geometric objects
that will be integrated into a World Wide Web browser
using Java Applets and/or ActiveX. This editor will use
be able to import geometric models from commercial tools
like AutoCad and ProEngineer using the MathBus term
structure.
See Richard Zippel
for further information.
- Search Engines for Web pages containing
equations and geometric models
Using the tools mentioned in the previous two projects,
we will be able to create web pages that contain
mathematical and geometrical objects that can be edited,
as opposed to bit maps which is the usual form. The next
step is to be able to search Web pages using queries
based on the mathematical and geometric objects. For
example, which Web pages contain quadratic equations and
pentagons? This project will create a new type of search
engine for the Web that will index pages based on their
mathematical and geometrical content.
See Richard Zippel
for further information.
- Empirical Evidence for the Hilbert
Irreducibility Test
This project is a combination of programming, data
warehousing and modeling. A number of important
techniques in computational mathematics use a theorem
called the Hilbert Irreducibility Theorem. However, the
precise constants involved in the theorem are not known.
This project will provide empirical evidence for the
values of these constants through large scale
computations using Maple/Mathematica and possibly Java,
which will be managed using data warehousing techniques,
and data reduction. The outcome of the test will give
evidence to bound the running time of a new polynomial
factoring algorithm. No special mathematical background
is required.
See Ronitt
Rubinfeld and/or Richard
Zippel for further information.
- Empirical Evidence that P=NP
This project will implement a new technique for solving
NP hard problems that may be much faster than known
techniques. The technique uses Monte Carlo sampling
techniques, but no special mathematical background is
required.
See Richard Zippel
for further information.
Last revised: August 26, 1998 by CUCS\rz@cs.cornell.edu