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.

Simulation Generation Projects

  1. 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.

Web/Java Technology to Support Collaboration

  1. 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.
  2. 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.
  3. 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.

Verification of Fundamental Conjectures

  1. 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.
  2. 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