CECM Research Projects

Technology -- Symbolic -- Numerical Computations
Visualization -- Philosophy

Technology

Most technology development projects fall under the umbrella of CoLab.

Symbolic Computation: These projects use symbolic computation in an essential way both in the process of discovery and proof. Each aims at producing robust software.
Inverse Symbolic Calculator (includes on-line demo)
Computationally Assisted Inequality Validation
Identity Checking
Computational Convex Analysis
Polynomial Greatest Common Divisors
Complexity Issues And Computational Phenomena: These concern the theoretical behaviour of analytic algorithms and the exhibition of unusual related computational phenomena.
Mathematical Constants: Computing pi and related matters
Complexity of Analytic Computations
Interesting and Unusual Computational Phenomena

Numerical Computation

The following projects involve differing mixtures of symbolic and numerical computation. The mathematics involved suggests the following classification:

Computational Classical Analysis: EZ-Face (Multiple zeta values, Euler sums); Fast Algorithms in Classical Analysis.; Hypergeometric Functions, Modular functions and q-Series.; Special Functions.; Complexity of Approximations.; Geometry of Polynomials and Computational Complex Analysis.; Analytic and Polynomial Inequalities.; Orthogonal and Markov Systems.; Rapid calculation of and new recurrences for Bernoulli numbers, Euler numbers and other Rational Poly-exponentials; Functional Equations
Computational Modern and Applied Analysis: Function Reconstruction, the MomEnt+ Project; Convex Programming and Maximum Entropy Optimization.; Moment Problems.; Projection and Relaxation Methods.; Fixed Points and Iterative Methods for Solving Inverse Problems.; Nonsmooth Analysis and Existence of Best Approximations
Computational Number Theory: Special Expansions.; Computational Diophantine Number Theory.; Integer Chebyshev Problems.; Irrationality Questions.; Partitions
Scientific Computation: Computation of invariant and inertial manifolds; Spectral methods for PDEs; Multigrid Methods; High Precision ODE Solvers; Automatic and Symbolic Differentiation

Advanced Collaborative Network Technologies

These projects explore issues arising from the CECM's role in the development of network-based, environments for research and education in the mathematical sciences.

M3Plexus: Multi-Modal Mathematical Document Delivery System

Organic Mathematics Project: Phase I of M3Plexus (see Proceedings of OM)

Inverse Symbolic Calculator(includes on-line demo)

PolyNet: Distributed Collaborative Networking

Digital Information Projects and Services

These projects explore issues arising from the CECM's role as a provider of online information thru Internet services.

CAMEL: Canadian Mathematical ELectronic Information Services

Organic Mathematics Project: Phase I of M3Plexus (see Proceedings of OM)

Document Vault

Digital Scientific Journals

Visualization of Mathematics

Closely connected to the philosophy of experimental mathematics, these projects represent explorations into visualizing a largely abstract domain of science which strongly constrains the bounds of rigorous knowledge.

Math Constants Visualization Project

n-Traces: Visualizing a Problem in Philosophical Logic

Zeros of Random Polynomials with Coefficients 0 and 1

Mathematical Visualization Resources

Mathematics and Art

Simon Fraser Art Gallery

Philosophy of Visualization and Experimental Mathematics

Issues arising from the use of and interaction with computers and computer software to do mathematics are explored.

Experimental Mathematics: A Discussion

Is Visualization Struggling under the Myth of Objectivity?

Mathematical Visualization: Standing at the Crossroads

A Methodology for Visualization

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