

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 online 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

EZFace (Multiple zeta values, Euler sums)

Fast Algorithms in Classical Analysis.

Hypergeometric Functions, Modular functions and qSeries.

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 Polyexponentials

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 networkbased, environments for research and education
in the mathematical sciences.

M3Plexus: MultiModal Mathematical Document Delivery System

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

Inverse Symbolic Calculator(includes online 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

nTraces: 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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