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CECM Research Projects
Technology --
Symbolic --
Numerical Computations
Visualization --
Philosophy
Technology
Most technology development projects fall under the umbrella of
CoLab.
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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.
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Inverse Symbolic Calculator (includes on-line demo)
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Computationally Assisted Inequality Validation
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Identity Checking
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Computational Convex Analysis
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Polynomial Greatest Common Divisors
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Complexity Issues And Computational Phenomena
- These concern the
theoretical behaviour of analytic algorithms and the exhibition of
unusual related computational phenomena.
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Mathematical Constants: Computing pi and related matters
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Complexity of Analytic Computations
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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:
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Computational Classical Analysis
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EZ-Face (Multiple zeta values, Euler sums)
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Fast Algorithms in Classical Analysis.
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Hypergeometric Functions, Modular functions and q-Series.
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Special Functions.
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Complexity of Approximations.
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Geometry of Polynomials and Computational Complex Analysis.
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Analytic and Polynomial Inequalities.
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Orthogonal and Markov Systems.
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Rapid calculation of and new recurrences for
Bernoulli numbers, Euler numbers and other Rational Poly-exponentials
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Functional Equations
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Computational Modern and Applied Analysis
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Function Reconstruction, the MomEnt+ Project
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Convex Programming and Maximum Entropy Optimization.
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Moment Problems.
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Projection and Relaxation Methods.
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Fixed Points and Iterative Methods for Solving Inverse Problems.
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Nonsmooth Analysis and Existence of Best Approximations
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Computational Number Theory
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Special Expansions.
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Computational Diophantine Number Theory.
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Integer Chebyshev Problems.
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Irrationality Questions.
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Partitions
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Scientific Computation
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Computation of invariant and inertial manifolds
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Spectral methods for PDEs
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Multigrid Methods
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High Precision ODE Solvers
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Automatic and Symbolic Differentiation
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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.
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M3Plexus: Multi-Modal Mathematical Document Delivery System
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Organic Mathematics Project: Phase I of M3Plexus (see
Proceedings of OM)
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Inverse Symbolic Calculator(includes on-line demo)
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PolyNet: Distributed Collaborative Networking
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Digital Information Projects and Services
- These projects explore issues arising from the CECM's role as a
provider of online information thru Internet services.
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CAMEL: Canadian Mathematical ELectronic Information Services
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Organic Mathematics Project: Phase I of M3Plexus (see
Proceedings of OM)
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Document Vault
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Digital Scientific Journals
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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.
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Math Constants Visualization Project
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n-Traces: Visualizing a Problem in Philosophical Logic
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Zeros of Random Polynomials with Coefficients 0 and 1
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Mathematical Visualization Resources
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Mathematics and Art
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Simon Fraser Art Gallery
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Philosophy of Visualization and Experimental Mathematics
- Issues arising from the use of and interaction with computers
and computer software to do mathematics are explored.
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Experimental Mathematics: A Discussion
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Is Visualization Struggling under the Myth of Objectivity?
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Mathematical Visualization: Standing at the Crossroads
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A Methodology for Visualization
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Monday, Dec. 30, 2024
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