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What is Mathematics?

Major Unifying Themes in This Document

Syllabus

Foundational Information

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Mind and Body Tools

Science of Teaching & Learning

Project-Based Learning

Computational Mathematics

The Future

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References

 Website Author
"Dr. Dave" Moursund

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Computational Mathematics

This page is under development. Some ideas and resources are listed below.

Click here for this Website's search engine.

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We now have theoretical, applied, and "computational" science. What is the parallel in math? A search for Computational Mathematician in Google produces a few hits.Computational is a wqay of representing and attempting certain types of both pure and applied problems. One might argue that it is a new component or way of looking at math. Hmmm.

http://link.springer.de/link/service/journals/10208/about.html Statement of Scope

Foundations of Computational Mathematics (FoCM) will publish research and survey papers of the highest quality which further the understanding of the connections between mathematics and computation, including the interfaces between pure and applied mathematics, numerical analysis and computer science.

 

http://www.damtp.cam.ac.uk/user/na/FoCM/What.html

Foundations of Computational Mathematics (FoCM) is a nonprofit organization that supports and promotes research on foundations of computational mathematics. It fosters interaction between mathematics, computer science and other areas of computational science through its conferences, workshops and publications. The FoCM journal, produced by Springer-Verlag, publishes highest-quality research articles treating various aspects of computational mathematics. The book series ``Library of Computational Mathematics'' is published by Cambridge University Press under the FoCM imprint. Major conferences of the FOCM take place every two or three years and deal with the entire spectrum of mathematical computation. Specialized workshops are held more frequently and focus on timely research topics.

 

 

http://www.iacm.forth.gr/num/ Division of Numerical Analysis & Scientific Computing

Since its founding, IACM has had considerable activity in the area of Numerical Analysis, which is the field of Applied Mathematics mainly concerned with the discretization of continuous problems of Mathematics (such as discretizing differential and integral equations, solving non-linear equations, approximating functions, integration, optimization etc.).

Research in Numerical Analysis includes the study of stability and convergence of the numerical methods and algorithms resulting for the discretization processes, and their efficient computer implementation. Therefore, Numerical Analysis is a branch of Mathematics which is of great importance to scientists and engineers who are interested in scientific computing.

The current research interests of the Numerical Analysis-Scientific Computing Group at IACM concern applied and theoretical problems in the numerical solution of PDE's occurring in Underwater Acoustics and Fluid Mechanics, in numerical linear algebra, in Scientific/Parallel computing, and also the development of the relevant problem-solving computer environments.

The group members collaborate closely with the Wave Propagation group on the numerical simulation of various wave phenomena. A considerable amount of collaboration has also been established over the years with many researchers in universities and research centres in Greece, Europe and the USA

 

http://www.vsppub.com/journals/jn-JouComMat.html Journal of Computational Mathematics

An international journal of Numerical Methods, Analysis and Applications.

Published by the Institute of Computational Mathematics and Scientific/Engineering Computing, Chinese Academy of Sciences, Beijing, China. Copublished and distributed outside of China exclusively by VSP.

Editor-in-Chief: Shi Zhong-ci Beijing

The Journal of Computational Mathematics is an international journal covering numerical methods, analysis and applications. The journal publishes original research papers in all branches of modern computational mathematics such as linear and nonlinear algebra, numerical optimization, numerical approximations, computational geometry, computational statistics and probability, Monte Carlo methods, numerical methods for ordinary differential equations, integral equations and partial differential equations including both direct and inverse problems, and computational-mathematical problems in diverse fields of science and engineering. Papers containing new ideas, creative approaches and/or innovative applications as well as invited reviews are expected to appear regularly in the journal.

A special feature of the Journal of Computational Mathematics is the publication of articles selected by the editors, and translated into English, from the Chinese-language journal Mathematica Numerica Sinica. This will be of great interest to many computational and applied mathematicians who up to now have been unable to easily obtain translated material on Chinese mathematical research.

The Map is Not the Territory

Alfred Korzybski coined the term "general semantics" in his book Science and Sanity. Korzybski had an interest in the way we as human beings interact with the world outside our own skins and sometimes take semantic shortcuts that lead us to false evaluations. He said "the map is not the territory" to indicate that we should not confuse the "map" of reality that we carry around in our heads with reality itself. Korzybski's system of general semantics gives us a set of tools that enable us to develop awareness of our own map-making process, and thereby to make more accurate and useful evaluations. It can result in clearer, more effective communication, more appropriate responses to events around us, and dealing more effectively with stress in daily life. Accessed 10/1/01: http://www.general-semantics.org.uk/frontpage.html

T he phrase "the map is not the territory" comes from Science and Sanity, by Alford Korzybski (there does seem to be some disagreement about spelling his first name).

Science and Sanity : an Introduction to Non-Aristotelian Systems and General Semantics by Alfred Korzybski (Hardcover - January 1995) [Amazon.com]

The idea that comes to mind for me is that modeling and simulation are a map, and they may or may not be closely enough related to the territory to help represent and solve a specific problem.

 

Maryland Virtual High School of Science and Mathematics [Online]. Accessed 1/16/02: http://mvhs1.mbhs.edu/.

This Virtual High School involves students from many campuses. Much of the "classwork" can be classified as Problem-Based Learning, , and the PBL routinely makes use of powerful computer hardware and software. Quoting from the Website:
Preparing students to "do" science in the real world of the future means guiding them in "doing" science now. The Maryland Virtual High School of Science and Mathematics entails bringing to the classroom the same team problem solving, technology rich approaches currently used in research and business. Computational science has become a powerful paradigm to complement other approaches. Computational tools, ranging from spread- sheets on microprocessors to advanced molecular modeling tools on supercomputers, are allowing scientists to model processes too costly or impossible to investigate in other ways.

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