Proof of algorithms by general snapshots

A constructive approach to the question of proofs of algorithms is to consider proofs that an object resulting from the execution of an algorithm possesses certain static characteristics. It is shown by an elementary example how this possibility may be used to prove the correctness of an algorithm written in ALGOL 60. The stepping stone of the approach is what is called General Snapshots, i.e. expressions of static conditions existing whenever the execution of the algorithm reaches particular points. General Snapshots are further shown to be useful for constructing algorithms.     

UMTS radio network evaluation and optimization beyond snapshots

A new evaluation scheme for universal mobile telecommunications system (UMTS) radio networks is introduced. The approach takes the complex coupling of coverage and capacity through interference into account. Cell load estimates, otherwise obtained through Monte-Carlo simulation, can now be approximated without time-consuming iterative simulations on user snapshots. The two cornerstones are the generalization of interference coupling matrices from user snapshots to average load and the emulation of load control by an analytical scaling scheme. Building on the new evaluation scheme, two novel radio network optimization algorithms are presented: an efficient local search procedure and a mixed integer program that aims at designing the coupling matrix. Computational experiments for optimizing antenna tilts show that our new approaches outperform traditional snapshot models     

Freud on math

The Mathematical Intelligencer -     

Whiteboard math movies

In this article, we discuss whiteboard math movies (a.k.a. mathcasts)and their applications to mathematics education. A whiteboardmath (wbm) movie is a screen recording of writing plus voiceand/or text explaining a mathematical concept or solving a problem.The movie is then produced to Flash movie format and distributedvia CD or Internet. The wbm movies are the ultimate in asynchronouslearning—providing a simple and inexpensive means of interactionat the teacher–student, teacher–teacher, student–teacherand student–student level. With wbm movies both the creatorand the viewer get to see and hear the mathematical thinkingstep-by-step. They get the process and not just the result andthey can have it when and as many times as they want. We talkabout how Tim Fahlberg came up with this idea over 8 years agoand describe the developments in technology—that are atleast partially the result of our team's work—that nowmake wbm movie making a cost-efficient, effective and even afun way of truly learning mathematics.     

Advances in math search

As digital libraries of mathematical and scientific contents become available, it is essential to have math-aware search systems. The search systems must understand math symbols and structures, and allow users to enter queries that involve not only text keywords but also mathematical expressions and fragments of expressions. In addition, the search results must be presented in a way that enables the user to find the desired information rapidly. This short paper gives a quick overview of the state of the art of math search, and focuses on the math search system that the author has developed for the Digital Library of Mathematical Functions (DLMF) project of the National Institute of Standards and Technology. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Abhandlungen zur Sammlung math. Modelle

Monatshefte für Mathematik -     

La preuve en mathématique

Proof and deductive method in mathematics have their origin in the classic model of exposition developed by Euclid in his famous book on Elements. The attitude of mathematicians towards this method has certainly evolved in the past centuries, but the relationship between understanding and acceptability of mathematical statements has not dramatically changed and still constitutes a characterising element of this discipline. This paper is aimed at explaining and discussing some aspects which may be considered at the origin of difficulties related to proof, in particular, it focusses on the tension between two poles, that of production and that of systematisation of mathematical knowledge.     

Network based math teaching using CAS

In the teaching of mathematics the CAS based knowledge-bank, placed on local network could be the link between the personal cognitive microcosmoses and the world of hypermedia. Modularization is one of the biggest didactical problems in connection with using of CAS in math teaching. Mainly the curricula and the role in enlarging of knowing representation net motivate working with module-types. There are some characteristic features of the CAS supported algorithm building we would like to discuss. The model-building has new and greater chances: decreasing the demand of the calculations and using compressed cognitive units, the CAS modules.     

The new math as an international phenomenon

The new math was a several-decade-long movement to update school mathematics that began in the mid twentieth century in many countries around the world. It took many forms, but much of it involved the preparation of new instructional materials, including textbooks. Much of the new math activity in Europe and North America was stimulated by conferences and seminars of the Organisation for Economic Cooperation and Development (OECD) in the early 1960s. Although the initial reform efforts addressed secondary school mathematics courses that prepared pupils for tertiary education, those efforts quickly spread to primary school mathematics, to pupils not headed to tertiary education, and to non-OECD countries. Mathematicians and schoolteachers were divided about the direction that the new math reforms took. Although the new math is often deemed a failed endeavor, it changed not only school mathematics but also the way people and countries viewed school mathematics.     

Revue semestrielle des publications mathématiques

Rendiconti del Circolo Matematico di Palermo Series 1 -