Abstract Bishop’s presentation of his informal system constructive mathematics BISH was on purpose closer to the proof-irrelevance classical mathematics, although a form proof-relevance evident in use several notions moduli (of convergence, uniform continuity, differentiability, etc.). Focusing membership and equality conditions for sets given by appropriate existential formulas, we define cert...

CS educators have paid a great deal of attention to Discrete Mathematics over the past several decades. Although there have been many suggestions for improving this course, it seems to us that the real purpose of Discrete Mathematics as a transitional course has been long forgotten. We believe that the most important objective of this course is to let students be familiar with the format and st...

The number of hits on Google on the term inverse problems has now exceeded 1.2 million. Yet, most of you have hardly met the term in any of the courses you have been through. The field of inverse problems is definitely a branch of applied mathematics, but deals with situations one tend to avoid in the traditional courses in mathematics. This includes less pleasant situations such as equations w...

RASTA (Rhetorical Structure Theory Analyzer), a system for automatic discourse analysis, reliably, identifies rhetorical relations present m written discourse by examining information available in syntactic and logical form analyses. Since there is a many-to-many relationship between rhetorical relations and elements of linguistic form, RASTA identifies relations by the convergence of a number ...

Since the 1970s, much attention has been devoted to the male advantage in standardized mathematics tests in the United States. Although girls are found to perform equally well as boys in math classes, they are consistently outperformed on standardized math tests. This study compared the males and females in the United States, all 15-year-olds, by their performance on the PISA 2003 mathematics a...

This article proposes an integrated theory of acquisition of knowledge about whole numbers and fractions. Although whole numbers and fractions differ in many ways that influence their development, an important commonality is the centrality of knowledge of numerical magnitudes in overall understanding. The present findings with 11- and 13-year-olds indicate that, as with whole numbers, accuracy ...

In his correspondence with Grigory Mints, the famous logician Georg Kreisel noticed that many results of constructive mathematics seem easierto-prove than the corresponding classical (non-constructive) results – although he noted that these results are still far from being simple and the corresponding open problems are challenging. In this paper, we provide a possible explanation for this empir...

We are now investigating an "executable" fragment of classical mathematics for testing formal proofs to make formal proof developments less laborious. Several theories of execution of full classical proofs are known. In these theories, some kind of abstract values such as continuations, are necessary. It makes them illegible from computational point of view, although they are mathematically int...

The control problem and Dynamic programming is a powerful tool in economics and management. We review the dynamic programming problem from its beginning up to its present stages. A problem which was involved in physics and mathematics in I 7” century led to a branch of mathematics called calculus of variation which was used in economic, and management at the end of the first quarter of the 20” ...

Although evidence suggests that individual differences in reading and mathematics skills are correlated, this relationship has typically only been studied in relation to word decoding or global measures of reading. It is unclear whether mathematics is differentially related to word decoding and reading comprehension. The current study examined these relationships at both a phenotypic and etiolo...