相关论文: What is good mathematics?

As an approach to a Theory of Everything a framework for developing a coherent theory of mathematics and physics together is described. The main characteristic of such a theory is discussed: the theory must be valid and and sufficiently…

We argue that, when establishing and benchmarking Machine Learning (ML) models, the research community should favour evaluation metrics that better capture the value delivered by their model in practical applications. For a specific class…

A critical examination of some basic conceptual issues in classical statistical mechanics is attempted, with a view to understanding the origins, structure and statuts of that discipline. Due attention is given to the interplay between…

Well-founded fixed points have been used in several areas of knowledge representation and reasoning and to give semantics to logic programs involving negation. They are an important ingredient of approximation fixed point theory. We study…

It is introduced the concept of Superiority Degree one competitive decision over another. On the basis of this concept the mathematics theoretic structure is developed, which is part of pairs comparisons branch in modern decision making…

Szemeredi's Regularity Lemma is a very useful tool of extremal combinatorics. Recently, several refinements of this seminal result were obtained for special, more structured classes of graphs. We survey these results in their rich…

In the report the approach to estimation of quality of planned experiments is considered. This approach is based on the analysis of uncertainty, which will take place under the future hypotheses testing about the existence of a new…

Mathematics as an area of study occupies an important place in higher education. Due in part to its utility in other disciplines as well as its role in student learning, institutions of higher education (IHEs) often have large numbers of…

We propose to address the problem of how to know students' knowledge in an entirely new approach called ?epistemography? which is, roughly, an attempt to describe the structure of this knowledge. We claim that what is to be known is made of…

The role of mathematical models in physics has for longer been well established. The issue of their proper building and use appears to be less clear. Examples in this regard from relativity and quantum mechanics are mentioned. Comments…

We show a possibility to apply certain philosophical concepts to the analysis of concrete mathematical structures. Such application gives a clear justification of topological and geometric properties of considered mathematical objects.

Recently there has been a dramatic increase in the performance of recognition systems due to the introduction of deep architectures for representation learning and classification. However, the mathematical reasons for this success remain…

It has been shown that a functional interpretation of proofs in mathematical analysis can be given by the product of selection functions, a mode of recursion that has an intuitive reading in terms of the computation of optimal strategies in…

A new generation of educational mathematics software is being shaped in ThEdu and other academic communities on the side of computer mathematics. Respective concepts and technologies have been clarified to an extent, which calls for…

What is Statistics? Opinions vary. In fact, there is a continuous spectrum of attitudes toward statistics ranging from pure theoreticians, proving asymptotic efficiency and searching for most powerful tests, to wild practitioners, blindly…

My purpose is to examine some concepts of mathematical logic, which have been studied by Carlo Cellucci. Today the aim of classical mathematical logic is not to guarantee the certainty of mathematics, but I will argue that logic can help us…

Since its existence, the computer tool has often supported mathematicians, whether it is to implement an approximation method (numerical calculation of a root, of an integral, ...) or to simulate a phenomenon (geometric in nature,…

In this paper, we study good semigroups of \mathbb{N}^n, a class of semigroups that contains the value semigroups of algebroid curves with n branches. We give the definition of embedding dimension of a good semigroup showing that, in the…

Is speculative mathematics dangerous? Recent interactions between physics and mathematics pose the question with some force: traditional mathematical norms discourage speculation, but it is the fabric of theoretical physics. In practice…

This paper discusses an approach with machine-learning probability models to evaluate the difference between good and bad data quality in a dataset. A decision tree algorithm is used to predict data quality based on no domain knowledge of…