相关论文: Mathematical conceptualism

We claim that human mathematics is only a limited part of the consequences of the chosen basic axioms. Properly human mathematics varies with time but appears to have universal features which we try to analyze. In particular the functioning…

Discrete mathematics is the foundation of computer science. It focuses on concepts and reasoning methods that are studied using math notations. It has long been argued that discrete math is better taught with programming, which takes…

The paper discusses fundamental problems in mathematical description of social systems based on physical concepts, with so-called statistical social systems being the main subject of consideration. Basic properties of human beings and human…

Development of several alternative mathematical models for the biological system in question and discrimination between such models using experimental data is the best way to robust conclusions. Models which challenge existing theories are…

Mathematical concepts and tools have shaped the field of visualization in fundamental ways and played a key role in the development of a large variety of visualization techniques. In this chapter, we sample the visualization literature to…

This is a draft of a chapter on mathematical logic and foundations for an upcoming handbook of computational proof assistants.

Mathematics is one of the ways our species makes sense of this world and I believe that it is inherent in our thinking machinery. The mathematics we do in turn is dependent on the way we view our universe and ourselves. Lakoff and Nunez…

At two examples dealt with in methodologically different ways it will be pointed out how the concept of an empirical theory (in the sense of the Structuralists) can be useful to specify contents relevant to maths didactics.

I discuss some general aspects of the creation, interpretation, and reception of mathematics as a part of civilization and culture.

In order to work with mathematical content in computer systems, it is necessary to represent it in formal languages. Ideally, these are supported by tools that verify the correctness of the content, allow computing with it, and produce…

Math is widely considered as a powerful tool and its strong appeal depends on the high level of abstraction it allows in modelling a huge number of heterogeneous phenomena and problems, spanning from the static of buildings to the flight of…

To adequately model mathematical arguments the analyst must be able to represent the mathematical objects under discussion and the relationships between them, as well as inferences drawn about these objects and relationships as the…

This lecture addresses some general ideas behind numerical computations ranging from representation of numbers in computers to stability and accuracy of standard algorithms for some simple mathematical problems.

Metaphysical interpretations of set theory are either inconsistent or incoherent. The uses of sets in mathematics actually involve three distinct kinds of collections (surveyable, definite, and heuristic), which are governed by three…

This article is devoted to the tactical game theoretical interpretation of dialectics. Dialectical games are considered as abstractly as well as models of the internal dialogue and reflection. The models related to the representation theory…

Mathematical proofs are often said to justify their conclusions by indicating the existence of a corresponding formal derivation. We argue that this widespread view relies on an under-examined notion of correspondence, or what it means for…

Axiomatizing mathematical structures is a goal of Mathematical Logic. Axiomatizability of the theories of some structures have turned out to be quite difficult and challenging, and some remain open. However axiomatization of some…

The paper provides a survey of semantic methods for solution of fundamental tasks in mathematical knowledge management. Ontological models and formalisms are discussed. We propose an ontology of mathematical knowledge, covering a wide range…

The goal of this paper is to extend classical logic with a generalized notion of inductive definition supporting positive and negative induction, to investigate the properties of this logic, its relationships to other logics in the area of…

Remarks on mathematical proof and the practice of mathematics.