Related papers: D\'e usted una buena pl\'atica de matem\'aticas
As the etymology of the word shows, logic is intimately related to language, as exemplified by the work of philosophers from Antiquity and from the Middle-Age. At the beginning of the XX century, the crisis of the foundations of mathematics…
This article aims at clarifying the language and practice of scientific experiment, mainly by hooking observability on calculability.
A number of topics in analysis are discussed, with emphasis on basic principles. There is some overlap with "Elements of linear and real analysis" (arXiv:math/0108030), with numerous changes in content and presentation since then.
The unity of mathematics has its power to compactify experiences in a form capable of being transferred and modified or adapted to new mathematical situations. Yet, we believe that the phrase "Unity of Mathematics" expresses a dream, an…
Math is constructed by people for people: just as natural language corpora reflect not just propositions but the communicative goals of language users, the math data that models are trained on reflects not just idealized mathematical…
These notes grew out of a mini-course given by the second-named author at Casa Matem\'atica Oaxaca in the Fall of 2022. Their purpose is to provide an exposition, directed at graduate students, of the basic properties of complex analytic…
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.
I discuss some problems related to extreme mathematical realism, focusing on a recently proposed "shut-up-and-calculate" approach to physics (arXiv:0704.0646, arXiv:0709.4024). I offer arguments for a moderate alternative, the essence of…
In this article, we suggest the use of Mathematical Relationships as a possible way to decrease the students' disinterest in Mathematics. First we made a consideration of the environment of the classroom from the perspective of teachers and…
Since information in electronic form is already a standard, and that the variety and the quantity of information become increasingly large, the methods of summarizing or automatic condensation of texts is a critical phase of the analysis of…
A review is given of some mathematical contributions, ideas and questions concerning liquid crystals.
Sometimes we obtain attractive results when associating facts to simple elements. The goal of this work is to introduce a possible alternative in the study of the dynamics of rational maps.
Formulaic expressions, such as 'in this paper we propose', are helpful for authors of scholarly papers because they convey communicative functions; in the above, it is showing the aim of this paper'. Thus, resources of formulaic…
Generating a concise summary from a large collection of arguments on a given topic is an intriguing yet understudied problem. We propose to represent such summaries as a small set of talking points, termed "key points", each scored…
Human tutoring interventions play a crucial role in supporting student learning, improving academic performance, and promoting personal growth. This paper focuses on analyzing mathematics tutoring discourse using talk moves - a framework of…
This article aims to provide a unified and technical approach to semantic information, communication, and their interplay through the lens of probabilistic logic. To this end, on top of the existing technical communication (TC) layer, we…
Courses in mathematical methods for physics students are not known for including too much in the way of mathematical rigour and, in some ways, understandably so. However, the conditions under which some quite commonly used mathematical…
The paper has a form of a talk on the given topic. It consists of three parts. The first part of the paper contains main notions, the second one is devoted to logical geometry, the third part describes types and isotypeness. The problems…
We outline the basic ideas and techniques underpinning the simulation of stochastic differential equations. In particular we focus on strong simulation and its context. We also provide illustratory examples and sample matlab algorithms for…
Formal logic has often been seen as uniquely placed to analyze mathematical argumentation. While formal logic is certainly necessary for a complete understanding of mathematical practice, it is not sufficient. Important aspects of…