Related papers: Matematika 1
These are the notes from my courses on the arithmetic of quadratic forms.
The purpose of this paper is (i) to expound the specification of a universe, according to those parts of mathematical physics which have been experimentally and observationally verified in our own universe; and (ii) to expound the possible…
This paper is a first step to chase the ambitious objective of developing a mathmatical theory of living systems. The contents refer modeling large systems of interacting living entities with the aim of describing their collective behaviors…
We describe various errors in the mathematical literature, and consider how some of them might have been avoided, or at least detected at an earlier stage, using tools such as Maple or Sage. Our examples are drawn from three broad…
Systematic literature studies have received much attention in empirical software engineering in recent years. They have become a powerful tool to collect and structure reported knowledge in a systematic and reproducible way. We distinguish…
This text is based on an invited talk at the Dedekind Symposium at Braunschweig in October 2016. It summarizes views from my recent commented edition of Dedekinds two books on the foundations of mathematics.
In this chapter, I discuss teaching mathematical tools specifically tailored for economics students. A typical one-semester course in this area seeks to blend a range of topics: from foundational elements of subjects such as linear algebra…
Contribution: We demonstrate that it is feasible to include field specific problems in introductory mathematics courses to motivate engineering students. This is done in a way that still allows large parts of the course to be common to all…
This paper discusses digital online mathematics examinations -- a discussion ranging from high school to university level examinations. In particular, we consider the nature of mathematical writing, what is distinctive about mathematical…
Recently delivered lectures on Self-Referential Mathematics, [2], at the Department of Mathematics and Applied Mathematics, University of Pretoria, are briefly presented. Comments follow on the subject, as well as on Inconsistent…
This book contains a large number of exercises related to different stochastic disciplines. Difficulty of the problems varies from the basic level in the first chapter up to the analysis of articles in Probability, Statistics and Computer…
This paper shares a classroom story from Fall 2022 to Spring 2025 about a learner centered routine in undergraduate mathematics. I use four steps: an opening question, a short mini lecture about meaning, structured small group work, and a…
Problem-based learning (PBL) is a constructivist learner-centered instructional approach based on the analysis, resolution and discussion of a given problem. It can be applied to any subject, indeed it is especially useful for the teaching…
Data-driven decision making is serving and transforming education. We approached the problem of predicting students' performance by using multiple data sources which came from online courses, including one we created. Experimental results…
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…
The textbook contains the problems in mechanics and special relativity for physics departments of universities. Many original problems were proposed by active scientists from the institutes of the Siberian Branch of Russian Academy of…
In this article, we identify the didactic conditions for learning mathematics in kindergarten. To do so, we rely on the framework of the theory of didactic situations (Brousseau, 1998) and the notion of problem-situation (Douady, 1984). We…
In this manuscript various components of research are listed and briefly discussed. The topics considered in this write-up cover a part of the research methodology paper of Master of Philosophy (M.Phil.) course and Doctor of Philosophy…
This is a reflection on the author's experience in teaching logic at the graduate level in a computer science department. The main lesson is that model building and the process of modelling must be placed at the centre stage of logic…
The goal of this chapter is to support teachers in holistically introducing graduate students to literature reviews, with a particular focus on secondary research. It provides an overview of the overall literature review process and the…