Fundamentals of Mathematics.

Fundamentals of Pure Mathematics

About the Course In this course we shall mostly talk and think about numbers, working carefully from definitions. The course will have the following components: 1. Proof and Mathematical Argument 2. Sets, Relations and Functions 3. Construction and Properties of Number Systems 4. Some Number Theory 5. Countability If you wish to read further about various topics covered in this course and relat...

Some layman considerations related to the fundamentals of mathematics

In the sequel some questions related to the fundamentals of mathematics as I understand them as physicist are considered. 1. Gödel’s problematics is shown to have a topological analog in real topology, which however disappears in p-adic topology which raises the question whether the replacement of the arithmetics of natural numbers with that of p-adic integers could allow to avoid Gödel’s probl...

Formalising mathematics in UTT: fundamentals and case studies

We give a detailed account of the use of type theory as a foundational language to formalise mathematics. We develop in the type system UTT a coherent approach to naive set theory and elementary mathematical notions. In the second part of the paper, we present a fully-checked example based on our representation of naive set theory.

Analyses of 10th mathematics textbook and teacher guide book based on context base Mathematics approach

Recently, the National curriculum of Islamic Republic of Iran has been developed by the Ministry of Education to provide educational policies. In this document, an implicit emphasis on so called context base aspect of the program can be seen in the mathematics curriculum framework section. In this paper, I first, introduce the different aspects of context base Mathematics Education, and then th...

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