This undergraduate course aims to introduce the fundamental concepts and properties of sets, relations, and functions, to teach how to reason rigorously and write the reasoning used in an appropriate manner, and, last but not least, to serve as an introduction to the art of proof.
This course aims to provide students with a solid understanding of multilinear algebra and the classification of linear transformations through canonical forms. By the end of the course, students will be able to work with tensor products, exterior and symmetric algebras, bilinear and multilinear mappings, and analyze linear operators using Jordan and rational canonical forms. The course emphasizes both the theoretical foundations and the practical techniques needed for advanced studies in mathematics.
In addition to the technical content specific to each discipline, it is essential to reflect on the origins and development of these concepts, as well as on the value of the methods used to produce knowledge, its very nature, and the ways in which it is validated. The central aim of this postgraduate course is for participants to develop their own understanding of the nature of science, which may serve as a guide for their pedagogical strategies.
This course presents the essential techniques and tools for the study of the theory of representations of partially ordered sets. In particular, it covers the differentiation algorithms of Nazarova and Zavadskij and provides the classification of all finite-type posets and all sincere posets of finite type.