Foundations of Mathematics

Catalog description

Mathematics is a convenient and powerful language, providing a deep, unified framework for all scientific developments. All existing results from the three fundamental categories of mathematics - geometry, algebra, and analysis - can be formally expressed in terms of set theory, predicates, quantifiers, and logical connectives. This course explores the axiomatic method, some elements of logic and formal languages, and set theory. In addition, the system of real numbers and all other fundamental number systems can be firmly established on the ground of natural numbers; therefore, the course introduces elementary arithmetic and the universal method of constructing new objects from already known sets by means of equivalence relations. Abstract concepts are introduced through basic but fundamental and universal examples or problems, carefully chosen as illuminants of broader ideas and sources of new theoretical and practical applications.