L211E: Logic and Mathematics

L211E: Logic and Mathematics

Norbert Preining
Term: 
2014 Term 2-1

Ideas and concepts of mathematics are infiltrated deeply into our science and technology. Highly abstract notions of mathematics can sometimes find unexpected applications. This lecture will explain them by looking back the development of logic and mathematics, and will discuss also the current of modern mathematics.

Aim of the course is the acquisition of basic understanding of fundamental mathematical and logical concepts.

Lectures

  1. Examples of Mathematics in the 20th and 21st centuries
  2. What is mathematics - from calculation to the theory of patterns
  3. What is a proof? - basic proof methods
  4. Induction
  5. Number theory
  6. Number systems - binary, octal, decimal, hexadecimal
  7. Logic - the language of Mathematics
  8. Geometry and algebraic constructions
  9. Axiomatic method in Geometry, Non-Euclidean geometries
  10. The infinite - counting and measuring
  11. Calculus - Functions and limits
  12. Graph Theory and internet traffic
  13. Models of computation
  14. Hoare logic and verification of programs
  15. Mathematics and Logic in the 21st century