# L211E: Logic and Mathematics

## L211E: Logic and Mathematics

Norbert Preining |

Term:

2014 Term 2-1Ideas 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

- Examples of Mathematics in the 20th and 21st centuries
- What is mathematics - from calculation to the theory of patterns
- What is a proof? - basic proof methods
- Induction
- Number theory
- Number systems - binary, octal, decimal, hexadecimal
- Logic - the language of Mathematics
- Geometry and algebraic constructions
- Axiomatic method in Geometry, Non-Euclidean geometries
- The infinite - counting and measuring
- Calculus - Functions and limits
- Graph Theory and internet traffic
- Models of computation
- Hoare logic and verification of programs
- Mathematics and Logic in the 21st century