Chapter 1 sketches the set theoretic construction of the natural, integer, rational, real and complex numbers. Chapter 2 gives an introduction to elementary number theory.  Chapter 3 gives an introduction to polynomial rings and provides a first contact with algebraic field extensions. Chapter 4 is dedicated to abstract ring theory.

The course continues next semester with group theory and Galois theory.

There are continuously updated lecture notes on  StudIP.

Lecture:

Tuesday       10:00 - 12:00 ITZ SR 004
Wednesday 10:00 - 12:00 ITZ SR 004

Exercises by Daniel Yoon:

Monday   10:00 - 12:00 IM SR 007
Tuesday   12:00 - 14:00 IM SR 007

Mathematical logic takes its origin in Gottlob Frege's Begriffschrift 1879, and was pushed forward by David Hilbert's program during the so-called foundational crisis of mathematics in the beginning of the 20th century. Today it is an established disciplin of mathematics with broad connections to other areas of mathematics, and in particular to theoretical computer science. Among the greatest achievements of mathematical logic, and generally mathematics of the 20th century, are Alan Turing's formal definition of the notion of computability 1936, and Kurt Gödel's proof of impossibility of Hilbert's program, namely his incompleteness theorems 1931. The course offers an introduction into mathematical logic, and in particular into computability theory and the incompleteness theorems.

Lectures

Tuesday       12:00 - 14:00 IM SR030
Wednesday 12:00 - 14:00  IM SR030 / JUR SR059

Exercises

Thursday 12:00 - 14:00 IM HS12

Literature

Ziegler, Mathematische Logik, Birkhäuser, 2010, Springer
Ziegler, Vorlesungsskript
Ebbinghaus, Flum, Thomas, Mathematical Logic, 1994 Springer
Ebbinghaus, Flum, Thomas, Einführung in die mathematische Logik, 2018, Springer
Shoenfield, Mathematical Logic, Addison-Wesley, 1967

This is an advanced seminar joint with Tobias Kaiser. It offers research talks of the respective groups and their visitors.  Advanced students who wish to deepen their knowledge in mathematical logic and/or complexity theory can give talks on jointly chosen and jointly elaborated topics.

Programme  pdf