Selected topics in mathematics (2026): Diophantine equation
Lectures
The lectures take place Mondays 17:15 - 18:45 in SR 11.32. We will discuss topcis such as linear Diophantine equations, Pythagorean triples, rational solutions to quadratic equations (in two variables), Rational points of certain curves of degree three, sums of squares, Pell's equation, and factorial rings and Euclidean rings. There will be an oral exam towards the end of the lectures.
Here are notes of the lecture.
Exercise classes
The classes take place Wednesdays 10:20 - 11:05 in SR 11.34. The content is closely related to the corresponding lecture Selected topics in mathematics 1: Diophantine equations (see above).
Evaluation: There will be 6 minitests during the semester, each giving up to 2 points. For the final grade, only the 5 best Tests will count. At least 5 Points from the Minitests have to be achieved to pass the class. There will be Tests every second week, and the first Test will take place on 25.03.2026. Each Test will last for about 15 - 20 Min.
Besides the Minitests, there will also be blackboard presentations. Each presentation will be graded with 0, 1, or 2 points. Every student has to present at least 2 presentations. Only the 3 best presentations will count for the final grade.
The final grade will be determined by the total sum N of the points from the Minitest, and the points from the blackboard presentations (i.e. N = points Minitest + points blackboard presentations) as follows:
If N ≥ 14, then the grade is 1.
If 14 ≥ N ≥ 12, then the grade is 2.
If 12 ≥ N ≥ 10, then the grade is 3.
If 10 ≥ N ≥ 8, then the grade is 4.
If N < 8, then the grade is 5.
Exercise sheets: