Five Bachelor's Degree Project Presentations in Mathematics

Time: 10:15 - 11:00

Place: 4003

Speaker: Eskil Worm Forss

Title: Infinite series and products

Abstract: Determining whether or not a series converges or not always trivial, therefore it is useful to have convergence tests that can be applied in different situations to determine convergence. This thesis will mainly encompass some properties of series, convergence tests with applications, and a little about convergence of products and how they relate to series. The main result of the thesis being a classification of which real values a specified hypergeometric series converges for, using Gauss’s test.

Time: 11:15 - 12:00

Place: 4003

Speaker: Oskar Ådahl

Title: Counting Cycles in the Uniform Attachment Model

Abstract: In this thesis we study the number of cycles in a special type of random graph, the uniform attachment model. Previous work have shown asymptotic bounds on the expected cycle count in a uniform attachment graph. We prove a theorem that gives much tighter bounds and then go on to explore some consequences of the theorem and demonstrate how it can be applied to approximate the cycle count in practice using Python.

Talare: 13:15 - 14:00

Place: 4003

Speaker: Felix Gustavsson

Titel: Anomaly Detection in Bernoulli Time Series

Abstract: In the industry, we might encounter a series of events that we expect to be independent, without being sure. At some point the events may stop being independent from each other. The thesis develops a way to identify anomalies where presumably independent events from a Bernoulli time series see rapidly changes in probability. Rapidly changing probability may indicate activity that is dependent. Bands similar to ordinary bollinger bands from finance are used.

Time: 14:15 - 15:00

Place: 4003

Speaker: Juni Drakengren

Titel: The group structure of rational points on elliptic curves

Abstract: Elliptic curves might be most known for their role in the proof of Fermat’s Last Theorem in number theory. They are also quite interesting from an algebraic geometry perspective, since it is possible to define a natural geometric group operation on them. To begin with, we will define elliptic curves, whereafter we define the operation addition on them. Then we are going to show that the points on the curve form an abelian group under the addition, to which the rational points is a subgroup. In the end we will show the idea of the proof to Mordell’s theorem, saying that the group of rational points on a elliptic curve is finitely generated. It can be used for certain diophantine equations to conclude that it is possible to genererate all their rational roots from a finite set of rational roots.

Time: 15:15 - 16:00

Place: 64119

Talare: Jakob Larsson

Titel: Clustering of playing styles

Abstract: Data analytics in football is becoming a crucial part of the modern football and machine learning has become a fundamental part of everyday life for many. Connecting these two seem like an self-evident choice, this is what this thesis will do with analysing clustering in regards to playing styles. The clustering used is K-Means and Gaussian Mixture Model combined with PCA-projection. The project dives into how these methods work and applies it to data from Allsvenskan 2023. The model showed that the there were four prominent clusters with the most successful in terms of output (e.g. xG and number of shots) being high risky pressure, possession based with safe passing. Another cluster which was quite unsuccessful but still the most original of the four was Low pressure, long vertical passing, the other were closer to the most successful cluster, both being possession based.