Presentations of independent projects in mathematics

Jessica Ramström, Independent projects for mathematics teachers, L6

Date and time: Thursday 5/2, 8:00
Place: Meeting room 25, Albano building 2
Student: Jessica Ramström
Supervisor: Pavel Kurasov
Title: "Sturm-Liouville theory"

Abstract

This thesis presents the fundamentals of Sturm–Liouville theory, which provides a framework for a class of second-order differential equations. Properties of the solutions of these equations, known as eigenfunctions, are discussed and proved. In particular, the orthogonality of eigenfunctions and Sturm’s comparison theorem are established. Furthermore, a method for solving Sturm-Liouville problems is described and illustrated with a concrete example. Finally, the influence of boundary conditions on the eigenvalues and the associated eigenfunctions is examined.

Gülhan Sariismailoglu, Bachelor's thesis, K3

Date and time: Thursday 5/2, 14:00
Place: Meeting room 9, Albano building 1
Student: Gülhan Sariismailoglu
Supervisor: Gregory Arone
Title: "Picks sats"

Abstract

"Pick’s Theorem is a classical result in geometry that provides a simple and elegant formula for calculating the area of polygons whose vertices lie on an integer lattice. Despite its elementary formulation, the theorem establishes a deep connection between geometry, combinatorics, and graph theory.

In this thesis, we present Pick’s Theorem and illustrate its use through a series of concrete examples involving both regular and irregular lattice polygons. Two different proofs of the theorem are given. The first is a constructive proof based on induction and the additivity of area, while the second relies on Euler’s formula for planar graphs and triangulations of lattice polygons.

Finally, we investigate a generalization of Pick’s Theorem to polygons with holes. It is shown how the original formula must be modified depending on the number of holes, and how the classical version of Pick’s Theorem appears as a special case. The results demonstrate that Pick’s Theorem is a powerful and versatile tool within lattice geometry."

Presentations earlier or later in the week

There are some more presentations the same week. Abstracts can be found in the calendar article for each day.

Calendar for the Department of Mathematics

Matilda Colarieti Tosti, Bachelor's thesis, K2

Date and time: Monday 2/2, 8:30
Place: Cramér meeting room, Albano building 1
Student: Matilda Colarieti Tosti
Supervisor: Alan Sola
Title: "Convergence of random series"

Carlotta Kvitberg, Independent projects for mathematics teachers

Date and time: Monday 2/2, 9:00
Place: Mittag-Leffler meeting room, Albano building 1
Student: Carlotta Kvitberg
Supervisor: Per Alexandersson
Title: "S-Kalaha: Solving a Swedish variant of Kalaha"

Melvin Segerman, Bachelor's thesis, K1

Date and time: Monday 2/2, 10:30
Place: Mittag-Leffler meeting room, Albano building 1
Student: Melvin Segerman
Supervisor: Yishao Zhou
Title: "Visibility Graphs för tidsserier: Matematiska egenskaper och tillämpningar"

Anders Lindberg, Independent projects for mathematics teachers, L3

Date and time: Monday 2/2, 12:00
Place: Mittag-Leffler meeting room, Albano building 1
Student: Anders Lindberg
Supervisor: Rikard Bögvad
Title: "Transcendenta tal"

Niklas Hellberg, Independent projects for mathematics teachers, L4

Date and time: Monday 2/2, 12:00
Place: Cramér meeting room, Albano building 1
Student: Niklas Hellberg
Supervisor: Boris Shapiro
Title: "Finite Fields: An Introduction"

Felix Nordgren Odhner, Independent projects for mathematics teachers, L5

Date and time: Tuesday 3/2, 10:00
Place: Meeting room 25, Albano building 2
Student: Felix Nordgren Odhner
Supervisor: Sofia Tirabassi
Title: "Polynomials of Degree 3 and 4: Classical Solution Methods and Their Significance"

Amanda Borg, Independent projects for mathematics teachers, L1

Date and time: Friday 6/2, 12:00
Place: Cramér meeting room, Albano building 1
Student: Amanda Borg
Supervisor: Per Alexandersson
Title: "Backtracking och n-queens: hur radordning påverkar sökningens effektivitet"

Fabian Lukas Grubmüller, Master's thesis, M1

Date and time: Friday 6/2, 13:30
Place: Cramér meeting room, Albano building 1
Student: Fabian Lukas Grubmüller
Supervisor: Anders Mörtberg
Title: "The Category of Iterative Sets in Cubical Agda"