Presentation of independent project for mathematics teachers

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"

Abstract

"This thesis examines classical solution methods for third- and fourth-degree polynomial equations, developed by Cardano and Ferrari in the sixteenth century. Using modern algebraic notation, these methods are derived step by step and framed in terms of polynomial rings, symmetric polynomials, and Viète’s relations.

The work emphasizes the underlying algebraic structure of the methods, showing how specific substitutions systematically eliminate terms and reduce the equations to simpler forms. In particular, Cardano’s solution of the depressed cubic is shown to form the foundation of Ferrari’s method for solving quartic equations via a cubic resolvent.

Finally, the thesis discusses the theoretical limitations of these classical approaches. Results by Ruffini, Abel, and Galois demonstrate that no general formula exists for polynomial equations of degree five or higher, as the symmetries of their roots cannot, in general, be resolved using radicals. The thesis thus illustrates both the historical development of algebraic solution methods and the structural reasons for their limitations."

Presentations earlier or later the same week

There are some more presentations during 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"

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"

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"

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"