Teaching

Winter term 24/25: Function fields (unisono)
Summer term 24: Algebra (unisono, moodle)
Summer term 24: Seminear zu Algebra und Zahlentheorie (Quadratische Zahlkörper), Ankündigung: PDF (unisono, moodle)
Winter term 23/24: Praktikum Computeralgebra (unisono, moodle)
Winter term 23/24: Algorithmische Algebra (unisono, moodle)
Summer term 23: Lineare Algebra II (moodle)
Winter term 22/23: Lineare Algebra I (moodle)
Winter term 22/23: Praktikum Computeralgebra (link)
Summer term 22: Algebraische Zahlentheorie (unisono)
Summer term 22: Praktikum Computeralgebra (link)
Winter term 21/22: Elemente der Algebra (moodle)

2019, Marvin Schierholz, “Rational points on elliptic curves and norm relations”, master's thesis
2019, Johannes Schmitt, “On an effective version of Eichler's theorem”, master's thesis
2019, Malte Hopfer, “Imaginärquadratische Ordnung mit kleiner Klassenzahl” (imaginary quadratic orders with small class number), bachelor's thesis
2018, Christopher Cullmann, “Diskrete Logarithmen und Gaußsche ganze Zahlen” (discrete logarithms and Gaussian integers), bachelor's thesis
2017, Marvin Schierholz, “Rationale Punkte auf elliptischen Kurven” (rational points on elliptic curves), bachelor's thesis
2017, Johannes Schmitt, “Lineare Algebra über Polynomringen” (linear algebra over polynomial rings), bachelor's thesis
2016, Robin Ammon, “Quadratische Funktionenkörper” (quadratic function fields), bachelor's thesis

2018, Jannik Mähn, Fabian Mäurer & Erec Thorn, “Zur Berechnung von Teilkörpern in Zahlkörpern” (computing subfields of number fields). Implementation of basic functionality for subfields of number fields using julia and Hecke, including the algorithms of Hulpke, Klüners and van-Hoeij–Klüners.
2017, Malte Hopfer & Christopher Cullmann, “Diskrete Logarithmen in endlichen Gruppen” (discrete logarithms in finite groups). Implementation of basic algorithms for discrete logarithms including BSGS, Pohlig–Hellmann, Pollard's Rho algorithm and Index Calculus using julia and Nemo.
2017, Johannes Schmitt & Marvin Schierholz, “Algorithmen für elliptische Kurven über Zahlkörpern” (algorithms for elliptic curves over number fields). Implementation of basic algorithms for elliptic curves over number fields, including rank computation via 2-descent for rational curves, using julia and Nemo.
2016, Robin Ammon & Sofia Brenner, “Algorithmen für elliptische Kurven über \(\mathbf{Q}\)” (algorithms for elliptic curves over \(\mathbf{Q}\)). Implementation of basic algorithms for elliptic curves using julia and Nemo. Including algorithms for point counting over finite fields (BSGS, Schoof's algorithm), division polynomials, torsion points, minimal models over the rationals (Laska–Kraus–Connell), local arithmetic data (Tate's algorithm) and periods.