Slides and Report from my first year presentation on the point counting problem.
Archive of posts filed under the Algebra category.
Mathematical tourism
In search of the quarternions.
A less very, very stupid way of counting points on elliptic curves
Sidestepping brute-force determination of the number of points over a finite field by construction of zeta functions.
Small defect types in Maple
Maple procedures for finding polynomials of a given trace and degree; hence for establishing the possible types of zeta function for small defect.
The Torsion subgroup of an Elliptic Curve
Yet more Maple code, this time for finding/classifying torsion points of an elliptic curve.
Implementing the Group Law Algorithm in Maple- finite fields
Extension of Maple code to finite fields.
Implementing the Group Law Algorithm in Maple- Examples
Sample problems from Silverman on the Elliptic curve group law.
Implementing the Group Law Algorithm in Maple- Code
Maple procedures for group law computation on Elliptic curves.
Lecture notes- Galois Theory
Notes from MA40037 Galois Theory, as pdf.
Moments of the Riemann Zeta function
Follow up of some ideas from Nina Snaith’s talk to the undergraduate maths club.
