My biggest project ever (so far) was my masters thesis. My task was to write a textbook on Gröbner bases that should be accessible for a student with only basic knowledge of linear algebra.

Gröbner Bases - An introduction.

A presentation of my Master Thesis on Gröbner Bases:

A common situation, not only in mathematics, is that a large and useful class of problems is known to be solvable in principle but no algorithm to actually solve the problems exists.
In this presentation I will show how Gröbner Bases can be used to construct and compute with objects derived from ordinary polynomials (more precisely, objects expressed as residue classes to a polynomial ring modulo an ideal).
As an application I will show how systems of non-linear polynomial equations can be solved using Gröbner Bases.

Gröbnerbaser - Ett verktyg för att konstruera och räkna med matematiska objekt.

A textbook (in swedish) on Gröbner Bases written as my Master Thesis.

Keywords (english): Gröbner base, Buchberger algorithm.

Keywords (swedish): Gröbnerbas, Buchbergers algoritm.