Open Math Notes

The notes correspond to the bachelor course Group Theory of the Vrije Universiteit Brussel, Faculty of Sciences, Department of Mathematics and Data Sciences.

Leandro Vendramin · Vrije Universiteit Brussel · Date posted: July 8, 2025

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The notes correspond to the bachelor course Ring and Module Theory of the Vrije Universiteit Brussel, Faculty of Sciences, Department of Mathematics and Data Sciences.

Leandro Vendramin · Vrije Universiteit Brussel · Date posted: July 8, 2025

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Notes prepared for a first course in Galois theory inspired by the classical book of Emil Artin.

Shuyang Cheng · University of Michigan · Date posted: June 18, 2025

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Our main aim with these notes is to introduce the combinatorial and symmetric function tools
that relate to the description of the Poincar´e polynomial of the triply graded Khovanov-Rozansky
homology of torus links, a.k.a. the (reduced) “superpolynomial” of these links. These where written in the context of the AIM Research Community on Link Homology.

François Bergeron · University of Quebec in Montreal · Date posted: April 18, 2025

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A first course in calculus/analysis, the first part of the course motivates the study of sequences and their convergence through problems involving calculating the area under a graph and the slope of the tangent at a point on a graph. The second part draws on observations from the first about structural differences between the reals and the rationals, and starts with some axioms for the reals. These axioms are then used to study continuity and properties of continuous functions on the reals.

Tulsi Srinivasan · Azim Premji University · Date posted: April 17, 2025

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