English
Abstract algebra
Notes on the structures that underlie modern mathematics — groups, rings, fields, and beyond. Covers foundational concepts like homomorphisms, quotient groups, ideals, and Galois theory, with an emphasis on building intuition alongside rigor. Each note breaks down one idea at a time, connecting abstract definitions to concrete examples. Written for anyone willing to think carefully about why the math works, not just how to apply it.
All the topics from the previous post about modern mathematicians' achievements sound intimidating. But are they actually that hard?
What helped me push through a 34-kilometer run on January 1st? Among other things — a podcast. On December 31st,…
We are approaching the midpoint of our experiment — each new post is shaped by your comments on the previous…
Once upon a time, probability theory was considered young and "audacious." In the 18th century, even D'Alembert called it "a…
Funny how things line up sometimes. Over the past three days, I've come across Cantor's diagonal argument twice — in…
As mentioned in a post about Michael Atiyah, one of his greatest achievements was K-theory. But what exactly is it?
In 1888, a young David Hilbert did what seemed impossible: he proposed an entirely new approach to one of the…
