This is my last semester at IITB and along with Fourier Analysis and applications, which is compulsory learning, I have chosen to study Algebraic Geometry, Algebraic Number Theory and Algebraic Topology. The smart reader would have probably guessed the algebraic connection here.

In a way, these subjects were inevitable to be studied. Algebraic Number Theory is my main research interest, my most likely dissertation subject and so my bread. That course couldn’t possibly be dropped.

Algebraic Topology is the interplay of Algebra and Topology that enriches our understanding of both, algebraic objects (groups) and topological surfaces. Each provides vital information about the other. The van Kampen theorem teaches amalgams and properties of free groups and also helps in finding the fundamental group of complicated topologies.

To me, algebraic geometry is algebra with a kick, said Solomon Lefschetz. I got my first algebra kick in today’s algebraic geometry class. The assistance algebra gives to understanding geometric properties and the fun it gives me, is ‘undescribable’. Neither shall I describe it, but surely I cannot die without learning it!

Fourier series and transforms were what I used to do (and enjoy) in my BTech days. It is good to learn it rigorously and thus make a clean job of it.

Having said that, let me resume what I left off before starting writing this post — algebraic geometry…

PS: This is my experience about these subjects after learning for the first time. The opinion may change as I learn further interesting things.