I really like Wolfram's theory of physics. It is easy to understand. At its core it is a bunch of graph theory with hints of everything else in the universe.
But I am biased because I am also a language designer, and we are both math literate. So I think in a lot of the same ways he does.
I am having a great time with calculus of computation. It reads like a math logic book, but there is a solid proof system that comes as a companion to it.
Type systems are pretty great. I am fond of these compilers
Some great stuff.
Purdue, and others are also trying out "Software 2.0". The idea is that programmers design a nice solid type system, proof code if you will. Underneath this are many machine learning algorithms to accomplish the difficult task of implementation.
Get it while its hot. Mathematical logic is a common element of compiler and formal language design.
A machine learning course that is more rigorous than average while still being not purely theoretical. Partake in the story of the world my friends, or whatever Descartes said.
https://engineering.purdue.edu/ChanGroup/ECE595/project.html
I am pretty curious about how to use automated reasoning systems to help discover new things, use and verify old ideas, and generally make my life easier.
Current events I try to keep up on
- Math Logic community (The Journal of Symbolic Logic)
- Statistics community (JASML, AoS)
- Algebra community (JoA, JoAG, JoPaAA, SIGSAM)
- Formal Methods community (CAV/TACAS)
Passing the learning curve up to current events
- Abstract Algebra (Dummit, Foote)
- Commutative Algebra (Eisenbud)
- Algebraic Geometry (Hartshorne)
- Mathematical Logic (Mendelson)
- Model Theory (Marker)