BTS III: Some loose ends
This is the last installment to the series sparked off by the SMO Open Q4 problem, which led us to introduce some basic learning theory.
Posts
BTS II: An introduction to learning theory
(David here.) In this blogpost, we'll go off on a tangent and explore what it means to learn from data . In the process, we will get slightly closer (but not quite there) to the context where Rademacher complexity emerges.
Too lazy to integrate
(David here.) A math teacher from Primary school once told me that "lazy people make good mathematicians". This is one story of laziness-inspired mathematics.
Coupling Arguments
(David here.) I'm going to explore various versions of an idea, starting from where I first saw it in Olympiads, and going beyond.
Inclusion-Exclusion
(David here.) In The Rising Sea , Ravi Vakil writes: When introduced to a new idea, always ask why you should care. Do not expect an answer right away, but demand an answer eventually. Try at least to apply any new abstraction to some concrete example you can understand well. We have something analogous for understanding proofs - with time, new perspectives show up and reveal new insight, and allows one to tackle problems that seemed impossible before.