Yash Jhaveri

Sequences/Series of Functions, Uniform Continuity, Weierstrass Theorem Fourier Series, Derivative in higher dimensions, Lebesgue measure

Langrangian, KKT, ODE, Calculus of Variations, Control Theory

I learned a lot of math and got better at solving complex abstract problems and writing proofs.

Mostly optimization problems, some ODEs, linear algebra review up top. Emphasis is on theory.

maximums, min problems with calculus 3 integrals, ODEs

Only take if you are willing to spend a lot of time on a very hard math class.

Kinda all over the place... some linear algebra, some ODEs, some calculus of variation, some constrained optimizatin

most people shouldn't take this course since they aren't prepared or it isn't useful to them, if they are interesting in math then I would definitely recommend 1 Columbia University: Arts & Sciences Fall 2021 Course: MATHGU4062_001_2021_3-INTROMODERNANALYSISII : MATHGU4062_001_2021_3 - INTRO MODERN ANALYSIS II Instructor: Yash Jhaveri

Linear programming, calculus of variations and control theory

In the first four weeks of the course we formally covered all of linear algebra and multivariable calculus. This was supposed to be a review but I ended up learning a whole of bunch of things at a neck-breaking speed: Jacobians, Hessians, Concave functions, Concave sets, tricky linear algebra problems, etc. This was crazy intense. Then we began learning optimization itself, things like the Lagrangian, the envelope theorem, and the Karush–Kuhn–Tucker conditions. To continue our study of optimization, the professor than taught us ODEs. When I say taught, I mean he covered a majority of an ODE course in two weeks. It was crazy, going from separable, linear, and exact ODEs to solving second-order non-homogenous ODEs. Once we covered all ODEs then we began studying control theory and calculus of variations, a fancy way of saying we were optimizing integrals whose integrand included ODEs.