did you read any interesting problems, theorems, proofs, textbooks, or papers recently?
what are you studying this summer?
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/mg/ = /math/ general: Completions Edition
Jack Roberts
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Owen Miller
Im studying about Illuminati.
Nolan Jackson
Studying basic tensor calculus (aka index shuffling for physicists) and trying to into abstract algebra.
Ryder Wright
How do you train you brain (besides solving multiple exercises)? Do you do anything specific? I think solving puzzles in general helps.
Ethan Perry
>What about his videos on algebraic topology?
They're good for the most part, same with the diff geo parts.
Isaac Wilson
How do I get into differential geometry and topology ?
Landon Wilson
Reading Abstract Algebra by Dummit and Foote. I haven't been too dedicated, only on chapter 5 since I started this summer (busy with programming things)
Aiden Wilson
Are semi math related jokes allowed? If so pic related is worth a look for a laugh.
I'm currently learning quantum field theory. I'm not very far, just coming to grips with interacting fields and Feynman diagrams. Been using Mandl/Shaw and Lahiri/Pal. Going to read some Zee and Peskin/Schroeder. Zee especially looks very interesting since he starts off with path integrals.
The important thing is to make sure you're trying difficult problems and content. Solving a bunch of exercises is pointless if they're too easy. Actually solving problems isn't necessary either. As long as you're thinking and making an attempt you'll learn. Pick a topic, theorem, or problem that interests you and try to learn/prove/solve it.
Start with Spivak's calculus on manifolds if you don't know that stuff yet. I lightly recommend Hicks, it's pretty old with awful typesetting but gave me good intuition. Lee's smooth manifolds is a much more modern and highly recommend text so give that a try.
Grayson Baker
You'll want a background in (multivariable) analysis and point set topology. If you don't already feel comfortable with that, do that first.
For Differential Topology, I'd recommend:
>Differential Topology by Guillemin and Pollack
>Topology from the Differentiable Viewpoint by Milnor
For Differential Geometry, I'd recommend
>Introduction to Smooth Manifolds by Lee
>Differential Geometry of Curves and Surfaces by Do Carmo
Ryan Hall
Heinrich Guggenheimer.