What are interesting subfields of math?
I'm planning on buying a book for summer and learn a new topic from scratch. What are good subjects/books for an undergraduate?
(ie: a book that doesn't require too much background)
Also, ITT discuss your summer plans and ask/give recommendations.
do a fucking internship.
Bit late for that innit
is it?
No paid ones remaining in my part of the US, I'm just working on my family's farm for the summer and self studying real analysis
>wants people to recommend books
>doesn't even post his major
We could assume you are a math major but... are you? Nobody really knows.
Building on this - are there any areas of math that I could jump into without any familiarity with lower levels of math? I obviously have basic calculus and algebra understanding, but I'd like to find a higher level area of math that I can learn conceptually without having to build on things that I've already learned. My purpose in doing this is to see how much I can learn autodidactically in a completely new area - intelligence cap is "irrelevant" if that would limit my options.
Set Theory.
For everything else you need top tier 10/10 understanding of Set Theory, but you don't need Set Theory to start learning Set Theory, and yet it becomes pretty complex.
So yeah, set theory. It is the only self relying field of mathematics.
Even ancient shit like Euclidean Geometry is built upon Set Theory.
get a machine learning internship
anyone has any suggestions for UK? considering amazon, nokia, asos, warwick
Thanks, I really appreciate it.
Don't listen to Set theory is used all the time in all different areas of math but you don't need a "10/10" understanding of sets for an introduction to abstract algebra, real analysis, topology, etc.
Most introductory books on these topics include everything you'd need to know about sets in an introductory chapter.
>I have a basic understanding of algebra and calculus, therefore I will now study topology
Great idea.
yeah sorry, math
If the highest math I have taken is ZFC and Linear algebra, what should I do next? Diff eq? What are some good differential equations resources?
Also, if a ZFC/Intro to abstract algebra/proofs course was kinda hard for me (i got a C), should I jump ship on a math degree? I'm 18 and had a lot this quarter.
Probably a good place to ask:
I'm finishing trig soon and going into calc summer term, what should I do in between? And would getting into number theory on the side be too much for my pleb brain?
Honestly, OP, learn more about counting. I don't know why it is at the top of the trench, and imo should be at the bottom, since there is never going to be the "fastest" way to count something given an arbitrarily complex rule for how you count.
To get an idea of what I mean, start trying to count things that are hard to count, see how long it takes you, then see if you can find faster ways of counting them. Start with easy things (obviously do it as fast as you can since conceptually it will be easy) like number of pebbles in a cylindrical shaped jar, triangular shaped jar, arbitrarily shaped jar, etc (be as creative as you want with the rules, the more unpredictable the better)
When I started doing this, I noticed my general numerical reasoning, and general reasoning got better, and thus writing proofs got easier, which is something many undergrads struggle with (and just people in general).
Counting things is fun because you can do it with other people, too. it's extremely accessible. Get drunk with some friends and challenge each other to count things with simple or hard rules. how many stools are on the table on a sunday at 7:00 PM, 8:00 PM, n-PM, any day of the week, every odd day of the week, etc. You'll start getting a much better, much more vivid intuition for numbers, and then later on "structures" (I don't like the word since its a buzzword but whatever).
also, sorry, forgot to mention. don't do any of this with pen or paper. you need to be able to do it all in your head, while your walking down the street, driving in the car, fucking your girlfriend, etc. don't make it easy.
Mathematical Logic: Recursion theory
underrated post
>vectors come right before diff equations
Graph theory
...
autism
...
dont post this image, it makes you look retarded
> Veeky Forums is srs business
>haha you call something retarded in Veeky Forums, you're so retarded hahaha
you're a retard with absolutely no self awareness
> being this srs
...
>Stroke's theorem
Lmao
> can't tell a joke
how's that autism going for you?
It's got fucking triple integrals at the bottom of the trench.
it's edited in with a different font, are you blind?
Are you?
There's other jokes in there.
>haha you don't realize P you autist
>P is false
>w-well! there are other similar things too!
kill yourself
P isn't false you dense autist.
getting a job, and probably working through "calculus: an intuitive and physical approach" and "the colossal book of mathematics" (i know it's popsci but it looks fun). If I have time also Euclid's elements and maybe some of Feynman's lectures.
accidental name from another thread
>vectors below matrices
lel
Haha, yeah, so funny. He's autistic because he is even TALKING about counting. Jesus, it's no fucking wonder east-asians are winning at everything. You realize that it's mostly Americans who think of talking about math as something that is shameful or "autistic"? Europeans (the educated ones) and especially east-asians (urban/coastal/educated) all enjoy talking about math and mathematical problems in their house at work in school because they realize that mathematical literacy is what separates humans from apes, as well as humans from lesser humans. Mathematical literacy gives you an advantage in a majority mathematically illiterate world.
Who do you think runs the world?
Kill yourself P is not false.
Any recommendations on special relativity/general relativity? Preferably with an introduction to the geometry required, or otherwise a differential geometry book too?
This is really misleading and depends on what you mean by 10/10 understanding. I'd say knowing the basic definitions at a rigorous level, knowing about cardinals and ordinals and the standard theorems are enough. To me, 10/10 in set theory means being able to prove everything in, say, Jech's set theory book. You certainly don't need to be able to do research level set theory, care about large cardinal axioms, etc.
Basics of special relativity require almost no advanced math. For General relativity, I'd pick up a book on smooth manifold then look at Barrett O'Neill's book "Semi-Riemannian Geometry." If you want the math perspective. Maybe a physicist can recommend beter books from a physics viewpoint.
"The Geometry of Spacetime" by James Callahan is good if you are coming from a math background
>Stroke's theorem
Tensors, optimization, partial differential equations and chaos theory are all very serious and difficult math.
Complex functions and complex analysis are the same thing.
Poly-dimensional topology is topology.
What the fuck are triple integrals doing at the bottom?
Try studying complex analysis. I started with an aim to finally master contour integration. Not even scratched the surface.
it's a meme you dip
Some of it is alright, some of it it wrong. I was simply pointing out some of the wrong bits.
b
u
bump!
Well the class I took on special relativity and electromagnetism did gloss over tensors a bit at the end but finished a bit too early, so I wanted to take it a bit further.
An unpaid internship is worth more than reading a book. Jesus christ. You're not going to make any money reading some stupid book and gaining no practical experience.
I am a hiring manager for a large manufacturing company. I would MUCH rather see "Internship for Jim and Pam's Frame Shop" than "I read quantum faggotology one summer..."
Get ANY job, seriously.
Any recommendations for a (soon) 3rd year math undergraduate for differential geometry? I heard it's one of the hardest courses at my university so I want to get a head start.
pic related is my curriculum
t. Undergrad
>curriculum
meant to say syllabus
what's the difference?
I think syllabus is what you're required to do, and curriculum is everything you do. Or the opposite, who knows
Bump