Differential Geometry

No one cares about that autistic shit.

Hilbert wasn't a physicist.

Who is that supposed to be? Newton?

no shit, that's why modern math sucks so much fucking dick and is ridden with redundant pseudo-intellectual jargoneering. physicishits are so fucking shallow and retarded they think they are reinventing math. stick to pre-19th century number theory and statistics if you want "real" math.

Know topology first, say Munkres. And basic linear algebra and calculus.

Lee's books on Topological Manifolds and Differential Manifolds are good. There's an incomplete manuscript by Robbin and Salamon I found online which is very similar to Lee, but I found slightly more clear for the tensor algebra/cohomology part. There's also a Dover book "Tensor Analysis on Manifolds". Both of these could be used concurrently with Lee for the algebra part. After those, find any handout on De Rham cohomology online, and then pick up a book on Riemannian Manifolds (say the springer one).

looks like that preprint got more developed; might be worth seeing if you can learn from it entirely, as the part I read was very clear.

if you want a self-contained and very precise, but dry treatment, get Lee's trilogy
if you're in for a fun ride, get Spivak's Comprehensive Introduction to Differential Geometry

interesting take; I actually found Lee to be pretty conversational in style. Even moreso than how people talk about Hatcher. He does a good job at telling you what things are like in practice vs general theory, and qualitatively why such and such constraints are imposed.

I'm recommending "Semi-Riemannian Geometry With Applications to Relativity" by Barret O'Neill for diffgeo. It's for some reason not well known, but it's a great textbook.

Choosing my first "final year" math subject for my math major.

Can Topology be applied for jobs?

If I dont like trig will i not like topology?

please be bait holy shit

No, I don't like trig, so I'm asking if there is trig in topology?

Watch this lecture series by physicist Frederic Schuller
youtube.com/watch?v=V49i_LM8B0E&list=PLPH7f_7ZlzxTi6kS4vCmv4ZKm9u8g5yic

I also recommend Sidney Coleman's book "Aspects of Symmetry"
amazon.com/Aspects-Symmetry-Selected-Erice-Lectures/dp/0521318270

Nakahara's book is a great text for grad students in theoretical physics, by the way.

There's also a book by Jose and Saletan which uses basic differetial geometry to study classical dynamics and Hamiltonian systems. Much better than the standard mechanics book.

oh and if you're interested in field theory,
"Anomalies in Quantum Field Theory" by Bertlmann is pretty good. I'm reading it now.

And if you're wanting to learn some group theory as well (which you absolutely should), then these are the books that my professor recommended:

*********************************
1. Group Theory in Physics, by Wu-Ki Tung
2. Groups Representations and Physics, by H.F. Jones
3. Lie Algebras in Particle Physics, 2nd edition, by Howard Georgi.
4. Quantum Theory, Groups and Representations: An Introduction, by Peter Woit (final draft version)
5. Semi-Simple Lie Algebras and Their Representations, by Robert N. Cahn.
6. Group Theory: Birdtracks, Lie's, and Exceptional Groups, by Predrag Cvitanović.
7. Lie Groups, Lie Algebras, and Representations, by Brian C. Hall.
8. A Course on Algebra, by Ahmet Feyzioglu.
9. Classical and quantum mechanics via Lie algebras, by Arnold Neumaier and Dennis Westra
10. Geometric Mechanics, Part I and Part II, by Darryl D. Holm.
11. Lie Theory and Special Functions, by Willard Miller Jr.

******************

Shamelessly stolen from his website. All of these can be found online, with a little effort.

When I was a teen, I used to wonder how people on forums could tell I was teen even when I tried not to sound like one. Years later I learned that trying not to sound like one is the easiest way to out yourself.

Finish up and do well in precalc before you even think about topology, champ. You want to be able to take calc 1 as a freshman next year.

I've done calc 2 and 3 with High distinctions.

I understand why you think I am a highschooler because I said I don't like trig. Sounds retarded but I actually just don't like trig identities.

The fact you ask this question shows you are not ready to study topology.

The real question is if you have already taken Analysis. I assume you have not, since you would not be asking said question. How can you be a math major without haven taken analysis? Your school is failing you user. Ask for your money back.

I'm taking analysis the semester after I take topology.

The reason is that I meet the pre requisite classes for topology but not for analysis yet.

:(

Topology will feel completely unmotivated unless you take analysis first.

The go to first examples for topology are metric topologies. And the go to example for that is the standard topology of R^n.

An analysis class will spend a good bit of time going through the topology of R^n, or at least the topology of R.

Thanks for the advice.

It's been a while since I've done analysis, but in elementary analysis, trig functions definitely appear as examples, however I'm pretty sure there's not much identity juggling so you should be safe.

In topology, the only example that comes to mind is the topologist's sine curve, but again you don't need trig identities at all.

Okay dope,

Thanks.

I don't remember a single trig identity from calc 1 other than the sin^2 + cos^2

>I don't remember a single trig identity from calc 1 other than the sin^2 + cos^2
then you're a shit mathematician

I like Boas.

>Sussman

Def recommend this book, it's free floating around too off his personal website i believe.

You write Differential Eq into scheme functions. This book and SICM, are both inspired by Spivak's tiny Calculus on Manifold's book where he lamented the state of ambiguous math notation so they decided to use scheme notation instead.

Who cares about double angle formula