hi

Hey

wow

that is crazy. I mean you must learned a lot if you could follow that pace.

As you can see, it was a bit tall to post int he main chat

Yeah, I'd say I learned a pretty good deal

very nice.

I came in sorta knowing a bit of what was going on, since I worked through some of Rudin. So the stuff on topology, continuity, etc

yeah.

But yeah, we mixed between Rudin and Sally to start, and then from day 23 on, we used Buck

nice. Very impressive guy.

In the meantime, we had been self-studying linear algebra, since our prof kinda wanted to do all of this, and doing linear algebra in class (which he didn't like teaching) would take up too much time

Second quarter professor is going to pick up from where Soug left off

Gonna start with differential forms and Stokes's theorem

Then, it's hard to say

Last year, he "reviewed" topics from 207

By talking about some stuff from linear algebra that they didn't know yet

I see.

Then did forms, proved FTA, did some homotopy, and then moved on to ODEs

Yeah your university is impressive.

I am pretty sure you will learn a lot in it.

Haha, yeah, this class is pretty good

Thanks!

And hopefully

But yeah, after ODEs, Schlag started functional analysis

Third quarter was measure theory, L^p spaces, a bit more functional, and a tiny amount of Fourier

Like, one day the prof just came in randomly and talked about the Fourier trasnform, convolution, Plancherel's theorem and all

Then they did Sturm-Liouville to finish things off

It is only one class that's like this though

cool.

But yeah, if I get an A in this class second and third quarter I'll hopefully be able to do grad analysis next year, along with algebra, and then grad algebra fourth year

Also gonna work in topology, possibly our intro to manifolds class as well

what do you take in grad algebra ?

Grad algebra is first quarter representation theory, second quarter is commutative algebra and algebraic geometry, third quarter is "Topics in Algebra"

I mean what is the outline for grad algebra and grad analysis ?

cool.

Ah

very nice stuff for grad algebra.

As for analysis

Grad analysis is first quarter measure theory, integration, L^p, differentiation, basic functional, and further topics

The guy used a book by Richard Bass, Real Analysis for Graduate Students, did chapters 1-19

Second quarter is functional analysis, I know when the professor I just had teaches that class he tends to use Brezis

The outline says weak convergence, compact operators, spectral theory, Sobolev spaces, and "some applications"

Third quarter is complex analysis

Basic complex analysis, Cauchy theorem in the homological formulation, residues, meromorphic functions, Mittag-Leffler theorem, Gamma and Zeta functions, analytic continuation, mondromy theorem, the concept of a Riemann surface, meromorphic differentials, divisors, Riemann-Roch theorem, compact Riemann surfaces, uniformization theorem, Green functions, hyperbolic surfaces, covering spaces, quotients.

So it's a good sequence, I'd say

The grad topology/geometry (which I'll take if I can, but I might not be able to) does algebraic topology, then differential topology, then differential geometry

So I'm pretty excited

If I have space, I'm crossing my fingers to do grad model theory

nice.

very exciting stuff.

If not, audit. Either way, if I can't do it, then that means I don't have space, so I'm doing other stuff :)

I see.

Well, what are your plans?

I am planning to go into algebraic geometry. Next semester I am taking quadratic forms, algebraic topology, and rings and modules grad courses.

Nice

However, I am working through allufi at the moment I would like to finish it completely by June 2017. My supervisor told me my master thesis will be something related to algebraic geometry, but we will extend it to something that need algebraic geometry in my PHD.

Hopefully by september 2017 I will have nice ground to start studying algebraic geometry. Hopefully Allufi chapter 0 will provide me with enough basic ground.

It seems like a pretty well-written book

@Daminark I am planning this year by july 2017 to finish Allufi chapter 0, Ted's book, John lee topological manifolds,john lee smooth manifold, abbot, and some book in functional analysis.

Nice

So what we're using second quarter is Kolmogorov and Fomin, Introductory Real Analysis

Yeah @Daminark Allufi is very well written and problem set are nice.

Which has also been titled "Elements of the theory of functions and functional analysis"

Wow, ambitious list

Good luck!

thanks :)

How far have you gotten up to now?

I have finished abbot and I have finished first 3 chapters of john lee smooth manifolds. Finished first two chapters of Ted's. I finished first two chapters of allufi.

I still have many work to do though.

I am planning to take my second functional analysis class in winter 2018. I am pretty excited for it.

Functional is fun, many of us are looking forward to it

How is Lee?

Lee is super good.

I would suggest going through John lee topological manifold first though. That is what I will do before John lee smooth manifolds.

Probably makes sense, will do

I think the immediate priority will be algebra, though

I anticipate that I'll probably end up being an algebraist

So now I'm gonna read either Aluffi or something similar

I really liked Herstein but it doesn't include Jordan-Holder, which Laci explicitly said we should look at

Before starting his algorithms class

So that's when I started roaming around (Dummit and Foote takes f o r e v e r)

Yeah. @Daminark I will put very hard emphasis on geometry and algebra. I want to understand them on a very deep level.

I want to improve my analysis skills to be able to delve into geometry very deeply.

Yeah, analysis is a subject I've been gaining more appreciation for

I'm reviewing some analysis and linear algebra now

I think on the whole I have a better grasp on stuff like multivariable calculus than I did before

My university that I did my undergrad in didn't have good analysis profs, so I am working on my analysis on myself.

Ah, I see

My hope is that this summer I'll be able to do the analysis bootcamp

analysis bootcamp ?

The professor in second quarter hosts a bootcamp which is analysis-themed

Started it last year

It's for good students in honors analysis

Last year they did Titchmarsh Theory of Functions, Sinai Probability, Shifrin Differential Geometry, and a 4th book I forget.

very nice.

And apparently, if you do honors analysis and the bootcamp, they'll let you right in to grad analysis

pretty cool university.

Along with possibly some CS, maybe topology and/or manifolds

cool.

I wonder what book the guy teaching manifolds this year is gonna do

They tend to bounce around a lot, I believe last year they used Lee

But they used Guilleman and Pollack before

Barden and Thomas as well

Guilleman and pollack I think isn't very detailed.

Huh

I like john lee more. It has more pictures they cover more things.

I'll keep that in mind for sure

Alright, I'm back, so thanks for the book suggestions, good luck on your journey, and see you back in the main chat!

thanks cya.

good luck to you as well @Daminark.

I gtg my sleep schedule.

nights