Based books

[Anonymous No.7242412]

Post your favorite textbooks in this thread

Maybe I'm a math noobie but this one stood out to me as exceptionally educational

[Anonymous No.7242414]

>>7242412
Love this book. Clearly written, lots of information, and nice compact size.

[Anonymous No.7242416]

[Anonymous No.7242420]

>>7242414
What things does it cover? An introduction to curvature and elementary differential geometry?

[Anonymous No.7242425]

this is one of my favorites

[Anonymous No.7242442]

>>7242420
1st chapter: Brief review of Analysis

2nd chapter: All about curves and their various properties

3rd chapter: All about surfaces and their various properties

4th chapter: Covariant derivatives, geodesics, Gauss equation and Theorem Egregium, more on surfaces, Gauss-Bonnet Theorem

5th chapter: All about Riemannian manifolds

6th chapter: Tensors, mainly the curvature tensor

7th chapter: Spaces of constant curvature

8th chapter: Einstein Spaces

[Anonymous No.7242459]

I recommend this one to all undergrads

Makes differential forms and manifolds intuitive and all it requires as a prerequisite are the first 5 chapters of Rudin

[Anonymous No.7242465]

>>7242416

>all those nuclear power books

Are you a terrorist, anon?

[Anonymous No.7242476]

>>7242459

>requiring Rudin.

Put it in the trash.

[Anonymous No.7242505]

>>7242476
Not necessarily Rudin, just an introduction to analysis in one dimension. Compactness, Continuity, Darbour sums, all that crap.

Why does everyone hate Rudin now?

[Anonymous No.7242568]

>>7242505
Nobody hates Rudin. >>7242476 is just a troll.

[Anonymous No.7242617]

>>7242568
>different opinion = troll
You're retarded

[Anonymous No.7242634]

Absolutely beautiful

[Anonymous No.7242637]

I'm pretty much a math and science noob, but I have recently found a great interest in personal studies and such so what would you recommend for required reading?

[Anonymous No.7242648]

>>7242637
Apostol

[Anonymous No.7242651]

>>7242634
Not particularly beautiful but just exceptionally solid. No real flaws and just all around an excellent textbook.

[Anonymous No.7242653]

>>7242651
An underappreciated gem, quantum computing as told by the master himself

[Anonymous No.7242655]

>>7242653
Physics poetry

[Anonymous No.7242661]

>>7242655
A friend's personal favorite, and I like it well enough also

[Anonymous No.7242664]

>>7242661
A forgotten classic

[Anonymous No.7242667]

>>7242568

>2015
>Liking Rudin

Who's the real troll?

[Anonymous No.7242684]

>>7242617
I really, really like Rudin (I think the later chapter leave much to be desired. I don't have the book next to me, but I think after chapter 8 or 9?). IMO Rudin and Pugh are the best undergrad analysis texts I've come across. I haven't used many, but I feel like most people would either like one or the other (they have VERY different tones).

>>7242425
This is a fantastic book for a bright undergrad's first exposure. The presentation is a bit unconventional to use for a reference, though. Still useful, though--I still flip through it now and again.

>>7242412
Oh, Lee. I used to LOVE lee so much. As you learn more and get more comfortable with everything in Lee, you begin to feel like he's too wordy (like Hatcher). It's one of those books that's terrific to learn from because of how detailed and thorough it is, but feels really wordy and even a bit disorganized when you go back to it (I think Spivak's Diff Geo volume 1 does a better job at not getting unweildy with the amount that's said, though it's less comprehensive).

As to the topic of the thread, I have a lot of books I really really like and can't decide which is my favorite:
Anything by Milnor
Bott & Tu
Voison's books on hodge theory and complex geometry
JP May's Alg. Top books
Hormander's books on Linear PD operators, also his book on Several Complex Variables.
Folland or Lieb & Loss (Like them more than Papa Rudin)
Kirillov Jr's Book on Lie Groups/Algebras
Every book I've read on Distribution theory--it's just so beautiful (esp. Schwarz's original treatise, in french only).
ANYTHING by Eli Stein
Griffiths-Harris
Petersen or Do Carmo
Demailly's notes on Complex analytic and differential geometry.
Most of Sternberg's books (Free on his website).
Cheeger & Ebin
Yau & Schoen
Salamon & McDuff
anything by Gromov
Everything by Novikov (I love russian style geometry).
Takhtajan - QM for Mathematicians
Arnold's book on Math methods of mechanics

I REALLY love all these books. Can't pick one.

[Anonymous No.7242690]

>>7242634
I was going to include this in gigantic list (see above) list. I really fucking like this book. It's literally how mathematicians think about physics. I have yet to read it all (it's huge!), as it's hard to justify the time commitment since I know most of the stuff in there. I still gotta find time to read it though just because it's so fun.

[Anonymous No.7242860]

[Anonymous No.7242880]

[Anonymous No.7242891]

>>7242412

[Anonymous No.7242916]

>>7242667
He's not a troll, he's just buying into the bullshit /sci/ feeds him.

[Anonymous No.7242924]

>>7242425
so overrated

[Anonymous No.7242936]

>>7242655
>http://www.reddit.com/r/Physics/comments/1dmxq7/our_beloved_landaulifshitz_books_are_available/
Psst, wanna get landau for free?

[Anonymous No.7242951]

>>7242442
Says on the book that you need only linear algebra and multivariable calc to get into, my multivariable calc experience was basically shit stewart stuff, can I still get it good or do I have to review?

[Anonymous No.7243162]

>>7242412
Some anon posted a bunch of awesome diagrams from a book on 4-manifolds recently.

https://archive.moe/sci/thread/7028662

I tried finding a scan of it somewhere but it's gone from everywhere I looked. I checked libgen, avaxhome, torrents, and just general internet.

Anyway, it looks really cool. Though I'm not sure if it's actually worth picking up a physical copy of.

[Anonymous No.7243518]

>>7243162
That book is pretty awesome but gets quite difficult in the later chapters as the number of quoted results (as opposed to results that are actually proved or where at least a summary is given of the proof) increases. Couldn't learn shit about Sieberg Witten invariants from it. But the first few hundred pages were really nice to get a good overview, and also learning obstruction theory, a review of curvature/differential geometry from the "right" viewpoint, etc. I think I need to try Gompf/Stipsicz next.

Don't you have a university library?

[Anonymous No.7243657]

>>7243518
I do, and they do have it in stock so I may drop by there and check it out. I generally check online first since I usually find it faster and more convenient than checking out books. Especially since my university fucked up with their libraries and so most of their books aren't kept in stock there (you have to put an order in a few days ahead of time and they let you know when it arrives to the library from storage). That means that I can't just browse the math book isles and for book browsing and end up having to look stuff up on the internet no matter what.

What is the mathematical background required for the book?

[Anonymous No.7243882]

>>7242951
Yes you should review and also make sure you are familiar with the basis of analysis.

[Anonymous No.7243906]

>>7243162
>>7243162
Hey anon, that was me! Glad you liked the thread. Here's a copy:
https://mega.co.nz/#!8cUglRYJ!6_RvKGs3s3eWtwo6up0bGGSHatbRU1RuYS_8vIiw1Kw
Cheers!

[Anonymous No.7243930]

>>7242651
>shankar

nigga that book is awful, thoguh granted I did use it in class and don't really know of anything better outta apathy.

[Anonymous No.7243936]

This is a fun book.

>>7242634
Best introductory physics book there is, I really hope to see the complete series one day.

[Anonymous No.7243977]

>>7243906
Thanks anon!!

[Anonymous No.7243982]

>>7242634
you have a download link for this?

[Anonymous No.7243984]

>>7243982
There's a .djvu copy on libgen

[Anonymous No.7244308]

>>7242684
BASED
Are you a PDE guy? Mathematical physics here, I have read most of those and agree with your taste. Except Hormander. Fuck that series, Taylor is far better.

[Anonymous No.7244321]

>>7242684
>Cheeger & Ebin

[Anonymous No.7244359]

>>7242634
I hope he keeps writing these.
Any news on volume 2?

[Anonymous No.7244444]

>>7244321
what?

[Anonymous No.7244866]

>>7244444
Ebin. Like the meme? Google Ebin meme and you'll get the idiotic joke the guy is making.

[Anonymous No.7244871]

>>7242648
>>7242637
Here we go...

[Anonymous No.7244893]

>>7242860
Wtf? Principles of Natural Science? What does this even cover?

[Anonymous No.7244914]

This book is my bible.

[Anonymous No.7244919]

>>7244444
fuck nice quints

[Anonymous No.7244928]

>>7244893
I saw it through a thumbnail by hovering over your quote and still didn't fuck it up. Maybe your favorite book should be "How to not be dyslexic".

[Anonymous No.7244948]

I read this last semester it was a good read

[Anonymous No.7244974]

>>7244359
Since it's labeled as Vol I he probably is writing more. But this one took him 6 years and came out in 2010 so it might be a few years before we find anything out.

[Anonymous No.7245034]

>>7244914
Really? I thought it was decent during my first exposure to algebra, but absolutely useless as a reference after that.

[Anonymous No.7245039]

>>7245034
I was never a fan of Gallian. On the other hand I've never found an introductory algebra text I've liked.

[Anonymous No.7245072]

>>7244914
>reading pleb tier shit

why not read the masters such as van der waerden, lang, jacobson, zariski? wtf is this garbage lel

[Anonymous No.7245148]

>>7244914
This is great. Got my groups, rings and fields down with this.

[Anonymous No.7245188]

>>7242476
>Hating on Rudin
Okay I fail to see the problem with Rudin books and yet I see this shit all over /sci/. Is it some dank meme I'm not aware of?

[Anonymous No.7245193]

>>7245188
notice how people who love rudin are always people who know and have reviews of 5 different analysis books and have obviously studied analysis extensively. the cleverness and lack of motivation is just not a good intro for most people, but great as a supplementary book or a book you go back to after you learn analysis from a less clever book

[Anonymous No.7245200]

I don't know why, but this thread makes me really happy. Feels like there's a life full of learning ahead of me. Also, anyone know any good Computational Chemistry books?

[anon !!SY79kyGCAYm No.7245208]

>>7244308
>>7242684

He is the PDE guy. He likes Evans, Gilbarg, Trudinger and Qing Han's Elliptic PDEs.

[Anonymous No.7245213]

Good books on differential topology?

>>7244321
>he's never had a class with the absolutely ebin Professor Ebin

[Anonymous No.7245217]

>>7242684
For Riemannian Geometry

Peter Petersen or Do Carmo?

[Anonymous No.7245225]

[Anonymous No.7246182]

>>7244914
Is this better to start with than Dummit and Foote?

[Anonymous No.7246232]

Best introduction for physical chemistry: Kinetics and Thermodynamics.

Weak on Quantum chem & spectroscopy, though

[Anonymous No.7246349]

>>7242651

[Anonymous No.7246353]

If I ever become rich I will buy this. Until now I'll stick with a pdf.

[Anonymous No.7246375]

>>7242442
As a mathematics major minoring theoretical physics, how good a book would this be for me to understand the curvature of space-time in general relativity? It seems to be a good book to read for the mathematical part itself, but could help with that too.

[Anonymous No.7246404]

this is probably one of the only books on statistics i've ever read that doesn't assume the reader is a statistician but also doesn't treat the reader like a fucking moron.

[Anonymous No.7246410]

[Anonymous No.7246479]

>>7246353
>95th

Not even once.

[Anonymous No.7246483]

[Anonymous No.7246629]

>>7242684

Do you work at stony brook?

[Anonymous No.7246635]

>>7244321

>he hasn't taken a class with the hyperintelligent Ashkenazi beret wizard David Ebin
>he hasn't had a laugh at something ebin with Ebin

[Anonymous No.7246641]

>>7242416
you also post in /sci/? you are oficially a meme

[Anonymous No.7246658]

Anyone have any info on this book?
Is it a good introduction for someone who hasn't had any graph theory before?
I've had intro analysis, algebra, intro linear algebra, group theory, topology, and topology of manifolds.
Is that enough to be able to work through this book? Pic related.

[Anonymous No.7246683]

>>7246658
It's a really good book, but I'm not sure it's the best place to start if you've never studied graph theory before. You could probably handle it, but that book is more about topics in graph theory than a well rounded introduction to the subject.

Douglas West's Introduction to Graph Theory might be better suited for you, but definitely check out Bollobas at some point.

[Anonymous No.7246696]

>>7246683
Very helpful. Thanks

[Anonymous No.7246699]

>>7246182
Depends on how mathematically mature you are. D+F isn't really meant to be read as a textbook, although it can be. It's quite terse at points and there's not always a lot of exposition (although it's top notch when it's there)

Gallian is the other end of the spectrum. Dude holds your hand through every single proof as if it's the first proof based course after "intro to proofs" or discrete math or whatever. He overexplains shit to a fault, and in doing so can't cover most of what you'd be expected to know after doing a year's course in algebra (no modules, almost no vector spaces, shit section on galois theory, sylow theory is a "special topic" at the end, etc).

I'd get gallian from the library and work through it quickly (the exercises are piss easy) and then grab Artin or D+F which will actually be useful books later on.

[Anonymous No.7246705]

>>7246658
>Is it a good introduction for someone who hasn't had any graph theory before?

Yes.

[Anonymous No.7246709]

>>7246683
No problem. If you find yourself wanting for a more broad and more rigorous exposition of graph theory, Reinhard Diestel's book is as good as they come (and free on his website, iirc) but it's quite difficult.

I hope you enjoy studying graph theory! It's one of my favorite branches of mathematics.

[Anonymous No.7246745]

>>7246699
>>7242684

Are you a professor or still in grad school?

[Anonymous No.7246764]

among many other wonderful books

[Anonymous No.7246778]

>>7246699
What I like in Gallian's way to do things is the use of inspiring quotes. I remember when I was having one of those deppressive periods and had both Gallian and Herstein's algebra books. The problems in Herstein's book somehow just seemed to be impossible, I was almost ready to quit and become a neet, until I opened Gallian's book. It was a lot different. And just seeing those quotes gave me some selfconvidence back and then I saw the other problems in a different way.

He's not the best author, but he sure is a man I'd go to if I needed help.

[Anonymous No.7246797]

>>7242412

hey /sci/ wtf is a manifold ?

[Anonymous No.7246884]

>>7246797
Intuitively: A manifold is something that acts like Euclidean space when you look at it up close.

The definition: A manifold is a second countable Hausdorff space locally homeomorphic to the Euclidean space.

Sometimes people throw out the second countability requirement. I do not.

[Anonymous No.7246892]

>>7242924
Completely agree. I don't like it at all.

[Anonymous No.7246895]

>>7246884
What does locally mean in this case?
And what properties of make the space Euclidean?
Just the metric?

[Anonymous No.7246908]

>>7244914
The best undergraduate algebra text.

[Anonymous No.7246910]

>>7246895
Local in toplogy means that for each point you can find a neighborhood with the property.

[Anonymous No.7247276]

>>7246895
The properties that make it Euclidean: 2nd countable, hausdorff, locally homeomorphic.

[Anonymous No.7247361]

Seriously, why am I the first to mention this one?

[Anonymous No.7247918]

>>7247361
Thanks for posting shit that you can find on the internet.

[Anonymous No.7248184]

>>7246895
Pic related.

[Anonymous No.7248186]

anyone have a book on smooth jazzifolds?

[Anonymous No.7248422]

>>7248186
I just googled 'smooth jazzifold'

[Anonymous No.7248904]

>>7248422
same, we've been bamboozled by the notorious hacker known as 4chin

[Anonymous No.7249059]

>>7248184
Can you explain the function f and f composed of the inverse of x?
They map onto R, but how is that a requirement of a manifold?

[Anonymous No.7249061]

>>7246641
>you are oficially a meme
>tfw you finally make it

[Anonymous No.7249144]

>>7249059
too lazy, just read the first chapter on OPs pic related

[Anonymous No.7249148]

Hammack's Book of Proof:
http://www.people.vcu.edu/~rhammack/BookOfProof/BookOfProof.pdf

free, and a very good primer on mathematical reasoning.

[Anonymous No.7249258]

>>7242412

[Anonymous No.7249263]

>>7249258
Downloading.
It better be good or I'll find you.

[Anonymous No.7249270]

>>7249263
link pls, dont habe de monies for the hardcover

[Anonymous No.7249277]

>ctr+f
>Den Hartog
>no results

[Anonymous No.7249290]

>>7249270
I'm on my fourth source.
All I've found so far is a teachers edition solution manual
http://gen.lib.rus.ec/book/index.php?md5=a7a3dd9c399df3a848c4c161b20f056f

[Anonymous No.7249301]

>>7249290
It is a fantastic book, totally worth the price for the hardcover. I've used the e-text for 2 semesters so far. Just too poor right now. But I will have it, I must!

[Anonymous No.7249307]

Does anybody know a good undergraduate introductory text about Lie Groups, Lie Algebras and their applications in QM?

[Anonymous No.7249324]

>>7249307
the selfish gene

[Anonymous No.7249333]

The most readable textbook I have ever encountered is one called Plants Beyond the Margins. It looks at the biology and life history of plants adapted to hostile environmental niches. A good read overall if you're interested in plant or evolutionary biology.

[Anonymous No.7249334]

>>7249301
whelp I've exhausted all my sources.
The book doesn't 't exist

[Anonymous No.7249336]

>>7249333
Also, Brady and Weil's The Nature and Properties of Soils. Fascinating work, lots of sections on applied soil science.

[Anonymous No.7249351]

>>7249334
Dont go for the 2014 edition, its impossible. I'm sure you can find earlier editions

[Anonymous No.7249361]

>>7249307

[Anonymous No.7249382]

>>7249333
>Plants Beyond the Margins
I can't find it on amazon?

[Anonymous No.7249395]

>>7249361
Thanks!

[Anonymous No.7249399]

is it just me, or are all topology books yellow

[Anonymous No.7249407]

>>7249399
All math books are yellow

[Anonymous No.7249434]

[Anonymous No.7249435]

>>7249434
Well meme'd

[Anonymous No.7249439]

>>7249399
Munkres, which is THE topology book, is green.

[Anonymous No.7249440]

>>7249351
I went by author and title like I always do.

[Anonymous No.7249443]

>>7249434
HHAHAHAHAHHAAHHAHAHAHAHAHHAHAHAHAHAHAHAHAHHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHHAHAHAHAHAHAHAHAHAHAHAHAHHAHAHA

[Anonymous No.7249453]

[Anonymous No.7249627]

>>7246884
I still haven't had anyone explain to me what second countability buys you in that definition.

[Anonymous No.7249639]

>>7249439
My Munkres is purple.

[Anonymous No.7249734]

>>7249627
There's something called Wikipedia and WolframAlpha.

[Anonymous No.7249944]

[Anonymous No.7249970]

>>7249434
Clearly I haven't been on /sci/ long enough; I thought it was pic related at first.

[Anonymous No.7250287]

>>7249382
Was giving it it's old title, sorry. Looks like it's been updated for climate change scenarios.
http://www.amazon.co.uk/Plants-Margin-Ecological-Limits-Climate/dp/052162309X

[Anonymous No.7250309]

>>7242412
Kinda off topic because its not really a text book but what do people think of godel escher bach?

[Anonymous No.7250320]

>>7242414
Do you guys have a link to download this book? I do I need to ship it from Amazon?
I'm a poorfag ;_;

[Anonymous No.7250364]

[Anonymous No.7250384]

the Chem E bible

[Anonymous No.7250392]

>>7242412

mmmmm...Smoooth Manifoolds

[Anonymous No.7250455]

>>7249399
Mendelson's third edition is orange.

Kelley is blue.

Dugundji is black.

[Anonymous No.7250463]

>>7246375
Pls respond

[Anonymous No.7250575]

>>7250320
>>7250320
http://libgen.org/search.php?req=k%C3%BChnel+differential&open=0&view=simple&phrase=1&column=def

[Anonymous No.7250582]

>>7250463
After a very quick glance at it it seems to be a nice book imho but there are probably better books for that.
Maybe a good combination would be to learn differential geometry from a math book like spivak, do carmo, lee, etc, use a general relativity book and complement with maybe nakahara or the fist part of baez/muniain gauge fields, knots and gravity but that's because i love the last 2 ones.

[Anonymous No.7250584]

>>7250582
Excellent recommendations. Anon, listen to this guy.

[Anonymous No.7250588]

>>7250582
Also be careful the differences in math vs physics differential geometry, for example the use of covariant/contravariant is reversed

[Anonymous No.7250594]

>>7246375
Yes, a lot of the last chapter focuses on General Relativity topics.

[Anonymous No.7250655]

>>7250582
Thanks for answering. I'll see if I can get my hands on those books.

>>7250588
What I've learnt is that one should always be careful when physicists make mathematical claims. They are often close enough, but sometimes false in some aspects.

[Anonymous No.7250665]

>>7250594
That I deduced from the last chapter's title. Now that I know it's good, I'll probably look for it.

[Anonymous No.7250783]

>>7247361
you mean, the old shit your grandpa used when computers werent available ?

[Anonymous No.7250837]

>>7250575
Thank you so much anon!

[newt !!kYVeUZiCFBb No.7250838]

>>7245188
Rudin has always been a shit book to learn analysis from.
The "dank meme" is recommending rudin as a learning resource at all when all it's good for is a reference.

[Anonymous No.7250855]

What would you guys suggest for an intro to differential geometry? What's the first book someone interested in the field should read?

[Anonymous No.7250858]

>>7250855
>>7242414

[Anonymous No.7251300]

>>7250309
It's paving the way for more popmath books. STEM undergrad sperglords eat that stuff right up.

[Anonymous No.7251442]

>>7244308
I'm primarily in Geometric Analysis, along with some pure PDEs. So I also dabble in some Differential and more Geometric style Algebraic geometry as well. When I was an undergrad, I used to want to be a harmonic analyst, hence you can see I still worship Stein.

I've only very recently become interested in mathematical physics. Eh, I've always liked (Or I guess I should say never minded) the way hormander writes. And those books were groundbreaking when they came out. Taylor is very nice though. But I've always preferred smaller books -.-

>>7245208
I do Like all of these books a lot.

>>7245217
Really hard for me to decide. Do carmo for a first exposure I'd say. But get petersen eventually?

>>7244359
I know he's supposed to be writing volume 2, but I don't know if he still is/has the energy. Like the other guy said, though, Volume I took 6 years. I know he was still writing volume 2 in 2012, and hopefully he hasn't stopped.
>>7246745
I'm a second year postdoc, though I'm pretty old because I took quite long to finish my PhD. It's not like I know everything in all of those books, though. I'm also not the other Gallian guy you quoted. I dislike gallian.

To the other guy who I don't feel like quoting: I don't work at stony brook but I work in nearby state and go their often (they have a ton of conferences now that Jim simons donated a damn research institute. Jim is so based). I would like to get a job there eventually as the strengths of the department are very pertinent to my interests.

>>7249627
THE MOST important reason for requiring second countable, which people don't emphasize enough: If M is a locally Euclidean Hausdorff space, M is second countable if and only if M is paracompact and has countably many connected components (exercise in Lee, if I recall). This is important because it also gives us existence of partitions of unity on M, one of the most important tools for proving basic facts about manifolds.

[Anonymous No.7251447]

>>7245213
Do you want more topology flavored differential topology, or are you looking more for a study of smooth manifolds as a prerequisite for geometric uses?

[Anonymous No.7251660]

>>7251447
The first one, please and thank you.
I'd assume the second kind is covered in books like OP's?

[Anonymous No.7251698]

What would you guys suggest for my first two books in abstract algebra? So far I've looked at Fraleigh and Gallian, neither of those seemed very good. Thoughts on Pinter's book (although it seems sort of elementary)? Thoughts on Artin's book?

[Anonymous No.7251764]

>>7251698

Artin is the Rudin of abstract algebra.

[Anonymous No.7251768]

>>7251698
In undergrad I used Rotman's Group Theory. I liked it a lot.

[Anonymous No.7251776]

>>7251768
It's up there.

[Anonymous No.7251797]

>>7242891
How is this? I'm currently browsing through Awodey and MacLane as time permits

[Anonymous No.7252042]

>>7251764
Really? I didn't think the exposition in Artin in was bad, and all the proofs felt pretty properly motivated without trying to rely on little clever tricks. Granted, I used it in a course with a pretty solid professor

[Anonymous No.7252130]

>>7252042
My class used artin but I never really read it.

I really liked Dummit and Foote when I went through it, but since I already knew a decent amount of algebra from my class I'm not sure how it is as a first book. It certainly seems to go into enough detail for groups though, and has tons of examples - to the point where now I look at it and half seem redundant because they are too obvious with a bit of experience.

[Anonymous No.7253395]

[Anonymous No.7253437]

>>7253395
>>7249434

[Anonymous No.7253463]

>>7249434
>>7253395
any dowload for this

[Anonymous No.7253547]

>>7251442
>To the other guy who I don't feel like quoting: I don't work at stony brook but I work in nearby state and go their often (they have a ton of conferences now that Jim simons donated a damn research institute. Jim is so based). I would like to get a job there eventually as the strengths of the department are very pertinent to my interests.

I'm always impressed that my cheap-as-fuck state school is actually good.

[Anonymous No.7253548]

>>7249439
Mine is purple.

[Anonymous No.7253553]

>>7249944
So fucking elementary

[Anonymous No.7253555]

>>7242667
>too stupid for Rudin detected

[librarian !a3WToVM2jg No.7253752]

Someone on /diy/ had an idea about collecting some essential books on /g/, /diy/, and /sci/.
What do you think about it? Any suggestions?

>>>/diy/811255

[Anonymous No.7253766]

>>7242684
Excellent authors.

[Anonymous No.7253821]

>>7253555
>too stupid for Folland
Well, I won.

[Anonymous No.7253858]

>>7251442
Do you work at a SUNY?

[Anonymous No.7254044]

Hello my friends. My "advanced calculus" course is a clusterfuck and I'm having a VERY hard time finding a book that covers all the things in the course. I need a text that covers: cardinality, zorn's lemma, axiom of choice, metric spaces and rudiments of normed spaces. The official bibliography doesn't have ONE book that covers all the topics.

[Anonymous No.7254094]

>>7254044
Imo it's better to have several books that combined cover your topics well as opposed to a single book that covers all of the topics poorly.

[Anonymous No.7254952]

>>7253752
>Mathematics: pre-calculus, calculus, linear algebra, discrete math
Don't give a shit.

[Anonymous No.7254975]

[Anonymous No.7255004]

>>7253858
I answer that in the post you quoted.

>>7251797
I really like Maclane. Borceux covers similar material, but covers some stuff in more detail than maclane (also includes more details in some of the more basic proofs), and Maclane covers some stuff not in Borceux (volume I, that is). If you're not going to be doing category theory super seriously, I think Maclane will serve you well, as it's nice and concise with good coverage. From what I've heard from others, the Borceux volumes are worth getting if you plan on doing a subject which heavily relies on categorical machinery. Not really my area of expertise, though. As I said, Maclane has been fine for me so far.

>>7251660
The more geometric type books are indeed covered quite well by books like Lee, Spivak (comprehensive intro to differential geometry, volume I), Tu's book, etc. There are quite a loot of books in this vein that I haven't touched on. But honestly, I don't know too many modern books that are more of an introduction to differential topology with the topologist in mind. I mean, there are books like Guillemin and Pollack, but most of that material is covered in the other books I mentioned. There's also milnor's topology from a differentiable viewpoint, which is far from a full course on the subject but is short and beautifully written. I guess I'd recommend either looking through Guillemin and Pollack (the beginning of this I don't think is too well written. It can be hard getting started), or just working through one of the many popular smooth manifolds books (maybe this is the better choice. They're more modern). Then, you will know enough about manifolds to study more in depth in differential topology: http://www.math.cornell.edu/~hatcher/Other/topologybooks.pdf

Also, for more advanced study is Hirsch's Differential topology.

[Anonymous No.7255021]

At points Leithold is super shitty in explaining certain things so I turn to other books/MIT lectures, but his exercises at the end of each section are really good

[Anonymous No.7256335]

This

[Anonymous No.7256384]

Great textbook on number theory that may also serve as an introduction to abstract/pure math in general.

[Anonymous No.7256478]

>>7242684
How much do I need to know before I start working through Cheeger and Ebin's Riemannian Geometry book?

[Anonymous No.7256535]

>>7251442
What a coincidence, I'm a mathematical physicist (not the guy you're replying too though) that wants to learn geometric analysis.

[Anonymous No.7256546]

>>7256335
Elon is shit.

[Anonymous No.7256717]

>>7249970
Paul Zeitz is a problem solving mob boss

[Anonymous No.7256718]

The one that made me a physics major

[Anonymous No.7256828]

>>7256335

[Anonymous No.7257195]

>>7254975
So what's meterology really about?

As a kid I thought it was cool as fuck but all I wanted to do was stand out in the rain and watch tornados

[Anonymous No.7257222]

>>7242416
That Fluid Mechanics textbook is terrible by the way

[Anonymous No.7257941]

>>7256718
I LOVE THIS BOOK!

[Anonymous No.7257943]

[Anonymous No.7257955]

>>7256718
> The one that made me a physics major
>physics major
I'm so sorry.

[Anonymous No.7257962]

>>7246353
Why would you want a non-searchable hard copy? Just use the electronic version through your library portal.

[Anonymous No.7257974]

>>7249258
I can't imagine him writing a quality text on fluid mech. His statics and SoM somehow manages to be so simplistic, long and convoluted, incoherent and incomplete all at the same time. I hate it. His books are better for doing tons crappy practice problems than understanding anything or having a concise explanation/derivation of the material.