books to learn a topic

>>7932577
>10th grade education
>tfw

>>7932577
here's a list for shitty garbage mathematics:

Morris Klein Calculus an intuitive and physical approach -> Spivaks Calculus -> Apostol's Mathematical Analysis -> Conway's Complex Analysis -> Aliprantis and Burkinshaw's Principles of Real Analysis (which is really a measure theory book) -> Kolmogrov and Formin's Introduction to Real Analysis (which is really a functional analysis book and should be pretty piss easy at this point)

congratulations, now you know the ugliest math we've come up with and you can strive to avoid such filth in your research.

>>7932577
For Linear Algebra you only need to know how to write a proof to read Hoffman and Kunze which will teach you all the LA you need for abstract algebra and applied stuff. After taking at least ring and module theory, Roman's Advanced Linear Algebra has everything you'd need to do pretty much anything in, say, Algebra or Combinatorics.

>>7932602
10 books on the same topic? how about this: spivak -> baby rudin -> spivak analysis on manifolds and some munkres. there that was easy

>>7932618
and you don't even know what a lebesgue integral is having done that.

>>7932626
Chapter 11 of Rudin: The Lebesque Theory

>>7932602
Can someone post a reply just like this one but that isn't so fucking convoluted!
I want to know what to read in sequence like OP, but dont tell me its for the ugliest math cause that just messes with me.
Also a list to approach combinatorics, and numerical methods would make me so happy...

>>7932681
What is your current background? You're right to want to study combinatorics. It is truly gorgeous mathematics unlike pig analysis.

If you are new to proofs, get a cheap old edition of Rosen's Discrete Mathematics and work through that. Then work quickly through Roberts & Tessman (or start here if you know proofs already).

That's baby combinatorics. Now you want to continue getting good at this stuff but broadening your horizon's too. Graph Theory is a good next step. Use West's Introduction to Graph Theory and focus on the algorithms.

Then, Van Lint and Wilson's text is next because it will make you good at everything you've learned so far and will also teach you design theory, which is beautiful.

Now you have choices. To work on some of the hardest shit you can reasonably tackle, get Stanley's Enumerative Combinatorics. A warm up to this might be his book on Catalan Numbers, which is really just practice in bijective proof but you learn a lot of neat facts.

For some fun and not too challenging but very ~weird~ stuff read Generatingfunctionology. You will then be a master of recurrence relations. If you like this stuff, it will get hard when you pick up Flajolet & Sedgewick which you will probably want to pair with an algorithms textbook.

Stinson's design theory text could be used now if you liked that part of Van Lint and Wilson.

Or you could brush up on abstract and learn some Algebraic Combinatorics. Sagan's book on the Symmetric Group is a good place to start but it's a reasonably difficult text.

Geometric combinatorics/tropical geometry could also be ventured into here, don't know good texts but you'll wanna be good at algorithms. Optimization too, again no texts.

Also how was that other post convoluted, just read the books in the order indicated.

>>7932709

I loved your reply, any other detailed lists for any topic from you would be a huge asset to some of us. I have screenshoted your reply, and have gotten access to Rosen. Beggining this NOW. You rock anon. any other reading you can suggest is deeply appreciated.
I will follow the book list you gave me. Any interesting applications you've found too?

As an undergraduate physics major, I find math to be an enjoyable subject but is not pushed enough in the curriculum. Suggest me some stuff to learn that is good for any physicist (under grad level please)

You need to buy authentic math scripts. I suggest The Elements as a starting place.

>>7932718
>Any interesting applications you've found too?

Eh, graph theory can be as applied as you want it to be. Analytic combo (generatingfunctionology and F+S) is useful in theoretical CS and algorithm design (you should consider these parts of combinatorics if you wanna git gud)

The best application is getting satisfaction out of solving good problems. I get the most satisfaction from combinatorics which can be a very problem oriented field.

I was slightly kidding in my other post. If you read those analysis books (or even other anons shorter list) you'll know most of the analysis you'd ever need to apply to anything including engineering if you learn diffeqs along the way. I dislike analysis but you should explore it.

>>7932725
Structure and Interpretation of Classical Mechanics

>>7932725

Algebra, Analysis, Differential Geometry, Probability, Topology

>>7932735
When is a physicist gonna design algorithms

>>7932746
Iunno man, but it would be challenging and mathematical while also serving to get you better at classical mechanics. I had fun with the first chapter but I'm no physicist.

>>7932753
Im not the guy you responded to but I think he would probably be better off learning group theory or something

>>7932756

I dunno, even if it's LISP I think programming is more marketable for a physics undergrad than knowing group theory would contribute to his theoretical understanding of physics. Group theory would be a lot more fun though.

There can never be too many book threads on /sci/ desu.

>>7932709
Combinatorics beautiful but analysis is "pig" ugly? Someone needs to read stein. And in response to your suggestions, generatingfunctionology is fantastic.

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>>7932577
I like the For Dummies series or Wikipedia's Simple English option. It's basics that you can build further understanding from.

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>>7932602
> Not appreciating how fun and creative elementary real analysis is
> Thinking that complex analysis is ugly
> Thinking that functional analysis is ugly
I have no words

>>7932735
Any guides for mathematics for scientific programming

>>7933770
Or sequence to get good at high performance computing

>>7933393
But I dont want to look like a dummy in front of girls in the library

>>7933943

Then find a corner away from the girls.

>>7933930
Bumping this

Advanced linear algebra: Lax of Roman?

>>7934513
>or
fix

>>7933402
I'll give you complex. Functional and elementary real though? Horrendous.

>>7933389
>Someone needs to read stein.
If that's such a good analysis book, why isn't it a meme?

>>7934513
never used lax but Roman is a very good text. I'd say it's utility is much more for pure stuff than applied though.

>>7933402
>>7933389

also tbqh senpai I shit all over analysis because despite studying it up to functional I have never found it aesthetically pleasing and therefore try to goad analysts into showing me that I'm wrong.

Any recommendations for micro- and macro- economics and financial maths?

>>7934538
I'm not even an analyst (much more of an algebraist actually) but I thought functional analysis was great. Granted, fractional Sobolev spaces left me snoring but spectral theory and Banach geometry are pretty cool.
For elementary real analysis, I just like to see how much can be proved with so little. I am still very impressed by what you can do with a drawing and a clever use of the mean value theorem.

Anyone know a good progression of books up to algebraic geometry? And maybe one for algebraic topology?

>>7934692
Probably something like that
Shafarevich - Basic Algebraic Geometry
Perrin - Algebraic Geometry, an introduction
Mumford - The Red Book of Varieties and Schemes
Matsumura - Commutative Ring Theory
Hartshorne - Algebraic Geometry
Now, there is a lot of overlap between these books but try to read at least one, that should take you long enough to figure out whether or not you like it.

But a better question might be, why do you want to learn algebraic geometry ? What interests you ? What is your background ? Do you want to learn it because all the cool kids are doing it or are you actually interested in learning about it ?

>>7934709
I meant from a more basic knowledge of abstract algebra, but it seems like a topic that might interest me and eventually do a PhD in, but I would first like to learn if I like it or not

>>7934716
You don't need much to start reading Shafarevich. Basically, if you are familiar with cartesian coordinates, polynomials and know what a ring is, you should be good to go (however the exercises are pretty hard).
If you really know very little algebra, then maybe start with Artin's Algebra and Atiyah's Introduction to Commutative Algebra.
Some basic knowledge of general topology would not hurt, but nothing too fancy (any book will do).
Then some familiarity with differential geometry and complex analysis could be interesting to have an intuitive idea of what is going on (what is a tangent space, a chart, a fiber bundle etc) and have another point of view on the objects (for example why the Riemann sphere [math]\hat\mathbb C[/math] can be seen as an algebraic variety and as a complex manifold and how the two visions relate), maybe read the beginning of Lee's Introduction to Smooth Manifolds and the first few chapters of Donaldson's Riemann Surfaces.

>>7934669
http://4chan-science.wikia.com/wiki/Economics_Textbook_Recommendations

>>7934741
And it goes without saying that you should be very comfortable with linear and multilinear algebra (but in any case it should be the case after you read Artin). It is central in differential geometry and it is a very important part of algebraic geometry (a lot of basic projective geometry is an easy consequence of general theorems in linear algebra).

What's a good introductory book for electronics? I want to work up to digital circuits and FPGAs eventually.

I have a degree in biotechnology, so I have a little background in baby physics and baby calculus if that matters.

>>7932626
are lesbegue integrals advanced math or beginner math

>>7934810
what is a good nook for biotechnology

>>7934877
Neither, it's actually very easy to use and prove things with, just complicated to define.

I would love any of you give me a reading list for all the maths leading up to graphics or maths present in a ssiggraph paper

>>7934884
>lesbegue integrals are complicated to define
Just wait until you get to Ito Integrals...

>>7934882
Honestly, it's a massively diverse field. I don't think I ever read a text book explicitly on "biotechnology". Molecular biology I guess would be the most general field you'll find books on, with lots of books on the specifics of cellular physiology, protein structure and function, genetics, virology, etc... You'd probably need separate organic chemistry books to understand a lot of the protein mechanics.

Can't really recommend any books since I just used the texts that were assigned to me and I don't think any of them were particularly great.

>>7934741
>>7934709
Thanks for the info, after I finish exams I'll look into the books, screenshotted your post

>>7934932
Bump

>>7932577
My diff eq professor said that "Schaum's Outline on Real Variables" is a pretty dope book for real analysis. I'm currently enrolled in real I, and we are using the book "kenneth a ross elementary analysis" and it sucks tbqh family. I've found a pdf of the schaums book, and it seems pretty good. More like a list of definitions, and a shitload of problems though. I think the problems have been pretty good but I've been seeing some weird typos, I'm worried that teh typos will actually confuse me at some point when I'm not following along as well as I normally do.

What's a good discrete math intro book? I found C. L. Liu on library.

>>7935076
Mathematical Conversations by Dynkin

Any good book which goes into depth on astronomy?

>>7935744
did you check the wiki?
http://4chan-science.wikia.com/wiki/Astronomy_Textbook_Recommendations

>>7935894
I have, there's no book about stars.

>>7935904
Fue dur

>>7935904
>Stellar Physics
>Compact Objects
>not about stars

>>7935059
Eh, Schaum and Ross both suck. Neither are good at really helping you understand analysis. For that, I'd check out
1. If the course isn't too sophisticated, something like Abbott's Understanding Analysis

2. If it is a bit of a harder course, tao's books, pughs book, and robert strichart's book are all very good, comprehensive introductions (I'm trying to avoid mentioning Rudin, because I don't think it's best for you right now).

If you don't care about content exactly matching what you learn (the above books all have a kind of "standard" content, except they all have some interesting extra topics), the books by Zorich on analysis are fantastic. They emphasize the Russian style which I am partial to--rigorous yet still linking mathematics with the other sciences, espcially physics.

>>7934877
depends on what you mean by beginner or advanced. All phd students (except some first years) know the definition and can prove statements about lebesgue integration, but it certainly isnt the first rigorous encounter with integration for most.

>>7934787
Benedict Gross used to say "you can never know too much linear algebra," within which I think he also includes multi-linear algebra.

>>7934716
>>7934741
Good recommendations here. I wholeheartedly approve. I would also mention that yes, Shafarevich is fantastic for him to get some basic knowledge in algebraic geometry without too many prerequisites, but that eventually he will want to know all of the topics you listed well. I'd also recommend a text on algebraic curves, like bill fulton's or miranda's book on algebraic curves and riemann surfaces.

>>7934692
So yeah, like the other guy said, Shafarevich is a good intro to a lot of ideas in algebraic geomery (not by any means easy though if you are just starting). Eventually, you will need a very solid foundation in basic algebra (look up any good grad level books and look for ones whose style you like), commutative algebra, as well as geometry (the language of topology, smooth manifolds, etc). As I said above, knowing algebraic curves and riemann surfaces will also be useful. If you are an undergrad, I wouldn't focus on charging ahead in the progression too quickly. It's more important to gain good understanding at each level than to get to an advanced level asap (I learned this the hard way, went back and read a lot of "easier" books over a summer as a PhD student, focusing on understanding, and gained a tremendous amount of intuition and motivation for more advanced stuff).

For algebraic topology, elitists and purists may scoff, but honestly HATCHER is a v. good introduction, for ppl who dont mind his chatty nature. People like JP may or Tom Dieck approach everything from a much more formal, categorical point of view. This may seem cooler and more sophisticated to both young and experienced mathematicians, but the difference is that experienced ones already have the geometric intuition while young students will not. Get some general top. w/ Munkres, dugundgi (sp?), etc, then go to Hatcher

>>7934683
Makes sense that an algebraist would like functional analysis, though. It's allllllmost as much algebra as it is analysis.

>>7934541
There are a lot of bad analysis texts out there. Analysis can seem very boring if you just look at it in terms of "what theorems are there, how is it proven," Eli Stein's undergad texts to a great job at addressing this. To >>7934538
They aren't a meme because they don't follow any traditional curriculum--only the complex analysis one could be used in a "standard course." Book I is almost too easy, and book III is too hard for intro to analysis, too easy for grad level. Yet I still think it's worth going through one of those books over a summer or something if you're in undergrad. His grad books are also beautiful.

But to be honest, I find geometry and algebra more beautiful than pure analysis most of the time. BUT, when seemingly boring but powerful analytic tools an be used to prove something in differential or algebraic geometry, I think it's incredibly beautiful. It always almost feels like cheating, and I want even more to figure out how it works.

However, there is but one area of analysis that I find to be the most unbelievably beautiful thing I can think of -- distribution theory. I think this is an unpopular opinion as most people just see it as a tool for PDE guys to use, and most people find PDEs ugly, but i don't know, everything from the definition of a distribution to deriving all of it's properties, to seeing how powerful they are in PDEs is really mindboggling to me. It honestly makes me giddy just thinking about it.

>>7934513
Both of these books are very nice. Lax definitely has a more analytic flavor, while Roman definitely has a more algebraic flavor.

>>7932681
If you're self studying I strongly recommend not reading books cover to cover in any sort of order right after the other.

1. Find a book/topic that interests you
2. Start writing proofs for theorems
3. Make sure you can justify EVERY step
4. If you get stuck on a proof go to another book/wiki/proofwiki

I take a notebook, pencil, and my kindle preloaded with the textbooks I use and just write proofs while waiting places. I have three books I read concurrently for analysis

Is there a good book on antennae? I have a bit of knowledge of electromag with about three years of dust on it to start from (from a unit based on Griffiths' Introduction to Electrodynamics).

The context is radio astronomy but more general isn't necessarily a bad thing.