god-tier math books you've actually read

[Anonymous No.12666020]

i feel that more often than not in math book threads people post books without never having cracked them open and taken the time to study them in the first place, just parroting shit they've seen elsewhere
as a remedy i propose we post in this thread books that we've actually read, used and studied, and found particularly well-written/useful/enjoyable in the process
i'll start: anything written by this man is gold, but this in particular helped things like field extensions and Galois theory "click" for me

[Anonymous No.12666024]

this one i haven't read in its entirety, still have to work through some chapters, but i've read around ~60% of it and it's one of the best algebra books written. while Stillwell's is good for intuition and understanding what's going on, this presents all the important results in an elegant and effective way

[Anonymous No.12666031]

>>12666024
picrel i've read less of than Vinberg, but as they are very similar in spirit and the bits that i have read were good, i think it deserves a mention

[Anonymous No.12666034]

currently reading this and it's a very clear introduction to general point-set topology, everything is really well-explained and motivated

[Anonymous No.12666067]

>>12666034
good book

[Anonymous No.12666186]

>>12666020
>i feel that more often than not in math book threads people post books without never having cracked them open and taken the time to study them in the first place, just parroting shit they've seen elsewhere
This happens on /g/ too, so I, a person who admits I don't read shit, post pic related.
Requesting exercise solutions kills the book larper.

[Anonymous No.12666838]

>>12666024
Did you do every exercise in that book? It's pretty readable for me, but sadly I lack geometric intuition since I barely touched upon it.

[Anonymous No.12666871]

>>12666838
>Did you do every exercise in that book?
like i said above, i haven't worked through the entier book. of the sections i read i've a fair amount, but they're pretty hard in general

[Anonymous No.12668570]

>>12666020
Do you guys have any recommendations for Linear Algebra? I traditionally struggled through math, and the same was true when I took Linear Algebra at uni, but I found it very interesting and would like to learn more.

[Anonymous No.12668638]

This is still the best book on forcing that anyone has ever written. My course used some shitty notes written by the instructor, if it wasn't for this book I wouldn't have gotten anything out of that class. The exposition is top tier and the exercises have so many good examples.

[Anonymous No.12668649]

>>12668638
>My course u
A graduate course?

[Anonymous No.12668665]

>>12668649
Yeah it was a first year grad course in set theory. We were expected to know basic set theory up to ordinals and cardinals.

[Anonymous No.12669585]

>>12666020
pretty easy to learn from this book, especially if you're a dumbass like me. text is nicely spaced and easy to understand.

[Anonymous No.12669613]

>>12668570
All you will ever need

[Anonymous No.12669756]

>>12668570
if you're not that familiar with the subject and generally struggle with it, don't try >>12669613 this, this goes into modules and umbral calculus, you won't understand shit
start off with Strang (he's the perfect novice text), graduate to Axler or Hoffman&Kunze. after that, if you're still interested, move to Roman and Greub. as a wildcard you could try Klaus Janich. i haven't read it myself, but it's very short and Janich is usually good at explaining stuff intuitively

[Anonymous No.12669834]

It's more of a survey, but it starts from the basics and takes you to very contemporary topics in number theory, it's pretty amazing. The writing is good, it doesn't have a lot of proofs but the important ones are there, and no exercises but lots of great ideas and thoughts.

[Anonymous No.12671213]

>>12669834
are you sure it starts from basics? iirc i took one look at the russian edition and noped the fuck out, shit was hardcore

[Anonymous No.12672202]

>>12671213
Basics as in what is needed to start research in number theory.

[Anonymous No.12672414]

>>12671213
It starts from the basics in number theory anyway. It's a graduate level book definitely, though. So you'll have already taken several algebra courses and such if you pick it up.

[Anonymous No.12673506]

>>12666034
well hello johni

[Anonymous No.12673508]

>>12669613
well hello mr johni

[Anonymous No.12673539]

>>12669613
johni

[Anonymous No.12673561]

All the books on complex anal I see go way too fast and seem to fall short because most people who are talking complex analysis have just come from a course in real analysis. I keep seeing stuff like Stein and Shakarachi or Conway recommended and frankly the fact this doesn't get a mention is criminal.

This on the other hand is perfect it goes through basics very thoroughly.

There are answers to the exercises

It's extremely well motivated and the proofs are very well explained.

[Anonymous No.12675014]

>>12673561
cool book, checking it out as i type

[Anonymous No.12675276]

>>12669613
>Steven Roman
Yo this guy was my linear algebra professor at UCI during undergrad, he was fucking great

[Anonymous No.12675474]

>>12668570
I liked Friedberg in undergrad, official textbook was Hoffman but I couldn't follow it at all.

[Anonymous No.12675476]

Yo what textbooks did russian high schools use?

[Anonymous No.12675490]

Linear Algebra book?

[Anonymous No.12675492]

>>12675476
if you're referring to the meme chart, i just hope you know no Russian school actually teaches that, just fyi

[Anonymous No.12675497]

Non-linear algebra recommendations ? Something hard before starting with matrices if possible

[Anonymous No.12675498]

>>12675492
Duh, what did they actually use?

[Anonymous No.12675607]

Differential Equations textbook, please

[Anonymous No.12675699]

>>12675490

[Anonymous No.12675705]

>>12675497
So graduate algebraic geometry or pleb tier middle school algebra?

[Anonymous No.12675734]

>>12675607

[Anonymous No.12676596]

>>12675607
Arnold's Ordinary Differential Equations.
Evans for PDE I wouldn't say it's 'god tier though' like Arnold.

[Anonymous No.12677630]

>>12675476
Regular ones
https://foatk.ru/documents/book1.pdf
http://school-zaozernoe.ru/files/10-11_kl._geometriya._atanasyan_l.s._i_dr_2013_-255s.pdf

[Anonymous No.12677636]

>>12675492
Post the said chart

[Anonymous No.12677948]

>>12669756
*strang*
t.Amerifat

[Anonymous No.12677969]

>>12666020
Baby Rudin helped me a lot to get an A in Real Analysis last semester.

It's a bit overrated meme.
But it's terse and concise style is quite good for self study compared to other real analysis books.

Tao was the required reading material for the course.

Tao is becoming popular among fellow zoomers.
I prefer good'ol Rudin tho.

[Anonymous No.12677979]

>>12677969
Neither of them give a satisfactory definition of the reals.

[Anonymous No.12677980]

>>12677948
what's your problem with Strang, mate? he's good at what he does: providing a calculation-heavy, theory-light intro to LA for non-mathematicians (engineers and so on, imo not physicists as they'd need more). i'm not saying it should be taught from to and read by actual math students, because it is clearly peanuts compared to more serious texts, but the dude said that he has struggled with math in the past, you can't seriously expect him to read H&K//Shilov or much less Roman/Grueb
i'm not a american btw and nice kitty
>>12677969
i think Tao writes well, although he introduces a lot of unnecessary/extraneous definitions (at least to my taste), shit like "eventually-epsilon" or w/e he called it, and its several variations. also the 2nd volume has barely any multivariable analysis, which is a bummer
imo Rudin's good as a terse set of notes to refresh your memory from, but idk if it's good for first-reading

[Anonymous No.12678016]

>>12677980
Yeah i am sorry. I couldnt advice any non german linear algebra book I've actually gone through. x3
It's ok. I use strang to keep my wrists warm. Havnt read shilov. First second semester course I took used Beutelspacher, Fischer and Waldmann. Which are all standard texts for 1st year linear algebra on german speaking uni afaik. Waldmann was lit.

[Anonymous No.12678028]

>>12678016
where'd you study? i just finished my first semester at FAU (bachelor), although i had studied some CS/self-studied math a little before
just let me preempt your impulse to switch to German, because i don't speak it so well

[Anonymous No.12678148]

>>12676596
Based and Arnoldpilled.

[Anonymous No.12678194]

>>12666186
I actually read the first 2 and they are actually good. I have sicp solutions only my GitHub but obviously won't dox myself.

>>12673561
did you try alphors?

[Anonymous No.12678532]

This is one of my favorites. Bott and Tu's book really helped me with understanding spectral sequences and Serre's theorem on homotopy groups of spheres.

[Anonymous No.12679309]

>>12678532
I got filtered hard by that book.

[Anonymous No.12679838]

Do you know something for developing geometrical intuition?

[Anonymous No.12679862]

>>12679838

[Anonymous No.12680890]

>>12677969
Tao is a pretty good book for a first intro to proofs (maybe even calculus if you can handle it).

>>12677980
Have you finished the book as well? I do agree that his auxiliary definitions can obfuscate the main definitions. But it's kinda cool how you can prove Theorem's using them in many ways.

[Anonymous No.12680995]

>>12679309
it's not an easy book, but it's disguised as one

[Anonymous No.12682712]

Best book to self-study abstract algebra as a high school student?

[Anonymous No.12682736]

[Anonymous No.12682787]

>>12682712

[Anonymous No.12682914]

One of the best intros to QFT and Supersymmetry for mathematicians

[Anonymous No.12682979]

>>12682914
>QFT and Supersymmetry for mathematicians
How much potential does this kind of math have for pure mathematicians?
And how well-developed is it?

[Anonymous No.12682991]

>>12682712
groups and symmetry
https://4chan-science.fandom.com/wiki/Mathematics#Group_Theory_Teaser

[Anonymous No.12683009]

>>12666020
Anyone know the prerequisites for this book?:
>Foundations of the Theory of Probability by Andrej Kolmogorov

[Anonymous No.12683044]

>>12682979

A hell of a lot. Symplectic Geometry/Topology is a pretty hot topic nowadays and Mirror Symmetry, a phenomenon motivated from string theory, is conjectured to provide a kind of dictionary between the worlds of Algebraic Geometry and Symplectic Geometry.

A lot of ideas that come into play here are ostensibly pure mathematics; I'm not an expert yet but as I understand, mirror symmetry has applications to the Geometric Langlands Program.

Hell, one of the formulations of mirror symmetry, conjectured by Kontsevich, is an equivlance of the bounded derived category of coherent sheaves and the wrapped Fukaya category of a Calabi-Yau manifold. If that's not "pure mathy" enough for you then I don't know what is.

[Anonymous No.12683114]

>>12682712
You should be taking it in your first year of uni if you're going into math.

Either way you MUST understand proofs. It's very difficult to self-teach proof-writing skills and you'll need others to read your proofs, it's challenging to self-validate. I recommend pic-related for proofs.

[Anonymous No.12683338]

>>12683114
i genuinely don't understand the concept of a "proofs" class. how the fuck do you do maths without proofs? do Americans really need an extra class to learn what a proof is?

[Anonymous No.12683363]

>>12683338

A lot of introductory classes are mostly "memorize formula and calculate" and are aimed at the rest of stem. Some students have trouble shifting from the calculation courses to proof courses. It's not universal that proof techniques are their own class, a first intro to proofs is usually folded into analysis or abstract algebra course, or students are expected to pick it up as the go along, like set theory or category theory.

[Anonymous No.12683416]

>>12683338
If you're lucky, you might do some basic Euclidean geometry proofs in geometry class in the U.S.
Otherwise most students have never even heard of the concept of "proving" things and get absolutely wrekt by higher level math courses.

[Anonymous No.12683571]

>>12683338
>do Americans really need an extra class to learn what a proof is?
Yes
>how the fuck do you do maths without proofs?
Only derive things algebraically.
>>genuinely don't understand the concept of a "proofs" class.
Introduces AND OR XOR -> <->, inverse is the contrapositive of the converse, weak/strong induction - infinite descent - well-ordering principle, basic naive set theory, set theoretic definition of relations and functions, cardinality, + filler taken from abstract algebra, analysis, linear algebra, number theory, combinatorics, or graph theory.
>i
>>12682712
>as a high school student
You have to be 18+ to post here.

[Anonymous No.12683620]

I am currently reading it.
I want to read Polya and Szego's Problems and Theorems in Analysis but the very first question is on diophantine equations and I haven't yet gotten that deep into number theory.
I am a failure.

[Anonymous No.12683654]

Anyone have a recommendation for a book that teaches Complex Analysis with a view towards Complex Algebraic Geometry?

[Anonymous No.12683661]

>>12666020
I'm reading it

[Anonymous No.12683712]

>>12682787
>>12682991
>>12683114
ty senpais
>>12683571
>You have to be 18+ to post here.
I am. Just looking for a book for a friend.

[Anonymous No.12683824]

Currently on chapter III, feels like there's no Algebraic Geometers on here :(

[Anonymous No.12683826]

>>12683363
>>12683416
>>12683571
>Introduces AND OR XOR -> <->, inverse is the contrapositive of the converse, weak/strong induction - infinite descent - well-ordering principle, basic naive set theory, set theoretic definition of relations and functions, cardinality, + filler taken from abstract algebra, analysis, linear algebra, number theory, combinatorics, or graph theory.
do mutts really spend a semester learning this? we were taught this in the first 1.5-2 weeks of our linalg class

[Anonymous No.12683865]

>>12683826
A good uni would go in depth on the theory of proofs. This can be incredibly helpful for writing proofs. It's also used to teach set theory and basic number theory, used in all abstract mathematics (not taught in U.S. public schools, lol).

[Anonymous No.12683940]

>>12683824

Algebraic Geometer checking in. Working through Chapter 4 of pictured

[Anonymous No.12683970]

>>12683940
Can you explain what a hodge theater is or is that not algebraic geometry

[Anonymous No.12684073]

>>12683970

Haha, no. That is Algebraic Geometry but it is kinda far beyond my current capabilities. I can sort of see what the geometric insight is but I'd be lying if I said I understood it.

To me it seems like theta links between Hodge theaters seem like connections on a principle bundle in that you're trying to determine how a structure deforms as you pass along a line.

Again, complete fucking retard here, so this could be completely fucking wrong.

[Anonymous No.12685065]

>>12683865
That's a shame really. We learn some proof techniques (induction, contradiction) in high school here. To be honest, besides this I don't really remember learning "how" to prove, that was how uni maths was done and I spent my degree just getting better at it.

[Anonymous No.12685077]

>>12683940
Nice one! My supervisor recommended me Huybrecht but I'm gonna try Lipman next.

[Anonymous No.12685146]

I want to learn more about non euclidean geometry, any suggestions?

[Anonymous No.12685490]

>>12683970
nlab doesn't even have adequate articles on Inter-Universal Teichmüller Theory

[Anonymous No.12685495]

>>12685146
Stillwell has several books on geometry and although they include secions on euclidean geometry, there's also a lot of non-euclidean there
check picrel out

[Anonymous No.12685792]

its funny seeing how everyone in these threads is either an algebracuck or a geometranny. where are the analysis chads?

[Anonymous No.12685856]

>>12685792
Busy making it big in quant and not jerking off to algebraic tranny structures.

[Anonymous No.12686258]

>>12685495
Thx anon

[Anonymous No.12686343]

>>12683654
I haven't read it but considering the background of the author and the contents this might be it.