/sci-lit/

[Anonymous No.11881259]

What should I read to understand math really well? (Anything past high school. I know calculus but I want a deeper understanding than what they taught at school.) Is pic related as good as people say it is? I really like the cover. (inb4 don't judge a book by it's cover. Sorry, I'm very lookist.)

[Anonymous No.11881261]

Learn analysis before topology, otherwise you'll end up wasting a lot of time like I did.

[Anonymous No.11881281]

>>11881261
<—Is this series good? I don't know what I'm looking for, how much does it matter which author I pick?

[Anonymous No.11881298]

>>11881281
Doesn't matter. They're all the same. Just pick a book and start reading. If you don't like it you can switch the book.

[Anonymous No.11881301]

>>11881261
Yeah.I agree.
One of my uni prof says "set and topology" class is is the root of evil for students being sick of the word "topology".My country's curriculum of math major has a class which teaches naive set theory and point set topology at once.Students only has experience of classes calculus with proof and linear algebra with proof.

[Anonymous No.11881312]

Google evan chen’s infinite napkin and spend some time on it to get a good orientation for what you like, then pick either a rigorous book on calculus (which will include some analysis anyway) or abstract algebra
Calc/intro anal - spivak probably
Algebra - Many choices desu, I’ve used Pinter and Gallian and they are gentle enough
etc etc. You need to learn linear algebra too but idk what book is good

[Anonymous No.11881319]

And dont listen to this guy,
>>11881298
You wont understand 1 thing from that book and its on a specific topic in analysis, not an intro to the subject lmao

[Anonymous No.11881349]

[Anonymous No.11881407]

>>11881312
Thank you for telling me about the infinite napkin thing that's really cool!

Why would I need to read an algebra textbook? Is there stuff I need to know before moving on that I wouldn't already know from high school?

[Anonymous No.11881411]

>>11881281
The Stein and Shakarchi series is excellent, but is very very difficult. I recommend Abbott's Understanding Analysis or Pugh's Real Analysis if you want a good starting point. Pugh is a better book but a bit tougher.
Also, here's the standard meme image which is obligatory for me to post but which you should ignore.
>>11881407
Infinite Napkin is pretty shit and is hopelessly biased toward le epin Category Theory. Evan Chen is a competition math hack. But whatever it's probably fine for a first foray.
Also check out 3blue1brown's youtube series on Linear Algebra.

[Anonymous No.11881417]

>>11881301
thats rough

[Anonymous No.11881421]

>>11881407
To read an algebra textbook, you merely need to be willing to accept some level of abstract thinking. It also would hurt to remember some basic facts about factoring numbers and divisibility, and about polynomials.
My recommendation for someone without experience with proofs and stuff is Fraleigh, A First Course in Abstract Algebra.

[Anonymous No.11881446]

>>11881319
He asked about the series, not that book specifically.

[Anonymous No.11881489]

>>11881446
ok my bad then, either way stein&shakarchi will discourage OP unless he is exceptionally gifted
>>11881411
The book is biased in some ways, I mostly agree with you but I really like the high-level overview it gives on different subjects.
@OP algebra is not the same thing as high school algebra, there is quite a bit more to it but you dont need to learn it right now desu

[Anonymous No.11881531]

>>11881259
if all you know is calculus, don't bother reading this book.

[Anonymous No.11881543]

>>11881411
>>11881281
it's not just that Stein and Shakarchi is difficult, it's not a book suited for a first reading in analysis. like, at all. just compare the first chapter of Abbott and of SS. two different games entirely.

[Anonymous No.11881566]

Intro to Analysis: Principles of Mathematical Analysis by Walter Rudin

Topology: Munkres is good

Algebra: lots of books, Algebra: Chapter Zero starts with category theory which could be useful

Complex: Alfhors book, just called Complex Analysis

Start there, especially "Baby Rudin" as its commonly called. Those books will lead you to other books. MAKE SURE YOU DO THE EXERCISES!

[Anonymous No.11881571]

>>11881566
>Algebra: Chapter Zero starts with category theory which could be useful
for god's sake anon, OP might hear you

[Anonymous No.11882068]

>>11881421
Oh, I thought algebra here was referring to the solve for x type, not the groups and rings type.

[Anonymous No.11882091]

>>11881489
I scored 4th in Québec in a Waterloo math competition in grade 10 if that counts, and got 100% on the senior year physics final exam for the first time in like a decade or something without any studying. (To be fair it was only mechanics and optics.) I should be far ahead of where I am in terms of knowledge but I'm kinda pathetic cause of being able to cruise through school. I'm willing to struggle if I can progress faster because I've decided enough relying on youtube and wikipedia for education (apart from school, speaking of which, cégep has not been that great) I'll be a failure if I do that. What I want to know is will I be able to understand Stein & Shakarchi without having to look anything up to know what they're talking about? I don't care if they're painfully rigorous or something like that, that would be a good thing in fact, I just want to know if that series is technically self contained if I already know basic calculus.

[Anonymous No.11882096]

>>11881543
So should I be reading a bunch of different textbooks on the same topic? Somebody should just make 1 big textbook so that people wouldn't have to go find a bunch of little ones.

[Anonymous No.11882105]

>>11881571
What's the big secret you guys are trying to keep from me?

[Anonymous No.11882173]

oh shit I think he heard you man

[Anonymous No.11882303]

>>11882091
ok if you're smart and serious about this, then just pick a serious *undergrad* book on analysis and go hard, it doesn't matter that much which one and no you don't need to use many it's just useful to see different perspectives on the material, if you just use 1 but understand everything there then you'll be fine 100%.
S&S is graduate level it's not intended as an intro
Also again if you are serious about this you will have to learn linear algebra and abstract algebra at some point as well.
I like the book "Vector calculus, linear algebra and differential forms - a unified approach", if you know calculus but not linear algebra you can check it out, if you do the whole book (not easy) you pretty much learned analysis too

[Anonymous No.11882572]

>>11882173
This seems so cool but I get that I sadly wouldn't be able to understand much without abstract algebra and stuff

>>11882303
Thanks for the recommendation. Will it go into detail on linear algebra? I've had a linear algebra course but it was garbage and probably pruned even further cause of covidnineteen.

[Anonymous No.11882655]

>>11882572
Yeah it very much will, it starts from 0 and quickly builds up to the serious stuff IIRC

[Anonymous No.11882995]

>>11881259
The figure looks like a svastika. I hope this book gets cancelled, i didnt like it for some reason.

[Anonymous No.11883108]

>>11882572
>I've had a linear algebra course
Oh. Alternatively, try Axler's Linear Algebra Done Right. It's a very rigorous and abstract book and all the material in it is absolutely essential to know.
You mentioned you don't care about painful rigor, Stein and Shakarchi will assume you know a lot of background but a book like Rudin Principles of Analysis is much more geared toward that. Rudin is the definition of painful rigor, but it assumes nothing outside of what you know now.

[Anonymous No.11883243]

>>11883108
>It's a very rigorous <...> book
kek

[Anonymous No.11884413]

>>11883243
The fact that no one can agree on anything almost makes me think that textbook preferences are entirely subjective.

[Anonymous No.11884489]

>>11883108
Would this be better? Once school reopens I can read this in the library. I have other books planned I could read beforehand anyways. Also thank you for recommending Rudin, I think I'll get that book you mentioned along with the others if I like it.

[Anonymous No.11884491]

>>11881301
yikes

[El Arcón No.11884497]

Long paper (very short book?) explains a lot of good stuff about math. Starts with Euclid and goes up through high school with an advanced application at the end.

Fractional Distance: The Topology of the Real Number Line with Applications to the Riemann Hypothesis
https://gofile.io/d/gV8m2B also https://vixra.org/abs/1906.0237

ABSTRACT: Recent analysis has uncovered a broad swath of rarely considered real numbers called real numbers in the neighborhood of infinity. Here we extend the catalog of the rudimentary analytical properties of all real numbers by defining a set of fractional distance functions on the real number line and studying their behavior. The main results of are (1) to prove with modest axioms that some real numbers are greater than any natural number, (2) to develop a technique for taking a limit at infinity via the ordinary Cauchy definition reliant on the classical epsilon-delta formalism, and (3) to demonstrate an infinite number of non-trivial zeros of the Riemann zeta function in the neighborhood of infinity. We define numbers in the neighborhood of infinity as Cartesian products of Cauchy equivalence classes of rationals. We axiomatize the arithmetic of such numbers, prove all the operations are well-defined, and then make comparisons to the similar axioms of a complete ordered field. After developing the many underling foundations, we present a basis for a topology.

[Anonymous No.11886426]

[Anonymous No.11887575]

>>11881261
You can learn them in either order. Learning topology first will provide more intuition for analysis at the expense of being unmotivated. Learning analysis first will motivate topology but requires some topology concepts that most analysis texts don't provide enough intuition on to use effectively.

[Anonymous No.11887707]

>>11887575
Yeah but is it actually gonna be advanced topology stuff or just stuff on the level of the reals' completeness?

[Anonymous No.11887769]

>>11887707
generally just open and closed sets and related concepts (interior, closure, boundary, limit points), compactness, completeness, connectedness and continuity in the setting of metric spaces for more general analysis.

[El Arcón No.11887835]

>>11887707
>>11887769
I would say topology is pretty simple and the stuff that might be called advanced topology is really just complicated applications.

[Anonymous No.11888040]

>>11887835
>I would say topology is pretty simple
so you finally understand how two point compactification of the real line works ? :^)

[Anonymous No.11888054]

>>11884413
Compared to say Roman's Advanced Linear Algebra or Lax's Linear Algebra and its Applications, Axler's text isn't "very rigorous and abstract" by any means. These things aren't entirely subjective, the heterogeneity of opinion you see is a mixture of meme'ing, motivated bias, and lack of experience with a wide array of texts that is typical of people that were forced to learn an undergrad topic one way from one text by a typical class.

[Anonymous No.11888075]

What book do I read to entertain myself with quantum physics or space? Preferably closer to the actual facts but with less formulas

[Anonymous No.11888117]

>>11888075
The Elegant Universe by Brian Greene is basically a no math approach to broadly explaining modern physics (relativity, QM, superstring theory). It's basically pop-sci but you did say entertain, and it's an enjoyable read.

[Anonymous No.11888126]

>>11888075
https://www.susanjfowler.com/blog/2016/8/13/so-you-want-to-learn-physics

good stuff for a lot of physics

[El Arcón No.11888417]

>>11888075
pic is not heavy on math but it follows the historical development of modern physics how one idea led to another which led to another, etc, and it has huge emphasis on explaining the important "hallmark" experiments which were crucial along the way

[Anonymous No.11889742]

>>11888126
cool site