book-recommendations

[pliant wadi]

Boy that's a hard question at this stage to make precise. Ig most of my background is in algebra and algebraic topology; done analysis upto functional analysis and a tid bit of ergodic theory and microlocal analysis.

Would be nice to have some stuff in model theory too

I am mostly looking for problems in analysis upto functional analysis and anything in algebra would be appreciated tbh

I'd try this, thanks

[lusty thistle]

check dms also

[pliant wadi]

Oh hey, thanks!

Heyy guyss thanks a lot!

This was really helpful

[mellow wren]

UCSD hosts all it's prior quals online

https://www.math.ucsd.edu/students/graduate/academics/qualifying-exams

there's a lot of them

[stiff crow]

bro WTH 😭

[raw jolt]

any good books for caluclus of variations and euler lagrange?

[remote sparrow]

gelfand/fomin and van brunt

[slate pilot]

Lol, I read that at first as Deportation of Math

[remote sparrow]

do they need to have solutions

[raw jolt]

which ones better?

[remote sparrow]

uw-madison has some qual problems in model theory (and they used to require set theory)

[remote sparrow]

gelfand/fomin is really cheap, van brunt may be more modern

[raw jolt]

which ones better for this stuff:

Existence and uniqueness theorem

Euler-Lagrange theorem

Lagrange multipliers

Conservation of energy and Hamiltonian formalism

Noether theorem

Kepler problem

Geodesic lines

Poincare recurrence theorem

[remote sparrow]

van brunt covers most of it

[sullen forum]

Does anyone has books (or any resources) on Differential Forms described in a similar way as in "Geometrical Vector" by Gabriel Weinreich and " Div Grad and Curl are Dead" and "Applied Differential Geometry" by William L. Burke? They present them as "density of papers" that vectors pierce.

[marble solar]

I'd avoid learning specific style of Qual Problem Sets for a few reasons: You're unlikely to attend that specific school; even at the same school different professors assign different problems, or emphasize different viewpoints.

If you want to learn "Qual" level problems, just pick a standard grad book and do as many problems as you can

e.g. if you're interested in analysis, Rudin's Real & Complex is a go to standard

[dapper root]

Mine doesn’t

Okay we do have a qualifying exam, but it’s oral, we don’t have exams like this

[cunning elk]

looking at phd quals really hammers home how absolutely dogshit my undergrad has been in terms of actually covering substantial content

[pliant wadi]

Nah it's okay, I can find/ask solutions from around me for the most part. That's the benefit of being an active student at a university!

[pliant wadi]

Oh that's a good point. I am not preparing for quals for the most part right now. I am just really looking for a question bank sort of thing which mixes up topics---won't point to what is used in the solution so that'd make it a bit harder ig? Idk thought that'd be nice. Grad books I can pick up yea true. Maybe I'd compile the ones we used for courses.

[manic cairn]

harvard has their archive, paul garrett has his archive for university of minnesota

but a fuller answer to this is given in a math stack exchange answer

[heavy egret]

what r some books for newly transferred high schoolers

[rigid trail]

william shakespeare has some good reads

okay whats the topic 💀

[dim pendant]

"Love and Math" by Edward Frenkel

[manic cairn]

https://math.stackexchange.com/a/270467

[molten gulch]

wish we could have this pinned

[fresh skiff]

usually how much background is needed to attempt these exams? (or atleast try to solve these problems) --- i have heard some poeple direct go for PhD from UG so i wonder how much background is needed

[shy bronze]

wott???

directly PHD from UG?

[fresh skiff]

yes, they choose elective subjects wisely i guess

[shy bronze]

but how

well im still UG, but how tf do they get all that background

like dont u need to do Bachelors and Masters

[fresh skiff]

wdym Undergraduate (UG) = Bechelors

i mean some people dont do masters

[dim pendant]

You know you're cooked when your brain replaces "David Gilmour" with "David Hilbert"

[tender river]

https://jonathanlove.info/qual/

[pliant wadi]

That's because the PhDs are longer and often the master's coursework is included

In comparison to Europe

[tender river]

https://www.amazon.com/Solutions-Mathematics-Universities-Qualifying-Questions/dp/9814304956

[slate pilot]

What are some comic books for math? Non-textbook maths, ideally with pictures

[tender river]

https://www.maths.cam.ac.uk/postgrad/part-iii/current/examinations-and-essays#Past exam papers

[pastel sparrow]

Best book for linear algebra

Basic to advanced with clear explanation

[pliant wadi]

Certainly. Now, there are also separate master's programmes but afaik they are just money grabs, even in a lot of places in Europe or Asia. PhD programs in the US are for the most part, extremely competitive.

(Especially if you are hoping to get decent funding and a decent work environment)

[vital bane]

In the US most PhD programs are basically like Masters + PhD

so the first 2 years is usually just coursework

like a master's degree

[fierce river]

https://tenor.com/b02Wi.gif

[remote sparrow]

https://tenor.com/view/epic-embed-fail-ryan-gosling-cereal-embed-failure-laugh-at-this-user-gif-20627924

[old elk]

nice, nice

I went crazy reading all these problems, from the different links, it's really frustrating not being able to understand hahahaha.

[vital bane]

Real and Complex Analysis by Walter Rudin (drawing pictures is left as an exercise to the reader)

[cunning elk]

my school so bad it ain’t even on here 💀

[fresh skiff]

FIS by beloved

People usually prefer Lays book for 1st course in LA. But i think starting with FIS isn't a bad idea. I used FIS as my first LA book (i haven't read Lay)

[pastel sparrow]

Thanks

[heady ember]

FIS my snoozefest

[last cipher]

Just started reading abbott's analysis

and I LOOVE it

and very fun

[vital bane]

HELL YEAH BROTHER 🗣️🔥🔥🔥🔥

It's AWESOME

Such a wonderfully written book

it's my favorite textbook of all time 🔥

[last cipher]

someone suggested me rudin and i was very close to buying it instead🌚

[vital bane]

Abbott + Rudin combo is great!

Rudin by itself is not very useful

[last cipher]

Oh yeah fs. Since im a beginner im taking the more gentle approach

[vital bane]

it's quite literally peak analysis exposition

[last cipher]

Interesting that rudin gets straight into dedekind cuts while abbott leaves it for the end

[vital bane]

well it's not about gentleness, it's just that Rudin doesn't teach you anything there's just barely any exposition

[last cipher]

Oh yeah I guess

[last cipher]

yes very beautiful

The explanations are great and theres none of this https://en.m.wikipedia.org/wiki/Abstract_nonsense

🤧🤧

[vital bane]

yes

and the exercises are awesome

especially the project sections at the end of every chapter, it's so fun

[last cipher]

I only read some parts of my discrete math book for proofs and the preliminaries really helped me with filling in the gaps especially as a self study guy

[vital bane]

and I cannot wait the get to the project chapter at the end of the book, chapter 8, it's just full of fun things that you get to do by yourself like Generalized Riemann Integral, Fourier Series, Gamma Function on R, and more!

[vital bane]

yea it's super helpful for beginners 🔥

[last cipher]

I have the first edition 😔🙏

Due to cost

But ill probably look at the newer exercises in a pdf

might actually look at the projects i cant lie

[fresh skiff]

i can smell cat theory (abstract nonsense)

[shy bronze]

i mean masters

[dim pendant]

I definitely need to forget that this channel exists

I've got a server full of nerds to do this work and I repeat myself on end when I could just be doing math

I shipping

Nah you but so I okay

[heavy egret]

thanks

[coarse rapids]

anyone have a good real analysis book recommendation for after i finish abbots understanding analysis

[vital bane]

Folland and/or Cohn

[pastel sparrow]

Whats FIS full form

[cunning elk]

friedberg/insel/spence

textbook industrial complex

😔

[vital bane]

Publisher industrial complex

[heady ember]

It does teach you ||to think for yourself||

[naive lava]

It also gives you substance abuse problems

[heady ember]

If the substance is math, then why not.

[vital bane]

No?

it doesn't teach you to think at all

[heady ember]

Skill issue

[vital bane]

Whereas Abbott teaches you to think for yourself

[fresh skiff]

Rudin teaches you to not think about maths ||joke its nice one||

[vale solar]

great book

[fresh skiff]

I wish i could read this book in this summer

[vale solar]

you can!

[fresh skiff]

I have some other plans, like revising analysis and Linear algebra then studying abstract algebra And cox book on ideal verities and algorithms

[naive lava]

If you want general info about topology, you can try janich as a quick read

you can finish it in a good day or two

[fresh skiff]

What

Lemme check the book, you made me curious lol

[golden salmon]

seconding this, even if you just read ch2 I think it's pretty solid still

[balmy folio]

Guys can someone send pdf of elementary linear circuit analysis by Leonard S , it will greatly help me 🙏

[dim pendant]

"There he is, Mr. President."

[dim pendant]

Stein-Shakarchi "Complex Analysis"

then you can be done with analysis and live your happy mathematics life 🙏

of course after a little manifold and measure theory later down the line

[naive lava]

you want ug analysis

or measure

or functional

or complex

or spectral

[dim pendant]

what da hail is spectral analysis

[gray gazelle]

De fourier'

[gray gazelle]

Why not Conway complex

[dim pendant]

Conway is fine

A more proper self-study might even use both to great benefit

[marsh moth]

chat have yall read change is the only constant

[remote sparrow]

#book-recommendations message

[lethal ibex]

....and justice for all

and justice for all.

[vague spruce]

Any books with nice "applied real analysis" problems lol

Along the lines of like, "proof f(x,y,) = ... is continuous using eps delta", not "proof differentiability implies continuity

[rigid trail]

Applied real analysis? Like..calculus?

Oh still proofs

[vague spruce]

I guess, but with eps/delta/anylytical techniques instead of "can you do the chain rule again here for the 500th time"

[rigid trail]

eps delta isnt very applied so I'm not sure what you mean

[dim pendant]

Epsilon-delta is what you use to understand the nature of stuff you're doing in calculus

if you want to apply it you literally do just memorize the formulas

to get intuition you work a bunch of word problems until it all fits together in your head

[marble solar]

I suppose stewart or thomas' calculus books in the multivariate section have some applied problems like this. E.g. prove that $f(x,y) = \sqrt{x^2 + y^2}$ is continuous

[hasty eagle]

MoonBears-C-

[marble solar]

But if you're looking for an emphasis on understanding epsilon-delta without getting into more abstract proofs, then I'm not sure there is anything really to look for. Even the mildest books, like Spivak's Calculus or Apostol's Calculus, have lots of more theoretical results than what you're looking for in this matter

[steel stag]

why was the proof in principa mathematica of 1+1=2 so long?

[dim pendant]

It was an attempt to prove such from first principles

In mathematics and science you have to start somewhere, with some basic assumptions

we've tried our best to make those basic assumptions as simple and correct and reasonable as possible

and it's such a far setback that if you start all the way from those basic assumptons, getting to modern math takes ages

this is a naive answer, but it gets the spirit right

anyone more knowledgeable is welcome to contribute

[rough umbra]

Ppl hear it's toward the back of the book and assume everything up till that point was to prove 1+1=2, it's like saying zebra is super hard to define bc it's at the back of the dictionary

[steel stag]

I assumed it required at least some of the book to prove

although I think you can derive Peano arithmetic from ZFC in like 2 pages now

[rough umbra]

This is the proof using some prior propositions yeah

but they prove a ton of things in the book, this is one of them

[dim pendant]

I, too, hate trees.

[sharp relic]

what

[gloomy spire]

what are some good alternatives to hatcher to learn singular homology and then some cohomology

[orchid otter]

Does anyone have any good recommendations on real analysis for beginners?

[vital bane]

Understanding Analysis by Stephen Abbott

[rough umbra]

#book-recommendations message

[dim pendant]

Oh my god I totally forgot about Dieck's book

It's been years since I've even seen it wow

[orchid otter]

Do you know if elementary analysis: the theory of calculus by Kenneth A Ross is good for beginners? I’m not amazing at proofs and already have the book.

[tribal crow]

@sharp relic welcome to the mathcord

[dim pendant]

Only you can know. Open it up and get going.

[rigid trail]

it's okay

i used the book for my analysis course alongside rudin

i feel like the first half is good but the second half is eh

it's worth looking at rudin too

definitely

[dim pendant]

Is that one of those books that does analysis on the line and then in Euclidean space

[rigid trail]

uh not sure what you mean

i dont remember that if it did that

[slender cargo]

At a glance, seems like it was made to be a gentle intro to analysis and proofs

[rigid trail]

it's more rigorous than abbott def

not rudin level though for sure

[dim pendant]

Is Abbott not terribly rigorous?

[rigid trail]

abbott is easier than ross

[dim pendant]

I thought it was basically Rudin but without the magical element to the proofs

[rigid trail]

nah abbott is a lot gentler

[gloomy spire]

Ross was the book i used for my first proof-based class, i thought it was a pretty good introduction

[rigid trail]

idk if i would recommend ross tbh

as much as rudin hurt me, i think it's smth everyone should go through 🗿

[slender cargo]

uh... idk about that

[dim pendant]

Maybe after a first pass..

[rigid trail]

it's part of the initiation process

[dim pendant]

As far as I'm concerned Rudin is a great book if you just don't read his proofs

Try them yourself and use another book to check yourself 🔥 🔥

[rigid trail]

yeah it better to conveniently ignore some of them

some proofs are just crank material fr

[slender cargo]

Rudin is good if you don't use Rudin to learn. Nice!

[dim pendant]

Yeah that's pretty much the idea

He's concise, orders most of his content nicely

But his proofs are magical for folks new to analysis

[rigid trail]

learning from one source is pretty much never optimal c:

i used ross+rudin

[slender cargo]

He does have some really slick proofs, which I like to check out sometimes

[rigid trail]

it worked well enough

prof also had some of his own proofs he used in lecture

[dim pendant]

I just remember having such a nice time following other books but I also hadn't done any analysis prior at that time

But I don't like first courses in real and complex analysis to the point where they make me want to write my own

Which I may or may not be in the process of doing...

[rigid trail]

lowkey im tempted too

writing math notes/material is so fun

[dim pendant]

Personally my passion is teaching

Math is secondary

So they fit together well

I like to assemble at most three texts on a topic

[slender cargo]

I just follow whatever the professor assigns, but I'll look at other books if the book I'm reading is confusing on a certain topic

[dim pendant]

Correct

Unless they're supremely curious

[rigid trail]

idk depends on the topic, for linalg im only gonna ever refer to LADR. for logic i have dozens of pdfs

[dim pendant]

I like to just collect books for all of my interests so I have a huge pool to choose from especially according to different levels of sophistication (1st sem of abstract alg vs 1st year of grad alg)

[rigid trail]

i also have so many pdfs on multivariable calculus from when i did that

👀

[dim pendant]

You should have a core book that you worship and stick to, and a supporting book or two or set of notes to fall back on when you hit a barrier

[rigid trail]

ofc

cmon rudin should at least be a supplement

it has such good stuff

[dim pendant]

Err.. I'll check out my collection to see what I'd do

[normal crystal]

[dim pendant]

Wtf

[fresh skiff]

Study Algebra

[dim pendant]

I just found out that Lang's "Undergraduate Analysis" does most of the basic topics in a first course in under 170 pages

[fresh skiff]

insising finally i decided to do Linear Algebra

[dim pendant]

No doubt I'd be only using that book and just coming to this server when I had an issue

[dim pendant]

(try to) have fun

[rigid trail]

https://tenor.com/view/luigis-mansion-sleep-gif-23758548

[dim pendant]

Probably but it's so dense that you'd hate yourself

[rigid trail]

the most awake person reading lang

[fresh skiff]

its fun until and unless infinite basis pop in

[dim pendant]

Anyway if Lang didn't exist I'd use uhhhh

[normal crystal]

Languigi

[dim pendant]

Main: A ProblemText in Advanced Calculus by Erdman
Support: Abbott & Tao

But the correct answer here is to use Tao as your main text and for support use this server and use Abbott

Excruciating detail

It's so much detail that I hate the book

When you hate the book because it's slow, you know you're doing ir rignt

[cunning elk]

what kind of induction

[dim pendant]

You should have the general idea of how a proof works

Then you fill in the details if you need to

But do not try to memorize proofs unless you need to for an exam

[cunning elk]

if it's just symbol pushing like they put in some precalculus textbooks ("pRoVE thIs iDentiTy !") then i'd suggest smth more substantial

[dim pendant]

When I peek at a solution it becomes stuck in my mind until I forget about the problem altogether and I become incapable of doing it myself

[cunning elk]

but the focus should be more on just getting familiar with the techniques yea

...

tao has exercises in his book too

[dim pendant]

Idk now that people are saying that Abbott is gentle I definitely don't want to be learning anything from the book

It's analysis you're supposed to cry and finish it and cry out in victory a new person

If you're studying analysis, you aren't there for fun

Or you don't value your time well

One of the two

[gray jungle]

If its your first time doing proof based math, a gentle RA book is what you NEED, and what will ultimately help you in the long run.

[dim pendant]

Basically I mean you learn analysis because you're a mathematician or you are learning it because you chose something random for no reason

No dude read abbott if it clicks with you

I just personally ain't touching it

[cunning elk]

or be like my analysis prof and use no book

[gray jungle]

The take that you need a book to be hard for it to be "real" math is absurd, if you want to challenge yourself thats fine, but if we want to be realistic, a well written book from a padagogical standpoint is the better book for you as a mathematician.

[dim pendant]

It doesn't have to be hard like I don't think anyone should read Rudin personally

[cunning elk]

for a lot of students a first course in analysis is practically hazing

[dim pendant]

It just should treat you like an undergraduate student

Not someone who is barely holding on

[gray jungle]

People can read rudin, but its not a book i recommend for multiple reasons, and its not for the terseness.

[cunning elk]

if you're doing fine with abbott i don't see a reason to drop it

[gray jungle]

The only good chapters are 3, 5 and 7.

[cunning elk]

supplement your reading with other texts, you're not confined to using just one

[dim pendant]

LMAO agreed

[cunning elk]

my analysis course would not have gotten out of chapter 2 of rudin

😭

[dim pendant]

Personally aside from typical critiques I just feel like the book isn't modern

[gray jungle]

Also good advise

[dim pendant]

He's using four books so he's covered

The main bit of advice I wanted to give him was to try to focus on one and only use the others when you meet obstacles

[gray jungle]

I mean i was using 7 books in one subject

[dim pendant]

Stick to what you are liking

[gray jungle]

use as many as you need, as long as you learn what you need to learn

generally its good to have one main book tho

especially at the point where you still have time to learn things slowly and really grasp conceps

some books explain certain things better than others, its good to see a wider perspective

[dim pendant]

This is precisely why we recommend using multiple texts, aside from other stupid things like authors forgetting to include exercises

[cunning elk]

nothing wrong with learning something for personal enrichment!

[dim pendant]

Only way to know is to contemplate why you're doing it and weigh your results against what's important in your life

Not everyone has to be a mathematician, but you don't gotta be one to like math

[gray jungle]

a good amount of math majors do it for fun, we're all wasting our time who cares

do what you enjoy for the sake of it

given you can fullfill whatever responsibilities you have in your life

[dim pendant]

I will say that, from an outside perspective, real analysis doesn't appear to be something that would be fun, unless you really liked calculus. It is really just the study of certain Functions to and from the real line. Without a more in depth understanding, functions of the real line sound pretty boring.

[gray jungle]

changing majors is still a option as well

idk what year you are in

[dim pendant]

Yeah idk man I wouldn't stay in the same major if I was enjoying it more than my current one

Screw them it's your life

[cunning elk]

fwiw i'm entering my final year as a piano/appmath major and deeply regretting my major choice

if i could do it all over again i would've done electrical or smth

in this economy???

[dim pendant]

I can't give you genuine advice because I'm emotionally disconnected from my family so I'd say "too bad for them, they expected wrong"

[gray jungle]

Idk what type of parents you have so its not my place to say this. BUT, if you are interested in math you can still have a convesation about switching majors, and there IS pretty convincing arguments for it from a "financial" standpoints if you want to avoid the "its what i like" talk.

good luck tho

[dim pendant]

The further we get into the future, the more arbitrarily true that is becoming

[worthy kindle]

stemlords in MY book-recs?

[golden salmon]

Just a wallfly on this topic, but imo, not a good plan on their part. That's essentially making you adopt all of their financial risk, which they might be able to convince you to do, but they can't guarantee you'd act as a rational agent. Do you plan to live with them through adulthood? Do they plan to live with you through adulthood? What if you move country (even if you get a nice big paying job like an oilfield engineer)? But also, sounds toxic, hate that for you, hope they cut it out.

THAT ASIDE, I would encourage you to plan for financial safety as an absolute priority - but do it for yourself, not for your parents.

That's not to say you shouldn't do academia - you can make a career out of it if you're a fan of writing papers, teaching, and are good at it. But academia is not a panacea bereft of financial influence.

[remote vortex]

Mathematics, being somewhere between philosophy and abstract art, should count as humanities

[rigid trail]

No need to cross that one out

STEM is a poor term

[golden salmon]

bundling them together at all imo is just lame

[cunning elk]

https://xkcd.com/435/

[rough umbra]

What are the pros and cons of using Rotman vs Weibel for a first book in homological algebra?

[ancient creek]

Do a side hustle on the side and go to grad school

The way I am setting up it for me right now

[worn reef]

Carl Friedrich Gauss said this, didn't he?

[subtle pecan]

Any book recommendations for functional equations for national olypmiads and imo?

[peak bluff]

not rlly books but evan chen has nice handout

[subtle pecan]

otis excerpts?

@peak bluff

[peak bluff]

ya that

And intro to functional equations

And Monsters

[subtle pecan]

yep im doing that

any other books?

[peak bluff]

idk then

Gl tho i also studying fes

[dim pendant]

Sadness and pain

[bitter raptor]

Anyone know where to find a typeset version of Borel‘s „Intersection cohomology“?

Or some nice set of typeset notes to learn intersection cohomology from?

Actually nvm Maxim’s book seems aight

[dim pendant]

Yeah on a second pass I guess it depends on how great the disparity is

[molten gulch]

meow

[heavy egret]

hola

[true sail]

I'm currently reading Foundations of Computer Science, I find it ok but I think that the text might not be the best explanation of the subject. Is there any other more modern books you recommend for subjects like iteration, induction, recursion, Big-Oh, combinatorics, and such for elementary CS?

[normal crystal]

I think that book covers stuff that is spread among different courses more commonly
so you would get more thorough versions in texts/courses of Discrete Math, DS, TCS

[little locust]

So I'm looking for books of subjects I've covered in school already to shore up my foundations as well, and one of my big weak points from my school days is geometry - what texts would you recommend that are good for self-study? I still have my old textbook that I used when I took geometry in 2005, and I know my library has a book available called Axiomatic Geometry by John M. Lee, but would a different title be more suitable to my purposes?

[true sail]

By DS you mean "Data Science", and TCS "Theoretical Computer Science"?

[vital bane]

Probably Data Structures

[dim pendant]

Khan Academy. You will find misfortune in spending any amount of real effort to use real books for this kind of content.

[vital bane]

Hot take, discrete math is awesome

[dim pendant]

I'll meet you guys in the middle. Discrete math is nice when it turns up in the completely "unrelated" math you're studying

Plenty, but they aren't about combinatorics, that's for sure

[dim pendant]

Hell nah

[rough umbra]

Matroids r pretty cool tho

Chromatic polynomials also

[livid lintel]

Graph theory is peak...

[sudden vale]

Hello. I have been intending to read Schnirelmann's proof for the smooth square peg problem. The presentation I'm reading uses some bordism arguments. I've encountered terms like unoriented bordism group about which I have no idea. As of now, I'm only familiar with the definition of cobordism and h-cobordism. Can someone recommend me some introductory text on bordism for my purposes that doesn't go into loads of build up?

Additionally, some text on homology and cohomology as well?

[heavy egret]

what books are recomended for med students(Which involves math)

[golden salmon]

Big question. What topics do you want to mathematise? Statistics are probably a safe place to look though.

[molten gulch]

Any homological algebra text and algebraic topology text should do this; I sadly don't know of anything for bordisms

[vital bane]

(it involves math)

[molten gulch]

that's not that funny

[heavy egret]

thanks

[heady ember]

That's a joke I would make

https://tenor.com/view/konosuba-kazuma-aqua-useless-finally-realizing-how-great-i-am-gif-16638578

[dim pendant]

This guy is just starting high school he has no idea it's a joke 😭

[molten gulch]

This

[golden salmon]

It's a harmless prank lets be so real here

[deft dome]

Recommendation for good topology books?

For self learning ofc

[rough umbra]

Point set or algebraic? If the former, do you wanna learn learn point set like separation axioms and stuff, or do you just wanna know enough to move on to something like smooth manifolds or algebraic

[naive lava]

main goal?

[dim pendant]

The first chapter of Bredon Top & Geo, if you're okay with dry definition-proposition style

[tender river]

what is your current math background?

[umbral spade]

Good starting books for DEs? I know integration and derivatives, but every DE book I checked out just seems above my level, is it really that much of a stepup?

[vital bane]

A little bit yes

[umbral spade]

Would love to hear of some good ones?

[vital bane]

you can learn basic DEs like first order linear DEs using seperation of variables

but in order to really get into it, you need to know multivariable calculus and linear algebra

I suggest Paul's Online Math notes for now https://tutorial.math.lamar.edu/Classes/DE/DE.aspx

These are great

for a DE book

"Differential Equations with Applications and Historical Notes" by George F. Simmons is great

[umbral spade]

Yea I did gilbert strangs linalg

Cheers though

[rain hound]

Croom Principles of Topology is one of the most comprehensive books and is really cheap since it’s a dover book. I enjoyed it a lot more than any of the other topology books I tried (better motivated and explained than Munkres imo).

[real marsh]

I thought dugundji was nice

[kind ruin]

I'm going to write a report on Applications of Linear Algebra in Graph Theory. Could anyone suggest me some books that combines the two beautifully and maybe I quote some of the materials from there in my report. Thanks.

[real marsh]

https://nmishra459.github.io/assets/An_Introduction_to_the_Applications_of_Linear_Algebra_in_Graph_Theory.pdf

[full cairn]

It came can confirm that springer.com is not a scam, and they actually do have free shipping

[merry sphinx]

Oh hey those are the guys who wrote the insanely long multivar analysis books

[tender river]

yeah the crazy thing is that the last about 200 pages of both volumes is just a huge collection of projects that will last you a lifetime so the text itself is quite shortish

[minor geyser]

found old math books from the UDSSR why is it all about dividing tho

[deft dome]

Thanks, I think I just needed this to be exact

[rain hound]

happy reading

[rough umbra]

is lee smooth manifolds just the accepted "correct" book? what else do people like for diff geo

[graceful moon]

People seem to like Tu as well

[rough umbra]

thanks

[full cairn]

Diff geo could mean lots of things, I feel like Lee is more diff top

Tapp is apparently good for diff geo: https://link.springer.com/book/10.1007/978-3-319-39799-3

Guillemin & Pollack is also a good alternative to Lee, it's a bit simpler and gets to the point quicker

[rough umbra]

by diff geo i mean smooth manifold theory, sorry

so like after a first course in diff geo (like following Shifrin)

[full cairn]

Yeah, then Lee is great 👍 I prefer it over Tu

[rough umbra]

thank you 🫡

[full cairn]

Btw, every Springer book I look up has like a 75% discount. Does anyone else get that or is it localised to me somehow?

This one too, is 18 EUR for me: https://link.springer.com/book/10.1007/978-1-4612-1278-2

[marsh ingot]

Yes, I also have that discount

[full cairn]

Crazy, I can't even get a used book for twice that price

Hmm, wait, maybe there's some money to be earned here

[normal crystal]

it's a sale on the yellow books in pb
I think for all of May/June

[gray gazelle]

Hey, does anyone have a recommendation for an extensive and comprehensive geometry book? I took geometry in 9th grade over 2 years ago, and I want to get back into the subject but with a much more advanced understanding.

[humble spire]

Gelfand?

Also i found that a nice sofa reading book for geometry is excursions in geometry in dover math books

[gray gazelle]

Would you mind sending a link to this book you’re referring to?

[humble spire]

yes, sorry. https://www.amazon.com/Geometry-Israel-M-Gelfand/dp/1071602977?crid=1KH3HQBD2695L&dib=eyJ2IjoiMSJ9.0lie_guKfFm1-Fz4lyeboHbWyebMqtz3haf2y95SaA8hjROy6W_vETjP7OjIMKwx_SoPm9ptyA1MKaXSncQDL9cvJ05okqvyFxN21okO2OwqygOjSmEawN3Fgds2yLEtk5QO-iqV1sm4g5Vg-LUON6jIZxAGgmxVM72C8VCmnhUSFraxSBXnMI-WZYEBW4wHJtBjs4hevBC8Yz9yYbhtzBSoV_DwqJIHgo7TVos4P8g.yT0FXtHeGwNxrsZVLmJ321EMELaYsZjQm2MExH7vFME&dib_tag=se&keywords=gelfand+geometry&qid=1748473187&sprefix=gelfand+geometry%2Caps%2C74&sr=8-1

[gray gazelle]

Thank you very much

[remote sparrow]

really?

ehh some only have their ebooks discounted

[remote sparrow]

fyi you can cut off the metadata at the end of amazon links to make them less messy

just delete everything after and including the "?"

https://www.amazon.com/Geometry-Israel-M-Gelfand/dp/1071602977

[full cairn]

well, I guess not every book, but almost every book I'm interested in atleast

I'm really tempted to buy this one: https://link.springer.com/book/10.1007/978-1-4612-1278-2

[remote sparrow]

just print out rotman instead

[full cairn]

hmm...

with lulu?

[remote sparrow]

yeah

[bright epoch]

Rotman is peak

[marsh ice]

Is it ok to share straight up PDFs here

[cunning elk]

no per server rules

[remote sparrow]

if it's legal to sure

[molten gulch]

if the pdf is legally offered, yes, else no

[sand path]

I am new to my study of undergraduate mathematics. What sources do you guys use for research papers and how do you go about finding something specific ? Right now I am just aware of arxiv. Any help is appreciated

[vital bane]

Do you mean you're new to your field or you're new to undergraduate mathematics as a whole?

[cunning elk]

typically you need to have taken analysis and/or algebra in order to do anything even slightly substantial

[sand path]

New to undergraduate mathematics as a whole. I am just starting with Apsostol and Shilov but I suppose I would like to get deeper insights into different topics as I work through them from those books. Idk if research papers are the best method but maybe they could provide discussion on topics I’m introduced to/how they relate to other things

[vital bane]

meanwhile people in combinatorics:

[dim pendant]

Your resources for navigating research papers is a strong undergraduate foundation and many months spent with your personal interests

[cunning elk]

im salty I didn’t just take graduate combinatorics my sophomore year

[vital bane]

You can try reading them, but I'm not sure if they'll offer "deeper insights" into a subject that's hundreds of years old

[cunning elk]

instead of undergrad combo where I didn’t learn much

(contest background and all)

[sand path]

I see

[dim pendant]

I study graduate level stuff here and there when I find motivation and research papers are still alien to me

[vital bane]

since research papers tend to cover new mathematics at the frontier

[dim pendant]

Might as well be Greek

[cunning elk]

the [10000 different names all concatenated] theorem

[grim ore]

Im only a ug, but similar to what Neamesis said, they are kinda on the "cutting-edge" so reading masters thesis papers helps a lot for getting a summary of the current work

Sometimes profs do their own little expository on topics too but rarely (atleast from what ive seen in stuff im interested in)

[gaunt flame]

can anyone recommend a beginner-friendly book for calculus? I might've failed my Calc 1, and I am in dire need of help🙏🏻

[grim ore]

Honestly, I feel like OpenStax textbooks are underrated for just understanding calculus

not the analysis behind it all

[gaunt flame]

thank you!

[grim ore]

Nws

[normal crystal]

flipping physics guy has another clone

[solar matrix]

best book for discrete math for undergrads? I've like 2-3 months to finish it before joining the college(I'm out of the HS)

sorry, the best is vague

I mean the books that cover almost all of the discrete math required in my CS undergrad, or enough DM needed for algorithm design

[normal crystal]

Epp or Rosen DM
or MIT's Math for CS course/text

[solar matrix]

what would you suggest between Epp and MIT's?

[normal crystal]

you should look and choose on personal preference
obviously, MIT has videos etc
Epp is a more beginner friendly text

[solar matrix]

I see, thanks

[vital bane]

There is no law against using both

You can go through a text while also watching video lectures from MIT OCW

[solar matrix]

I know some beginner stuff(propositional logic and quantifiers; basic number theory and combinatorics)

[vital bane]

me too

[solar matrix]

cool, I'd go with Epp's I guess

[golden salmon]

The stacks collab has some fucking banger sections but others are impenetrable for me. Anyone else used it?

[real marsh]

stacks isn't meant to be used as a book that you like read from cover to cover?

[small perch]

Hello, does anyone have favorite book about sheaf theory?

[past girder]

hey people, whats a good introduction to complex anal apart from the needham one?

[rough umbra]

#book-recommendations message

[round minnow]

I'm learning RCA by Rudin, should I be doing every exercise? They're a great mental workout but some are very time consuming

[graceful moon]

In an ideal world you would do every problem in every book, but you only have so much time. Doing a good selection of problems should be enough

[loud plover]

Hey does anyone have any recommendations for a more advanced alternative to strogatz dynamical systems? I'm liking how the book is applied and not proof based but I'm finding it too basic and undergraduate-focused, and the book seems terrified to present anything abstract

Any "graduate" recommendations for dynamical systems books that I find are all theorem-proof style

[tender river]

ypu can look for website of some course online that used rudin and do the assigned problems from that

[dim pendant]

Just as @graceful moon said, only a subset of the problems is usually good. What I like to do is skip all of the easy problems that seem obvious or become obvious while I'm doing them and to try to work through the harder ones. Anything I can't get done gets added to my little notepad of problems that have bested me

[real marsh]

"little" orz

[vital bane]

I just skip every problem

because they all seem easy

[vital bane]

@timber mesa

[real marsh]

If you need to do the exercises its because you weren't smart enough to get the material the first time ||/j||

[naive lava]

probably

the book doesn't explain anything

so if you wanna learn something from that book

you have to put a lot of effort in doing problems imo

[round minnow]

"the book doesn't explain anything"? it's terse, but it explains things

[naive lava]

no it doesn't

gives you 0 intuition

[graceful moon]

As a different approach, I usually do all of the easy ones to make sure I actually do know the basics, I just keep a notepad next to me and do them as I go, and for the harder ones I just try to pick what looks like a reasonable selection (I.e. does it look like the problem is getting at a bigger idea, or are you deriving some results about some specific ring/function etc)

If I get utterly stumped I usually put a little sticky note on the page if I have the book, and if it’s a PDF I’ll just write a note of it somewhere

[naive lava]

has none to little discussion of some important topics

[graceful moon]

I then either come back to it (this happens less often than it should) or ask about it here

[naive lava]

and treats some topics as mandatory which are usually considered highly optional

[golden salmon]

Which topic would you like more discussion on? I like Rudin but it assumes a certain perspective and it's not in general the best first book imo. If you specify what you'd like expanded on we can make specific suggestions.

[graceful moon]

RCA is the second Rudin book btw

I can’t say I’ve ever looked at it but the first one is terrible so

[golden salmon]

Yah I know - I think of Rudin as a series of 'second books' if that makes sense

[naive lava]

for example it just puts an entire section in folland(the premeasure) in a single proof and never even mentions the name

[graceful moon]

Baby rudin is an incredible reference text for someone who already knows the content, but idk that it goes over and above enough to be considered a great second text

It’s just a good source of problems and a good way to refresh your rusty analysis

[naive lava]

Baby rudin is fine even maybe as a first book imo

but RCA is just brutal

[graceful moon]

If you have a lot of support, sure, as a book on its own I think it’s terrible

[golden salmon]

Measure theory is an interesting one because I learnt it after complex analysis. It gets moved around a lot - but if you adopt the perspective that Rudin's use of measure theory is a 'preview' rather than a proper treatment you may hate it less.

[graceful moon]

I actually think the book is great for me, but that’s only because I know everything in it already

[round minnow]

I tried folland and didnt like it

not enough foundational structure before he jumps to Borel on Rn

[golden salmon]

If you are sure you want measure theory in your complex analysis, first of all bizarro, but second of all maybe try Amann and Escher.

[naive lava]

this might just be my opinion, but I tried baby rudin for my first analysis book and it went smothly, but for measure

[round minnow]

and generally not abstract enough for me

[naive lava]

I spent hours on some proofs and still got nowhere

[golden salmon]

but again, Stein and Shakarchi or even Brown and Churchill would be my recommendation for Complex Analysis

[naive lava]

Going from the most general to most specific might be a good idea for a reference book

[round minnow]

ive done brown and churchill already

[naive lava]

but not for learning imo

[round minnow]

I don't like how many books jump to intuition before abstraction so

[golden salmon]

I think it's truly just taste so I don't think that's a bad thing

[round minnow]

I'm Bourbaki-inclined in how i think about math, in many ways

[golden salmon]

Bourbaki I find very hit-or-miss

[round minnow]

not literally saying i read Bourbaki i meant the approach of rigor before all else

[golden salmon]

Oh gotcha

[round minnow]

But Munkres shows its possible to have both rigor and intuition

alas, most books don't have such a nice marriage of both

[golden salmon]

Munkres is fun

He gets 'distracted' a lot I find

which is fine but sometimes it feels like he's just going for a walk in the park rather than to a destination

[round minnow]

yeah i hear that

[vital bane]

I love stuff like that

because it's about the journey, not the destination 🗣️

[dim pendant]

So I've just looked at Bourbaki Algebra I and it looks like a dream

I think I will update my list of writing projects to modernize Bourbaki

[vital bane]

Bourbakize Bourbaki

[dim pendant]

Lmao

[merry sphinx]

also like the presentation of topics in rca (first 2 chaps) is pretty unusual

[golden salmon]

IT STARTS WITH MAGMAS HAHAHAHA

nice

i take it back bourbaki is kino

[round minnow]

I found it intuitive and the order in Renee and Schilling and Folland counterintuitive

¯_(ツ)_/¯

[merry sphinx]

i think folland has the right topics but is just a bit annoying to read at times

cohn is slightly easier to follow

[vital bane]

Cohn glaze

[vital bane]

But Cohn's font is annoying

but I suppose I need to stop caring about things like that

[merry sphinx]

yeah stuff like that does slightly annoy me tbh

[naive lava]

don't judge a book by it's cover

judge it by it's font

[merry sphinx]

i mean math book covers are usually all plain as hell

[vital bane]

How's it going dogu?

[merry sphinx]

so yeah

[vital bane]

except D&F

and Munkres

🔥

[merry sphinx]

goes to show how low the bar is

lmfao

[vital bane]

or maybe I'm just biased

bro wants mona lisa on his math books

[digital pumice]

physics books have way better covers in general

[naive lava]

eh not bad

started going trough deligne

cos i was bored of maths

[vital bane]

isn't that also math AG?

[naive lava]

oh no

the IAS lectures

I have realized to learn the math, I have 2 choices

either spend 20 years studying math

or learn the basics and learn rigorous stuff as it comes along

[vital bane]

Noice!

[digital pumice]

https://pup-assets.imgix.net/onix/images/9780691177793.jpg?w=365&auto=format

[naive lava]

what have you been upto

[vital bane]

during the summer I will finish Abbott and I will learn group theory and ring theory

[naive lava]

you haven't finished abbott?

I tought you did

[vital bane]

that's my plan for now, oh and I have to get into a master's program after summer

[vital bane]

I'm about to finish chapter 6 ! only 2 more chapters after that

[naive lava]

hope you get in to somewhere you want

[naive lava]

js skip and learn diff geo

you don't need multi dimensional analysis

[vital bane]

I hope so too, but even if I don't, I can't let that stop me

[vital bane]

I could, but I'd like to first learn a bunch of other stuff

[naive lava]

But there's an important question left for you to answer

what are you gonna do in terms of physics

[vital bane]

Learn it, and then get into a hep-th PhD program 🫡

I'll restart physics once I begin my master's, until then I will focus on math

[naive lava]

since you have a math degree

wouldn't it be eaiser to get in a math-phy program

[vital bane]

math-phys PhD?

let's see

[naive lava]

Yep

So your instructor can force you to read hartshorne

[hollow peak]

[random estuary]

This doesn't really have to be a book but does anyone have resources to read math online

[spiral sky]

Im finding undergraduate commutative algebra by miles reid really good, doesn't give you details but its complementary for whatever the main deal is on alg geo books/even some class field theory standard books, only glimpses (this is in the goodbye chapter)

[remote sparrow]

there's a bibliography in the back

you can look at hirsch, smale, and devaney too

[timber mesa]

Hirsch-Smale-Devaney and Robinson are both good introductions, there's also Katok-Hasselblatt if you're insane lol

[vestal crane]

insane as in “good”?

[grim ore]

looking through the books they stated, the first two look very introductory and "good for engineer" as its reletively simple examples and easy to understand math and formulas

The latter seems lowk intense even for a ug math person lol

But not terrible if you come from that background

[grim ore]

not even intense, its going into the analytical perspective which actually would be crazy for an engineer to learn lmfaooo

i didnt even know this was possible for an engineers text

[daring wolf]

are backgrounds on undergrad abstract alg, category theory, general topology, smooth manifolds enough to get into alg top?
if so what do you recommend? or not what should one learn first?

[jovial sky]

Hey, do you all know a good algebra book (preferably covering Algebra 1 and 2) that includes challenging problems? I don’t remember much algebra, but I want to review and practice again to build a strong foundation.

[quick hornet]

just to clarify since "algebra" is kind of an overloaded term in mathematics: do you mean high school algebra (solving equations, factoring and solving polynomials, linear systems, etc.) or abstract algebra (groups, rings, fields, etc)?

[jovial sky]

Yeah high school algebra

[quick hornet]

yes this sounds fine, youll want to pick up commutative algebra but you can learn it concurrently

[quick hornet]

ah, then i dont have good recommendations unfortunately but hopefully someone does

[daring wolf]

okay thanks

[dim pendant]

I have no idea what the problems look like but try Basic Mathematics by Serge Lang

[cunning elk]

AoPS has a decent treatment of the HS curriculum specifically oriented towards challenging contest level problems

[jovial sky]

Thanks! Im going to check it out

[dim pendant]

El Richardo probably did better than I did for finding you problems but in any case have fun

[naive lava]

usually in AT, we focus on rings and groups

so like an ug course on those should be enough to get an intro

but as things progress, AT becomes less T and more A

cat theory is usually introduced in alg top book

general topology is good to have, any standard book will do

[gray gazelle]

Conway or Rudin for functional analysis?

[dim pendant]

Both!

[rough umbra]

whats ur recommended measure theory book?

[dim pendant]

Stein-Shakarchi

[round minnow]

Rudin's RCA, so far

[gray gazelle]

I really liked Royden

But Taylor's Measure Theory and Integration is good as well

[rough umbra]

ty

[naive lava]

what are you looking for?

why do you want to learn FA

[gray gazelle]

To do a masters project in either functional or harmonic analysis

Conway seems really nice

[naive lava]

conway is nice

even tough it leaves lots of important stuff as excersize

rudin is like a more pumped up and terser version of conway

I'd get the basics from conway than use rudin as a reference

it might be also worth looking at yosida

[gray jungle]

what type of harmonic analysis? classical or fourier analysis on groups?

Rudin is general better if you're doing more abstract stuff related to Fa

i really like it

if your doing more applied stuff or PDE related directions id checkout peter lax or yosida as mentioned.

[gray gazelle]

I looked at that. It doesn't have exercises though

[naive lava]

as a reference

FA is huuuge

[gray jungle]

Brezis is also really good, probably my main recommendation

[naive lava]

you can just spend 3 volumes of pre 1970 stuff

[gray gazelle]

I can't stand algebra, all the homies love analysis

[naive lava]

hate both as gods suggest

[dim pendant]

someone get this guy the hell out of here!

[gray gazelle]

The real hot take: combinatorics is good but both algebra and analysis suck

[dense pumice]

Any recommendations for learning about Hopf algebras?

[vital bane]

wait really?!? I thought you just needed undergrad alg for alg top

[grim ore]

Yeah I second this lol

If you go more into homologies and cohomologies youd need comm alg, but most standard alg top classes dont get that far in a sem

[vital bane]

cohomology IS what I want

but I guess that makes sense, for intro alg top, you'd just need intro alg like UG group theory and ring theory

[quick hornet]

They asked what they needed for alg top, not what they needed for a first course in alg top

[grim ore]

I sat in a homologies class this spring sem (not long tho) and the prof used a good amount of topics from comm alg, but went over them with the class bc he understood ppl didnt take it likely

[grim ore]

Ah yeah then def

[quick hornet]

Hence why I said you could take comm alg concurrently

You don't need it to start but you'll need it eventually

[vital bane]

makes sense, I guess as you go deeper into alg top, you'll start using more advanced algebraic tools

[dense pumice]

Can this conversation happen in another channel?

[grim ore]

I sometimes think back to how my alg top prof didnt know how to solve ps top questions and said they havent taught or used ps since their ug

I find it hilarious

They are also pretty established in alg top community (just giving credibility to her)

[dense pumice]

Any recommendations for learning about Hopf algebras?

[grim ore]

Ive heard ppl read Montgomery on this, but I wouldnt be able to vouch for it myself

But according this channel, most ppl seem to recommend it

[dense pumice]

Great, thanks!

And checked out from the library, cool

[grim ore]

oop

[dense pumice]

Oop?

[grim ore]

dont mind it lol just a saying bc of memes

[vital bane]

It means Object Oriented Programming

Zyphen invented it

then he perfected it

so that no man can best him in the ring of honor

[dense pumice]

Aight

[sudden tendon]

i need books for ioqm and rmo

without being to large

[dense knoll]

which class are you in?

[sudden tendon]

9th

i can do until like the 7th question but then everything else in the paper is too time taking

in ioqm

[sudden tendon]

i dont know abt rmo tho

didnt try yet

[glacial mica]

any recomendations for differential equations textbooks for somone not interested in physics and just wants the more pure math part of it

[vital bane]

Have you checked out Arnold?

But the physics flavor of the subject is inseparable from it as it quite literally arose from physics

[marble solar]

I think a standard book in ODEs is like Boyce & DiPrima. There's a necessary amount of grunt calculations you must get through

[golden salmon]

Maybe Smooth Manifolds by Loring Tu is a good place to look? He's relatively maths-flavoured

You could try John Lee as well

Oh differential equations im illiterate

[vital bane]

DG brainrot moment

but we love DG, so all is forgiven

[golden salmon]

I have sections on one monitor and cobordisms on the other

[ancient creek]

Tu and Lee books complement each other good

[tepid merlin]

recommendentation fr euclid geometry fromintermediate to advanced

[sudden vale]

Any suggestions?

[cunning elk]

no.

<@&268886789983436800>

[dense knoll]

yeah in last year's ioqm the first 5 questions were pretty much free marks following the hardest paper in 2023

[dense knoll]

pick up one book- either Challenge and Thrill in Pre College Mathematics, or Excursion in Mathematics, both by indian authors

Start solving it with full effort, just one book, youll easily qualify ioqm

apart from challenge and thrill, solve the book Mathematical Circles and Pathfinder by Prashant Jain you'll easily have enough backend to get into inmo

And qualify it

if you can do atleast two of these books by end of class 10th, you'll pretty much butter through ISI, and start very strong for jee

[jovial tree]

should i solve all of theses books or only one em

cuz they all have same chapters

[dense knoll]

keep syllabus completion a priority, so first go through one whole book end to end (preferably challenge and thrill)

the others will then be just practice problems

the more you do, the sharper you get

[dense knoll]

usually you'd go through a book, finish it, by the time you finish it you know what chapters you're weak at and what you're strong at. If you have ~3 months left till the exam, pick up another book, start with your weaker chapters. if youre planning for next year definitely pick up another book and solve. If you have ~1 month left, then do not go for one more book, rather practice previous year qstns

[sudden tendon]

hello guys, im planning on writing ioqm

any idea what are the minimum for getting selected for rmo??

also any good books that suit the level of ioqm?

i saw a book called mathematical olympiad challenges, and its harder than the ioqm papers

[timber mesa]

maybe ask in #competition-math or the math olympiads server https://discord.gg/3sbwZdh

it's more likely someone'll have a better idea there

[sudden tendon]

what abt this

[dense knoll]

i think i gave the answer?

[dense knoll]

.

[sudden tendon]

sry i didnt read any older messages

thanks

[dense knoll]

you're welcome

[sudden tendon]

👍

also in the website it looks like in a few of the years ioqm and rmo were combined

[quasi dagger]

hello guy, I've learned angle and shape and other similar thing, but until now i still cant understand the concept of shape.Do your have any recommendation about this topic? Would really appreciate

[rough umbra]

Hopf Algebras and Their Actions on Rings by Montgomery

You could also try Hopf Algebras, An Introduction by Dascalescu, Nastasescu & Raianu, or A Course on Hopf Algebras by Kashaev

[vocal kraken]

Hey everyone, I’m in Class 10 right now and I’ve been struggling with math ever since Class 6 — like regularly getting 0s or 2s on tests.
This summer vacation, I really want to change that.

I’ve realized my foundation is super weak, so I want to start from scratch, relearn all the basics properly, and finally build some confidence in math.

I’m planning to buy this book to help me get started:
https://www.amazon.ae/Ace-Math-One-Big-Notebook/dp/0761160965
It’s called “Everything You Need to Ace Math in One Big Fat Notebook” — it’s a middle school study guide.

Would you guys recommend this book for someone like me?
Also, if you know any other books, resources, or learning paths I should follow to really fix my foundation — I’d really appreciate your suggestions 🙏

Thanks in advance!

[inner needle]

Hey everyone, does somebody know a good book to get into tropical geometry? 👀

[placid dawn]

Trying to learn calculus I before my semester starts in college. I know Stewart’s book is supposedly one of the better ones, but there’s a bunch on Amazon. Can anyone direct me to the actual one I need to get?

[dense pumice]

If you want the one that'll be for your class, there's often textbook lists you can find via your university library or student services

Otherwise though, calc is one of those topics that are so widely studied and taught that there's gonna be tons of potentially good resources. If Stewart's speaks to you then go right ahead! Just don't worry too much about learning everything this summer, that's what the class is for! I recommend taking your time with the foundations and early chapters in order to get a running start in the fall

[dense pumice]

That book looks to be decent and well reviewed, so I'd say go for it! You might want to also look into additional help, maybe talk to your parents or teachers about finding a tutor?

[strange wyvern]

any good book recs on braid groups?

[rough umbra]

ive heard good things abt Braid Groups by Kassel and Turaev but haven't read it myself

supposedly its the standard reference

[tawdry escarp]

Foundations and fundamental concepts of mathematics, what a book

[true sail]

Hello back

[dim pendant]

It's Back

[tropic nacelle]

good book btw

haven't read it myself though

[left sinew]

Im looking for a good Algebra book and I'm not sure bc i have also seen books with 160€ and I wonder if it is worth to pay that much

[dim pendant]

Use a book by that same title, by Chartrand et al.

[dim pendant]

Are we talking high school algebra? If not, pick up a copy of Pinter or Jacobson's "Basic Algebra I".

[strange wyvern]

thank you!

[trail hemlock]

jacobson is great

[jade cape]

hey guys

what kind of book do yall recomend to read for university type of math

[left sinew]

Yes high school algebra

[novel solar]

Oh, I'm learning from the same kinda book "Mathematical Proofs A Transition to Advanced Mathematics" by Gary Chartrand

But I think if you become comfortable reading or making proof, it will be good in the long term.
Btw, what do you want to study ?

Im too in CS major

Oh I got it, CS majors don't need to study proofs, haha

[normal crystal]

to be a full sized potato
obviously

[sterile pelican]

Velleman’s How to Prove It was the book I did and I wholeheartedly recommend it

[jade cape]

hey guys, what book is good to learn calculus and pre-calculus?

[vital bane]

They do

[novel solar]

Tell this to my college 😭

[scenic pewter]

Guys any recommendations for a book that has a lot of problems on multivariable calc?

[heady ember]

duistermaat and kolk multidimensional real analysis

That one is liked by some, though others are put off by its length.

See whether it suits ya needs

https://www.cambridge.org/core/books/multidimensional-real-analysis-i/3571CF78491A53C281FB72A07A55970F

https://www.cambridge.org/core/books/multidimensional-real-analysis-ii/40569A7E17929121FB43EA362BAB3C4A

[vital bane]

pretty cool

[normal thunder]

Hi, so I did some Linear Algebra in college but was more so to do with graphics programming and vector manipulation, I was wondering if there were any recommendations for learning more about the topic? I realize the actual mathematics of LA are a bit different to how I used it

If I need any other topics to understand before diving in I'd appreciate being let know

[vital bane]

Gilbert Strang's LA books

[normal thunder]

Much appreciated

[vital bane]

Also check out: https://www.youtube.com/playlist?list=PLZHQObOWTQDPD3MizzM2xVFitgF8hE_ab

and his calculus and differential equations series are pretty cool too

[normal thunder]

Will I need those for studying LA?

I did CS in college so I don't have a strong mathematics background but a strong desire to learn

[naive lava]

is this a Lang book?

[heady ember]

No its duistermaat and kolk multidimensional real analysis I

[normal thunder]

That looks painful

[naive lava]

if i had a penny every single time i saw an ift proof I'd probably be a hundredier right now

[real marsh]

My main question here is why would you write that book

[heady ember]

IFT?

[vital bane]

Intermediate Falue Theorem

[naive lava]

inverse/implicit function theorem

[heady ember]

I'm guessing this was made in Asymptote

[naive lava]

they are the same anyways

[heady ember]

Ah I see

[vital bane]

Least pain derivation in electrodynamics be like:

[heady ember]

There's a reason why I'm not doing Phy*ics

[naive lava]

derivation? who has time for that

[vital bane]

You're missing out

physics students who never study pure math and math students who never study physics have one thing in common

they're both missing out hard

[naive lava]

I whish I had gone to med school or become a businnes major or smth

[heady ember]

https://tenor.com/view/jakobglanc-gif-26492901

WTF this looks epic; it looks like our server's icon too!

[naive lava]

hopf vibration mention

[heady ember]

Do not tempt me, book. I am distracted enough. DO NOT TEMPT THEE

[naive lava]

hopf vibration is probably at the same level of cool as cauchy's theorem

[heady ember]

Which Cauchy's theorem?

[naive lava]

the cohomology version

[heady ember]

,w Cauchy's theorem

[hasty eagle]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by grass1977

[heady ember]

[orchid otter]

What topic and book would you recommend for someone who just finished learning proofs?

[full cairn]

I was so confused, because I thought that was an illustration of im(h) Here is the full question. I guess the seeming contradiction is that h is C^1 but the image is not a manifold

[novel solar]

Also state that, what are your goals of studying math, I mean, is it just for the sake of understanding numbers and structures or you want to apply in some engineering such that, some eligible person can answer you

[orchid otter]

Im mainly just doing it for the sake of studying numbers and structures, not applications of it

Maybe some applications of computer science

[naive lava]

you can probably jump into both algebra and analysis here

which are the "main" branches of math

provided you know calculus

[orchid otter]

Yeah, I just finished calculus 1 and 2

And abbots understanding analysis is good for analysis?

[silver shoal]

Any suggestions on book for upcoming college ?

[vital bane]

combinatorics:

[vital bane]

yes it's literally so PEAK

https://tenor.com/view/it's-just-so-peak-peak-panda-peak-panda-it's-just-so-peak-gif-10789048890486755182

me reading Abbott ^

[orchid otter]

What’s so good about it exactly? I constantly hear amazing things about it

[heady ember]

You can spend 2.5 years on it and still have more to learn

[vital bane]

It's insanely well written, amazing exposition that really expose what makes analysis tick but also makes you think for yourself, really great exercises, and super fun project sections at the end of every chapter and the final chapter of he book is entirely full of those "project sections" 🗿

[orchid otter]

Amazing, are there any abott level abstract algebra books?

[vital bane]

tbh there are lots of great intro analysis books you can choose any one of them and learn analysis perfectly fine, but to me Abbott is da GOAT 🗣️

[vital bane]

I'm not sure if I'd call it Abbott level, but I'm going through Dummit and Foote right now and it's amazing!

[orchid otter]

Oh cool, I’ll check it out

[vital bane]

I love D&F, though recently I haven't gone through much of it I need to do more algebra

[real marsh]

Artin is a bit of a more gentle book as well

[vital bane]

The same goes for intro algebra as well ^

Honestly I haven't really read any algebra books except D&F, Gallian and Herstein, so I can't speak of the other intro books like Hungerford , Artin, Jacobson. I think Gallian is a really fun book to read, but I'm biased towards D&F

Herstein is a good book but everything about it is too old schooled for my taste

[orchid otter]

Yeah, I’ve also heard good things about Charles c Pinter

[naive lava]

irrelevant tp pysics

implying irrelevant

[naive lava]

I'd go with aluffi

it's harder than DF buuut

you see category theory

which is the coolest thing ever

[molten gulch]

🐱 egory theory

[vital bane]

There's cat theory in D&F too

perfectly fine amount of it

[orchid otter]

What’s cat theory

[molten gulch]

google is your friend

[naive lava]

uuuh

lemme check again

[vital bane]

Category theory, it's a tool used for.... make simple things more complicated

jk

[naive lava]

4 page appendix is not nearly enough

also

[vital bane]

it's enough for an intro book🗿

[naive lava]

cat theory simplifies most proofs

AND

it teaches you a new way to think

[vital bane]

I'm not saying it's bad, I'm saying it's fine if your first course in algebra is not 40% cat theory

[novel solar]

I have heard about category theory somewhere, is it related to structuring sets or maybe not ?

[naive lava]

it's about understanding an object or sets of objects via it's relation to other similar objects

[vital bane]

it's really cool

[novel solar]

Like a graph ?

[vital bane]

Like looking at specific algebraic structures more generally

[naive lava]

uh kinda

[vital bane]

like instead of looking at a single group or a vector space, you look at a category of vector spaces

or a category of groups

which is basically every single group and every single morphisms between them that ever exists

[novel solar]

So it is a study about general structures of various distinct objects, right ?

[vital bane]

you put those into a single object called a "category" and study more general ideas using this

[naive lava]

Doing it this way makes generalizing things a lot easier

[vital bane]

Yes but you can also study category theory for the sake of studying category theory

[novel solar]

😂

[vital bane]

and define higher categories like 2-categories and maps between them like 2-functors

[vital bane]

But I'm pretty sure these are actually used in alg top and alg geo

[gray gazelle]

hi yall

what are the best book recommendations for like...

high-school math

[novel solar]

U know, I heard about it when I was trying to get to know about hilbert hotel, category theory tried to encompass every real number in a system but failed to do so.

I heard about way before so I don't if what I just said is true or not

[dim pendant]

no need to buy anything for algebra. as your brain continues to develop, it will get easier and easier and then you'll be like "man.. I bought a book for this but now I won't need it ever again..." just use khan academy

[novel solar]

Precalculus- the mathematics for calculus by James Stewart is the overall good book

[gray gazelle]

what are the contents?

[novel solar]

Can I be able to send photos in discord ? I'm new to discord thing

[dim pendant]

you have to get the active role

it gets assigned to you after you spend a relatively significant amount of time talking in this server

but in some channels you indeed can send photos even right now

[novel solar]

Ohhh, thanks

[gray gazelle]

this channel doesnt allow you to send photos though

youu could just directly message me

[dim pendant]

Just want to say that "category theory tried to encompass every real number in a system but failed to do so" doesn't really sound like it means anything to me

category theory generally is not concerned with numbers or with encompassing numbers, whatever that may mean

[novel solar]

Thanks for the clarification. That means, the category theory is worth studying as I don't know anything about it

[dim pendant]

noooo

assume that nothing is worth studying

new ideas should be demonstrated to be useful to you

if I tell you that number fields are cool, you should say "on what grounds?", not "sign me up!"

category is about abstracting the general process of studying mathematical structures away from their individual qualities and taking a more relationship-based perspective of them

from here you can prove very powerful things about aspects of mathematical structures

and eventually, once you've sold your soul, you can kind of forget about this original intention and do new things, like homotopy theory

so the lesson to take away is that category theory, in a naive sense, is only important if you already know a ton of abstract algebra and topology

[dim pendant]

someone might pick a bone with this and say "well it's okay to be interested in new ideas" but it's important to remember that being interested in a buzzword is not the same as being interested in a mathematical idea. just because something's name sounds cool doesn't mean that the actual theory resonates with you. know what something is about before deciding to commit months to it

[novel solar]

Ohhh, this is the reason why I'm in this discord channel. Thanks a lot for the advice

[tiny pebble]

I am planning on doing Zill's Advanced Engineering Mathematics for advancing my Math foundation for undergraduate physics. Does anybody have any other recommendations or tips?

[fallow junco]

hello, im going to start a masters in math next year, and i saw on the courses prerequisites i needed to have knowledge on topology and measure theory
im planning on studying them on the summer, do you guys have recommendations for books on these two subjects

[molten gulch]

munkres, folland

[fallow junco]

Thankss

[heady ember]

Some books I have seen recommended:

1. Dietmar A Salamon Measure and Integration (EMS Textbooks in Mathematics)
2. Folland
3. Bass
4. Axler

[dim pendant]

Love and Math, by Edward Frenkel

That one is more of a story about Edward's life with a good amount of "casual" math

If you want a sort of "easier" book that actually teaches you math, Elliptic Tales is a good choice

It assumes nothing more than partial derivative calculations and takes you through algebra and projective geometry so you can mess around with some light algebraic geometry, some elliptic curves, and some L-functions

[vast leaf]

Just started reading Algorithmic Randomness and Complexity by Hirschfeldt.

The proof that there is a minimal pair of computably enumerable Turing degrees by the priority infinite injury is one of the prettiest proofs I have seen.

Highly recommend

[willow merlin]

which resource explains affine subspaces

[gray gazelle]

does anybody have any recommended resources for someone taking calculus next student year? as the school year wraps up [American] I have so far completed Geometry and Functions [sort of a mesh between algebra/functions/extremely tiny calculus] and want to get ahead

there are so many resources it's overwhelming and many seem to overlap but none contain a well-rounded curriculum

[dim pendant]

Khan Academy "Differential Calculus"

[willow merlin]

maybe check out the openstax calculus books, are free and open source

[pastel sparrow]

Best book for trigonometry

[deep moat]

If you want a classic and focused on a classroom level, Schaum's Trigonometry books would be the best to go all the way :)

I mean, there are other trigo. books out there, but I think Schaum's might be the best option. It really depends on what kind of book you choose and all books have the content but other go all out :PPP

[pastel sparrow]

Thanks I'll check it

[dire cargo]

Is "Challenge and Thrill of pre-college mathematics" going to be enough for RMO?

And IOQM

Also I need tips for solving questions faster, I can solve questions in IOQM, but I'm not fast enough

[dire cargo]

Do you know any shaum's books for IMO?

[heady ember]

Prove all the theorems yourself

Actively ask yourself questions

[deep moat]

Well, for IMO preperation, I guess Schaum's wont be much of help as there are other resources. However, fortunately enough, someone I know made an entire list of resources to prepare for competition maths. It consists of loads of textbook recommendations and contest sources.
https://tinyurl.com/ContestGuideIntlGDrive

[dire cargo]

Thank you!

[dire cargo]

Also what does CL A1 A2 B1 B2 C1 C2 D1 D2 E1 E2 refer to?

[deep moat]

CL = Classroom Level
A1 - E2, they refer to the level of contest math.
A1 being introductory and E2 being the IMO (or undergrad MIT math student) level

[spare pivot]

Hello guys I have looking to improve my “general” math, and I know it’s broad but I just want to hear if people have some good recommendations for either books, websites or just any kind of place/thing I can use to improve.

My level is around 10th grade.

[toxic willow]

what is mathematics
https://www.amazon.com/Mathematics-Elementary-Approach-Ideas-Methods/dp/0195105192

[spare pivot]

Okay I Will Give it a shot thanks

[toxic willow]

i read it after undergraduate
i think i learn a lot

[dim pendant]

Sure. You don't have to stick exclusively to Tao. You can do problems from other books, too.

[dim pendant]

that happens

it's good to do it anyway to get different perspectives

lots of objects can be realized in different ways

e.g. vectors and tensors

[fallow junco]

thanks man

[heady ember]

Np

[pale mica]

Tao has problems at the end of each chapter, but personally I ended up doing half of them while reading the chapter to get a better idea of what the next paragraph of reading was about, instead of doing all of them after reading the entire chapter

[pliant pollen]

hey does anyone have a good book recomendation for an indepth guide on subjects in maths it can be any I want to expand my knowledge in the subject

[sterile pelican]

I agree with this currently doing Bloch's real analysis with supplement to Spivak's exercises

Currently in the e-d chapter and I must say I am not used to the proofs but I am at least starting to familiarise with the "backwards" approach of proving

[dim pendant]

this goes kinda hard

[last arrow]

A recommended book for differential equations?

[molten gulch]

is this just an introductory class? theoretical? dynamical systems? PDE's? If PDE's, what level

do you know functional analysis

[last arrow]

An introduction, I am in my third semester

[scenic sequoia]

You guys recommend Jaynes for a first introduction to Statistics ?

[heady ember]

Third semester of what

Ug?

If you have taken analysis before, then maybe Arnolds ODEs---I can't rmb the exact prerequisites off the top of my head. It's pretty well-liked for the theory of ODEs.

If you just wanna get a very foundational understanding and get some computations in, then Pauls' Online Math Notes is a start.

[dim pendant]

^

[rough umbra]

What's a good theory/pmath oriented ODEs book? I have real analysis

[fresh skiff]

Maybe Arnolds?

[dim pendant]

And why is that

[normal crystal]

you need a smaller phone screen
to optimize the learnin'

[dim pendant]

Lmao

As in they're kicking you out? Or as in they're making you do crap

Oh dang

Well if you can squish out two hours a day you should be able to get through a book or two even with a full time job

If you want of course

Usually for my parents it's enough for me to look like I'm trying to write and think when they walk past my door

That's okay

You'll be back before you know it

[normal crystal]

get a job at a library

moving books is menial labor

but also, you seem to be going through a thing
don't make any rash decisions

[slate dagger]

[sterile pelican]

Serge Lang’s Short Calculus comes to mind and you can do proofs at the side

Truth be told though you would need to do precalc first either way

[sterile pelican]

I am recommending Lang due to that he briskly go through the needed precalc to later on go to calculus

But honestly a proper precalc book is better in the sense of building familiarity, and it may require 600 pages if needed. I know it feels tedious but that can at least solidify ones foundation

And Lang has another book for that called Basic Mathematics that goes through all that you need but it is as you feared, which is about 600 pages

That is my two cents though, and the other is to do Gelfand's Functions and Graphs, and his trig book

It is like 3-400ish total if you go for the Gelfand route

[dim pendant]

Hopefully you won't end up raising kids this way, "I suffered so you have to, as well"

Absolutely horrible parenting

The fact that they're choosing from you bro this is the reason why a lot of people abandon their parents when they move out

[fresh skiff]

Lang has an undergraduate algebra book

Is it a prerequisite for his ALGEBRA book ?

[molten gulch]

no, for that you should just know some algebra out of like artin or something

also his not its

[fresh skiff]

Thank you i edited it

[fresh skiff]

Oh i see

[sterile pelican]

Lang's Algebra book...