book-recommendations

[sturdy shore]

[remote sparrow]

[gentle arrow]

godspeed you beautiful cat

[sturdy shore]

oh that is moon??

I saw that page in his measure theory book yesterday

[remote sparrow]

in the acknowledgements page

[gentle arrow]

godspeed

[remote sparrow]

@jovial parrot new edition of LADR just dropped

the print version is cheap at least, and the pdf quality is great

the pdf quality for the fifth ed. of friedberg is awful

feel free to update your review of LADR when you find the time

https://www.csulb.edu/mathematics-statistics/comprehensive-exam-preparation

[gray gazelle]

holy shit this looks cool

thank you

[languid kettle]

https://x.com/axlerlinear/status/1718659014593261627

new edition of LADR dropped, and it’s free!

https://linear.axler.net/

[remote sparrow]

we just discussed that above

[sudden kindle]

New LADR dropped

[remote sparrow]

https://ww3.math.ucla.edu/past-qualifying-exams/

again, tons of graduate programs release past qualifying exams

they are very easy to search for on the web

i only sent a couple of examples

[steep root]

need sum books on writing proofs

[remote sparrow]

#book-recommendations message

[maiden halo]

And I just bought the 3rd edition earlier this year 😕

[remote sparrow]

the 4th edition is sufficiently different that picking up the newest edition is worth it

you could probably resell the third edition

do it ASAP while used prices are still good

[maiden halo]

mine is still in excellent condition so that's a good idea

[remote sparrow]

what's the "best" undergraduate abstract linear algebra book then?

that includes all the material you want

looking through the fourth edition pdf of friedberg (which is searchable; the fifth edition pdf on the web are just image files), i don't see any material on finite fields.

[sage python]

I updated the review quite a bit @remote sparrow

Reworded some of the other ones to save space, and indicated that Katnzelson-Katznelson, Greub, and Roman were more impressions than anything else

But yeah as for what the best is... it's hard to say

I guess tbh the advantage of books like HK and FIS over Axler is more that Axler internalizes this sentiment of first course = computation and second = theory

So Axler is not really a second course since it's self-contained, and frankly seems rather gentle. But it also misses Gaussian elimination and whatnot (though it seems like it now does some matrix factorizations and whatnot that it didn't before which is good)

[remote sparrow]

can't that sort of stuff be made up for with notes

[sage python]

I mean the fact that you have to make up for it is a point against it compared to some others

It is no longer imo a bad book for what it's worth

Before, if you gave me the explanation for real char poly that Axler does on an oral exam I'd dock a lot of points since that's just brain worms.

But it still comparatively is a point against it. Hoffman-Kunze went into some detail about polynomials vs polynomial functions (which Axler doesn't) that would be mostly a factor over finite fields, though tbh I don't remember him actually doing cool problems or applications involving the stuff

FIS... when I graded for a class using it, it didn't go very far, so I'm not sure

[rare estuary]

When you say that "clever" students who want to move fast might use Artin or Knapp, do you think that's actually a good idea? What sort of LA specific content would you miss if you went that route?

[sage python]

I haven't looked at them in a ton of depth, they do seem to hit the main points

SVD seems missing in both at a glance

But yeah my clever comment was more, some people may find it tricky to do algebra and linear algebra simultaneously

[rare estuary]

I see, thanks

[fast pawn]

Any YouTube recommendations for undergrad topology?

I’m reading through the university of Toronto notes on topology as well

[remote sparrow]

@vital bane

[narrow relic]

I don't care if it's dry, I just care that it's precise

Have you tried Lang's Linear Algebra book?

[vital bane]

OH MY GODD YOOOO NEW EDITION!! MULTILINEAR ALGEBRA LETS GOOOO

damn damn so cool

very good improvments

this has definitely bumped up LADR from a 7/10 to a 9/10 for me

[narrow relic]

Thanks for this update, I might have to check it out again... really didn't like the book back when I looked at it a few years ago

I remember really preferring Lang as the book I used after Poole

[halcyon scaffold]

Babe wake up, new LADR edition just dropped

[fierce hedge]

No, in that comment I meant like Lang Algebra level dry

[manic cairn]

Holy fuck this is based

[hollow shore]

https://press.princeton.edu/books/hardcover/9780691206080/the-proof-stage

@remote sparrow

also @vital bane

[vital bane]

:(

[vital bane]

lol yea i've seen this, stephen abbott is interested in theather as well

[hollow shore]

that explains a lot about his writing style

[gray gazelle]

<@&268886789983436800> spam across multiple channels

[leaden quarry]

suggest some book which goes through the topics of linear algebra from informal introduction to formal definition .

in the style of ian stewart ,david tall's. "The Foundations of Mathematics "

are there books like that for fields of group theory and linear algebra.

[nocturne marsh]

book for olympiad-level inequalities

and one for functions too

anyone knows one?

[nimble ruin]

Check Titu Andreescu.

[gray gazelle]

any introductory number theory book?

[stuck zephyr]

https://play.google.com/store/books/details/Tom_M_Apostol_Introduction_to_Analytic_Number_Theo?id=3yoBCAAAQBAJ

[finite gale]

The person who asked is pre uni so I'm not sure whether they were looking for analytic nt or elementary nt

The first chapter of apostol is elementary but might go a bit fast

[crimson leaf]

Yeah the book in theory according to Apostol could be read by a high schooler

Maybe for pre university Burton's Elementary Number Theory would be good

[finite gale]

Perhaps yes but I'm not sure how much maturity the book requires and whether a high schooler would be prepared for that

[halcyon scaffold]

The first chapter doesn't even cover quadratic reciprocity

[finite gale]

That's later...

[narrow relic]

Okay

[narrow relic]

This looks so much better than the 3rd edition of LADR

[remote sparrow]

this looks like a pop math book

[remote sparrow]

#book-recommendations message

for group theory, pinter or judson

[umbral peak]

Is this the stephen abbott who wrote flatland?

[gray gazelle]

not even pre uni lol

I'm still in elementary school

[finite gale]

You have pre uni role

[gray gazelle]

what

[remote sparrow]

elementary school clearly precedes university

[gray gazelle]

i'll remove it

[umbral peak]

Sheldon Axler's Linear Algebra Done Right 4th edition is open access: https://link.springer.com/content/pdf/10.1007/978-3-031-41026-0.pdf

[arctic dew]

When was this book published?

[umbral peak]

Quite recently, I'm not sure when exactly.

[arctic dew]

Okay so it's relevant then, cause the first edition was written like 30 years ago, so that's why I'm asking

[graceful moon]

I believe it was published like yesterday lol

[rigid barn]

Dear lord, he's actually defined the determinant properly this time

[gray jungle]

eh , idk chief

[umbral peak]

what your thoughts on shilov?

[rigid barn]

what, the "top multilinear form" is a completely valid approach taken by many authors, starting with Halmos back in the 60s

[harsh mango]

What is the best book for an absolute moron like me to self-teach number theory?

[gray jungle]

its not the idea i have a issue with , thats how i learned it too but its just the way he delivers this idea is just bad? i prefare hoffman kunze simple approach and it makes more sense straight away , while axlers definition just feels weird to me , maybe someone can provide more reasoning as to why he phrased it the way he did.

[vital bane]

pretty good

[cursive orbit]

i mean for one it avoids picking a basis, which is all nice and good

but really by avoiding picking a basis, it tells you why the determinant is the correct thing to measure

[remote sparrow]

https://case.edu/artsci/math/esmeckes/math307/

I found a course webpage for Meckes' Linear Algebra. It's actually created by Elizabeth Meckes, one of the authors of the book.

[manic cairn]

Depends on what else you know

[nocturne marsh]

Is there a book that focuses on proving through induction?

[leaden quarry]

any book which discusses the history of constructing techniques to solve integrals and intuitions behind them which also goes on to classify all integrands and methods to solve them analytically and discussing proofs of unsolvability under elementary operations. also tell a book on real analysis to cover pre requisites.

[heady ember]

I don't see any reason to write, or read an entire book about induction on the naturals

[leaden quarry]

maybe he meant induction in general

[leaden quarry]

i read a book on logic by enderton which used the induction in proving almost all theorems

[heady ember]

Transfinite induction (on well-ordered or well-founded sets) doesn't take up even a section (the way I learnt it) though?

But well, if you want to learn transfinite induction perhaps try Enderton's Elements of Set Theory if you have little to no mathematical maturity. I liked it.

[leaden quarry]

a section is defining ? or just a section in application?

[leaden quarry]

kek

[heady ember]

Proving that transfinite induction works

Applying it follows shortly afterwards

[leaden quarry]

there is a lecture series on yt too

on the same book

[heady ember]

Yeah, personally I didn't use it

[nocturne marsh]

"Use induction to prove the following statements. 1. For each n ∈ N, 1 + 3 + 5 + · · · + (2n − 3) + (2n − 1) = n2"

This type of induction

[heady ember]

Yeah so induction on the naturals

[nocturne marsh]

oh yea

[heady ember]

I doubt anyone would write a book on that but there are many places/resources to learn induction from. E.g. look at loch's intro to proofs pinned in #proofs-and-logic iirc, or Spivak's Calc (1st or 2nd chapter can't rmb), etc

[nocturne marsh]

Bc like I finished "How to Prove It" but I still suck at proving stuff through induction lol (which is the bulk of the course that i'm taking this sem"

[heady ember]

Well, perhaps a good start is checking what you're stuck at when doing induction proofs

[nocturne marsh]

Gotcha, thanks

[heady ember]

Yeah it is a possibility, that for instance, it isn't actually you not knowing induction but, say, the inductive step gives you trouble

[leaden quarry]

someone reply to this

[heady ember]

Me:
> Ah yes I can do transfinite induction in Enderton
> Also me: Can't do the necessary inductive steps in school questions because they involve slightly funnei algebraic manipulation

For real anal, Dami recs Schroder or, if you have some mathematical maturity, Browder

[leaden quarry]

me: checks the identity holds for 1,2,3. to get satisfied that its probably tru

[heady ember]

People also like Abbott

[heady ember]

Ah yes, by proving for 1,2,3 we have successfully proved the statement is true for all ordinals alpha . What's the probability that it only holds for 1,2,3 anyways pffftt

Fyi... I was simply making a joke

[magic spade]

The Induction Book https://g.co/kgs/YRXdqu

[cedar flume]

Can you recommend a book where I can find the dual space of lp & related theorems

[grave thorn]

find an intro to Banach space theory

[cedar flume]

Ok thank you

[halcyon scaffold]

Not an induction book but a coinduction book https://www.cambridge.org/core/books/introduction-to-bisimulation-and-coinduction/8B54001CB763BAE9C4BA602C0A341D60

(great book btw, would recommend)

[dusk wind]

Have you read the Open Logic Project

[topaz thorn]

does anyone know where I could find a source for a proof of the crystallographic restriction theorem in 2 dimensions

[hasty eagle]

Removed the studying! role from you.

[tender river]

#bots

[harsh mango]

Up to calculus and linear algebra

[remote sparrow]

#book-recommendations message

[harsh mango]

We are there already lol

[remote sparrow]

you think these books are too hard?

[harsh mango]

Oh I thought you has said the channel didn't realize it lead to a post mb

[remote sparrow]

https://www.amazon.com/Friendly-Introduction-Number-Theory-4th/dp/0321816196

https://www.amazon.com/Elementary-Number-Theory-Its-Application/dp/0321500318

these books are popular too

[harsh mango]

Thanks Ill check them out

[remote sparrow]

https://bookstore.ams.org/view?ProductCode=AMSTEXT/61

this was very recently published in 2023

i just happened to see it in the library

[dusk wind]

do you scrape your books?

[zealous cedar]

honestly mathematics books are so expensive these days

libraries are so stingy too

and most often than not there's tons of lectures online these days

from calculus to more complex noptions

[wintry abyss]

anyone got any good books for undergraduate complex analysis

[remote sparrow]

what does scrape mean

like use a web scraper?

[remote sparrow]

gamelin or bak and newman

[dusk wind]

yea

[remote sparrow]

no

[gray gazelle]

Is there any book that you can recommend for a high school student that wants to learn discrete mathematics with some basic logic and sets knowledge?

[dusk wind]

ehh maybe just take the discrete math by itself

probably better to get another book for the logic

[dusk wind]

https://www.amazon.com/Discrete-Mathematics-Computing-Peter-Grossman/dp/0230216110 (easy)
https://discrete.openmathbooks.org/dmoi3.html (free)
https://www.amazon.com/Discrete-Mathematics-Applications-Ali-Grami-ebook/dp/B09ZKXCZHL (recent)

you can also look at rosen or epps

[gray gazelle]

yes i looked at them. They are so expensive for my budget for now

[dusk wind]

they aren't that good anyway imo as they are polar opposites

take the free book and do some practice problems online I suppose

[gray gazelle]

Nice, I bought a course from udemy and i think this book will be a nice fit for practicing concepts. Thanks for your answers.

[dusk wind]

maybe they have one of them at your local library, good luck

[gray gazelle]

I think there's no math book in my city's libraries fr :d

[dusk wind]

for logic this is a nice early book https://www.fecundity.com/codex/forallx.pdf

bigger one is the open logic project but it has many changing hands/heavy

[dusk wind]

I heard there was a certain library by anna

[gray gazelle]

this book looks so clear and nice

[dusk wind]

yea ikr its difficult to find books like that

[gray gazelle]

for sure

[narrow relic]

This looks pretty good. It uses Fitch natural deduction which I wholeheartedly recommend

[remote sparrow]

https://forallx.openlogicproject.org/

this is the newest version

[dusk wind]

that's false advertising

written by completely different authors

[final sluice]

has anyone here read sheldon axler's measure theory?

[remote sparrow]

@sturdy shore

[crimson leaf]

It has the same person as the first author as the one you sent?

[dusk wind]

the original was open source so anyone can add themselves onto a new document

if you read both they look completely different and there are other similar projects

[remote sparrow]

maybe i should rephrase, the fork i sent is one of the newer ones

there are several different forks of forall x

[dusk wind]

and they all suck

a massive circlejerk of appropriation

[crimson leaf]

You're making it sound like they stole it when what you said makes this clearly not the case

[dusk wind]

that's just your perception

but if you write something and then someone else comes along and 'improves it' when what you wrote achieved the necessary goal, then eh

at the very least, I would want any adaptations of my own not to be changed so completely from the original work

[remote sparrow]

You are free to copy this book, to distribute it, to display it, and to make derivative works,
under the following condition: Attribution. You must give the original author credit. — For
any reuse or distribution, you must make clear to others the license terms of this work. Any of
these conditions can be waived if you get permission from the copyright holder. Your fair use
and other rights are in no way affected by the above. — This is a human-readable summary of
the full license, which is available on-line at http://creativecommons.org/licenses/by/4.0/

[crimson leaf]

I mean you used the word appropriation which means to take usually without permission

[dusk wind]

it means more than that

imagine starting off with apples but then you throw in lemons later

like sure they gave permission but that doesn't mean they 'wrote' the adaptation or had any involvement in derivative works

[remote sparrow]

uhh, okay

seems like a rant about nothing then

[dusk wind]

not sure why they thought it was stolen tbh

[crimson leaf]

Because you called it false advertising and claimed it was appropriation which is synonymous with stealing in that context

Both of which are false very clearly lol

[dusk wind]

it's not stealing, it's just using the original work for the adaptation

words have more than one meaning

[magic moth]

theres a thing called hermeneutics and mathematics has as one of its goals being free of hermeneutics as far as I know

[olive bloom]

Pls explain

[magic moth]

hermeneutics has to do with the issue of interpretation, mathematics is a language that has as one of its goals to have unambiguos interpretation, that is no hermeneutics.

[olive bloom]

So there's only one way to interpret it

But for ex some people consider 0 being part of N and some others don't

Is this hermeneutics for maths

[magic moth]

normally u choose N depending on what ur working

dont quote me on this but if ur an analyst N does not contain 0

if ur doing number theory N contains 0

that kind of thing

[sturdy shore]

parts of it sure

[fickle whale]

What's some good clifford algebra books pls

I'm looking for material at the graduate level

One Name I've heard along the lines of what I'm looking for is Clifford Algebras and Spinors by Lounesto

If that helps

[glass badger]

I just finished watching a video that mentioned the subject and thought it seemed really cool (though I don't know how handy-wavy it might have been).
I'd like to know too if that's okay.
Edit: Sorry I pinged; forgot to remove that as I was collecting my thoughts.

[fickle whale]

What? No! Don't ping and then apologize, read my about me I want the ping

[glass badger]

Oh lol, sorry I wasn't aware. I just assume people don't like to be pinged randomly as a default.
P.S. The video is called "Why can't you multiply vectors?" by Freya Holmér - if you happen to want to check it out (though it's quite long).

[covert zealot]

Does that video apply to the vector space of real numbers?

[fickle whale]

I skimmed the video

Glad Freya finally caught on to GA after spending so long extolling LA

But I didn't watch it all the way through, not a Freya fan, her videos just pop up on my autoplay so I'll watch portions.

Have you seen Sudgylacmoe's videos on the subject

Bivector and Hamish Todd are also some YouTube channels with good info

If you're looking for introductory material in books, I recommend LAGA by Alan MacDonald

[fickle whale]

Yes it does

[fickle whale]

Eigenchris also has some videos about clifford algebras and spinors

Though with less of a GA flavor to it

But still good

[wheat trout]

Lam has a book called introduction to quadratic forms over fields. It has a dedicated chapter of Clifford algebra of a quadratic space. It is purely algebraic though, do not know if you are interested.

[bold sequoia]

Hello, I'm an undergrad sophomore physics major. Can someone recommend me books on special relativity that give me intuition, mathematical intuition specifically. Maybe like a geometric perspective on lorentz transformations, length contraction and general concepts of SR. Thanks.

[fickle whale]

Thank you, looks like exactly the kind of thing I want from the toc

Although I am interested in it in slightly more generality than fields

[naive spindle]

Whats a book that gets recommended about calculus?

[zealous fjord]

Hey! Dota! Used to play a lot of that. Spivak's Calculus gets recommended a lot, though that's supposedly a bit on the pure side, and is more an introduction to analysis. The typical college calc book is Stewart's calculus, though I personally don't like it.

[north heron]

Hello, i'm looking for a book talking about Gauss method for quadratics form and his applications to conics and quadrics ?

that is part of my course on linear algebra, but the books i got don't talk at all about that ( Serge Lang linear algebra, ... )

and the course pdf is not very good at explaining that

[keen orbit]

it depends

if you want it computational then you can go for something like stewart's book

if you want a rigorous/abstract calc book then go for spivak

[glass badger]

I have not, but I'll be sure to give the videos (and the text; thanks for the recommendation btw) a look.

[alpine rover]

What is the most famous text on Algebraic Number Theory?

[stray veldt]

do you think we are keeping sale charts?

neukirch is pretty standard

[finite gale]

Also famous doesn't necessarily imply good / worth using, e.g. baby Rudin

[arctic dew]

Guys, is there any book that teachers linear algebra for specifically data science?(so not paying that much attention on things that aren't significant for data science)

[crude sage]

I have an opportunity to buy a physical math book instead of an online one for once. What book would an undergrad have use for for the longest possible period?

[magic spade]

https://math.mit.edu/~gs/learningfromdata/

[arctic dew]

Thanks very much

[fickle whale]

Geometric Algebra for Physicists

I forget who wrote it tbh

I think it was Doran and Lasenby

I haven't read it, and I don't know physics, but I know a guy who knows physics who read it because I always talk about GA, and he's commented about how it made relativity and some other equations clearer/more concise

[shadow hedge]

Is there a good book for improving study habits and studying effectively specifically for math majors. I just started college and am struggling to manage the classes especially the proof ones

[manic cairn]

whether that book will be good depends on who is reading it

there are myriad problems that it could be

i would ask the professors teaching the class, or the grad student TAing it, or the undergrad TAing it

[ocean spindle]

Follow a specific textbook for a topic, can be your course recommended textbook or some other textbook too

And just be a good student by being disciplined in terms of work ethic

No book is going to teach you how to improve study habits realistically speaking

[fierce hedge]

It'd probably be a book that works as both a decent textbook and a reference book. The most obvious that comes to my mind is Abstract Algebra by Dummit and Foote.

[crude sage]

That sounds like a good idea. Plus D&F would look great on a bookshelf lol

[remote sparrow]

https://www.amazon.com/How-Study-as-Mathematics-Major/dp/0199661316/

https://www.amazon.com/Think-About-Analysis-Lara-Alcock/dp/0198723539

https://www.amazon.com/How-Think-About-Abstract-Algebra/dp/0198843380/

[knotty basin]

suggest some books that contains some difficult trigonometric problems

[silk sigil]

How does Volume III from the Stein & Shakarchi series compare with Measure, Integration & Real Analysis by Axler for learning measure and integration theory? Are both good, or is one preferred over the other?

[orchid mortar]

MIRA being perma free will never not be an advantage

Apparently they are quite comparable, but I wouldn't really know. I've only peeked at MIRA a bit, and definitely not went through Stein Shakarchi

[arctic harbor]

hey guys im new here , and i wanna start with calc , someone told me that
just start with limits then derivatives then integrals then multivariate vector calculus then real analysis then complex analysis/topology, but im concerned about the reources , can anyone help pls

[hearty steppe]

You’ve tried these?

[magic spade]

Most people recommend calculus by Stewart or calculus by spivak to start

[sudden granite]

http://www.apexcalculus.com/

good free calc book

👍

not very proof based but thats okay chat

[arctic harbor]

do i need extreme expertise in functions and graphs for starting calc? i k them at a decent level only , @sudden granite @magic spade

[sudden granite]

idk what level youre at

read the chapter about limits and see how much you understand

[arctic harbor]

ik functions but not those graph transformations and stuf

[sudden granite]

you should review gaps in your knowledge before doing calc

calc requires strong algebra foundation

[remote sparrow]

yeah i've read them

[shadow hedge]

Are these really helpful?

[remote sparrow]

they're fine

whether they're really helpful partly depends on you

i don't love how alcock insists on writing down symbols in proofs rather than prose

[hasty eagle]

Removed the studying! role from you.

[keen orbit]

tbh transformations of graphs arent something to worry about

i mean dw if you or dont know them well

but the book you should use depends on what you want

if you something more computational then stewart's calc is a very good choice

if you want something proof based instead then spivak's calc is the best choice prob

[dry elm]

im using a pdf to do my precalc self study, but i would like a real book in front of me, what book would you guys recommend for precalculus?

[magic moth]

are there any books on fuzzy logic that are recent?

all the books that i have that touch the topic only do so in a limited manner and dont mention sources which are recent.

[hasty temple]

Does anyone have any books that could provide an intro to linear algebra or something similar to a full course

[fleet karma]

so I'm reviewing precalc right now and was wonder if there were any good books or etc on polar graphing or polar coordinates?

[narrow relic]

For a book that is an intro where you've never seen linear algebra before: #book-recommendations message

[haughty pilot]

Do anyone know about the book "No BS guide to math and physics"? I want to get the reviews on that book but I found out that it isnt much popular.

[remote sparrow]

#book-recommendations message

#book-recommendations message

meckes has a full solutions manual available if you know where to look

[stray canopy]

is there a pinned list

of the best recommended textbooks

or some sort of archive

[remote sparrow]

consider checking your university library and worldcat

[remote sparrow]

there are some in pins

don't know if they are "best"

also #books-old and #books

[stray canopy]

it would be smart to do a comprehensive list that people can add to

[remote sparrow]

4chan /sci/ wiki is good

[remote sparrow]

as i mentioned, /sci/ wiki exists

but lists have elements of subjectivity to begin with

[stray canopy]

oh i do not browse that website

but thanks anyways

[remote sparrow]

https://4chan-science.fandom.com/wiki//sci/_Wiki

[remote sparrow]

you don't need to participate on 4chan at all

i don't

it's just a fandom wiki

[stray canopy]

great, thanks for the link, i'll check it out

[arctic harbor]

for now i need a conceptual one to get the essence of it , then i wanna build my way up to higher problems and stuff

[willow adder]

Hmm...I'm looking for some books with like, really worked out solutions, higher level. A lot of the books in real analysis or abstract algebra don't seem to have worked out solutions/proofs through the problems, for a reason obviously, but i find like, i learn more from observing a process and getting a general idea of how the pipeline is supposed to go, does that makes sense? Like I find it more productive than staring at a problem mindlessly not knowing what the hell to do or think about it or google it and be like 'oh, this example works as a counterexample' or, 'oh, this method feels sorta out of nowhere'. Something that really holds your hand and guides you through the definitions with examples and what not

hope that makes sense

[gray jungle]

i think this is a bad mindset staring at problems and trying to do them is very productive to your problem solving skills and understanding why certain methods work rather than memorize them

[willow adder]

I mean, how would I figure out what methods work though without like, seeing more thorough sort of examples, if that makes sense

I mean often I just sorta stare at a problem, then get into very handwavy arguments for why something must, or must not be true

[gray jungle]

there is usually plenty of examples and proof in the book to serve that purpose , exercises are meant to be solved by the reader

just depends on the author if they are good or bad exercises

[willow adder]

i mean that's a relative term too? 'good' for some people, bad for others

[gray jungle]

there is some general rules everyone understands to what makes a good exercise

[willow adder]

like someone was talking earier about how copying proofs is a good way to get an idea of how to make good arguments and what not, forget the exact point

[gray jungle]

for example most rudins books have "good exercises"

[willow adder]

what does make a good exercise?

[gray jungle]

depends on the subject , but it generally needs to build some intuition and be "solvable" and instructive

some exercises are just routine computation , some use a clever trick technique thats useful in other places

some are just challenges ofcourse

[willow adder]

I guess having 'labels' on those sorts would be nice then

[gray jungle]

but anw you will find most books do have solutions online somewhere , and those that dont you can ask about here or on mse

you do have some books with solutions ofcourse

only remember andrew pressley diff geometry on top of my head

[willow adder]

because sometimes the author just sorta tosses them in there and its sorta feels like 'oh these are all supposed to be of equal difficulty'

if that makes sense

[gray jungle]

i think most are ordered relative to difficulty but again it depends , and once again its good to learn to get a "feeling" for exercises

so you can judge for yourself whats important and whats easy/hard

[gray jungle]

a list of topology exercises from utoronto (i think?) labels exercises in terms of difficulty , if that interests you

[willow adder]

Hmm...I guess. I guess I also just find it hard to self motivate through these sorts of things. I have a masters and bachelors and I feel like I should but I just...dont? and yeah maybe that could be good. I did some TDA in my undergrad/grad and maybe planning on doing more of that

it's all sorta an aimless void rn

[oblique trout]

E

[dapper junco]

Do you know of any book useful for getting a good understanding of calculus? Bearing into mind that I'm just an economics student and, though I'd like the material to be comprehensible, I wouldn't mind learning things I don't actually need in my field.
In the lack of a similar book, one which introduces well to the math behind stat would also be much appreciated.
Thank you in advance.

[gray jungle]

spivak is a common recommendation for calculus , tho you might be interested in a topic called real analysis which has many good books such as apostol

[remote sparrow]

apostol has both a rigorous calculus book in the same vein as spivak and an analysis book

[vital bane]

if they dont have a solutions manual, solve all the problems and create a solutions manual for it

[vast jackal]

Hey, why is there approx for pi is different the one in a mir book is 3.1416

Send the screenshot to math-discussion

The tables are different

[remote sparrow]

baby rudin has a full solutions manual written for it

[magic moth]

have not read that much of mir stuff to know

[vast jackal]

Well im still in the table and it's my first time reading one lol

[vast jackal]

My brain is not braining

[manic cairn]

The proofs of theorems and examples in the text should be where your ideas come from

[hasty eagle]

Removed the studying! role from you.

[dry elm]

what would y'all recommend me to get for a Precalculus book?

[stuck zephyr]

It's OK if it's textbook?

[dry elm]

I'm sorry what's the difference between a book and a textbook?

[stuck zephyr]

good question

I think textbook used to have in schools and book for reading on your own or smth

What else can be

[dry elm]

Doesn't matter to me

[fast pawn]

Currently working my way through the UToronto notes on topology. Any YouTube playlist recommendations to go alongside them?

[sinful bolt]

hello guys can u suggest some books for computer science students with problems and solutions

[mellow wren]

isn't there a big book of C programming

[remote sparrow]

computer science is a pretty broad field

[trail hemlock]

hey yall sorry if this question has been answered already, but I am looking for a book to learn intro real analysis . i only have calc 1-3 knowledge, and im looking for a book that teaches it really intuitively (like the aops calc book) and in depth. any recommendations?

[remote sparrow]

and books in CS can range from programming manuals to books that pretty much teach math

[sinful bolt]

do u have any suggestions?

[sinful bolt]

m looking for maths books

[remote sparrow]

https://4chan-science.fandom.com/wiki/Computer_Science_and_Engineering

[sinful bolt]

oh thank you

[remote sparrow]

intuitively? introductory real analysis is about putting calculus (roughly speaking; some parts of analysis hardly concerns itself with calculus) on a rigorous foundation. there might be friendlier, more reader-friendly treatments, but they all have the same goal

[trail hemlock]

haha makes sense. any self-study friendly books

[remote sparrow]

#book-recommendations message

[trail hemlock]

tysm!

omg i love jay cummings books

[dapper sorrel]

books for (relations,groups,sets,functions) or maybe called abstract algebra idk ,thnx

[gray jungle]

@hasty rose this is the course that was used in my undergrad uni for "algebra 1" (yes idc if people know)

[dapper sorrel]

i appreciate that thank you!

[tame plaza]

https://www.goodreads.com/book/show/1045726
what do you think of this?

[vast jackal]

I'd recommend you to just watch some codeacademy or any YouTuber to learn C

[fluid estuary]

lebanon :0

[subtle mango]

trying to read Vakil’s alg geo notes but the god awful font is making me angry

anyone know another link to vakil’s notes with a normal font?

[cursive orbit]

it's a better font than computer modern

[subtle mango]

nuh uh

i don’t like the math letters

[woeful ravine]

Tao's books (Analysis I & II) is also great. Lots of examples, exercises, and isn't too formal

[trail hemlock]

oo cool

[lime vessel]

[willow adder]

very cute pfp :)

[lime vessel]

You too :p

[subtle mango]

u cannot tell me these math letters r appealing

granted they r not as bad as hatcher’s varphi

[lime vessel]

They look fine

[subtle mango]

i miss computer modern

🤬

that being said i am willing to overlook this in lieu of vakil’s funny jokes

[vast jackal]

I can't send pictures

[lime vessel]

You need active role

[vast jackal]

How?

[finite gale]

be active

lol

[vast jackal]

Kek

Im finding S.M. Nikolsky and M.K. Potapov Algebra pdf

Anyone who has links?

[fierce hedge]

Best option is to send pics in #chill and refer them here

[vast jackal]

I uhh don't have access to it

[fierce hedge]

Please remove your studying role, it cuts access to few channels

[vital bane]

bruh what 4chan has a book recommendation message board now??

[vital bane]

this is a problem because of the new welcome screen thing

[fierce hedge]

They have already changed the welcome screen which is why I am surprised. They probably joined before the change.

[patent ruin]

Does anyone have book recommendations for beginner trig, algebra 2, and high school geometry? Like seperate books for each topic.

[gray gazelle]

@patent ruin There are really good online resources for each on openstax, although if I'm honest rather than going through all that just watch Professor Leonard's precalc series. He goes through everything you need to know (and believe many people forget) up to a point where you will have sufficient knowledge on not just how to solve problems but the properties of things you're learning and why.

[patent ruin]

Where do I find the precalc series?

I actually also just found out about openstax 😅 looks like a good resource

[gray gazelle]

https://www.youtube.com/watch?v=9OOrhA2iKak&list=PLDesaqWTN6ESsmwELdrzhcGiRhk5DjwLP DO NOT get intimidated by how many videos there are. Just do one or two a day or less than 2 hours and you will have a very strong foundation in 2-3 months. He's a really good teacher that also teaches other subjects if you like it. First 20-30 videos are elementary, meaning he literally starts from the fundamentals of functions that you probably know but I'd recommend against skipping, In the future even they'll be helpful when you come to Logarithms and for example why we can only use half of the unit circle in inverse identities.

[patent ruin]

That looks like an amazing resource 😮 also can’t believe it’s available on yt. Thanks for that. I was also wondering if openstax sells the books as printed, or just as ebooks?

[gray gazelle]

I think they sell but hnsetly you don't need a lot of resourcs printed for trigonometry. There's an avalanche of good content on the web about them.

[magic zenith]

Hi. So, i've been studying (vector) calculus with Thomas Calculus 14th edition, and someone mentioned studying linear algebra concurrently since it would be useful for the vector calculus. The book i have been studying is Keith Nicholson Linear Algebra with Applications. It's demanding in the exercises, but good. So far so good. Overall the coverage i've seen so far for differential equations seems relatively superficial and i was taking a look at Nagle's "Fundamentals of Differential Equations", 9th edition. It seems ok as well, but if someone has some other suggestions, i would appreciate it. The crux of the matter is this: I have no idea which book to use to study statistics and probability, nor which one to deal with stochastic calculus, or which to deal with transforms, mostly Fourier, but not only, and convolution in the DSP context for images, but not exclusively, though images would be the biggest application. Any teacher here has good recommendations for these 3 topics? Fourier/convolution/transforms/DSP, statistics, and stochastic calculus? It's a hobby for some years now, i've been studying at my own pace, but without a well defined direction.

also, what the hell do i do with Ricatti equations, other than transforming them to Bernoulli equations and into standard form?

[vast jackal]

Online resources might be good i recommend The organic chemistry tutor, khan academy and if the two of them confuses you just search it in youtube maybe Google or what and you can learn lol

[patent ruin]

Thanks for that @vast jackal : )

[vast jackal]

Lot of resources out there

[patent ruin]

Definitely is! I just found out about openstax a few minutes ago and I’m amazed! Organic chemistry tutor look’s very promising

[gray gazelle]

any good last-minute review resources for the amc 12?

[gray gazelle]

I wouldn't recommend organic chemistry tutor, i think his examples are way too surface and aren't based on a lot of intuition. Also the examples are somewhat 'stand-alone', as in they don't build up to anything but more a piece of information within each other.

[remote sparrow]

no? it has a wiki separate from the site

[mortal crater]

Hi everyone! I'm learning to integrate and I realized that I have difficulties with manipulating rational functions. Do you have any good suggestions on where I could learn and understand rational functions better? I am interested in understanding deeply partial fraction decomposition, solving cubic equations, the fundamental theorem of algebra, and division of polynomials. I can solve most cases but I would like to be more confident with more complex polynomials

Thank you very much in advance

[hasty eagle]

Removed the studying! role from you.

[finite gale]

What is with people and using this channel for bot commands

[kind pilot]

Hello everyone. I'm a 9th grader currently going into competitive highschool math, like AMC10 and AIME. I have competed in MATHCOUNTS and AMC10 before. I struggle a lot with algebra. What algebra books do you recommend? I've looked at AoPS volume 2, but I find it too fast-paced and hard to understand. However, I am proficient with AoPS volume 1. Thank you!

[cursive shoal]

What do you struggle with? Just the manipulations? Solving equations? Graphing?

[kind pilot]

Manipulations and graphing

[cursive shoal]

If you’re disciplined and self-motivated I think working through Serge Lang’s Basic Mathematics should get your algebra skills up to a college level very quickly as long as you’re actually doing the problems. However, he has a very terse and theoretical writing style which you might not enjoy. Stewart’s Precalculus is a good alternative from what I’ve seen, but I’d definitely recommend at least checking out Lang first to see if you vibe with it. For graphing I’d recommend I.M Gelfand’s The Method of Coordinates and his Functions and Graphs book. They’re in the Dover series so you can get them both for less than 20 bucks. His Algebra book is a good companion to Lang.

[kind pilot]

Thanks! I'll look into that.

[cursive shoal]

No worries! Don’t count out khan academy either. grinding out a couple dozen problems there can really help.

[kind pilot]

What Khan Academy courses should I look into? Precalc?

[cursive shoal]

I’d suggest starting at Algebra I and seeing what gaps you have. If you take the diagnostic test and get over 90 on that you should be good to move on to Algebra 2. Same for that and Precalculus.

[kind pilot]

thanks!

[limber marsh]

are there any good math books that accomodate people who need to know the "why?" in solving things? i just feel like i'm at a roadblock, because teachers will teach you what to do and not why you do it

I'm currently in the equivelent of Algebra 2

i just feel like i learn a certain way and memorizing steps to factor complex fractions, and this, and that is not satisfactory for my mind

[manic cairn]

what do you mean by "why" here?

do you mean an engineering application or something like that

or a logical justification

[limber marsh]

a. just a logical justification
b. sometimes a real world example

[sonic dawn]

"a" sounds like proofs

[limber marsh]

are those common to review in highschool mathematics?

[sonic dawn]

Yes. The mathematical rigour demonstrated in proofs seems to be important to at least preface in high school mathematics courses.

https://math.berkeley.edu/~hutching/teach/proofs.pdf

This is a good, quick read into proofs

[sonic dawn]

I reread your text, and on second thought proofs doesn't exactly sound like what you're describing, so I might have misled you. I completely understand wanting to know why you do what you do for math, especially algebra. Make sure to use all your resources; look a concept up and see if you find an explanation that works for you. Also, sitting down and just working with the numbers or the process for a bit can go a long way. That way you find out for yourself why you do what you do.

[limber marsh]

Thank you!

Are there any good resources or books suggested for Algebra that kind of help with this?

I’m trying to find something to accommodate my math textbook and go more in depth or explain things in a different way?

[sonic dawn]

I'm sure there is, somebody help me out here

I actually don't know many math books myself, I just wanted to mention proofs lol

I don't I can answer adequately

[magic spade]

See if this book is right for you. If its not, let me know and I'll find you something else

https://www.stitz-zeager.com/Precalculus4.pdf

[restive geyser]

any reccomdantations for books about algebra 2 currently enrolled in that and need help on some of it

learning about polynomials right now

[river helm]

how do you guys feel about analysis II by tao? i've been using volume 1 as a supplement to my intro analysis course and i've been enjoying it so far

[fierce hedge]

I've heard that, it's not as good at volume 1. But it's better to just try it and see, maybe you'll like it

[magic zenith]

What's the top-notch self-study book for statistics and probability, for those comfortable with multivariable calculus and some linear algebra? (all the way to eigendecomposition, et cetera). The ones i could find seem a bit "dry". And while at it, anything good for stochastic calculus? Most seem to deal with financial applications. Is there anything else stochastic calculus is used for?

[river helm]

sounds good!

[stuck elk]

I'll only do probability and stats since I haven't touched stochastic calc yet:

1. All of Statistic is a nice overview of probability theory and statistics, though it misses out on stochastic processes and sometimes goes too fast.
2. Introduction to Probability by Bertsekas is what I used at first. It does cover stochastic processes but not as in-depth as All of Statistics when it comes to learning theory, doesn't cover divergence, or non-parametric stats.
3. Introduction to Stochastic Processes with R. It makes use of linear algebra and is a nice balance of probability theory and numerical computation.

[scarlet steeple]

A natural introduction to Probability Theory is a great pick

[gray gazelle]

https://ocw.mit.edu/courses/6-041sc-probabilistic-systems-analysis-and-applied-probability-fall-2013/

[patent ruin]

I watched a few today and I love how engaging he is! Really makes the lesson fun. I’m self learning this area of maths, and I’m wondering if you have ideas on how to put what I learn in each lesson into practice to help it stick? There are a few generic tests online, but won’t necessarily be at the level I’m learning at the time.

[mortal crater]

Hi everyone! I'm learning to integrate and I realized that I have difficulties with manipulating rational functions. Do you have any good suggestions on where I could learn and understand rational functions better? I am interested in understanding deeply partial fraction decomposition, solving cubic equations, the fundamental theorem of algebra, and division of polynomials. I can solve most cases but I would like to be more confident with more complex polynomials

[magic zenith]

@stuck elk @opaque zinc thank you, i'm going to take a look at your recommendations.

@Alex that looks interesting as well, thank you

[gray gazelle]

Rather than generic school tests, especially considering you're self-learning I would recommend solving few nested real problems that would require you to use all the properties you know about topics in pre-calc. You can find load of good ones in the internet, or searching for the last topic thought to you. You can also use Wolfram Alpha to create problems for you and solve them. Other than that in terms of 'making it stick' Professor Leonard already makes you more than enough prepared with his examples and takes the time to make you understand before the next topic. I never needed to re-watch a video. Other than that I can recommend two rather obvious things for pre-calc, one is do not shy from using a calculator. It is not cheating to do so, and you will use one for the rest of your Mathematical life, just make sure you understand the logic. Second is much newer but you can use AI for your in demand tutor. It is very capable in explaining basic concepts or parts you don't understand. Sorry for the long response, and good luck!

[trail hemlock]

wait you can use wolfram alpha to create problems?

oh its paid 😭

[ionic portal]

are there any books on infinite. i heard there are different levels / sizes of infinite and would like to learn about that. im not reffering to a text on infinite series

[daring lake]

What you are searching for is cardinality. You can probably read 2nd Chapter in Jay Cumming's Real Analysis. He talks about Cardinalities in a nice simple way.

There are many videos on YT regarding this too if you basically just want the idea of how this can happen.

[mortal crater]

Hi everyone! I'm learning to integrate and I realized that I have difficulties with manipulating rational functions. Do you have any good suggestions on where I could learn and understand rational functions better? I am interested in understanding deeply partial fraction decomposition, solving cubic equations, the fundamental theorem of algebra, and division of polynomials. I can solve most cases but I would like to be more confident with more complex polynomials

[patent ruin]

Don’t apologise for a long message! I’m not only learning this area of math, but I’m also learning how todo it in a way I haven’t before! I really want to thank you for taking the time to share your knowledge on it.

I’ve got some great resources now. Thank you 🙏

[mental spruce]

hello folks, I need some books for algebra a special for engineering ,Do you have any recommendation ?

[gray gazelle]

Can anyone help with this?

I saw a response earlier but I can't see it anymore

[manic tendon]

Recommend me a book that talks about topics such as algorithms to get the inverse of a triangular matrix

[analog lava]

just practice

first u learn about those things in the general setting

and then u practice hard integrals

u develop a tool box

and then use it

[covert zealot]

Matrix Computations by Golub and Van Loan. Once you have a triangular matrix, should be easy to check its determinant to see if invertible. If it is, would be numerically better to solve by back substitution instead of computing its inverse and applying.

[manic cairn]

how deep do you want to go?

this is basically the study of cardinals

books on set theory will have stuff on them

[restive hawk]

Good book on diophantine equations (no calc pls)

[manic cairn]

lang has a book on this

haven't read it

but i assume it's good:

https://link.springer.com/book/10.1007/978-1-4757-1810-2

[restive hawk]

alr ty

[manic cairn]

it might have calculus stuff

[manic cairn]

don't actually go out and buy this if you don't know calculus

it was a joke

[restive hawk]

oh

[manic cairn]

looking through it, there is technically no calculus

[restive hawk]

alr ill have look

[manic cairn]

these are the first two pages:
https://link.springer.com/chapter/10.1007/978-1-4757-1810-2_1

of the first chapter

[ionic portal]

very deep but starting from fundamentals

maybe u could link a sequence of books

if one doesnt have everything

[lime vessel]

"Very deep" could be Jech's Set Theory

@gray gazelle

[stuck zephyr]

try with khan academy then

do you have your own textbook?

from school

maybe your parents wants you from that if it's not online

but like can't you tell them online is better because it has videos?

;-;

yeah it's good

[lilac raven]

any good book recs for self studying odes? professor for the course is using boyce and diprima elementary differential equations and boundary value problems

[vast jackal]

Get a mathematical handbook refresh your brain with some soviet era books and yeah serge lang too it's great (just tryed it) old and modern is the best to supplement

Quadratic equation is easy i say

[vast jackal]

You get everything you need in there but better to reset and do the foundations

[surreal meadow]

any book suggestion about set theory and proof writing?

[stark bone]

What're the best sources, books that contain the best exercises tho for Complex variables?

[grand thistle]

can you guys give me some recommendations on some relatively easy to digest books to help me get back into math

i just rlly lost interest in the last few months or so with school and everything

something at the mid/late undergrad level please

i think the last time i read hatcher i lost interest because it was a bit too difficult/unmotivated for me and also cuz i just didnt rlly feel that much interest in algebraic topology

i would also like for it to be a textbook in a field not just some like history of math thing

[daring lake]

Jay Cummings or https://www.people.vcu.edu/~rhammack/BookOfProof/

[grand thistle]

im thinking of something like generatingfunctionology by wilf except preferably outside the realm of combinatorics, i dont rlly mind the field as long as it’s outside of combi

[remote sparrow]

https://www.amazon.com/Mathematical-Logic-Oxford-Texts/dp/0199215626

[grand thistle]

ok wait sorry i shoulda clarified

im looking for smth adjacent to or close to algebra analysis topology or geometry

rather than like combi or logic or foundations

ive already got experience in basic algebra, (real) analysis, measure theory, point set, and i guess im acquainted woth algebraic topology so something aside from those would be nice

[hazy elk]

Maybe a more problem oriented book might interest you? How about Problems in algebraic number theory- V Ram Murthy, its a DIY ANT book.
"Office hours with a geometric group theorist" and "Dynamics done with your bare hands" are also cool problem oriented books.

[remote sparrow]

functional analysis, measure-theoretic probability theory, dynamical systems, and differential geometry are some directions you can go off in

some basic category theory wouldn't hurt (pretty algebra adjacent)

[hazy elk]

You could actually look into Michio Kuga's https://link.springer.com/book/10.1007/978-1-4612-0329-2 , it covers some interesting material

[gray jungle]

a less advanced option but a lot of fun nontheless is hoffman kunze linear algebra

[hazy elk]

And might get you motivated to study alg top again

[pure walrus]

any book recommendations for igcse ?

[manic cairn]

What’s a brisk introduction to ODEs that’s both rigorous and covers everything that would be required for an intro ODE course

same thing for PDEs

(also, please ping me, I won’t get it otherwise

)

[remote sparrow]

Intro ODE can mean different things. It could mean a classical course that focuses on analytically finding solutions (as represented by Boyce and DiPrima), or it could be a more modern course that emphasizes modeling and qualitative analyses, with an eye towards a dynamical systems perspective (as represented by Blanchard, Devaney, and Hall).

[manic cairn]

I mean mostly a classical course, so I can do physics questions by hand

[remote sparrow]

undergrad PDE mainly focuses on the analytical solution of a very restricted family of PDEs (although they appear often), while a graduate PDE course will depend a lot more on functional analysis, and the main concern is proving theorems about existence and uniqueness of solutions

[remote sparrow]

boyce and diprima is good enough for your purposes

there are lots of choices out there though

one that's free online is the one by william trench

[manic cairn]

Does the edition matter?

[remote sparrow]

tenenbaum and pollard is good

[remote sparrow]

not really

my professors recommend the 10th edition

[old elk]

I have on my amazon to buy
Differential Geometry by Don Carmo and
An Introduction to Manifolds Loring W. Tu
Which of the two should I buy to start studying this branch ?

[grand thistle]

oh interesting thank you these are what i was lookin for

[old elk]

[remote sparrow]

do carmo is a curves and surfaces book while tu uses some topology

kristopher tapp is better than do carmo if you want a curves and surfaces book

[old elk]

[round pelican]

I’m taking an intro to real analysis class this semester. After this class I want to continue learning real analysis and practicing proofs on my own. What are some good books? I’m interested in a book that is rigorous enough for me to grow but not so rigorous I won’t understand anything lol.

[finite gale]

you're going to have to give a bit more information on what your intro real analysis class is covering this semester

[round pelican]

According to the syllabus the chapters covered are:

Chapter 3: The Real Numbers

Chapter 4: Sequences

Chapter 5: Limits and Continuity

Chapter 6: Differentiation

Chapter 8: Infinite Series

So far we’ve gone over neighborhoods, deleted neighborhoods, The sup, inf, the completeness axiom, open sets, closed sets, boundary points, interior points, accumulation points, sequences, convergence, infinite sequences, monotone sequences, heine-borel theorem

[stuck elk]

1. Basic Analysis,
2. Elementary Analysis by Ross,
3. Understanding Analysis,
   Are all good and very introductory. For something more friendly and somewhere between calculus and analysis, Spivak's Calculus is pog.

If you need lectures, I liked these https://youtube.com/playlist?list=PLUl4u3cNGP61O7HkcF7UImpM0cR_L2gSw&si=SBVueGFLn3mN_AzT

Can be a little dry at times

[round pelican]

Sounds good. I’ll give these a look. Thank you for your recommendations!

[old elk]

Real analysis elon lages lima
Real analysis Jay Cummings
Mathematical Analysis A Concise Introduction

[analog spruce]

Intro to Analysis by Rosenlicht

Is quite neat as a supplement

[remote sparrow]

https://www.youtube.com/watch?v=yosbdRp6qws

[heady ember]

Schroder or Abbott would probably be good picks

If you're using Schroder, just an fyi that there's an error in chapter 3 that's not covered by the author's errata

The error is in the theorem's statement

(ignore the two proofs down there, those are mine that i used to illustrate the importance of L to the theorem)

[west ore]

Hey I've recently started studying Computer Science and am thinking about getting a Calculus book. I've searched a bit online and found 2 I can get used:
Calculus: A Complete Course by Adams and Essex and Calculus: An Intuitive and Physical Approach by Morris Kline. I can try to find others if you find them more suitable

[vital bane]

arnold for ODE and evans PDE? (if you're looking for the classical rigorous treatment of both those topics)

[vital bane]

hey sean how's func anal and QM going?

[grand thistle]

i

did not learn those after all

cuz i lost motivation

after school began

[civic python]

I can’t speak for the other book, but Calculus: A complete course won’t really teach you the inner workings of calculus. Rather, the focus is on learning how to compute by example. Though, which book would suit you best depends entirely on your previous background, so I can’t tell you which is best.

[vital bane]

https://tenor.com/view/discipline-you-lack-discipline-south-park-gif-12150185

[west ore]

The thing is, I like this stuff and would like to go deep into it, but at the same time I need to pass my classes so I have to be a bit pragmatic.
My background is basically regular high-school math and now uni, I've just learned the Fundamental Theorem of Calculus (learned perhaps a strong word lol)

[undone finch]

hoi

shot in the dark kinda, but thoughts on "Using the Borsuk-Ulam Theorem" as someone with a bit of topology background who wants to be introduced to topological methods in combinatorics?

i'm like way more of a combinatorics person than topology

[pure walrus]

hey so I am an IGCSE student so do u have any book recommendations for mathematics IGCSE books? if plz do let me know @everyone

[mystic orbit]

My brother in Christ, did you just attempt pinging 200k members just for that?

[gentle arrow]

discord.gg/math

[gentle arrow]

177k*

[heady ember]

177,968*

[keen orbit]

177,972*

[gentle arrow]

177k±5%

[gray gazelle]

is there any book that focuses just on lines. So lines in 3D, and 2D. It needs to cover skew lines, all types of distances

so basically geomtry

but it needs to cover distance between a point and a line in 3D

and closest point problems

[slim bramble]

I don't think there is any book of that kind
you can read calculus books for that
single variables calculus for 2D lines
and Multivariable calculus for 3D
of course if lines are your focus you probably will just need to read the first couple of pages from each
or even just watch yt videos or read some article on it
or my personal favorite ask chat gpt

[vital bane]

I guess you're looking for a coordinate geometry book (aka analytical geometry)

[median saffron]

over the reals??

[shadow hedge]

Can anyone identify the differences between linear algebra done right by axler and linear algebra by friedberg. I started working on the axler book but in a while I will join a class that uses the friedberg. Will I have any missing knowledge if I just work through axler and will I later be able to solve the problems in friedberg after finishing the axler book?

[gray gazelle]

could I get some recommendations on which architecture books to buy as a first year?

[alpine rover]

what's a gentle book that provides an intro to algebraic geometry and covers algebraic curves?

[vital bane]

use both!

work through axler on your own time and in class work through friedberg

[shadow hedge]

I’m not sure if I will have enough time to work through both. Is the knowledge from axler not transferable to the other book?

[vital bane]

lol of course they're transferable, math isn't like currency

it's both linear algebra

use axler's 4th edition btw

[shadow hedge]

I would like to do both but in case of I do only one would that be enough to solve the other books exercises?

[vital bane]

of course

[shadow hedge]

And axler’s exercises are supposed to be harder right?

[gentle arrow]

shilov

[gray gazelle]

The simerilion

Forgot how to spell it. the nerd bible

[undone rapids]

What is the best book to study calculus by yourself? (no college or school classes)

[vital bane]

roman

[gentle arrow]

what do you want out of this

[vital bane]

honestly I'm thinking instead of finishing axler, I should just do dummit and foote and then do roman

[undone rapids]

uh

maybe the basics?

[vital bane]

spivak is good

[undone rapids]

im not sure

[gentle arrow]

do you care more about like

applications

or do you just wanna learn it for the sake of learning it

[undone rapids]

[high tulip]

I’d start with YouTube videos for basics. They usually incorporate a lot more visual techniques for teaching fundamentals and are less wordy

[vital bane]

you can still apply it if you learn it for the sake of learning it

[gentle arrow]

True...

[vital bane]

spivak's "calculus" is good

[gentle arrow]

calculus on manifolds

[vital bane]

yes

[gentle arrow]

im kidding dont use calculus on manifolds that's a different thing

if you want a rigorous treatment of calculus, use spivak

[vital bane]

spivak's calculus is more like sitting midway between a normal calculus book and a real analysis book lol

[high tulip]

Would anyone recommend “the pleasures of counting”

[gentle arrow]

tbh spivak is a good book

[high tulip]

As a pre uni book

[gentle arrow]

but i feel like its in a weird place

where its like

[vital bane]

spivak's "comprehensive introduction to differential geometry" all 5 volumes for learning hs calculus

[gentle arrow]

"if you want to seriously learn mathematics you should probably read a full blown analysis book like rudin/abbott/etc."

"if you want just the applications of it spivak is probably overkill and you will be fine with something like stewart"

[vital bane]

Lol yea it's right in between both of those

[gentle arrow]

good book but intended audience a bit weird

[vital bane]

I guess it's written for "serious high schoolers" or something

[gentle arrow]

i would still suggest to read an analysis book

[vital bane]

CoM

[gentle arrow]

neam i dont think suggesting CoM is a good idea to someone who has 0 background on calculus

[high tulip]

Any help guys?

[vital bane]

I have never read that book so

[high tulip]

I’m choosing between Abotts understanding analysis and A number theory book

[vital bane]

read the preface, that usualy states the intended target audience for the book

[high tulip]

I have

I think I just need to accept the struggle lol

And that it’s not going to be intuitive at first

[vital bane]

indeed, you'll get used to it

[undone rapids]

ok ima gonna chack spivak

btw it can be in my home

[frosty carbon]

It's been a long time since I've taken linear algebra and am thinking of returning to grad school for machine learning. My linear algebra and probablility knowledge is lacking. Any book recommendations for each topic?

[civic python]

Yeah, then you should probably stick to a book that favours computation. Though, i'd recomend you to check out the math sorcerer, he does plenty of book tips.

[sand crescent]

Anyone know a good accessible reference for deriving the semicircle law for wigner matrices?

preferably an analytic proof without graph theory or combinatorics arguments 😭

or random coulumb gas results applied

strong assumptions are ok

Don't need weakest assumptions possible if it makes the proof smoother

[mossy shell]

Anything i can learn about the why in math instead of just learning the subject and process of solving (algebra 2)

[formal bronze]

What do you mean by 'why'? Also for algebra check out 'Abstract Algebra' by Dummit and Foote.

[mossy shell]

Like im just taught the unit and what to do not why it happens like i dont even know why x^2 bounces on a graph i just know it does

[crimson leaf]

I would not recommend D&F to someone in Algebra 2

[formal bronze]

Isn't algebra 2 like field and galois theory?

[crimson leaf]

No

Algebra 2 is like highschool math

[formal bronze]

oh ok

[mossy shell]

What would you recommend?

Or even youtubers

[crimson leaf]

Probably khan academy

[lusty ermine]

hey guys

can anybody recommend me a good resource for cracking this:

,tex Let ( S = {(1,0,2,1),(0,1,1,0)} ) and ( T = {x \in \mathbb{R}^4 \mid x_1 + 3x_2 + x_3 + x_4 = 0; x_1 + x_2 = 0} ).
Find, if it exists, a subspace ( W \subset \mathbb{R}^4 ) that simultaneously satisfies
( S \oplus W = S + T ) and ( T \oplus W = S + T ).

[hasty eagle]

レナト (renato , ping if reply)

[stray veldt]

this is #book-recommendations ?

so any introductory book on linear algebra?

[clever tree]

New oxford maths 7th edition level 1

Question

Find 3.086107÷5.001

What is De Morgans Law?

[gray gazelle]

Can someone recommend me book for learning contour integration and complex analysis application from basics

[vernal eagle]

I need a book recommendation for self-studying general topology. It will be my first encounter with the subject. I am comfortable with real analysis, group theory, and ring theory.

[gray jungle]

Not a book but the following lecture notes from a course at utoronto are great , comes with a large list of exercises from various books https://ctrl-c.club/~ivan/327/?resources @vernal eagle

[dim sierra]

I’d also recommend Tom Leinster’s lecture notes (can be found on his website). He also has problem sets with them and in my opinion he motivated stuff very well

[dire torrent]

Topology without tears ..? I haven't read it. Just came to my mind. Most say that it's good and also is in accordance with its title. That is, I think, suited for self-study.

[dire torrent]

Munkres is pretty famous and most say it's actually really good. I don't know if it's suited for self-study. I should say, I haven't read it either. In fact, I have read no topology.

[finite gale]

@mystic orbit

[dire torrent]

Boyce and Diprima or Shepley L. Ross? Which is more focused on theory and explanation?

I do want problems but they should not be the focus because I can always look for problems from other resources.

Any other book that does the job too?

[mystic orbit]

my time to shine, babyy

[mystic orbit]

lee's intro to topological manifolds

100%

dont' believe those munkres shillers, lee's just perfect especially if you were more interested in manifolds and manifolds-esque things and especially if you were self-studying

[gray jungle]

Warning!! The person above is being a bit silly

[mystic orbit]

Warning!! The person above is a munkres shiller!

[sage python]

DarQ is correct

[sage python]

@3trunk first off no need to insult over nothing, second it's because Lee focuses on the more important examples

[dusk wind]

libretext math

instead of Munkres you could use something that was made around 2020

that way you're not shilling anything and actually progressing current works

[zinc lantern]

Hey guys. I’m a sophomore self studying for bc calculus. I have online lectures which are really great. But as a supplemental textbook, I was torn between early transcendental 9th edition by James Stewart. Or calculus by Gilbert strang.

Any recommendations would be greatly appreciated

[mossy shell]

Ive got the pdf if you’d like for the 9th edition transcendental

[zinc lantern]

That would be wonderful thank you

[mossy shell]

👌 just give me a min and ill dm you it

[mossy shell]

Sent it

Has anyone read a mind for numbers?

[mystic orbit]

for someone that speaks so authoritatively you'd think you'd bring better arguments than "that is really dumb"

[turbid fox]

munkres kinda boring

[sturdy shore]

willard clears both

[dim sierra]

Lee >>

Also who cares about anything but manifolds

🥱🥱🥱

[sleek hawk]

The entire field of algebraic geometry

[wary igloo]

Recommendations for stochastic calculus?

Steele vs Shreve's texts?

[manic cairn]

munkres is what i used when self-studying topology myself

it's really good

[remote sparrow]

@orchid mortar

[ocean spindle]

I used early transcendentals for calculus and strang for linalg iirc

[zinc lantern]

I see thanks

[tardy oasis]

I will second the munkres hate

[indigo mesa]

Those are morally manifolds

[smoky zephyr]

morally?

[gray jungle]

what i understood is that "morally true= technical details aside it should probably behave this way"

[stray veldt]

a big part of algebraic geometry is rebuilding things from differential geometry using only algebraic tools

[orchid mortar]

I'm not qualified to compare, and I have not looked at Shreve's solo textbooks but these are finance-looking textbooks. You can opt for a purer approach with Karatzas Shreve Brownian Motion

[marsh ingot]

Book recommendatios of Hörmander where talks about his method for Dolbeault operators?

[gilded ferry]

My friend has two topology books: 'Topology' by Munkres and 'Topology and Modern Analysis' by George Simmons. They want me to pick but I don't have much experience with the field besides kinda doing 'Intro to Topology' by Bert Mendelson. Which one should I choose for a proper first course seeing that I have some background in algebra and analysis?

[mystic orbit]

proper first course in what?

I would pick munkres just coz it makes for a phenomenal reference even after finishing a course in general topology

[gilded ferry]

Topology. I used Mendelson's book a while back that's why this time I said proper

[mystic orbit]

oh.

tbh besides munnkres I'm not familiar with any of the references you mentioned

[gilded ferry]

[wary igloo]

Thanks. I'll check out that text this weekend.

[orchid mortar]

By the way, finance-looking isn't a bad thing. They are indeed more concrete

So it depends on what you're looking for

[wary igloo]

I was looking for something with both flavors - I thought Steele's text was a good fit for that. The text you referred to is more pure, which will act as a good reference if I move into the more ambiguous territory with the more application-based texts. Thanks again.

[ocean mulch]

@fossil arch wanna share you experience?

[fossil arch]

Munkres is boring and horrendously slow

Lee is just slow, but if you get bored of lots of chatter then you’ll still get bored lmao. But I liked it

Maybe I get hurt for this but I think topology is best taken after some analysis :D having a concrete framework in which you can place concepts makes it a lot easier to understand

But yeah can’t go wrong with Lee

[remote sparrow]

maybe try gamelin?

[fossil arch]

Isn’t that complex anal

[remote sparrow]

https://maa.org/press/maa-reviews/introduction-to-topology

no

[fossil arch]

YOOO ROBERT EVERIST GREENE??

Descendant of Galois?!?!

Kidding

Isn’t he Evariste anyways

[remote sparrow]

https://maa.org/press/maa-reviews/general-topology-0

also willard

both cheap and more concise than munkres

[fossil arch]

@vernal eagle these r for u bb

[fossil arch]

I’m already a topology pro dw

[gray jungle]

my professor topology notes are basically 40 pages and have everything you will ever need if anyone is interested lmn , probably the easiest to read top book out there

[gloomy fractal]

hy

[dusk wind]

professor shill

[marsh ingot]

No book recommendation about Hörmander? :c

[somber aspen]

Land of stories

Best book series if your 8-13
Full of excitement and very addicting to read

[snow flower]

Does anyone have a good recommendation for resources on computational complexity theory?

[rustic grove]

Ill take them...

[remote sparrow]

https://4chan-science.fandom.com/wiki/Computer_Science_and_Engineering#Automata,_Computability_Theory,_and_Complexity_Theory

https://www.logicmatters.net/tyl/

#book-recommendations message

[remote sparrow]

oh, you only mentioned complexity theory

i thought you wrote computability somewhere

diligentClerk's reading list doesn't have anything for computational complexity theory

[fierce hedge]

That sounds a bit too concise? I think Hatcher's notes are still 60-70 pages

[willow adder]

👀 (perhaps I will take as well)

hmm...i'm surprised there are not many math audiobooks out there, but I guess it would be hard to convey one purely with audio

or maybe there are and I am just not looking

[tardy oasis]

i think an audiobook would be miserable for math

please, explain to me how this nightmare diagram looks

[formal bronze]

Pontryagin

[crude sage]

Simple: Just read the .tex file aloud

[remote sparrow]

@sturdy shore after you finish axler measure theory, do you plan to read a more general book like folland or bass?

do you feel like you're missing something from only reading axler

[sturdy shore]

I'm only using axler's book because of a class, I know pretty much all the stuff in it already

there's stuff in folland not in axler that you'd need for measure theory, but you can just look them up as you go

also, bass is less general than axler

[remote sparrow]

really now

good to know

guess i won't buy folland too soon

i'll just get axler as my main text with bass and schilling as supplements

schilling especially since he has a full solutions manual

https://www.reddit.com/r/math/comments/10tqj46/resources_for_measureintegration_theory_and/j78ixw0/

i found a review for wheeden and zygmund

https://maa.org/press/maa-reviews/the-lebesgue-integral-for-undergraduates

https://maa.org/press/maa-reviews/a-user-friendly-introduction-to-lebesgue-measure-and-integration

https://maa.org/press/maa-reviews/a-radical-approach-to-lebesgues-theory-of-integration

these measure theory books seem cool for undergrad

https://maa.org/press/maa-reviews/real-analysis-theory-of-measure-and-integration

someone in the statistics server is a big fan of this book (not for undergrad)

https://www.amazon.com/Problems-Proofs-Real-Analysis-Integration/dp/9814578509

there's also a companion volume to yeh with solutions

[sage python]

Wait really?

I guess idk Axler but

I felt Bass was pretty "standard fare" somehow

[halcyon scaffold]

Just read sipser

[remote sparrow]

sipser might be a good introduction but arora and barak would be more thorough, no?

[median saffron]

https://tenor.com/view/that-one-there-was-a-violation-that1there-was-violation-violation-that-one-there-was-a-violation-personally-i-wouldnt-have-it-that1there-was-a-violation-personally-i-wouldnt-have-it-gif-20040456

[thick monolith]

Hello, I haven’t taken any formal classes of mathematical logic, but want to read about well ordering principle and mathematical foundations of logic, where can I find this?

[lime vessel]

^

[remote sparrow]

https://www.logicmatters.net/tyl/

also a good choice

[gritty sparrow]

Hi, I'm studying discrete mathematics right now and I would like to have a book to supplement my university's syllabus. Which one would you recommend?

[gray gazelle]

I remember mendelson was pretty nice

[gray gazelle]

Discrete math is a very wide topic. Can you tell us a bit more about the content of your course?

It could be anything from combinatorics, graph theory, posets, polya theory, ramsey, t-designs, even logics and a million other things

[raw juniper]

Are there any books that specifically help with cancelling fractions?

Trying to reassure and master my arithmetic

[gritty sparrow]

The course has the following chapters: integers (rings, order, prime numbers, Chinese remainder theorem public key cryptography), graph theory, generating functions and recurrence relations

[vast jackal]

looking for hardcore algebra 1 book with fast progress

[dusk wind]

wdym by hardcore? you could probably rep through khan academy tests

[sturdy shore]

so is axler

but it does cover some more stuff from what I've seen

[vast jackal]

i don't like video ones. Maybe im gonna miss something if im gonna skip it

pretty much time consuming for me (for my opinion)

[sturdy shore]

well, bass does have caratheodory extension theorem and I don't believe axler has it, so that is one edge for bass

[dusk wind]

thats fair and I agree with you

[sturdy shore]

okay bass also has riesz rep which axler doesn't , so that is a very important edge

[dusk wind]

you won't miss anything by doing lots of problems so you'd want a book with good ones and possibly a quality answer sheet

[sturdy shore]

otoh, axler has spectral theorem for compact self adjoint operators

[vast jackal]

i only use videos if it's a bit confusing to me

[sturdy shore]

I don't believe bass has egorov, axler does

[vast jackal]

eh

[sturdy shore]

?

bass has egorov or?

I am guessing you pinged me mistakenly

[willow adder]

Now i'm even more curious if there are any blind mathematicians? Like born blind or w/e...do they just get whole book in braile or smth? Audiobook? Braile diagram?

[vast jackal]

no,no i though you are talking to me lol since you didn't reply to any other messages....

[sturdy shore]

so I'd like to revamp what I said, it might be the case that bass actually covers more ground for measure theoretic stuff, since riesz is such a big deal
but axler puts so much effort into pedagogy, so I'd always recommend it over bass for a first time (i.e. knows nothing about measure theory) reader

you can always use both though, bass is also free online right?

[dusk wind]

but it's algebra 1 so maybe khan academy would be enough but some suggestions for you

https://www.openalgebra.com/
https://math.libretexts.org/Bookshelves/Algebra/Advanced_Algebra/01%3A_Algebra_Fundamentals
https://2012books.lardbucket.org/pdfs/advanced-algebra.pdf
useful for later https://www.stitz-zeager.com/Precalculus4.pdf, https://www.stitz-zeager.com/szct07042013.pdf

that 3rd book says 'advanced algebra' but it's mostly just a compilation of content from the same author, but has decent accessible diagrams

[dusk wind]

there's also openstax https://openstax.org/subjects/math#Developmental Math @vast jackal
probably the fastest option

[sage python]

@sturdy shore Yeah I think Bass has Egorov as well. And in the last few chapters he does some spectral theory, though idk how deep he does into it since the last few chapters are more just intros to various things than serious excursions, so maybe at that point just do functional analysis

[umbral peak]

Is Serge Lang's A First Course in Calculus a good resource to review single variable calculus?

[sturdy shore]

yeah it does seem to have Egorov

[cinder tundra]

anyone have any suggestions for discrete geometry books that isn't Zieglers, Grünbaum, Gelfand, Cox & Little & Schenck?

i've already read most of the sections and solved most of the problems in all of the books that are relevant to my course exams this winter, and i would like more practice. is there anything that deals with a lot of computational questions? i want to practice dealing with the very dull, computational stuff as i am highly prone to mistakes in those.

also something that covers balanced fans, weighted fans, and push-forwards in relation to this would be very appreciated

[remote sparrow]

i'm actually using this for a reading course i'm taking right now and it's pretty dull

[gray jungle]

Just have to randomly throw that Taos introduction to "Why learn Real analysis" in his first analysis book is phenomenal , went back to it and wasnt aware of how well written it is

[gray gazelle]

Hm yeah i totally see why it can be dull especially if youre self studying

I was lucky enough to have an amazing professor who motivated everything and i just used it as reference

[gray gazelle]

Hmm i really dont know what to suggest here ... generally discrete math books which cover such different topics are really poorly written, so i would be inclined to recommend a specific book for each subject, however its bot reasonable to cover that much in one course ... i would suggest you try to get any professors notes or just try to look for the stuff you encounter online

[remote sparrow]

I rather don't appreciate how much emphasis is given on writing down proofs in Hilbert systems (at least, my professor seems to like assigning these problems)

seems all rather technical and unintuitive. maybe my professor should instead have assigned problems that exploit how easy it is to prove metalogical results in hilbert systems rather than doing things directly with the syntax

may as well have chosen a book that uses natural deduction instead

e.g. van dalen

[glacial helm]

i'm a computational mathematics student really curious about fluid dynamics
just finished calc 3 and algebra 2
and i wanted to start learning more about it
in my uni (brazil), there's no introductory books specially about it (the applications into computational physics)
and when i search in the internet for some guidance
it's just content or some really advanced stuff that i fr dont understand yet
so i dont know where to start
does someone have a reference or smth?

i know it's early but i really wanted to start getting a grasp out of it

[lusty ermine]

hi guys

do you guys have any practice for direct sum of vector spaces or learning latex

[remote sparrow]

https://tobi.oetiker.ch/lshort/lshort.pdf

https://en.wikibooks.org/wiki/LaTeX

[distant spear]

https://texnique.xyz/ -online game

[gray gazelle]

Hello. I am looking for Real Analysis textbook recommendations.

Like a second course in the subject

[elder python]

Tao, Bartle, Rudin

[gray gazelle]

don't like either of em lmao

[elder python]

Lol why?

[gray gazelle]

just didn't vibe

[elder python]

Hnn you like use pdf or physical copy?

[gray gazelle]

I use both

[elder python]

What kind of book would you prefer then?

Like vibe, what kind?

[gray gazelle]

something which is a bit serious. not those books which are written to appeal to freshmen.

[elder python]

So like for early grad?

What about apostle?

[gray gazelle]

upper undergrad

[elder python]

Let me check my lib there was one more

[gray jungle]

have you tried apostol ?

[elder python]

So yeah Rudin again the advance one complex and real, and Fitzpatrick real analysis

[gray jungle]

also i should mention that if taos first book wasnt "up to pace" he does have a 2nd book thats a bit more advanced

[elder python]

I haven't read Fitzpatrick but its recommended a lot

[gray gazelle]

no

[gray jungle]

i have a hard time believing rudin is not a serious book , it is quite professionally written with little handholding

i dont know what would be more advanced thats not just straight up measure theory

[gray gazelle]

I think I might give rudin a shot

but is smth like pugh a better alternative?

[elder python]

1st one if is like soft analysis, building intuition which i really enjoyed, 2nd is like extention of it, has more topological stuff like metric spaces, Lebesque measure which was also enjoyable read for me

[gray gazelle]

going through forums I found some recs

[elder python]

Try Fitzpatrick

[gray gazelle]

amann escher, pugh, zorich

[elder python]

Zorich is nice read a bit dunno about others

[rustic grove]

You would find that if you used Bartle as a reference and another book, say Ross or Abbott, you would get a lot out of it.

[dire torrent]

I will preface by saying that I have read no amount of Analysis whatsoever.
In my opinion, the book that looks the most dense packed with content, advanced(graduate level) and has good writing is Terence Tao's 1 and 2.
I personally plan to learn from Apostol, then Royden and then finally Tao.

[gray jungle]

I think tao is a great book but i think its neither dense nor "graduate level" , it covers roughly the same things apostol does if not less

royden is a graduate book on the other hand

[dire torrent]

Never knew..

[dire torrent]

I mean two volumes but then also so dense. So I just assumed..

[gray jungle]

When people say "Real analysis" really falls into roughly "3 levels" , you have books that cover just rigorous calculus on the real line (such as taos first book) you have books that work on general metric spaces (like rudin , abott* and taos 2nd book) and then graduate real analysis is a whole different subject that covers measure theory , topology and functional analysis (such as royden)

[dire torrent]

Functional Analysis is a sub-topic of Real Analysis?

But I guess you use it to study real Analysis..

[gray jungle]

not really but many graduate "real analysis" books will cover functional analysis

[dire torrent]

why..

[gray jungle]

its important

sorry

its very important

[dire torrent]

I mean if it's not about real analysis..then..

[gray jungle]

thing is , graduate real analysis starts with measure theory

and measure theory very naturally starts going into functional analysis territory

[dire torrent]

I thought you use functional analysis to analyse real-valued functions and thus they include it in real analysis books.

[gray gazelle]

how much of analysis should one typically cover in undergrad?

[gray jungle]

eh , not really

[gray gazelle]

real and complex analysis?

[gray jungle]

and arguably measure theory and basic functional analysis ( at least some elementary hilbert spaces)

[dire torrent]

That's what my college does. Two courses in Real analysis and then one in Complex Analysis.

[gray gazelle]

I have 2 years left 🥲

[gray jungle]

that is enough time to cover the basics of every branch of analysis

[dire torrent]

are you saying it's too much or not enough time..?

[gray gazelle]

I graduate in 2025

[gray jungle]

real , complex , measure , functional , numerical , vector etc

[dire torrent]

hey same..

[gray gazelle]

how much time would each take?

[gray jungle]

like you can be done with basic real analysis in 3-4 months --> cover complex analysis and numerical analysis in the next 3-4 months --> measure theory and some functional in 3-4 months

and you still have time to take other stuff

[gray gazelle]

hmm

[dire torrent]

It takes a quarter of a year to learn RA basics?

[gray jungle]

on average

[dire torrent]

holy

[gray gazelle]

RA was hard asf to begin with

https://ocw.mit.edu/courses/18-100b-analysis-i-fall-2010/

ig ill do this to begin with

[dire torrent]

Do y'all feel powerful after having learned RA? like intellectually?

[gray jungle]

@dire torrent if you want some motivation to "why do real analysis" i highly recommend reading the first chapter in tao book analysis I

[gray gazelle]

[gray jungle]

he gives some motivation as well as some situations where a knowledge of real analysis is helpful

[gray gazelle]

hey james, tell me about tao

[gray jungle]

starts here and then gives a bunch of examples

[gray gazelle]

like I have heard lots of criticisms of it in mse

[gray jungle]

i personally used tao and i think its very good if you dont have a solid proof foundation

it teaches you the way of thinking as a analyst before diving into the meat of the subject

and you have to learn how to walk before you can run

take in mind i was using it as my "learn proofs" book cause i was using hoffman kunze for linear algebra

but if you are already familiar with proof writing or have taken a discrete math course etc