book-recommendations

[timid cosmos]

Cap

(Share if you fr though)

(please share though)

[heady ember]

Paid services go against the rules iirc

[crystal lion]

recall again

[rapid lily]

Yes

At least from what I've heard it can

[loud cradle]

the book has an appendix that briefly covers riemann integration and a few related topics, but it does implicitly assume that you know some other notions from analysis, in particular comfort with series, uniform convergence, etc

you don't necessarily need a full blown analysis course, but comfort with rigorous calculus at the level of say Spivak would be good to have

[outer nest]

ok what did that link do...

and wtf was it

[uncut tusk]

what is a good linear algebra book that is easy to understand I want to try to learn it during the summer

[remote sparrow]

#book-recommendations message

[uncut tusk]

isnt this book and explanation covered on youtube?

by a channel

[remote sparrow]

can you link me the video

[uncut tusk]

https://www.youtube.com/watch?v=JnTa9XtvmfI&t=303s

Uses the same book recommendation u gave me and explains all topics

he also has marked specific problems for u to solve in his version of the pdf

[remote sparrow]

oh yeah, dr. hefferon. yeah, he has all that stuff online. he has his own youtube channel, by the way; his online presence is not limited to freecodecamp.org's youtube channel.

a great self-study resource for linear algebra

[uncut tusk]

lmao i jsut wanna study this course before i take it so i can take another math class

Any books for Discrete math?

I already taken a intro to discrete math course

[uncut tusk]

https://notesack.files.wordpress.com/2017/07/ebooksclub-org__discrete_mathematics_with_applications.pdf

^ this is a great book for beginners for discrete mathe

Explains all topics very well and understandable even if your bad at math

[candid creek]

Any book recommendations for practising sigma/summation notation?

I want to be able to adeptly use all of these identities

https://en.wikipedia.org/wiki/Summation

[rapid lily]

You can look each one up

You don't really need a book to specifically teach you those

But if you want to learn about sums in general, you can take any real analysis book. It should have a section on sums.

[gray gazelle]

^you don't really need one but if you still do then there is "Sums and Products" by Titu Andreescu having all sorts of olympiad questions with techniques.

[gray gazelle]

rosen is what everyone follows unless you are in a maths degree

[heady ember]

Rosen is very boring imo

I did about 30 pages of it last time and it was

[sudden kindle]

Ireland and Rosen?

Yeah I got bored with it too

When I first started reading it, I didn't read much either

[gray gazelle]

Kenneth Rosen

Ireland & Rosen is the NT book i think

[maiden halo]

RE linear algebra: Mike X Cohen's book, while very clear/understandable, is very basic IMO. There aren't many exercises and they're pretty straightforward. It's really cheap as far as 500+ page books go, though, so I recommend it as a supplement

[sudden kindle]

Oh i like his number theory brook

Elementary Number Theory

[mellow wren]

Idk I find rosen very fun

I've gone through like 200 pages of the book up until now and I'm having a blast ngl

Ooohhh

rosen

not the NT rosen lmao

Fuck ok lol I take it back I haven't read discrete math rosen only NT rosen

[rapid lily]

How can it spend over 1000 pages covering discrete maths?????

[hollow fjord]

What is the best book on Linear Algebra? I have researched quiet a few namely: LA done right by Sheldon, Linear Algebra for everyone by Strang, Intro to Applied LA by Boyd
So far am finding the new book by Gilbert Strang: Linear Algebra for everyone very good. The professor has poured in his lifelong learnings from teaching LA into this book. A very novel approach.
And yes, I am learning LA from the point of applying it towards my AI/ML journey.
Sorry, shall I post this in the book recommendations channel?

[heady ember]

Yeah I was talking about discrete Rosen, but all's good

[heady ember]

Yeah I don't get it either. Instead of that you should spent 2000 pages covering an incredible amount of axiomatic set theory that you wouldn't need unless you're gonna be a set theorist / specialise in foundations stuff

[remote sparrow]

linear algebra is such a ubiquitous subject that any one book cannot possibly hope to cover everything, and because it is so diverse, there isn't really a perfect book.

[hollow fjord]

thats true, it requires an eclectic reading. but still some books are much better than others

[hidden fractal]

I would like book recommendations on integral and multivariable calculus

[remote sparrow]

#book-recommendations message

[swift dome]

found this book from sale any reviews for this one " Foundations of the Theory of Probability - by A N Kolmogorov"

[brave pivot]

Isn't he the guy who founded the probability axioms. I might be wrong. As far as old texts go, they are quite rigorous- not quiet intuitive. I haven't read that particular book, so please don't take my word for it.

[gray gazelle]

any book recommendations to learn graph theory and finite fields?

[sage kelp]

What series of books would you recommend to have a solid foundation on real analysis

[gray jungle]

What level of real analysis are we talking?

[sage kelp]

Going from basics to understanding standard material. From zero to half-hero lol

[ocean mulch]

Tao

Or rudin

I guess Princeton's Lectures on Analysis is fine, but the level is quite high. Not for freshmen, unless you're Tao.

But they explain things extremely well. That series saved my ass in Measure theory.

[ocean mulch]

depends on your level. Ig graph theory and finite fields are two separate things, you won't find them in the same book.

[gray gazelle]

i wanna learn both things at an introductory level. which book can i refer to?

[ocean mulch]

I'd say it's best to learn them separately. Also depends on what you know already about each of the topics

[sage kelp]

Something not that advanced. Seriously, for a true beginner

[ocean mulch]

I heard good things about Tao's Analysis series, except that he goes very detailed and conversation-like. Might be your taste, idk.

[gray gazelle]

my knowledge about those two topics can just be equated to "being aware of their existence"

so what books can i refer to

[ocean mulch]

I always like Herstein for algebra in general. Chapter 5 of his Topics in Algebra, 2nd ed is about fields and everything up to Galois stuff. It seems light enough.

As for graph theory... this one's tough, because I didn't learn from any books or courses.

I guess there are books that discuss both in a more informal setting, which is great as a primer and not to scare you away. But then I have no clues on that.

[maiden halo]

I read "Introduction to Graph Theory" (Dover Books on Mathematics) by Trudeau years ago. It's pretty short and definitely introductory so it wouldn't be a good standalone book IMO

[ocean mulch]

There's also Graph Theory by Diestel, I just checked, everything's in there, and it seems light enough.

I hate that no books have much emphasis on trees. I mean, I learned graph theory from algorithm side, and trees are a great toy to build intuition, before moving on to more complex graphs.

[heady ember]

Dover books are normally reasonably priced too iirc

But you can always use... creative ways you get a copy. Then print it out at a local shop

[ocean mulch]

You should never have to pay to get books.

[heady ember]

My copy of Jacobson I bought last Christmas was only $18, an absolute steal

[swift dome]

What's your thaughts " Foundations of the Theory of Probability - by A N Kolmogorov"

Should I be getting it

Just drop books pdf

Yep most of the sites are blocked for me , i use vpn for that

I looked through the pdf , i should definately purchase it

Thanks man

[heady ember]

Latex, which can be run with a wide assortment of various applications. Like VSCode

[sage kelp]

Someone? Some other suggestions? Like even if the books are not your typical ones such as Abbott, Bartle, etc. ?

[remote sparrow]

zorich. amann escher is considered a viable text in germany. duistermaat kolk for multivariable calculus specifically. there aren't really many multi-volume series that i know of, though. a single textbook is already a substantial achievement; a series even more so. you can look here for more series in analysis: https://4chan-science.fandom.com/wiki/Mathematics.

[sage kelp]

Or not necessarily multi volume series, even books from different authors. Thanks for the link! I will check it out

[gray gazelle]

Cannot do better than rudin (if you are doing a course simulataneously) and bartle (for self study, although questionable choice). There is also a nice book by david brannan which doesn't cover as much as the other two but the topics are really well explained. There is another one by Apostol (two volumes), i have heard good things about it but haven't read personally so cannot vouch for it.

Some other books my course recommended however I haven't read any. Only listing since you asked about other texts:
An Introduction to Real Analysis, by W. Wade; Prentice Hall
Real Analysis with Real Applications, by K. Davidson and A. Donsig; Prentice Hall
Real Analysis, by J. Bruckner, A. Bruckner, B. Thomson; Prentice Hall
Elementary Real Analysis, by J. Bruckner, A. Bruckner, B. Thomson; Prentice Hall
Real Analysis: N.L. Carothers, Cambridge University Press

[remote sparrow]

the two volume apostol books are not quite analysis per se, more like rigorous calculus plus some linear algebra

he does have a real analysis textbook, however, separate from his calculus textbooks

a sequence of books in analysis you can do is abbott > carothers > schilling/axler mira/bass. abbott for single variable real analysis, carothers for metric spaces and an introduction to lebesgue theory, schilling, axler, bass for more in-depth measure theory.

multivariable calculus is interesting. you can do a relatively elementary approach, such as the way hubbard or shifrin might do. munkres or spivak are standard for many colleges. or you can approach them as manifolds, generally covered in something like tu's Introduction to Manifolds, which i think covers up to stokes' theorem

[vital bane]

that is not multivariable calculus that's basically diff geo (loring tu thag is)

[gray gazelle]

yeah i meant that one

[gray gazelle]

have you studied all of these?

[rapid lily]

Real Analysis by Carothers is ok for a second course. I don't know about the others.

Although it does not cover differentiation and assumes a previous course in real analysis

So it doesn't work too well for a first course unless you are prepared to learn other theorems or assume them on the run

[narrow relic]

Have you read Carothers, Sour Drop?

[rapid lily]

What kind of calculus? Is this single variable calculus? With proofs or without?

[cinder quiver]

Introductory undergrad books for probability

[sage kelp]

Thank you! Would you consider though other alternatives to Abbott?

[rapid lily]

Calculus by Spivak may work well. I've also heard good things about the suggestion by amiya.

[hearty steppe]

I think Abbott is pretty self contained. I mean it’s hard to find an analysis book more broken down than that.

[drowsy thicket]

Does anyone know both Stochastik (probability theory) by Georgii and Wahrscheinlichkeitstheorie (probability theory too) by Klenke?
If so, which one would you say is better?

They are originally german, maybe there is a translation for them though (I think there is one for Klenke)

[grand thistle]

klenke does have a translation yeah

imo it looks very dense and complete

a reference text for sure

[sage kelp]

But is Abbott good for the exercises?

[hearty steppe]

I think so

It’s not as difficult as a lot of analysis books though

[sage kelp]

Oh okay, the thing is that I’m not so fond of Abbott, so just looking for alternatives

[remote sparrow]

multivariable calculus and manifold theory are closely connected, and tu does get up to stokes' theorem, which is what multivariable calculus classes get up to. it can work for someone who has a particularly strong background in real analysis (say, from baby rudin), linear algebra (something like axler, hoffman kunze, or FIS) and algebra (you'll need to know what a module is, which dummit and foote covers). knowledge of point-set topology is optional, as the necessary topology knowledge is covered in the appendix.

[vital bane]

Honestly when someone says "multivariable calculus" the only thing that I get reminded of is classes that cover calculus on R^3 and curl, divergence and gradient etc.

But I guess what you mean is analysis on R^n

[remote sparrow]

why don't you like abbott?

[vital bane]

oi mate you have a problem with abbott? then you'll have to go through me

[gray gazelle]

Recommend me a calculus book

I'm beginner btw

Book recommendation: The god of small things
its a really good book tbh

[remote sparrow]

#book-recommendations message

[swift dome]

Stewart Calculus might work

[remote sparrow]

#book-recommendations message

#book-recommendations message

[sage kelp]

Idk, just the exercises I don’t like. The text itself I think it’s good

[vital bane]

The exercises are good what dont you like about the exercises?

[rancid hollow]

abbott is like the friendliest real analysis test ever

disliking abbott is like disliking ur best friend

[sage kelp]

Have I been mi judging Abbott then?! Like seriously!

[fast thicket]

CGPBOOKS.CO.UK

[hearty steppe]

Yea Abbott is super easy compared to 90% of analysis books

[remote sparrow]

my recommendations were written with the assumption that everyone has seen partial derivatives and stokes' theorem from a lower-division multivariable calculus class that doesn't involve proofs. of course, the multivariable calculus recommendations range in abstraction and difficulty. for example, hubbard and shifrin were designed for strong students with solid background in single variable calculus, usually from ap calculus bc, but they are also used as analysis textbooks.

also, real analysis classes often last about a year. topics covered in the second semester may vary, but some professors or schools choose to give greater emphasis on multivariable calculus over, say, fourier series. i'm not sure if most manage to reach stokes' theorem, though.

[ocean mulch]

Mine does the exact opposite I'm having a Math degree without knowing exactly wth Stokes' theorem is.

[zinc ginkgo]

anyone read Calculus Made Easy by Silvanus P. Thompson?
are there other authors like him in math?

[remote sparrow]

https://calculusmadeeasy.org/

if the website's creator is to be believed, then the books listed in the "What Next?" section are in the same vein. abbott and cummings might be the equivalent for introductory real analysis. for abstract algebra, pinter. for linear algebra, meckes and mike x cohen. for calculus-based probability, probably blitzstein and hwang's book. these are books that have a similar flavor to calculus made easy in that they are very good at providing intuition and motivation for the topics. of course i have recommended more concise and rigorous books, but these are books that are similar to calculus made easy.

[rapid lily]

It's a good book for what it does, although it's not ideal for everyone to follow that path.

What are the problems with the exercises?

[crimson leaf]

Well for a Stewart like book you'd probably be looking at Gilbert Strangs book and MIT OCW lectures, but if you're a math major that won't be sufficient and you should check pins for the linear algebra book reviews those will be proof based but you'll end up using the knowledge you learn a lot

[sage kelp]

Idk, I believe it has like 10 per section? That feels like very few. Also it seems like he leaves some important ideas to the exercises. Personally, I don’t like that about a book

[rapid lily]

That sounds like an ok number as it often takes a bit of time to solve them. For the second point, that's quite common among most books and is also quite important to become used to. The issues you are describing are common features of most books.

I can recommend other books if you would like, but they're going to have the same features.

[sage kelp]

Interesting. Then I guess I should just get used to that. It just feels weird. I would truly appreciate if you recommend other books, even if they have the same features

Still I’m trying to find a book with which I feel comfortable

[heady ember]

Look in pinned

[rapid lily]

Here is a list of many common books:
Analysis I by Amann and Escher
Analysis I by Tao
Mathematical Analysis by Browder
Mathematical Analysis: A Concise Introduction by Schröder
Principles of Mathematical Analysis by Rudin
Postmodern Analysis by Jost
Undergraduate Analysis by Lang

I like Analysis I by Amann and Escher although the book is somewhat long and doesn't cover integration. Any of the above books should be fine.

[remote sparrow]

cummings

https://www.amazon.com/Real-Analysis-Long-Form-Mathematics-Textbook/dp/1077254547

[gentle forge]

Can anyone recommend any good books for trig?

[sage kelp]

Schroeder looks interesting to me. I’ll give it a shot. Thank you for those references

[sage kelp]

I would love to read it if it had a pdf version. I know I could buy it on Amazon, but sometimes I study at work and it is less uncomfortable people watching me read on my iPad than actually having a non-related book on my desk.

[gentle arrow]

and another joins the schroder cult

[rapid lily]

You're welcome. Hopefully you will enjoy the book. I have heard a lot of good things about it.

[sage python]

Lmfao

[swift dome]

just get any calculus book , you will get better in trig eventually

[gentle forge]

Actually, I don't know calculus yet, I'm in grade 7 so

But I'm studying grade 10-11 stuff

so

[crimson leaf]

Use khan academy

For k-12 I would say it's as good as any book

[sage kelp]

Why do you like Schroeder?

[gentle arrow]

great way to transition from calculus to analysis

doesn't really assume much going in either

you can say that for another book like tao but dami introduced me to schroder

[sage kelp]

So are you going through it by yourself?

[gray gazelle]

thomas calculus early transcendentals
or
steward calculus

[frosty yarrow]

larson 11e is also good

stars with basics ends with stokes thm

[remote sparrow]

it's worth noting that schroeder also leaves a lot of results to the exercises, especially as the book progresses

https://www.youtube.com/playlist?list=PL4d5ZtfQonW10k_fkbX-9Jj7HGAqRZbM3

found this youtube playlist

could go well with something like carothers

[gentle forge]

Yeah, I'll do that but if anybody has good book recommendations for trig, pls let me know!

[remote sparrow]

adding to my previous post on reliable sources of math history, judith v. grabiner is a credible historian of calculus and analysis.

[gray gazelle]

Methods of Solving Nonstandard Problems, Ellina Grigorieva. Should have a chapter on Trigonometry.

[gentle forge]

any other good book recommendations on trig?

[gray gazelle]

what are you looking for?

What trig? Any standard book will cover whatever you need to know

[gentle forge]

As I mentioned, I'm in grade 7 and am currently doing grade 11-12 trig, so I need to increase my knowledge

I'm learning from Eddie Woo as of now

[gentle forge]

So a book which covers a whole lot of math and isn't that hard to read

[heady ember]

The progenitor of the Schroder cult

[heady ember]

Yes he is #1037160979198378024

[robust belfry]

https://www.c82.net/euclid/

Jo Boaler - Limitless Mind https://www.youtube.com/watch?v=Z0k8F9m2pJ8

Harold Jacobs - Mathematics, a human endeavor : a book for those who think they don't like the subject https://archive.org/details/mathematicshuman0000jaco

Discover the Art of Mathematics books https://www.artofmathematics.org/books

these are awesome books

[sage kelp]

Like Abbott? I mean, Schroeder would still be a good introductory book?

[heady ember]

If you don't like it just blame dami

[sage kelp]

I mean, the table of contents of Schroeder looks very interesting. And if it is indeed a book that assumes no knowledge, I hope he sticks to his word haha

[heady ember]

I haven't read that much of it yet (focusing on another book rn) but generally I heard good comments about Schroder. Though one person did tell me that they found Schroder's pace after Part I a bit sus (looking at toc)

In the sense of number of pages vs content

Can't speak for the accuracy of that remark though

[gentle forge]

Can anybody give suggestions for trig?

[heady ember]

Khan Academy

[sage kelp]

College Trigonometry by Aufmann worked fine for me

[gentle forge]

Can someone in grade 10/11 refer to that?

I'm not in grade 10 or 11 or 12 though, I'm in grade 7

But if it is of that level, I'll understand

[gray gazelle]

you are in grade 7, how old are you 13?

[gentle forge]

Yep

@gray gazelle

[sage kelp]

@gentle forge For trigonometry you should have a fair of understanding of algebra, so if you can handle that I believe you’re ready. If not, focus first on algebra

[sage kelp]

A bit sus? Like thins escalate too quickly lol

[heady ember]

The number of pages covering that amount of content seemed abnormal to them (looking at toc only). But again, I can't comment on this personally

[sage kelp]

Oh yeah, it seems like he devotes 3 pages tops to each topic

I mean, after Schroeder I would like to go through Carothers

[heady ember]

I already bought the physical copy so if part II is bad I'll just blame it on Dami ez

[sage kelp]

Lol

[drowsy thicket]

Did you mean Artin's Algebra with this?

[sage python]

Nah I meant Strang

[wise rune]

Does anyone have any book recommendations for precalculus? I want to selfstudy

[drowsy thicket]

So you would say that Artin is good for math majors, right?

[sage python]

My impression is yes

[drowsy thicket]

Thanks

[gentle forge]

I do know a lot of trig

But I want to expand it more, and yes, I have a quite good understanding of algebra

[drowsy thicket]

A single book won’t make you a master anyway
Hm, if you solve all the problems and read it thoroughly, it could, depending on your definition of master

[gray jungle]

I think you should have a main book and as multiple other references around you

No reason to rely on a single book , so if you are learning abstract algebra , even if you arent using D&F just keep it around to get more insight lol

[remote sparrow]

assigning theorems or parts of theorems as exercises doesn't make it like abbott

schroeder, for one, is obviously a bit more dense than abbott

he does walk you through on how to prove things in analysis, but so does abbott

[crimson leaf]

Yeah a lot of books assign proofs or parts of theorems in the exercises I think it's D&F that leaves the first isomorphism theorem as a proof

[sturdy shore]

do you mean like a first course in analysis?

knapp is not meant for that

[remote sparrow]

^

[sturdy shore]

he basically does the first half of baby rudin (and prob more than that) in its first 80 pages, and baby rudin is considered among the more difficult books for intro analysis

[crimson leaf]

Yeah he does make the weird statement that like a student who has done honors calculus or a course in linear algebra should be fine with chapters 1-4 if they know proofs

I'd imagine it's pretty good if you took a course that used something easier or was lacking and you want to get a more rigorous foundation

[thorn cloak]

is abbott a good prep for rudin? my intro to anal uses it and im a bit worried

[sturdy shore]

yes

but you don't need to be that worried, rudin is fine when there's a professor to go with it

the book's just hard to tackle if you wanna self-study and don't have the math maturity to go along with it

on the other hand, it's always a good idea to have a book like abbott on the side

[thorn cloak]

I see

[glacial heath]

Anyone know books to read to qualify for AIME through amc10

[remote sparrow]

there's a guy that wrote a full solutions manual to abbott if you're interested: https://github.com/UlisseMini/understanding-analysis-solutions. also, abbott has written the official partial solutions manual.

[rose bridge]

I would like to learn more about special linear group, the KAN decomposition and their geometry, from an elementary point of view (without necessarily getting into representation theory and lie theory). Does anyone have any resource suggestions?

[fallow cypress]

for what it's worth, abbott is a good and well written book on its own regardless of rudin

[remote sparrow]

if it weren't for the fact that rudin is required, you could read carothers after doing abbott

[blazing canopy]

For what it's worth I read Carothers as a first course in analysis and it seemed fine

It seemed to start from the basics

[remote sparrow]

were you reading it for a class or on your own

[blazing canopy]

For a class

[remote sparrow]

also, carothers doesn't cover differentiation (not talking about lebesgue's differentiation theorem)

[blazing canopy]

I guess not, though I guess in the context of functions of real variables I had already learned this in calculus course

[remote sparrow]

are you european or american

[blazing canopy]

American. But my calculus course was already for math and physics majors only so it was maybe almost like an intro to analysis

[remote sparrow]

yeah, it makes perfect sense you can move onto carothers then

was the book for that class spivak or apostol?

[blazing canopy]

Apostol

Good guess haha

[remote sparrow]

yeah, taking calculus out of spivak or apostol is unusual for most american students

[blazing canopy]

That being said, I'm not really a believer in following specific books, especially in the digital era with so many resources

Apostol wrote his book specifically for my course

[remote sparrow]

you went to caltech then?

[blazing canopy]

I did yes

But more to the point I think that it's worth using multiple books so that you can understand a slightly larger picture

So maybe one book doesn't cover X but another does, doesn't mean you should completely not use that first book until you finish some previous book on the same topic

[sage python]

Don't let catbread see this I'm having him go through Schroder lol

And for now I'm not letting him jump the gun too early on complex analysis lol

[remote sparrow]

well, besides that, most people learn calculus without seeing very many proofs at all. so even though carothers is still a comparatively gentle book, it's still too big an ask to throw that book right at someone that has only had calc from a book like stewart.

so yeah, you don't HAVE to use abbott only right after calculus

[sturdy shore]

lebesgue differentiation?

[remote sparrow]

*lebesgue's differentiation theorem

[sturdy shore]

probably don't need to add that as a caveat when you are talking about differentiation, but fine

[remote sparrow]

@ Cat Bread

[heady ember]

Dami I bought Schroder because of you

If anything goes wrong I'll just put all the blame on you

[ocean mulch]

Imagine buying books

[remote sparrow]

buying physical books is okay

[swift dome]

I don't buy hard copy , i just printout the whole book at cheap price

[remote sparrow]

buying ebooks/pdfs 👎

[remote sparrow]

yeah i would love to do that, but lulu's project creation process is too finicky

local print shops, i don't know how they bind their books

[warped wave]

I'd like to buy original books but they're too pricy

not trying to sound cheap or anything but they're super pricy for my currency

Like 1.5-weeks groceries kind of pricy for one book

[ocean mulch]

Just read chapter about Homology in Hatcher

What a mess!

I heard good things about it, but now I seriously doubt myself. No books have made clear of the motivation, relationships, and the differences between types of complexes.

Definitely not Hatcher

[fierce hedge]

Anyone who has used Pinter confirm if it does simple groups. I couldn't find it in table of contents, index or even by ctrl-f

[sage kelp]

But then what? Schroeder is just more dense?

[remote sparrow]

i saw one mention of simple groups in judson, and it didn't really go into any depth on it. so i imagine a book like pinter probably doesn't talk about simple groups at all if it's not in the index (and if it was accidentally omitted from there somehow, i doubt there's any deep treatment beyond giving a definition and discussing why they're interesting).

[sage kelp]

What do you mean?

[fierce hedge]

There's around half a page defining simple groups and 2.5 pages dedicated to show that An is simple for n>4 in one of the most computational proofs of simplicity of An. Maybe it comments more on it later.

[fierce hedge]

Dumb question - Are homology and homological Algebra very different things or say different ways to look at the same thing?

[remote sparrow]

schroeder also doesn't really discuss tangential things like the history of analysis and doesn't try to impart a sense for why learning analysis is important. a minus for me, but others prefer a book that gets to the point. he also doesn't really add much surrounding context for why you should expect a theorem to be true.

[remote sparrow]

i was talking to chriz

but carothers is a great book to look at after doing abbott. it does all the metric space material that rudin does but with more motivation. also, it covers more stuff than rudin does at a similar, relatively leisurely pace.

[sage kelp]

Oh okay

Yeah, I would actually like to go through Carothers at some point. I think it’s a good second book. My issue at the moment is getting started D:

Decided to start Spivak though

[remote sparrow]

i think spivak suppresses topological arguments and sticks purely to epsilon-delta

but you'll get exposed to topology again in carothers

👍

should be no issue

[sage kelp]

I hope to get more confidence by going through Spivak first

[remote sparrow]

abbott does a really good job at organizing chapters around and discussing interesting/weird/pathological examples, which were pretty much why people developed analysis in the first place.

[remote sparrow]

well, you might lose confidence by doing some of spivak's problems they are generally regarded as quite difficult. spivak has written a solutions manual, though it's still skimps a bit on details.

http://alpha.math.uga.edu/~pete/MATH2400F11.html

btw this guy has written notes for spivak calculus

huh, all the links are dead. at least the homework assignments are still directly on the webpage

https://www3.nd.edu/~andyp/teaching/2020FallMath10850/ClarkNotes.pdf

well, it is here

[hearty turret]

whats a good book for introductory abstract algebra?

[sage kelp]

Well, let’s see how it goes

Thanks sour

[warped wave]

For someone who just finished Thomas/Stewart (all of it), do you think Spivak is the next step?

or do I need to take Analysis first

[crimson leaf]

I would just go straight to analysis

Spivak usually comes before analysis

[dapper root]

If you took analysis you don’t need to do spivak

You’re regressing

[crimson leaf]

Doing spivak after the calc sequence is doing all of calculus then taking honors calculus

[formal bronze]

What is a good resource for studying about graphs, specifically about chromatic numbers and problems related to vertex and/or edge colourings?

[crimson leaf]

I can't really recommend it because I haven't read it but my advisor has a book called "Chromatic Graph Theory" by Chartrand and Zhang

I think he's mainly used it for students who are interested in rainbow coloring and complete colorings since I know he isn't too into the subject

[ember slate]

I have studied the subject but didn't use any book but, IIRC discrete mathematics books might have a section on graph theory

[formal bronze]

Yeah, but what I was looking for was more along the lines of a resource that focuses on graph colourings.

[formal bronze]

Looks nice, thanks. I'll check it out.

[remote sparrow]

fwiw, institutions like caltech and university of chicago have "honors calculus" classes for people fresh out of high school that took ap calculus using books like spivak or apostol. similarly, hubbard and shifrin (who only cover multivariable calculus, but of course from a rigorous standpoint) both designed their books for "honors calculus" classes. but yeah, OP can move straight to analysis if they want.

[crimson leaf]

Yeah my school uses Apostol ours is more so for people who already know calculus but have to take it again (maybe didn't pass ap exam or something) that why I said it's like doing all of calculus then doing honors calculus

[sage python]

Well

You don't need to have taken AP Calculus to do Spivak there

[remote sparrow]

thanks for the correction

[orchid cobalt]

im gonna get thomas calculus's early transcendentals 14e

will this help me on self studying calc 2?

i have already learned majority of the basics of calc 1

[nova lotus]

hey are any linear algebra problem books that are pure math centered?

i did start doing halmos' linear alg problem book and am done with it and wanted to know if there were any more like that or better

[heady ember]

Look in pinned ig

[nova lotus]

i found lots of new books to discover ..thanks 👍

[ocean mulch]

Homological algebra is the abstract version of homology. You deal with algebraic objects and relationships between them alone, which need not have any topological significances.

[mellow wren]

Does anybody have books that cover elliptic curves

More specifically within that range they also talk about modular forms and eichler Shimura theory

[mellow wren]

Hmmm I kind of forgor that existed

I'll look over it then come back

Tho I haven't heard anyone really talk abt it

so idk what to expect really

Ahh interesting
I know he also has an algebra book?
But idk anything abt that

[fierce hedge]

yes, 2 volume books on algebra

also two books on analysis

[ember slate]

Should I skip book of proof in favor of a discrete math book? I was planning on reading book of proof then a discrete math book but alot of their content overlap, so I want to know if it's worthwhile to continue studying book of proof of if I should skip it.

[alpine mulch]

Dork Diaries is the best book

[swift dome]

For linear algebra i would advise to prefer gilbert strang- linear algebra and it's application

[gusty quest]

Which is the best foundation IIT book for class 10

[swift dome]

what ?

[remote sparrow]

why read both? these sorts of books are both used as introductions to proof.

rather redundant

[ember slate]

I thought of it as the next logical step, but now that I look at it, it is kinda redundant

[vagrant sedge]

Not a book recommendation, but do you people know of any set of recorded lectures on numerical methods for PDE's? I mean, covering the usual finite differences, finite elements, the related function spaces, etc...

I mean from a mathematics stand point... There are several, for example, finite element methods/analysis recorded courses from a mechanical engineering point of view.

[crude lava]

Good books for non-Euclidean geometry?

[thorn sparrow]

Good books for numerical analysis?

[remote sparrow]

idk, but my school uses burden and faires

seems like a standard choice

[gray gazelle]

hello might be outside of the scope of this channel

but what would you recommend as a resource for learning power systems?

for an introductory level

[remote sparrow]

what are power systems

[gray gazelle]

easiest definition i can give i suppose

basically focuses on all the aspects listed in the little boxes

and how they interact (convert)

[fallow cypress]

allaboutcircuits online textbook

unironically

[remote sparrow]

not sure if this would work, but maybe The Art of Electronics might help

you might also get better recommendations in the physics server

#old-network

[snow gate]

and CHERUB

[alpine mulch]

Never heard of this book before

[snow gate]

oh boy, that's great

CHERUB is an underrated series

like dork diaries

which book are you on

It's far rarer in India, I got two books in the series at an exhibition while out of town.

same lol

class A was dope

and max security was great too

it's just hard to get here because most adults aren't interested in it, most teens don't even know it exists, and lil kids can't touch that

Absolutely. Despite all the horrible things James and the gang grow through, they still make themselves into something.

man, cherub would be far more popular if it were distributed to more teens and libraries

kerry is a good foil to james

and lauren too

yeah, i noticed, it's big

and tons of characters

im just scratching the surface of the series, i should get back into it

it's also very realistic, and doesn't shy away from the parts of growing up most people don't talk about

james also needs to keep it in his pants

he can be a real dum dum at times

but he's a well made character

bruce is the dude who feels like a phony but is actually really good at his job when he wants to be

cherub is also far better than those cringe books like alex rider

or artemis fowl

aight sure, have a good day

nice to see another cherub fan, ttyl

[pallid yew]

Oh cherub

I've read that

It was good

[thick monolith]

Hey anyone into math competitions?

[stray veldt]

#competition-math

[grizzled tulip]

Now I do need some good inorganic and organic chem books

[coral prawn]

U should check out chem server they have great reccs

[swift dome]

Didn't know we have chemistry server too

Isn't it hilarious

[gray gazelle]

the first maths book ive bought is calculus by spivak, W or L

im halfway through finishing it

[swift dome]

Spivak is really good in intro to calculus, but you can still refer to different books too.

[covert shard]

What do you guys think of the Patterns and Practicalities books?

[viscid comet]

What books do you all recommended for learning about electronics, like components and such

[orchid mortar]

Horowitz Hill seems standard

[remote sparrow]

there's a lab manual for that book too that can be used standalone

[remote sparrow]

any fumo book recommendations?

[cinder quiver]

Need me a comprehensive geometry book

Beginner to advanced

Or like

Beginner to intermediate

Whatever that means

Good for an undergrad student

Undergrad compsci student

[faint nebula]

There's this great book

It's called

Uh

Lemme think

Wait

Hold on

I forgot

I'll type if I remember

[red river]

just read euclid bro

[cinder quiver]

Whar

[remote sparrow]

https://www.amazon.com/Classical-Geometry-Euclidean-Transformational-Projective/dp/1118679199

[tribal sapphire]

hey yall

[remote sparrow]

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

[elder stratus]

Looking for a reference/ textbook that covers Brownian Motion, Continuous sample path Martingales etc. We are using Durret for the course I’m in but I’m not loving it’s coverage for Reflection Principle and Martingales. Preferably a book with good exercises. Thank you

[crimson wolf]

I want to learn real analysis. I think I'm going to go with either Abbott or Spivak, but I can't decide between those. I worry Spivak's problems might be harder than Abbott's and maybe a bit out of my reach. Maybe I'm wrong. Between those two, which would you recommend??

[remote sparrow]

if you've just finished calculus, spivak is partly redundant

abbott is better in that case

google "x book recommendations" and look around i guess

[raven fossil]

Are there any good books for beginners number theory?

[remote sparrow]

dudley or burton

[raven fossil]

Sure, thank you

But one question

What if I cannot solve most of the problems from the exercises

[remote sparrow]

i mean, get help? you can ask questions here. look for videos or lectures to follow.

[remote sparrow]

look for another book i guess

[crimson leaf]

Andrews is good

Cheap too

[sage kelp]

I’m going through Spivak (just started) so let me know if you want to discuss it!

[grand thistle]

does anyone have experience with Lawrence Evans's "Measure theory and fine properties of functions"?

looking to use it for geometric measure theory

[swift dome]

would you specify more what do you mean by " problem solving book ".
If you are asking for problem solving for maths olympiads i would recommend try looking into #competition-math , you might get useful resource there.

[frank nacelle]

Thoughts on these books? :

Godel, escher, bach - hofstadter

The feynman book of exercises for his physic lectuers (the one he did I assume)

Cosmos- Carl sagan

If you've an experience with even 1 of these pls let me know what u thought of it 😁

[vivid gust]

fr i done read all those nd they wus ass

[warped wave]

Good books on Abstract Algebra?

[finite gale]

see pinned messages

[mighty yew]

read lang

[remote sparrow]

lang undergraduate algebra? yeah that seems like an okay choice

maybe a bit too fast for some

surely you were not recommending GTM lang

[mighty yew]

read GTM lang

[mighty yew]

I really hope the lang I've been struggling to get through is whatever the hard one is or I'm in for an ego check

[ocean mulch]

the Red Book

[mighty yew]

I thought that was chairman mao's memoirs

woah I butchered his name no I didn't or did I I have no damn clue

[crimson wolf]

have you gone through Abbott?

[rancid hollow]

L cus it's easy to pirate but good choice as a book

[sage kelp]

Yes

[crimson wolf]

what do you think I should go with, Abbott or Spivak?

[coral prawn]

As others said already if you have done calculus spivak is redundant. Spivak is like a mix of calculus and intro to analysis

[past flame]

I have been trying to start learning some analysis in preparation for my first course in analysis at university, and I am considering using the MIT OCW: https://ocw.mit.edu/courses/18-100a-real-analysis-fall-2020/pages/syllabus/. Which uses this text: Lebl, Jiří. Basic Analysis I: Introduction to Real Analysis. I hear a lot about authors like Rudin and Folland, would I be better off trying to learn from a textbook of theirs (if so which book?), or does anyone think the textbook used by the OCW would be a good resource?

I have used the OCW for linear algebra and differential equations and enjoyed the access to lectures and a more structured learning environment, I've never really learned strictly from a textbook before. Just wondering what opinions on analysis books / learning for a beginner would be?

[loud cradle]

i've never heard of this book.. for a generally well regarded intro you could look at Abbott "Understanding Analysis". (Baby) Rudin covers similar material but is not very user-friendly for self-learning. Folland is higher level and not suitable for a first course

[past flame]

Hi Bungo, alright thanks for the feedback I'll look into those two books. What do you think about learning from a book versus an online course?

[loud cradle]

never a bad idea to do both!

for analysis, you might try checking out the lecture series by Francis Su (I think I got the name right).. I believe he roughly follows Baby Rudin

rudin becomes more accessible when there are corresponding lectures btw

[past flame]

It looks like the course I will be taking will use "Advanced Calculus" by Folland

Should I maybe try learning a bit of that?

[loud cradle]

ah, i forgot he wrote such a book, when you mentioned Folland I was thinking of his "Real Analysis" which is graduate or upper-level undergraduate

i'm not familiar with his AC book, but he's a good author in general

and sure, if your course is using it then that would be a great place to start

[past flame]

are you familiar with complex analysis by Gamelin?

It looks like the course will transition into that book aswell

[loud cradle]

yea, i may be in the minority but i don't care for it

btw, i took a course from Gamelin himself which used that book

[past flame]

Oh very cool!

I wish Folland still taught where I will be going to university

[loud cradle]

washington?

[past flame]

Yah

[loud cradle]

that was one of the places i applied for grad school, he's one of the profs i chatted with when i visted, very nice guy

[past flame]

That's really cool, what was your opinion on UW as a school for math?

[loud cradle]

overall they seemed quite solid

one thing i recall was that their qual system was quite nice, in that you could bypass a certain number of them by excelling in the corresponding courses

that alone was tempting haha

[past flame]

wdym by qual system?

[loud cradle]

phd qualifying exams

[past flame]

oh lol

[loud cradle]

one of the more annoying hurdles of grad school life

[past flame]

sounds stressful

are they more difficult than the GRE?

[loud cradle]

generally yes, they cover material in first-year grad courses, usually analysis, topology, algebra

the (math) GRE just covers basic undergrad stuff, it's not too hard

[past flame]

so are they qualifying you to enter a PHD program? or to finish a PHD program?

[loud cradle]

the general GRE is just a redo of the SAT, basically trivial if you're smart

[loud cradle]

they're qualifying you to "continue" usually

you have to pass them within the first couple of years of the program typically

[past flame]

oh I think I have heard of that before actually

[loud cradle]

are you starting in the fall at washington?

[past flame]

yes

[hollow shore]

If you are self learning then the ocw course is what you should do!

if you wanna do it in a time bound manner

because the course has a schedule planned out for you

I tried to sit down with a textbook (Bartle) and slogged through it and it really sucks

one is not supposed to read every section and solve each and every problem. A course like this already does the job by assigning sections to read and exercises to do.

[past flame]

thanks for your feedback, I think that's a fair assesment

[remote sparrow]

@past flame https://github.com/UlisseMini/understanding-analysis-solutions

this guy wrote full solutions to understanding analysis by abbott

also abbott has written an official partial solutions manual

[orchid mortar]

I think OCW uses the text because it's open source, so that's one thing the other texts aren't

[gray gazelle]

oh no ik, i like have 20 different books pirated

i just wanted this one irl

[dusk crater]

I have started a book of mathematics which has over 1010 pages but after a week i am only at page 40 like how do i grap the speed

[alpine rover]

best learning resources on field extensions and (introductory) galois theory?

[hazy elk]

Rotman has a small book on Galois theory, haven't used it tho

[maiden halo]

the book they used to use for that course was "Introduction to Analysis" by Arthur Mattuck, who taught the course

[candid sedge]

does someone have a good pdf of the formulae required for Jee level ( indian entrance exam)

[alpine mulch]

Try find it in Anna Archive or Z-Library

[swift dome]

Don't know much but if you need it for maths Olympiad look into #competition-math

[summer lagoon]

don't say that, instead say "Please buy the book 99$ instead of checking this [link]"

it would be illegal otherwise

[crimson jewel]

Hi, I wanted to learn about differential algebra, specifically about how it can be used to prove that some functions have a primitive that can't be expressed with fundamental functions. I glanced at Ritt's and Kaplansky's books on the subject, but I wonder if any of you know of any other that would be suitable to learn about the topic and that specific result

[wheat tendon]

there's a very good 13 page paper on this exact topic by brain conrad

[past flame]

I didn't realize they had an analysis course by Mattuck, that's awesome though I love him I'll look for that one.

[sand crescent]

Does anyone know resources for an introduction to large deviation theory?

most of the resources when I look them up don't seem to be introductory at all

[ocean mulch]

Herstein all the way

I recommend second edition. He explains stuff quite in depth and goes slowly

[fierce hedge]

Why not the more recent 3rd edition?

[ocean mulch]

There's a 3rd ed???

I know there's 2nd ed cus I have it in my hands rn 😄

[fierce hedge]

Yeaaaaah, although I think it's mostly bug fixes

[crimson jewel]

Thanks! That paper is exactly the sort of thing I was looking for

[sand crescent]

Bump

[ivory rivet]

Best math book for noobs?

[coral prawn]

Please be more concise.

[ivory rivet]

for beginners?

[ocean belfry]

Yo I never stuck with reading math, I always gave up until I started reading Grimaldi's book on Discrete and combinatorics maths , there are so many examples. A good book.

[coral prawn]

There are different types of "beginners", and a variety of topics which a "beginner" would like to cover

Perhaps share your experience with mathematics?

[ivory rivet]

High school, gunna go to college soon and I wanna do a math book I will enjoy. I really liked this book called measurement by Paul Lockhart and he just proposes issues and gets you started on problems but never tells you the answers. It taught me a lot about mathematical thinking and I kinda wanna do a book like that again.

[desert oriole]

@ivory rivet
do paul zeitz or arthur engel

the problems are fun to do

i think zeitz is easier

[remote sparrow]

https://www.amazon.com/Proofs-Long-Form-Mathematics-Textbook-Math/dp/B08T8JCVF1

[swift dome]

Intro to proofs, then analysis by tao.

[alpine mulch]

Lol okay

[alpine mulch]

Immediately delete the message before I got into prison

[merry pier]

i didn't know z-library was still active

[alpine mulch]

It is back

[merry pier]

nice

[alpine mulch]

Mhm

But I don't know how Z-Library can be back and it's illegal

[ivory rivet]

Is this book suitable for someone like me who isn’t really familiar with all the symbols and formalities yet?

[remote sparrow]

absolutely

[near wagon]

What is your PhD in? Just mathematics?

[past flame]

omg I wish lol! I will be going for undergrad!

[fierce hedge]

wdym "just mathematics" PhD is done in only 1 subject

[past flame]

also incase it wasn't yet clear I don't have a PhD lol

[fluid skiff]

He wants people to do 3 or 4 PhD atleast

[past flame]

I will be majoring in mathematics if that is what you meant to ask though

[past flame]

like the hulk

[fierce hedge]

the credible hulk who always cites his sources

[gusty smelt]

some tv shows show off ppl with multiple phds but it makes no sense bc like

you usually just start doing research/learning about the other thing, you dont need a phd to like, give you permission kek

I have infact heard multiple phds would be a redflag: makes you look like someone who is better suited as a student then a researcher

[fluid skiff]

Nowadays people want to do double PhD because no jobs available

[fierce hedge]

true, unless there are very special circumstances. The only guy I knew who had 2 PhDs was just teaching us CS101 and always looked sad

[gusty smelt]

I can kinda understand if your transition from say math to hard experimental science ig

[fierce hedge]

Like going through 1 PhD is enough low paid labour, going for 2 is torture

[gusty smelt]

maybe the research is just so different you need to learn it

yeah getting paid 20k for another 5 yrs

who would do that to themselves lol

[sour venture]

What if they are not getting two degrees for pay, they got two because they got lost learning something for years and accidentally end up with two phd

Also, help me get lost in a book that help me get two phds by accident

[cursive wren]

Looking for a book i could use for my algebraic structures class, my professors book isnt that great. The topics covered are divisibility in Z (chapter covers euclidian division, chinese remainder theorem, ...), introduction to group theory, modular rings (idk the translation, in dutch its restklassenringen), dual vectorspaces and bilinear and quadratic forms. The professor explained that the class is like an introduction to abstract algebra but also some extra linear algebra

[alpine rover]

Try Gallian's Contemporary Abstract Algebra

Anyone know any Complex Analysis books written like a Pearson textbook? Something beginner-friendly and standard with a lot of concrete examples and problems

[maiden halo]

my old advisor got a PhD and then a MD-PhD. crazy

[sage python]

I should say if you learned analysis on manifolds out of chapter 9-10 of Rudin? You didn't actually learn the material. Rudin doesn't teach the stuff well at all

Also if you learned linear algebra from Axler you'll need to learn characteristic polynomials and determinants differently

Chapter 9 is okay for differentiation on R^n. Not perfect but okay

But chapter 10 is like... if I were giving someone an exam and they defined differential forms the way Rudin does?

I'd fail them

[heady ember]

lol

[sage python]

Do read chapter 7 of Rudin, it's pretty decent. But for calc on manifolds you should probably use Spivak. For ring theory... Idk many dedicated books on ring theory, a lot are general algebra books that include chapters on rings/modules

My impression of Munkres is quite bad

[mellow wren]

for calc on manifolds there is also...
Hubbard...

It's kinda weird

[sage python]

If you read 1-6 of Rudin and esp if you've done linear algebra there's no point in Hubbard

[mellow wren]

some ppl like it

[mellow wren]

hubbard leans a lot into the manifold stuff that's why I mentioned it

[sage python]

I figure, but the organization is very interspersed

He mixes linear algebra with multivariable calculus with Rudin-lite topology

Proves theorems out of order

There might be a case for it (or really at that level I prefer Shifrin) if it's your intro to the material but if you've seen a large subset of it before it's better ot have these things sectioned off a bit

[sage python]

So, probably use one of two books both titled "Basic Algebra", one by Knapp, the other by Jacobson. Lang if you're more daring. You're probably mostly fine on the group theory, maybe glance through the topics to make sure (also you'll wanna unlearn Herstein's convention for composing maps). Linear algebra, some stuff you'll be fine on but you'll wanna know how shit works over a general field, and on top of that you need to learn determinants and characteristic polynomials correctly.

Knapp in particular I think is mostly self-contained with respect to the linear algebra bit

So my point is, you can skim through but some topics you'll wanna review

[alpine rover]

bump

[rain moss]

anyone recommend some random chess book?

[swift dome]

What

[sterile harness]

what’s your rating

[fierce hedge]

What's MD-PhD?

[maiden halo]

a "joint degree" program. in some schools, the student will do X years of med school, then do their PhD, then finish their 4-X years left in med school. or some other combo. usually the PhD will be in some biomedical science related to what they want to do in medicine (but not always). and at least in my experience their PhD can be shorter

[fierce hedge]

I had a guess that MD was indeed the medical degree but MD+PhD didn't made sense to me lol

[maiden halo]

Accessible? Then try Blitzstein & Hwang

why would it be a troll? Also, check out Stat110 lectures from Harvard, the book is based off the course

[rain moss]

1k

[alpine rover]

Bobby Fischer Teaches Chess (since you said you were new to chess in #chess-go-shogi)

[vital bane]

shiffrin

[deep epoch]

i'm not very familiar with what pearson books look like, but have you tried looking at Complex Variables and Applications by Brown-Churchill or Complex Analysis by Gamelin?

[alpine rover]

just stumbled upon the Gamelin book

[deep epoch]

The former is written with a non-math major audience in mind with the latter being more rigorous without assuming too much background (vs. something like Stein-Shakarchi)

[alpine rover]

yep, looking through this one as well as Zill

thanks a lot!

[paper cape]

Any good books for UG math?

[near wagon]

I meant is it in mathematics in general or some sub field of it.

[remote sparrow]

your phd is titled after what your broad focus is, like physics, philosophy, psychology, etc.

but it is almost always awarded for completing research in a very narrow, highly specialized topic

there's no such thing as a math phd for "mathematics in general"

[near wagon]

Yeah good point. You’ll end up doing research in a small part of the field.

[upbeat vine]

If you like a book which addresses possible complications and stuff like "Why did they do this and not this", check out Complex Made Simple by David Ulrich. It's very beginner-friendly, explains everything in detail. One caveat is that it doesn't have many problems, but the author provides solutions for whatever problems it has.

[ocean mulch]

An author that actually provides solutions?

Impossible!

This guy must be a Saint

[loud cradle]

I like Ullrich's book, but it (at least my copy) doesn't contain solutions. Are they on a website somewhere? The author doesn't appear to have one

[upbeat vine]

Sorry, it’s not by the author : https://www.scribd.com/document/111294981/Complex-Analysis-11111

[loud cradle]

nice, thanks!

[marble frost]

Does anyone have a translated version of Freudenthal's thesis on his theory of ends

https://dspace.library.uu.nl/bitstream/handle/1874/7437/1930-freudenthal-dissertatie.pdf?sequence=1

[brisk ice]

Looking for a good ODE selfstudy book as a first course for the topic.

[remote sparrow]

for books that focus on closed form solutions, consider morris and tenenbaum, boyce and diprima, and goode and annin. goode and annin include a full treatment of linear algebra. boyce and diprima is the only one that has an edition that includes boundary value problems. two books that emphasize qualitative and graphical analyses more would be blanchard, devaney, and hall or judson's recent, work-in-progress draft.

[fossil arch]

How is Visual Differential Geometry by Tristan Needham as a supplement to Tu’s Introduction to Manifolds?

[vital bane]

woah feather doing diff geo? based

[fierce hedge]

Neam would you be joining for the diff geo group with DarQ?

[vital bane]

when are they starting?

[haughty holly]

anyone from maldives??

[fierce hedge]

I think mid June, till then I'd also have my exams over

[vital bane]

what book are they starting off with?

Lee?

[haughty holly]

is it IGCSE?

yes or no??

[fierce hedge]

No

[haughty holly]

where u from?

[vital bane]

Lol wrong channel for this

this is #book-recommendations go to #discussion for talking to people

[fierce hedge]

I think they're gonna follow some diff geo course from UCLA

[vital bane]

I see

[haughty holly]

fu

c

k

y

oo

u

g

u

y

s

[fierce hedge]

[vital bane]

<@&268886789983436800> please deal with this user

[stray veldt]

@haughty holly try again tomorrow

[coral prawn]

💀

[grand thistle]

wait what whats the diff geo group

lemme in

[fierce hedge]

It's not a surety, DarQ has it planned

I'll let you know if the group comes into existence

[grand thistle]

aight

james was also planning a functional analysis reading group

so my summer's gonna be packed with math

[fierce hedge]

Interesting, what are the prerequisites?

[grand thistle]

check dm

if you don't mind me dming you the course details, that is

[fierce hedge]

Sure

[gray gazelle]

Hey guys. I just want book recommendation to learn basic maths such as averages, ratio proportion etc.

[umbral peak]

Basic Mathematics by Serge Lang is a good one imo

What's a good first book to learn topology?

[vagrant sedge]

Hi. What is a good book proving, introducing, etc, Green's Theorem as it's used in PDE theory (like for regular open sets of class C¹, for Lipschitz domains, etc)? I know where I can find the theorem for smooth manifolds (like in Spivak's book).

[gray gazelle]

I checked this book out. It unfortunately doesn't have the topics I want.

[umbral peak]

Is it too advanced or too basic?

[gray gazelle]

It is a good book for topics it was dealing with like algebra, geometry.

[finite crane]

I would first search along Evans' PDE or Evans' Fine properties of functions.

Or Google Trace theorem and Sobolev
http://www.ltcc.ac.uk/media/london-taught-course-centre/documents/Applied-Computational-Methods---Notes-4.pdf

If you need the most general, look for The Bible, Triebel's Theory of functions. Lipschitz domains are covered in the 3rd volume

[maiden halo]

so basic statistics?

[gray gazelle]

Quantitative aptitude stuff like alligation mixture, speed time distance etc

[vagrant sedge]

Thank you

[grand thistle]

what is your opinion on evans' fine properties of functions?

me and a friend are planning to use it or some similar text for GMT

[plucky fable]

Suggest some good books for beta and gamma function

[finite crane]

Probably decent for a working analyst, but specialists in GMT know where else to look

[sage python]

GMT books tend to have pretty different flavors

You're more looking for the diffgeo side of GMT, and the nicest looking book there that I know of is probably "Sets of Finite Perimeter and Geometric Variational Problems" by Maggi

But Evans-Gariepy seems pretty good at a glance too, as is Krantz-Parks "Geometric Integration Theory"

[formal bronze]

Does anyone have any recommendations on resources for studying about unit distance graphs, and possibly variations of the concept(other 'fixed' distance graphs, unit distance graphs on metric spaces other than ℝ^k with the standard metric, maybe further generalizations)?

[teal siren]

I'm looking for resources for Linear Algebra. But I need a book that covers the subject of 'groups and objects' before the subject of 'matrix'. Does anyone have a resource recommendation in Turkish or English?

[remote sparrow]

hoffman kunze briefly defines groups, but not before defining what a matrix is. roman does talk about groups in the preliminaries section.

[finite crane]

upon searching I found these recommendations.
what ML book would be best for a professional mathematician looking for deep / important problems in ML ?

as opposed to books written for non-mathematicians

[upbeat vine]

https://mathoverflow.net/a/395177/145526 This has quite some pointers, I doubt there are books written catering specifically to mathematically trained audience

[chrome yacht]

For deep learning, Ovidiu calin deep learning architectures seems nice

[gray gazelle]

Looking for a good beginner's book on undergraduate statistics

[chrome yacht]

Also for DL (although not a textbook) this https://arxiv.org/abs/2105.04026 and this associated video https://youtu.be/u7a9YZ9kDcQ

[teal siren]

Thanks. I will review your suggestion.

[thorn sparrow]

any good books for differential topology

[remote sparrow]

#book-recommendations message

[remote sparrow]

statistics covers a lot of things. what did you have in mind? have you had calculus yet? have you previously had a course in probability?

[gray gazelle]

Not yet

[remote sparrow]

neither calculus nor probability?

[subtle mango]

khan academy is your best bet then

[gray gazelle]

Yeah ive had none in undergrad. Stats is going to be my first class

[gray gazelle]

Oh ok I'll check it put thanks

[remote sparrow]

so will it be like a statistics and probability concepts class that only uses algebra?

https://apstudents.collegeboard.org/courses/ap-statistics

[gray gazelle]

Yes

[gray gazelle]

Thank you

[maiden halo]

You can try Statistics by Freedman, Pisani, and Purves as well

[gray gazelle]

Thank yoi

[grand thistle]

right ill check that out

[desert falcon]

i thought this would be an actual book recommendation channel not a textbook recommendation channel 💀

[gray jungle]

what?

[remote sparrow]

are textbooks not books?

also the channel description says, "Use this channel to ask for book recommendations. Tends to be mostly math but feel free to ask about other literature (YMMV)."

[fossil arch]

Okay I hate Visual Differential Geometry by Needham

Is there anything just a bit more formal lol

to build visual intuition

I was skimming through this lecture series and I really like it

https://www.youtube.com/watch?v=mas-PUA3OvA&list=PL9_jI1bdZmz0hIrNCMQW1YmZysAiIYSSS

[upbeat vine]

How would you develop visual intuition via formalisation? If you really need some formal definitions to keep in track, pair Needham with Lee's book on diff geo.

[fossil arch]

I'm using Tu's ITM to learn

[upbeat vine]

thats good too

[fossil arch]

I meant more like

[fossil arch]

I was watching the video on exterior algebras & I really love the pictures for k-vectors & the wedge product

[upbeat vine]

Pretty nice pictures ngl, I doubt you would be able to find these in books

Needham is the closest who will explain stuff with pictures

[fossil arch]

[heady ember]

Lmao reminds me of Hatcher

Manga

[vital bane]

physics books have a lot of pictures for math

[fierce hedge]

Aren't these like specific to the discrete setting or does he does he show intuition for the general setting also?

[fossil arch]

Idunno I'm not actually using them to learn really lol

[remote sparrow]

the lecture series IS for discrete diff geo

[fossil arch]

Just for the nice pictures, and I like the intuition he gives, but I haven't actually watched them fully

[fossil arch]

Ok big man give me a physics book with pictures for dg shenanigans :3

Time to learn general relativity!

[vital bane]

[fossil arch]

(I still struggle with high school mechanics problems 😻)

[vital bane]

Gravitation by MTW

Lol that's a graduate level book but has lots of pictures

I know you dont hear those two things in the same sentence everyday

[fossil arch]

What is MTW

Okay

LOL

Will do

[vital bane]

misner, thorne and wheeler

[fossil arch]

What are the physics prereqs

I'm very familiar with Newtonian mechanics, next to no Lagrangian, zero Hamiltonian

[vital bane]

i would assume undergrad classical mechanics and electrodynamics and special relativity

[vital bane]

you can easily pick it up from taylor

[fossil arch]

Electrodynamics is not just classical E&M right lol

[vital bane]

no i do mean classical electrodynamics (griffths EM)

[fossil arch]

I don't know any special relativity besides v = csqrt(1 - (t'/t)^2)

[vital bane]

special relativity and lagrangian/hamiltonian mech you can learn in like a month

classical EM might take longer

[fossil arch]

I've taken E&M

just don't remember much lol

[vital bane]

this is the first place where students see what a field theory is and they first encounter tensors

[vital bane]

oh nice then just flipping through griffths EM and doing a few problems here and there should be enough then

he also teaches special relativity

he has very good chapters on SR and relativistic electrodynamics

[vital bane]

but do keep in mind this is more of a reference book lmao it's 1300+ pages

[fossil arch]

Yeah everyone loves Griffiths

[fossil arch]

LOL

Yeah well I've got a maths book to learn from

I just want pretty pictures

Some writing to elucidate what's going on would be nice too though

YO WAIT

I KNOW THORNE

THIS IS THE DUDE FROM INTERSTELLAR

[coral prawn]

Eyo whaaaa

[vital bane]

yes 🗿

kip thorne

[remote sparrow]

@fossil arch sean carroll has written a textbook on general relativity

heard it's good

[desert falcon]

i realize it's a math server but i was expecting fiction of some sort when i clicked on lol

[fierce hedge]

You can ask for fiction recommendations also, no one's gonna stop you

[desert falcon]

does anyone have any recommendations for sci-fi novels/series similar to the hyperion cantos by dan simmons?

[stoic nova]

Dune by Frank Herbert was a great read. Would recommend personally.

[gray gazelle]

I recommend you guys "Think and Grow Rich"

[signal fable]

Honestly I woudln't really recommend any self help book

[gray gazelle]

This is the only good one others are thrash, also every book is thrash depending on your goals. I stopped reading too

[signal fable]

Why do you believe it's good?

[gray gazelle]

Because it helped me

As simple as that

[signal fable]

Oh wait I misread that again

I'm too tired

[gray gazelle]

That's okay man

[ionic mica]

my fav novels r
1 - Six Crimson Cranes
2 - A Seven-Letter Word

[fierce hedge]

I had gifted a copy of it to my mom, she would read a paragraph and then tell me how stupid it was. To be fair it a translated copy so may be it had a lot of translation errors.

Plus didn't the author Napoleon Hill pretty much faked everything?

[gray gazelle]

I don't know much about the translation but I don't agree with law of attraction either. Other parts are worth to think about

It helped me determine a purpose for life, not only making moneu

I am not aiming money stuff anymore tho

[fierce hedge]

I see, I see. I'll check it someday

[snow gate]

have you guys read sapiens

[gray gazelle]

Uh does anyone know a textbook on Game Theory intended for Mathematicians?

[thorn cloak]

That is what is rumored

Well, speaking that his story doesn’t really make any sense

[fierce hedge]

As far as I have heard/seen, his autobiographer himself have said that quite a lot of stuff he said was baseless.

[remote sparrow]

#book-recommendations message

[coarse arrow]

What are some books which guide you and ask you to prove everything (almost) yourself?

[gray gazelle]

Yeah thanks a lot! I'll try to find something. This really helps

[remote sparrow]

https://www.amazon.com/Topology-Through-Inquiry-AMS-Textbooks/dp/1470452766

inquiry based books like this ^

google some topic plus inquiry approach

[coarse arrow]

Thanks

[gray gazelle]

Uh, ok I did look in all of them, and even though a lot of books are recomended and very good destinctions are made. Well something I have to ask, that is not answeared is ... well as a mathematical object what is a game or well a non-competitive game.

I did see a lot of definitions in like regular language. But as an Object we can construct with sets, functions and Binary Operations, what is a Game ? Or is there such an aprouch?

Maybe I'm asking too much but it is such an aprouch that I'm looking for, if there is any

Something like that would be a good starting point to find what I'm looking for

[desert falcon]

ive read that, anything else good?

[smoky schooner]

griffiths haters rise up

[ocean mulch]

Ironically the best math intro books I found are the ones for physicists

Functional analysis, Algebraic topology, Differential Geometry, and so on

[vital bane]

[fierce hedge]

Drop some recommendations especially for alg top and diff geo

[ocean mulch]

Nakahara's Geometry, Topology and Physics

Best intro to both topic I have in hands

It's soooooo easy to read. Damn, I found harder times reading comics.

[fierce hedge]

Is that the name of one book?

[ocean mulch]

Yes

[fierce hedge]

Ohhh big hype, yo @vital bane check this

[vital bane]

Lol yes Nakahara is based

[ivory rivet]

Damn textbooks are expensive

[vital bane]

I know right

why the hell they gotta be so expensive damn publishing companies

[grand thistle]

only if u get them legally

[ivory rivet]

Is there an underground market for textbooks or do you pirate

[stoic nova]

1. The Foundation Series by Isaac Asimov
2. Red Mars by Kim Stanley Robinson
3. The Left Hand of Darkness by Ursula Le Guin
4. The Fifth Season by N.K. Jemisin
5. The Long Tomorrow by Leigh Brackett

[grand thistle]

🏴‍☠️

[ivory rivet]

Arggg

[sleek python]

Pirating is illegal and shouldn't be encouraged. That is why you should definitely not use Libgen to download textbooks you're looking for instead of paying hundreds of dollars for them.

[vital bane]

[grizzled tulip]

[sudden granite]

for classic literature what publishers do you guys buy from

or do you buy depending on the translator

[ocean mulch]

y'all buy books?

[fierce hedge]

Physical books are easier to read for longer time

[coral prawn]

Yeah

[spare ridge]

penguin

[thorn cloak]

Also can study with then late at night w/o blue light

[sudden granite]

ok thats wgat i usually buy

sometimes vintage

[remote sparrow]

it's worth noting that some dedicated e-readers, like kindle, or dedicated writing tablets, like a remarkable, also have this advantage

[crimson leaf]

The kindle is nice but harder to flip back and forth

I prefer printing books for math

My school gives 1500 pages a semester so you can get a good amount

Kindle is great for casual reading though much nicer than a phone I didn't think the size difference would help much but it's actually great and the backlighting makes it amazing for when you're laying in bed at night

[remote sparrow]

not all classic literature is non-english

but i try to find it by translator

different translations have different goals

some are more literal, some more interpretive

scholarly accuracy might be more important for a philosophical text, but a more literary translation might be more appropriate if you're just looking to enjoy, say, the odyssey

[sudden granite]

real

[remote sparrow]

if you're doing a close read of some translated non-english literature, you might want to pick up a scholarly translation

[sudden granite]

i just judge a book by its cover for editions tbh

at end of the day reading in a different language there will be some drawbacks

[jade field]

what happened to the typeface modernization project here?

[gray gazelle]

Anyone recommend a good "light read" on the history of mathematics?

[azure salmon]

any recommendation for a good intro to linear algebra book?

[remote sparrow]

#book-recommendations message

[ocean mulch]

Try the biography on Hilbert, it's for non-mathematician (though some background on Maths will allow you to better appreciate the context).

I also once read an exposition book on Fermat's Last theorem, a bit heavier, but still good.

Other than that, Idk any books that cover the whole history of Math. It's pretty wild, and it blew up quite early.

[frosty coyote]

Thanks I’ll check that out!

[maiden halo]

I haven't read them yet but Boyer (1949, Dover) and Bressoud (2019, Princeton) have written books on the history of calculus. Maybe they have other history books, too. Jeremy Gray also has a couple history books I've heard of, I think one differential equations and another on analysis

[fierce hedge]

I have a Kindle and it's good for ebook formats, pdf is harder to read not to mention djvu isn't supported at all.

[marsh veldt]

hello guys! do you know a nice substitute for Patrick J. Ryan's Euclidean and Non-Euclidean Geometry book?

that one's tough for me without proofs

[marsh veldt]

🪰

[ocean mulch]

What do you wanna know exactly?

[marsh veldt]

rn I just want a softer attack on the chapter 1 of the book. I guess more proofs and a slower pace

chapter 1 is on plane euclidean geometry

[marsh veldt]

↖️ ⬆️ ↗️

[spare ridge]

hi gmz

[mellow wren]

Idk if you'd be interested in it but i have a couple of book that are pretty light mathematically but historically very heavy
Ala they're written a lot like history papers

[mellow wren]

Idk if that was ever affiliated with this place but there still is a project of typesetting older math books in latex

(notably the texromancers)

[primal sorrel]

Hot Mess
Matt Winnnig
good book about climate change and having a baby

[gray gazelle]

Studying math can be overwhelming for me as I have ADHD. Do you have any advice?

[smoky schooner]

recommendations for abstract algebra?

[deep epoch]

check pins

[remote sparrow]

is this your first time studying abstract algebra?

if so, pinter and judson are good

[jade field]

hi Oxide

[summer raven]

What math specifically are you trying to study? I have adhd too btw

[grave harbor]

I'm not diagnosed with adhd but I suspect i have It. What I do is turn of any music or any distraction around me, and after that i find a good youtube lectures and copy everything that the teachers writes. Then I find some good practice problems and practice putting the concepts into action.

[gray gazelle]

Arithmetics

[rigid barn]

Wtf, where do you study? We get only 300 per and I thought that's a lot.

[remote sparrow]

this website is a nice resource for abstract algebra: http://www.math.clemson.edu/~macaule/classes/f22_math4120/. lecture videos are also linked.

also this same guy has neat stuff in general: http://www.math.clemson.edu/~macaule/

[crimson leaf]

SE USA

[gray gazelle]

WOOOOWWW THANKSSS!!!!!!!!

[narrow relic]

I watched a bunch of this person's linear algebra videos but they were riddled with unclear things and ultimately wasted a lot of my time

I do not recommend his linear algebra content if you want something rigorous

[remote sparrow]

those videos are for a graduate course in linear algebra, so he is assuming you have seen linear algebra before.

[fickle bough]

Is there any RA book that not only doesn't assume completeness of R but also builds up the other sets starting from N?

I guess I'd be looking at a set theory book but whatever

I mean Rudin doesn't assume completeness but he starts from Q

[sturdy shore]

amann escher

[narrow relic]

His derivations are sloppy

I worked through many of them line by line

I have books that contain the material he was trying to explain that do a way better job

[sturdy shore]

fwiw I've watched many of those lectures and, while they weren't amazing, I certainly have a much more favorable view of it than you seem to have

[narrow relic]

Did you work through the derivations line by line, not just lightly watching the videos?

[sturdy shore]

as it has been aforementioned, the lectures assume you know linear algebra already

[narrow relic]

Yep, I already took linear algebra

I worked through over half the lectures, every line, documenting his mistakes, and for a while I was doing every problem in the recommended textbook. It was ultimately a pretty big waste of my time

I probably still have all the notes from that somewhere

I should have just gone with a book that actually derives the relationships between X, its dual, and its bidual, properly

Rather than that prof's handwavy explanations

[sturdy shore]

I'd have to see concrete examples of these mistakes then, because I thought they were largely good and I do remember it giving me important intuition on some things

although they also felt disorganized

[narrow relic]

At some point maybe I'll go dig that stuff out

May I DM you?

[sturdy shore]

I won't defend these lectures to death but I'm also not willing to let this criticism slide like that

sure

[narrow relic]

Fair enough! 🙂

[north aurora]

I've been reading Avram Davidson

Not only is he a magnificent author,

But his beard is glorious.

Just gonna drop that there and get out.

[lapis sundial]

Uh any recommendations for graded Lie algebras?

[sudden kindle]

No recommendations

[remote sparrow]

tao

parzynski and zipse

bloch i think

[ocean mulch]

Yeah, Tao comes to mind

a bit too rigorous, but he def did what you want

[remote sparrow]

https://www.maa.org/press/maa-reviews/calculus-with-applications
https://www.maa.org/press/maa-reviews/multivariable-calculus-with-applications
i recently found these two calculus books, and i think they look pretty interesting. reals are understood as infinite decimals. treats transcendental functions like sine and cosine early, as is common nowadays. they're more rigorous than the competition (of course more difficult results are stated without proof); however, both contain many discussions and applications to physics. the single-variable calculus book has a slightly unorthodox ordering of topics, preferring to treat sequences and series of numbers and functions prior to differentiation and integration. it also talks about completeness of the reals (via lub property) and cauchy sequences.

[fierce hedge]

Talking of calculus reforms there was this website that was recommended in a different server where the authors express their disagreement of how calculus is taught particularly integration as it presented in form of Riemann integral. The point being Riemann Integral is obsolete and shouldn't be taught in universities. They present some alternatives for the RI after which they make their way to Lebesgue integral. There's also the more traditional analysis books that they have.
More importantly, all of their books are free and cover a lot of material so, it's a worthwhile check. The website is -
http://classicalrealanalysis.info/com/Home.php

[gray gazelle]

where was this book when i needed it

[finite crane]

Peter Lax is a name I can trust

At least more than the randos who write calculus books nowadays

[fierce hedge]

Hmm... There's no mention of compact sets or any topological properties of R. Is it intentional, ie by design? Or is it standard for calculus textbook

[gray gazelle]

What are some books you can recommend to people who want to learn advanced math?

I know the basics, ofc, and want to move on. However I don't know where to start.

I only know some high school stuff, and even that, a little bit.

[finite crane]

Try Tao's Analysis 1 and 2, together with a book on linear algebra (see pinned)

[gray gazelle]

It's a bit above my level I think

[finite crane]

It starts from scratch with natural numbers

[gray gazelle]

There are signs and concepts I don't find familiar

[finite crane]

Skip the introduction if that's what you're thinking about

[gray gazelle]

I will look at it again, thanks!

[smoky schooner]

wdym by advanced math

khan academy works for c1-3 iirc

[gray gazelle]

High school/college stuff

[smoky schooner]

if you want to learn calculus use khan academy

[gray gazelle]

👍

I will bookmark the stuff in here and see what fits my needs the best

Thanks yall

[remote sparrow]

well, it's not an analysis textbook. it's just supposed to be a calculus textbook.

[fierce hedge]

Fair enough

[bold cave]

Hi. I could use a gentle introduction to game theory that goes into details on strategies in simultaneous games. For context, I'm writing a general game-playing AI. One for sequential games is relatively easy for me; Minimax is simple enough, and the tree search optimizations (alpha beta pruning, quiescence search) are not relevant to my question. But now I have a game's graph, and need to evaluate the available move options, and I'm a bit stuck.

[fossil arch]

Do you guys think Lee's ISM is better than Tu's book for an introduction?

I like the sequence of content much better

I've gotten to Section 3 on Tu

[rancid hollow]

Pretty partial to the Generalized Riemann integral myself