book-recommendations

[orchid mortar]

As for this I'd ask what kind of inequalities, because I don't think Hardy's Inequalities book (for example) would be desired

[remote slate]

for the basic inequalities

like the first course

[hasty turret]

Spivak calculus

You don't need any math afaik

[sturdy shore]

the book has a fair bit of calculus in it, and also asks you to prove stuff sometimes

technically you don't need the calc knowledge but it would help

same with rudimentary experience with complex numbers, polynomials, number theory

not necessary but will make it an easier experience if you've worked with these before

[gray gazelle]

So High School Algebra?

[oblique dove]

it aops intermediate counting and probability a good replacement for discrete math books

[random raptor]

A question: is Burkill and Burkill's Second Course in Mathematical Analysis hard to get a hold of? It seems to retail for a pretty penny online.

[alpine rover]

good book but not a good replacement, there's a lot more to discrete math than counting and probability

[oblique dove]

what are some topics in discrete math that aren't in this book?

[alpine rover]

have a look at the contents of this book: https://notesack.files.wordpress.com/2017/07/ebooksclub-org__discrete_mathematics_with_applications.pdf

everything except chapter 9 (counting and probability)

[oblique dove]

thanks

[undone thorn]

hello every i am new here can anyone suggest me any book about quantum mechanics or math used in it

[prime oak]

hey

anybody know books on the history and development of islamic mathematics?

[graceful dawn]

How hard math u need?

[prime oak]

@graceful dawn thanks bro

[gray gazelle]

did you try asking here? https://hsm.stackexchange.com/

also I think you mean Arabic?

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

you could also search in references here

[prime oak]

didnt know that existed

[prime oak]

thanks

[prime oak]

opinions on the book "All the Mathematics You Missed: But Need to Know for Graduate School"

[solar anvil]

does anyone know of any books for order theory ?

[gray gazelle]

about partial orders and stuff?

[solar anvil]

mhm

[gray gazelle]

there's Gratzer

[solar anvil]

ive looked at that

is that the best option?

[gray gazelle]

also Birkhoffs book about lattices

idk. What kind of properties of partial orders are you interested in

[solar anvil]

well im trying to learn more about this for my program analysis course

[gray gazelle]

you shouldn't need a lot then

you can probably find everything you need in some introduction to set theory book or wikipedia

I don't think they require much more other than the definition

[solar anvil]

alright thanks, ill look for some intro to set theory books then

[gray gazelle]

unless it's some really experimental course

[solar anvil]

I was just unsure if I needed more

[solar anvil]

the book we are using is principles of program analysis

its pretty dense so I was worried I needed to read up on a lot of stuff

[gray gazelle]

ah you've probably encountered partial orders when talking about sorting algorithms?

[solar anvil]

I have yes

[gray gazelle]

yeah you just need the basic bare down definition and maybe write few examples of what those kind of orders can look like

just use wikipedia tbh

[solar anvil]

alright, thanks for your help

[flint sleet]

Not a book but a NIST pub. Ha what a gem https://www.govinfo.gov/content/pkg/GOVPUB-C13-47662724baf87597656507c28c7fd8e4/pdf/GOVPUB-C13-47662724baf87597656507c28c7fd8e4.pdf

[fast pawn]

As someone who’s forgotten nearly everything from my college Differential Equations class, would Schaum’s Outlines be a good book to relearn with?

[remote sparrow]

probably paul's online math notes too

[fast pawn]

Thanks for directing me to the notes! They seem like they’ll be pretty useful

[pulsar junco]

Any good book suggestions for combinatorics? Begginer level and I don't want it to go too much in depth.

[gray gazelle]

Combinatorics and Graph Theory by John Harris

DM if you want to get the pdf

[wicked trout]

I just discovered how brilliant are the for dummies series.
Simple language. No assumed implicit knowledge. Are there any
other good simple one explaining complex stuff and its practicalities?
Interested in abstract algebra, mathematical logic, model theory.

[split bluff]

I heard otherwise about the "for dummies books". That they only explain at most superficial knowledge to give you notions about certain topics without going in depth to allow you to understand the implications about those topics

But i guess that if notions is what you are looking for and bot anything too complex, then they may be useful

[desert oriole]

arabic ≠ islamic

[hollow shore]

is there any strict pre-requisite for picking up pugh's analysis text?

like do we need to do some analysis beforehand?

[hazy elk]

It'll be good to know some calculus and have some experience writing proofs (this isn't strictly required of course)

[hazy elk]

Nah, but be prepared to work hard (especially on excercises and a few proofs )

[hollow shore]

okay

I would pick it up!

[sullen raptor]

whats a good comprehensive multi topic engineering math book

i heard advanced engineering mathematics by kreyszig is good?

[topaz rune]

These 1500 page books usually suck

Also inconvenient to use aside from eBook / pdf

[remote sparrow]

a walk through combinatorics by miklos bona

[narrow relic]

Very much agree

[desert oriole]

never said that anything is wrong with islam?

i just said that arabic isnt the same as islamic

[gray gazelle]

🍿

Have you tried counseling or therapy?

It's just internet chat. Don't take it too seriously.

[gray gazelle]

https://math.stackexchange.com/questions/3143162/introduction-to-geometry-books

[remote sparrow]

https://www.wiley.com/en-us/Classical+Geometry:+Euclidean,+Transformational,+Inversive,+and+Projective-p-9781118679197

i saw this at my university bookstore

[golden veldt]

Would rudin be good prep for a class like this? https://math.berkeley.edu/~rieffel/202A-F18/202AannF18.html

[gray gazelle]

Won't a good prep is to track the people who took the class with the same prof before? And get the problem sets, solutions, past exams, etc.

[golden veldt]

I haven't formally learned analysis yet, so I guess I'm interested in resources to get to that point

[gray gazelle]

book recommendation for graph theory?

[sage python]

@golden veldt baby Rudin chapters 1-7/8 would work. But what is your current background?

[gray gazelle]

I mean, it's obviously a joke.

[golden veldt]

As far as proof-based math goes, I've done a couple chapters of spivak calculus, axler la, and the first two chapters of munkres topology. Also taken all undergrad lower division courses

[gray gazelle]

Alright, so a bit of a disclaimer. I am simply a high schooler(junior) who is deeply passionate about maths and has recently decided to formally self-study maths. With that out of the way, I have found a series of books that I currently am reading and enjoy, of which I can not recommend enough. They are free/open source and are used within a university setting. Moreover, while some of them are very proof heavy and thus do not contain many solutions, they contain practice problems that are perfect for self-study and assessment. These are the books published by the Open Logic Project(https://openlogicproject.org/)

I have done a bit of research and the first three books(Forallx: Calgary, Sets, Logic, and Computation, Incompleteness and Incomputability) are all required reading for Richard Zach's Logic I, II, and III courses at the University of Calgary. I have completed the first book, and it is, in my opinion a relatively strong introduction to formal logic systems(e.g predicate Logic, first-order Logic, and modal logic albeit very briefly). The second book of which I am currently on discusses naive set theory and begins to introduce the relationship between maths and logic. As such, it is a much more proof heavy book than the last. It ends by discussing turing machines and the problems of computability. The final book discusses Gödel's incompleteness theorems.

There is also a book that is distinct from the first three, in so far as it is not related to Richard Zach's logic course — Set Theory: An Open Introduction. It has peaked my interest mainly for the fact that it attempts to formally describe set theory along with the axioms of ZFC.

There are, in my opinion really good books, which are freely available and I would hate to see them fade into relative obscurity

[near wagon]

This looks very cool. Thanks for sharing. What branch of math are these topics good for? All?

[wicked bronze]

Could anyone suggest some books on existence, uniqueness and stability for systems of differential equations?

[glacial crypt]

trying to solve navier stokes I see

[wicked bronze]

I need it to elaborate my bachelor thesis

[karmic thorn]

Differential Equations and Dynamical Systems by Perko could be a good place to look into

Chapter 1 gets straight into the system of equations with constant coefficients case iirc

[narrow relic]

Thanks for sharing your thoughts on these!

[turbid mural]

number theory book recommendations ?

[gray gazelle]

any books/texts that you can look up math definitions properties and important theorems?

like what is that kind of text called?

[lean pagoda]

Encyclopedia perhaps?

[gray gazelle]

i asked around and says handbook, reference book, and encyclopedia

[gray gazelle]

yeah

those exist for like every mathematical field out there

math is way too large for just one single book of this sort

[jade meteor]

lemme recommend a book

VERITY BY COLLEN HOOOVER

[gray gazelle]

you could at least give it a short description

[gray jungle]

its usually called a reference book , and as mentioned there is too much math for there to be 1 single book , for example real analysis has walter rudin "principle of mathematical analysis" as a common reference , and you have to keep a reference(or more) for each topic usually.

[gray gazelle]

I don't think that's a good example of a reference book

it's as good of a reference as any textbook

reference texts usually contain lots of information and are pretty terse

like Lang's Algebra or Federer's Geometric measure theory

there also exist books specifically made for this, usually called handbooks or encyclopedias

such as handbook of combinatorial designs

[gray gazelle]

any textbook can be used as one but not necessarily is the best of a reference

[gray jungle]

fair enough i understand what you mean.

[runic snow]

What book should I get if I want to learn how to prove geometric properties from scratch without relying on intuition alone? I think that the way I solve for them is messy and makes me to prone to mistakes.

Any suggestions?

[sudden kindle]

Whst level

What topic

I have lots of recommendations

If you have no abstract algebra background but want to get exposed to algebraic number theory i recomend Cuoco&Rotman's Learning Abstract Algebra through appemts to prove fermatls last theorem

[turbid mural]

undergrad

[sudden kindle]

Ok

What topic in number theory

[turbid mural]

idk

[sudden kindle]

I think the book i recommended is very good if you have little background

It can be read by highschoolers even, id say

[remote sparrow]

burton or dudley are elementary number theory books

a lot of people recommend silverman

[sudden kindle]

There are tons of options

For elementary nt

[remote sparrow]

niven, zuckerman, and montgomery is elementary for the first several chapters

[sudden kindle]

NZM is a huge book

Has tons of topics

[turbid mural]

thanks

[remote sparrow]

@sudden kindle would you like to give your thoughts on audrey terras' abstract algebra book? i used it as a class text

as a student

[gray gazelle]

No idea. Never seen one.

[sudden kindle]

Havnt read that book but have heard of the author Audrey Terras i think

Yeah I know them from their harmonic analysis book

Which is great, and also includes many applied math and number theory applications, which I appreciate seeing in a pure math textbook

[gray gazelle]

Interesting

[small canopy]

Hello i a new here but I really like Calculus Algebra, Trigonometry and I was curious if there is any workbooks out there that would go into more detail of these topics. Pls and that you

Also sorta beginner but I would like to learn more on these topics

[minor hinge]

same i need some workbooks for trig and calc

[fierce hedge]

How the Schroder compares to baby rudin in terms of content and terseness ?

The first chapter seems very similar but I haven't read either one enough to comment

[loud cradle]

I've only skimmed through Schroder but have read the first 8 chapters of Rudin several times. To me it seems that Schroder is a bit more detailed in his proofs, while still being reasonably terse so as not to bore the reader. I like how he provides useful brief discussions about "standard proof techniques" which Rudin invariably uses without comment. Example:

[fierce hedge]

I see, maybe I'll use Schroder as a reference text then with baby rudin. Thanks for the info

[sage python]

Yeah Schroder starts off with more of these side comments and tidbits

By the end it covers more than Rudin does

[remote sparrow]

<@&268886789983436800>

[sage python]

Still beaten

[fierce hedge]

Umm... seems like a made a mistake. I meant browder

[sage python]

Browder I think just beats Rudin honestly. Covers similar content but more on manifolds/forms

[fierce hedge]

Is it better to just do Browder only compared to Rudin

My only problem is that it does a bit measure theory even before integration

[sage python]

As it should

[fierce hedge]

alright, thanks

[heady ember]

[gritty zodiac]

I'm on a gap year after high school rn, and have lost touch with pretty much all the math I knew. I worked through stewart calculus and half of strang's lin alg ~8 months back but extremely rusty now.
rough areas of interest are statistics, probability, logic, and combinatorics, but open to literally anything. primary goals are to just get a headstart in college to graduate early and be able to at least understand some research, if not work on it; and to develop problem-solving skills for putnam and such.
looking for recommendations on what to study and approachable (preferably v rigorous) books for my level.
edit - lmk if this is the wrong channel, will delete.

I was thinking of skimming through calc and lin alg, and then multivar calc -> introductory abstract algebra. not sure though and would love any suggestions at all :)

[dense hamlet]

You don't need multivariable calculus for abstract algebra, if you know the basics of logic you can just take a crack at a text like dummite and foote @gritty zodiac

[gray gazelle]

Book recommendations for jee organic?

[grand thistle]

any short books or pdfs on number theory for competition math

i'm not looking for like basically modular arithmetic or divisibility only, but rather kind of covering undergrad number theory as well

i.e. uses of things like quadratic reciprocity, modular arithmetic with polynomials, etc.

should also have a bunch of problems and exercises that are around like intermediate AIME level - USAMO level (but maybe harder ones too)

i'm looking for something around the range of 50-100 pages long, i.e. not just a list of theorems and has a bit of exposition/motivation, but not a full fledged textbook like burton's book or something

[runic snow]

Any recommendations for books on geometric proofs ect?

[remote sparrow]

try reading hubbard and hubbard or shifrin's book on multivariable calculus

two good intro books on abstract algebra are those by pinter and judson

[remote sparrow]

geometry or geometric methods of proof

and by geometry do you mean euclidean synthetic geometry?

[runic snow]

A way to rigorously prove geometric properties (both euclidean and non) like I can algebraic and set properties

[remote sparrow]

geometry as a discipline is very broad

there's stuff like differential, algebraic , and arithmetic geometry

you're gonna have to narrow things down

[runic snow]

I'm not really sure. I just want to be able to prove things I derive from intuition.

Like being able to prove the formula for the shortest distance between two points on a sphere along the surface of said sphere of being able to prove classic theorems from scratch (angle theorems ect)

Aka: I just want to know how to use axioms to prove geometric properties

[remote sparrow]

you can look at kiselev's geometry volumes or that book i recommended the other day

[runic snow]

I can do most regular proofs just fine just get lost when things get more abstract (like in geometry)

[remote sparrow]

https://www.wiley.com/en-us/Classical+Geometry:+Euclidean,+Transformational,+Inversive,+and+Projective-p-9781118679197

kiselev is meant for students below college, above is an undergrad level book for ppl that weren't really exposed to geometry in say HS plus some more topics

gelfand also has a recently published geometry book

[remote sparrow]

i think zorich is sort of like a less concise schroder (though partly because it proves most things in detail) sans abstract analysis and measure

[runic snow]

I'll look into it thxa for the help!

[fast pawn]

Can someone recommend books on Magic Squares? I’d definitely like to learn more about their inner workings and learn more about how to solve larger sized squares and rectangles

[graceful dawn]

Any good electronic circuit design books?

[remote sparrow]

does The Art of Electronics qualify

[lean pagoda]

Jeremy Avigad recently released his Mathematical Logic and Computation text. I only now got my hands on it, so I only managed to skip through some chapters but it does look very promising. Thought this was worth mentioning since questions about logic books come up every so often.
What makes the text stand out is that it diverges quite a bit from some of the "classic" books you'd otherwise see mentioned (think Mendelson, Ebbinghaus, Enderton, etc). It's slightly less focused on model theory and set theory and instead pays a lot of attention to constructivism, proof theory, computability and even touches on type theory. That should also make the text especially attractive to computer scientists.
The first third covers the basics of propositional logic and FOL but a bit differently from the more traditional books. Handling intuitionistic and classical (and even minimal) logic in parallel, introducing hilbert-style, natural deduction and sequent calculus systems for each of them, providing translations between the logics, covering both algebraic and kripke semantics, disjunction property in intuitionistic logic, a chapter on cut-elimination, etc
The middle part is mostly on computability and arithmetic. With a chapter on undecidability and incompleteness, (simply typed) lambda calculus, combinatory logic, curry-howard, realizability, etc
The last third (except the very last chapter) is basically an introduction to reverse math and the book ends with an introduction to type theoretic foundations

(TOC and preface: https://www.andrew.cmu.edu/user/avigad/mathematical_logic_and_computation_toc.pdf)

(This sounds like I was paid to shill it lol, but it's nice to see a text that isn't just a slightly modernized version of some older text)

[remote sparrow]

would you like to take a look at mileti's book, Modern Mathematical Logic when you have free time? it was recently released just last year through CUP as well. mileti also has a draft copy on his site.

[lean pagoda]

From a quick glance it looks to be a lot more like a traditional mathematical logic book (like the ones I mentioned above). So I don't think the two texts are comparable if that is what you were asking

[narrow relic]

Woah, a book that actually covers natural deduction? Thanks for describing this for everyone

[narrow relic]

Have you seen the Stanford "Introduction to Logic" course/book?

[remote sparrow]

good to know

i was more wondering about the quality of exposition of mileti compared to some of its competitors

[lean pagoda]

I mean that would require someone to actually read or work through most of the book (or use it in class) and considering how new it is that might take a while. But it's not like you can do much wrong with a book like that and no book is perfect. Considering it's all fairly standard material one could just supplement with other similar books if something isn't clear

[remote sparrow]

https://www.logicmatters.net/2022/09/30/avigad-on-mathematical-logic-and-computation/

peter smith has also reviewed avigad's book

[lean pagoda]

That is something completely different. It seems to be a "baby logic" (that's not meant in a derogatory way) course aimed at students with little experience in higher mathematics. Like a course you'd take as a first year philosophy student (presumably, I don't know really).
It's not a mathematical logic text

[lean pagoda]

He seems to have written even more on the text while going through it more carefully: https://www.logicmatters.net/category/books/mlc/

[narrow relic]

Thanks for the feedback.

[remote sparrow]

hmm, seems like it's not so good as a first text

but your discussion about topic choices makes it seem like a worthy reference

[wise plaza]

But say you already own several texts on FOL and non-classical logic?

Would it be worth getting into if you aren’t totally naive on the subject matter?

Say you already well versed in the “baby logic” as Neverbloom refers to?

[remote sparrow]

usually math logic books invoke a bit of abstract algebra and assume some familiarity with mathematical proofs

[lean pagoda]

Due to the nature of the book, some topology and lattice theory is helpful too
The appendix includes some stuff, but a lot of it was also just included in the exercises

[wise plaza]

Okay I may add it to my list regardless

If I get accepted in the MA program that I applied for some of the topics may be covered in a grad level logic course or at the very least I will have access to profs who specialize in philosophical topics within mathematics who may be able to help me if there is something I don’t understand.

I been required to provide proofs in classes before when I took non-classical logic given all the various logics we learned required a shared metalanguage

[fierce hedge]

Zorich does most things in full glory, although take that with hint of salt as I've only read first few chapters. There are places where Tao is better than Zorich but for most others Zorich is very good. My main issue with Zorich is a slight disconnect between chapter content and exercises which seem much harder compared to what's in the text. Sometimes there are things you have to figure out on your own which can be an advantage or a disadvantage depending on the person.

[tawny copper]

Books for multivariable calculus?

[foggy gorge]

What do you guys think about the book: Discrete Mathematics With Applications by Susanna?

[solemn rover]

it's very common. it's a standard textbook for discrete mathematics at universities

[humble tusk]

Has anyone read Mathematical Thinking: Problem Solving & Proofs by D’Angelo and West?

[mystic orbit]

Spivak's calculus on manifolds if you want something terse

And hubbard's vector calculus, linear algebra and differential forms if you want something more talkative

These are the ones I know and i quite like

But Hubbard is in dispersed with linear algebra which you might already know

So you might have to study through to find the calc knowledge you need

[fossil arch]

I was going to ask about something similar

I think what I'm looking for is a book on doing calculus on arbitrary curved surfaces in arbitrary coordinates...

...which I think is called calculus on manifolds? or is that under the umbrella of differential geometry? or is that just multivariable calculus or "advanced" multivariable calculus?

all of the books I've found are really analysis-esque or focus heavily on theory and proofs or similar, I want something oriented towards an engineer or physicist desiring a strong math background, with either computations or just lots of examples or similar

Context: Interested in learning in order to study dynamics (fluid dynamics in particular, but also interested in robotics)

I've already taken calculus up to ODEs and a linear algebra class, as well as fluid mechanics & dynamcis classes

[hearty steppe]

Knot theory book recs?

I thought I had a note somewhere typed down in my trello board but couldn’t find it

[sage kelp]

Thoughts on Elementary Real Analysis by Thomson, Bruckner, Bruckner?

[marsh lodge]

Can i get any recommendations on books on prob and statistics?(preferably pdfs as well)

[sage kelp]

Mathematical Statistics by DeGroot

[remote sparrow]

blitzstein and hwang for just probability

wackerly, mendenhall, and scheaffer for probability and stats

[vagrant mason]

is stewart precalc a good option for recapping mathematics before taking a calc class?

[remote sparrow]

yes

you can also check khan academy or paul's online math notes

[remote sparrow]

zorich is one

browder and schroder as well

duistermaat and kolk, but that seems like too much content

[gray gazelle]

Excellent

[hollow nymph]

Anyone have any suggestions on dynamical systems books?

[gray gazelle]

I like Strogatz but it might not be quite what you want. It's a fantastic book on the topic though.

It is a book that belongs on every shelf though, so you might wanna pick it up 🙂 There's even free problem sets, quizzes and solutions on OCW. (to be clear, i mean "Nonlinear Dynamics and Chaos ")

[hollow nymph]

I would absolutely love to learn abour chaos theory, a little.

Strogatz is a good author in general so maybe I'll pick it up anyway 😄

I have Infinite Powers

[gray gazelle]

Like it certainly won't teach you control theory (which I'd like to learn some day) but (and this is memories more than 15 years ago)I seem to remember that course as being the main undergrad dynamical systems class in general.

There were problem sets about determining stability of systems using linearizations, it covered period doubling, orbits, ... other stuff. (crap, I thought I could remember more! maybe I need to retake it too)

Also, just throwing it out there Dr. Strogatz is/was (when I took the course) a fantastic lecturer as well. Dr. Strang as well. So maybe there's viodeos for ya, if that's helpful.

[hollow nymph]

I may have learned a little of that control theory you mentioned through my undergrad. My undergrad is Mechanical engineering but I want to go back to school for a master's in applied and computational math. I've always been a math guy stuck in engineering :/

At least I think I learned some control theory in my system dynamics class

And measure theory (not actual measure theory in theoretical math)

I miss my advanced calc class a little

It was my first adventure into theoretical math lol

[fossil arch]

Same

[fossil arch]

Bump

[fossil arch]

I'm a mechE major too, but I'm a third year undergrad

[hollow nymph]

It's nice to know you're not alone lol all my mechE friends disliked math, more or less. Love them to death but I was sad when I couldn't share my love of math with them.

But I thnk I'll just force it on my other friends during our monthly presentation night >:)

[fossil arch]

Interested in systems & controls :)

[near wagon]

Is this book good by Tao? What is the suited audience? Solving Mathematical Problems: A Personal Perspective, by Terence Tao

[vagrant mason]

What is a great calculus book that is more for someone who isn’t a beginner with calc? Like something more detailed and and sophisticated but it covers all of calc 1 and 2

[fluid bay]

any intro analysis book

maybe abbott's "understanding analysis" is what you're looking for

[vagrant mason]

Is this a response for me? Sorry I can’t tell

[fluid bay]

ye

id look into abbott's text

[vagrant mason]

Thank you!

[fluid bay]

Npnp

[remote sparrow]

spivak or apostol

[gray gazelle]

Hello I want to read algebra by serge lang since the content looked quite good and i have familiarity with linear algebra by lang and so i wanted to know if there are any video lectures that follow algebra by lang or any close video lectures online?

[silent sonnet]

Do you guys know some good basic book for beginers about number theory, or about logic or about proofs?

[indigo mesa]

One of the mods wrote an intro to proofs

check the pins in #proofs-and-logic

[gray gazelle]

intro to topology: gamelin & greene or mendelson?

and I'd also like to read Proofs by Jay Cummings, but it seems to me to be less of a textbook and more of a "the universe in a nutshell"-ish book for math.

[gray gazelle]

Does anybody know good Statics books

preferably with answers in the back

[sage kelp]

Logic and proofs check out Velleman

[heady ember]

Schroder's analysis book is one you could check out as well

[sage kelp]

Any thoughts on the Zakon series on mathematical analysis?

[gray gazelle]

I wanna learn calculus from the scratch

Any recommendations?

[rose heron]

It's expensive but, you can also find it for free on the Internet Archive, The Calculus by Louis Leithold

[rose heron]

I'm assuming your Trig and Algebra skills are really good. Use Stewart or Spivak or if you can find it for cheap Louis Leithold.

[gray gazelle]

[gray gazelle]

Why did you assume?

[rose heron]

To get good at Calc you need good Algebra and Trig skills that's all

[gray gazelle]

Ok!

So it's impossible to learn calc without algebra and trig?

[rose heron]

Not that its impossible more so it will be harder a lot harder

[gray gazelle]

Ohk

Thanks for the warning

[rose heron]

Anytime

[pseudo forge]

same and I am in EE 3rd year uG

the beauty of controls

what is the general math prerequsite knowledge for going fairly deep into control theory?

[fossil arch]

ODEs & LinAlg

[pseudo forge]

makes sense

no PDEs tho?

aren't those required when you get to non-linear

[fossil arch]

I have no clue

[sturdy sail]

Is Manin's book on schemes any good?

[dapper root]

Manin has a book on schemes???

[sage python]

Oh huh he does

https://link.springer.com/book/10.1007/978-3-319-74316-5

[sage python]

Looks pretty good ngl

[coral prawn]

any recommended book(s) to learn set theory and/or matrice algebra, vectors, cross products and all that? Trying to learn those so that I can go further into calculus and physics

[heady ember]

I suppose naive set theory? In which case most (math) books should cover the necessities you need to read them. Otherwise, for the basics I'd imagine Khan Academy works as well

[still umbra]

??? Do not read a set theory book to learn matrices, vectors, etc

What even

What you are interested in learning is the topic of "linear algebra"

There's some good suggestions in #books-old

[heady ember]

I don't think he/she's trying to read set theory to learn lin alg

I think they mean they're trying to learn both.

[coral prawn]

yep

[still umbra]

mm

If the intention is to learn further calc/physics then reading a linear algebra textbook is still the way to go imo

the set theory stuff can be learnt on the way

[coral prawn]

yeah basics of set theory is ezpz

[still umbra]

It might mean you can't read a proof-heavy linear algebra text

but that's probably fine for your purposes

[heady ember]

Yeah

[coral prawn]

makes sense then, time to look up on linear algebra wait what abt non linear algebra? Surely such a thing exists?

[grand thistle]

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

[coral prawn]

[heady ember]

Multilinear algebra also exists

[coral prawn]

okay smth to look into after linear algebra

oh damn

[heady ember]

Tensors

[coral prawn]

ok gonna have to look at all 3

[heady ember]

Tensors is under multilinear iirc

Another reminder of how little I know

[coral prawn]

.... now to ask for recommended books for all 3 topics- wait I should check out #resources 1st

[heady ember]

Tensors are also used in uni math quite a bit I think

[lapis heart]

me who has never done tensors

[fickle whale]

tensors are multilinear algebra yes

I need a good book for tensors

I have a terrible book already

so I don't need any mid books

[cobalt arch]

are there any axiomatic books of trigonometry?

[karmic thorn]

Zygmund

What do you mean by an axiomatic book though?

[cobalt arch]

something that treats trigonometry from explictly stated axioms and derives everything else explcitly from said axioms

[mossy flume]

A book on just trig would be quite small. Hard to do alot with trig without looking at seeing how it's applied to other things. And then do you want all those other things to be covered axiomatically as well? then that'll be alot of material and probably too much for one book

[cobalt arch]

is hobson's a treatise on plane trigonometry good?

I don't think that anyone has read it but nevermind

Seems like a good book

[cobalt arch]

I don't want a lot of other applications just enough to be a good sized book

[restive falcon]

there is not enough trigonometry for a full book

the best thing would probably be a real analysis book

[cobalt arch]

So are there any books that treat trigonometry within the context of real analysis?

There are books that treat trigonometry by itself

They are just old

Hobson's book is one example

[restive falcon]

if you want an axiomatic treatment of most of school maths you will need a real analysis book

[cobalt arch]

So any recommendations?

[restive falcon]

mathematical analysis: an introduction by andrew browder

[cobalt arch]

Any good books for rigorous calculus?

Not analysis

[karmic thorn]

How do you distinguish the two?

Rigorous calculus and analysis, that is

[cobalt arch]

Rigorous calculus should derive all of the theory from a calculus book like thomas

I don't think analysis texts do that

[sage python]

Many do I'd say? Anyway try Spivak Calculus

[rose heron]

Stewart is good too but Spivak is probably best

[sage python]

Stewart doesn't cut it for rigorous which Forsaken wants

[rose heron]

Ah I missed the word rigorous

I have a couple of old Soviet Calc books that are pretty intimidating

[karmic thorn]

Zorich Volumes 1-2

[foggy relic]

Loomis-Sternberg is very nice

better than Spivak/Apostol

[cobalt arch]

could you explain why?

[remote sparrow]

not just rigorous but essentially a bourbakian development

axioms are given explicitly at the very beginning

everything is written in complete logical order (even if it may benefit many readers to see an idea developed intuitively before formalizing and making it rigorous)

this is what forsaken is looking for

[vague wren]

Hello everyone. I would like to improve my basic understanding of math (know some geometry, can solve quadratic equations, and have a very bare knowledge of trigonometry) by reading a self-study math book. Do you have any recommendations for such books?

[rose heron]

start with Algebra and work your way up. I really trust the math sorcerer's videos. You don't have to get all these books but look at the books he recommends at the beginning: https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=&cad=rja&uact=8&ved=2ahUKEwiqidjsipv9AhV0DjQIHWs8Ae8QtwJ6BAgQEAI&url=https%3A%2F%2Fwww.youtube.com%2Fwatch%3Fv%3DpTnEG_WGd2Q&usg=AOvVaw0YIaE1JG1o2QWPaJhmerxX

[vague wren]

Thank you! Will get one of those books as a start.

[buoyant halo]

Is James Stewart Calculus a good calculus textbook?

Asking before I drop $$$ to buy a hard-copy

[restive falcon]

a lot of them do

browder definitely does

and you'll get a lot more proofs from his book than for example spivak

[remote sparrow]

you can buy an old edition

substantially cheaper

it's a good book

[cobalt arch]

Well dieudonne's books are really good for an axiomatic treatment of analysis 😆

[dapper root]

[narrow relic]

Is the Reed Simon functional analysis book (Methods of Modern Mathematical Physics - Volume 1 Functional Analysis) readable or difficult to read (like, does it skip steps in arguments, etc.)? Could one read it without a lot of trouble after reading Axler's Measure Theory book?

[gray gazelle]

any good books for logic/ proofs

[rose heron]

Book of Proof is a good one and it’s free and Proofs by Jay Cummings is a good one as well

[narrow relic]

Could anyone share their thoughts on this book from the Table of Contents? https://www.amazon.com/Fundamentals-Functional-Analysis-Universitext-Farenick/dp/3319456318

[gray gazelle]

ah yeah heard of it from the math sorcerer haha

[forest sleet]

if Axler measure theory is like Rudin Real and Complex Analysis then probably yes

[grave thorn]

looks ok

[quasi dock]

Haiya! is richard johnsonbaugh discrete math good?

[main void]

Any resource to read about haar measures and fourier analysis on locally compact abelian groups?

I know Stein Shakarchi talk about it in their book on fourier analysis but J was wondering whether there was a more specialised resource

[vagrant mason]

Is Single Variable Calculus: Early Transcendentals by James Stewart a reliable calculus book?

[ember slate]

Are you okay with lectures?

[vagrant mason]

yes

[ember slate]

Alright

Mit ocw has a course called single variable calculus

Its not proof heavy

Hope that helps

[vagrant mason]

alright ill look into it

[narrow relic]

Okay thanks.

[narrow relic]

Thanks for looking at it.

How much about complex variables does one have to know to read a functional analysis book like the ones I was mentioning? (or in general?) Do I have to go through the material of a full complex analysis course? Or do I just need to know some things about how complex variables work?

[sage kelp]

I have been teaching trigonometry from College Trigonometry by Aufmann and I have found it neat so far

[sage kelp]

Velleman is great

[sage python]

@narrow relic generically not much unless you do shit with resolvents in spectral theory

[river tangle]

guys what are some good books for Olympiad number theory?

like I'm a beginner in nt

[candid dagger]

Hello,

does someone has the following book?

CONAMAT. MATEMATICAS SIMPLIFICADAS / 4 ED.

is in Spanish made in Mexico

[broken meadow]

Maybe deitmar harmonic analysis?

[main void]

Thanks for the rec but I think Ill just read Fourier Analysis on Number Fields, I think its the most direct route for my objectives

[vague wren]

Thank you for recommending, will keep it in mind!

[forest sleet]

You don't need the complex analysis part of big rudin,

[forest sleet]

Just standard undergrad complex analysis

[atomic crystal]

what is like THE complex analysis textbook

[remote sparrow]

for undergrad or grad

[hollow shore]

Invitation to Number Theory by Oyestein Ore and Modern Olympiad Number Theory by Aditya Khurmi are standard recs

[unreal token]

Are there any good book recommendations for a college student in calculus 2? Like a book explaining the intuition of math, not comprehensive textbooks like Stewart’s calculus

[finite gale]

i guess if you really just want intuition and not rigor, paul's online math notes are pretty good resource

[narrow relic]

OK I see.

[narrow relic]

Is the last two chapters of Shilov's Elementary Real and Complex Analysis enough?

[forest sleet]

never heard of that book sorry

[sage python]

For undergrad complex generically I like Gamelin and Freitag-Busam

[narrow relic]

I'm not really interested in the subject at this point I just wanted to be able to read this (except for Chapter 9): https://www.amazon.com/Fundamentals-Functional-Analysis-Universitext-Farenick/dp/3319456318

@forest sleet Here is the part of the table of contents I was asking about: https://a.uguu.se/XlVgTZGH.png

(I don't know anything about complex analysis so I can't tell if these two chapters cover fundamental stuff, necessary stuff, are missing important key things, or anything)

[sage python]

So if you're doing functional calculus, resolvents, etc you might need, say Liouville's theorem

But if you're not then arguably you don't need any complex analysis tbh

[narrow relic]

OK I see. That "Fundamentals of Functional Analysis" book defines most of the functions as mapping to the complex numbers, but flipping through for example the measure theory part, it looks like most of the results are the same as when I learned that material for real-valued functions

[sage python]

Oh yeah measure theory over C doesn't really change it's more differentiation

[narrow relic]

I'll probably just stick with these two Shilov chapters for the time being then. Thanks for your advice!

[remote sparrow]

something that invokes infinitesimals like Calculus Made Easy by silvanus thompson might work

and doesn't precisely state things in nonstandard analysis language

[rose heron]

Leithold’s The Calculus Book

[chrome yacht]

i want people's thoughts on David Betounes' textbook Ordinary Differential Equations: Theory and Applications. how does it compare with other textbooks on the theory of ODE from an analysis perspective, anyone have better recommendations?

[gray gazelle]

just want to come here and say that schroder is an absolute fantastic introduction to real analysis or even calculus

[atomic crystal]

undergrad

[gray gazelle]

What would be a good book about logics that also covers gödel's incompleteness theorems?

[sturdy shore]

mendelson, rautenberg

[slim wind]

Check out Peter Smith's website logicmatters.net, there are a lot of free books written by him. If I remember correctly, there are two books on Gödel's incompleteness theorems and some primers on formal logic (propositional and predicate logic).

[remote sparrow]

gamelin i guess

[turbid mural]

any undergrad category theory book recommendations ?

[finite crane]

have you at least learned group theory, linear algebra, ring theory, modules and topology?

you need working examples to understand the ideas cat theory are trying to generalize. I just read MacLane for category theory, but maybe Awodey is a more modern guide

[remote sparrow]

awodey, lawvere, leinster, riehl

[desert oriole]

opinion on:
How to solve it - G. Polya?

[hasty turret]

It's a good book wrt what it's trying to do ig

[fast pawn]

Could someone give me an opinion on Munkres’s Topology book? ChatGPT said that would be a good next step after I finish Abbott’s Understanding Analysis

[grand thistle]

it's very popular

for a first course in topology

anyone know of a good resource for chemistry from a mathematical perspective? (if it exists)

[fickle bough]

lf a complex analysis book but not computation based

[grand thistle]

i'm kinda looking for something like spivak's "Physics for mathematicians" but for chemistry

[fickle bough]

it's fine if it has a few contour integrals here and there but not if they're half the book

[grand thistle]

@fickle bough

[fickle bough]

ty

has anyone had experience with the lang one

that one was one that also came up while I was looking not really mentioned here wondering if it has a good treatment aswell and doesn't require much outside of real analysis

[wheat remnant]

I noticed that strang isn’t listed on the linear algebra recs? Anyone care to enlighten me?

[sturdy shore]

haven't managed to spot a single proof in any of his linear algebra books to date

[fickle bough]

I looked at the first pages it looks like it starts from the beginning and builds up doesn't seem to require much prereqs and covers a decent amount of content

It seems worth it

might wait to see if I can snag a copy for a bit cheaper on amazon

[wheat remnant]

Gotcha. Yeah super curious as to why it’s the MIT required one then, I’m unaware of what the other unis use

[glacial crypt]

probably because he works at mit

[distant spear]

its used for an intro/first course in LA, which is taken by everyone not just math majors

[hollow shore]

yeah

MIT does have a proof based LA course which follows Axler

but there are no lectures of it sadly

[chrome yacht]

is loomis and sternberg a calculus textbook or is it an analysis? would it be recommended to someone with some real analysis experience and linear algebra experience

[vital bane]

I mean not everyone wants proofs physics and chemistry and engineering students exist

[sturdy shore]

and?

someone asked why it isn't recommended in a math discord, I believe my answer is adequate

maybe in engineering discord they do recommend it

[sturdy shore]

an analysis textbook and a pretty hard one at that, your background should be sufficient to at least give it a try though

[hearty steppe]

Sternberg is rough to read through, I didn’t like his dynamical systems book. I guess it’s more for the pure math crowd

[foggy relic]

no prereqs starts with basic logic

great calc book covering a bit of analysis

[sage python]

Well officially it assumes you know single variable calculus but otherwise yea

[chrome yacht]

ok thanks @sturdy shore and @foggy relic

[timid crane]

anyone know a good book for sturm-liouville problems, incl legendre and bessel problems (+ maybe their use in solving pdes)?

[wheat remnant]

Ahhh, so it should be good then starting out? Or should I just go into friedberg

[wheat remnant]

Yeah I’m comp sci

[distant spear]

go friedberg!!
check out the contents, if it doesn't seems to be of much use to u, then strang

[wheat remnant]

Okay awesome, thank you lots!

[remote sparrow]

boyce and diprima with boundary value problems

[remote sparrow]

#book-recommendations message

[narrow relic]

if you've never studied LA before and think Friedberg is confusing when you're trying to read it, there's a book that covers similar stuff to Strang but is much better written in my opinion, called Linear Algebra: A Modern Introduction by David Poole (https://www.amazon.com/Linear-Algebra-Introduction-Available-Enhanced/dp/0538735457)

[remote sparrow]

all of my recs are lower level than friedberg but significantly more proof-based than strang

[near wagon]

Any opinion on Terrance Tao’s LA notes?

[remote sparrow]

no opinion

[fickle bough]

came across the topology book by singh apparently it has full solutions

by the author

but I've never seen it mentioned people mostly recommend munkres I don't know if it'd be a better option

[gray gazelle]

people are crazy about Munkres for no real reason

its okay

theres actually plenty other books which introduce you to topology

any professor could probably recommend you one good introduction

[sage python]

Lee Intro to Topological Manifolds

[narrow relic]

I have never read the book but I had a pretty good impression of it (I saw the first edition, the one with the blue cover). I think it's like Munkres with less extraneous topics and editorializing, it assumes you know how to do proof-based math already.

(side note: you should not rely on solutions)

[narrow relic]

Another benefit of it is it uses nets directly in the content

[fickle whale]

I thought we like proofs in comp sci

[remote sparrow]

"umm, but i thought comp sci was supposed to be a direct pipeline to a software engineering job, not an academic field of study with actual depth!"

[fickle whale]

I'm sick of software engineers flooding my major

We need to build a firewall

[gray gazelle]

I think diversity and inclusiveness is important

[sage python]

I don't see the connection

[wheat remnant]

I personally want to learn as much as I possibly can to make me the best computer scientist/software engineer I can be, and while I’ve just stepped in to this world load me up with it all as far as I’m concerned

[wheat remnant]

Yeah I’m a passionate person personally, and so I love learning and value the craft for craft’s sake, but I definitely gotta pay my bills and have $ 🤣😫

But people that just get into this to try and get that I feel never get good enough as they could be, but anyways yeah thanks for those recommendations I’ll absolutely check them all out

[rose heron]

Can someone recommend me books related to these topics for both computational solutions and rigorous proof solving:

Formal treatment of limits of functions and sequences of continuity, including a thorough training in constructing rigorous proofs of the epsilon-delta type. Convergence tests for infinite series. Radius of convergence, differentiation, and integration of Taylor series.

[topaz rune]

can u guys recommand me a book for my IIT collage

its about physics

[grand thistle]

any analysis book

smth like abbott's "understanding analysis"

[heady ember]

Try Schroder

(Proofs)

[light solar]

I know this is for book reccs but does any1 have some reccs for basic calculus?

Im starting my 2nd semester and i have no idea what to do

[heady ember]

Paul's Online Math Notes/ Khan Academy for an intro to calculus (not books)

If you wanma learn with a bit more rigor and proof-based exercises, then try Spivak

[gray gazelle]

Can anyone recommend a book about non-Euclidean space or/and about the works of Nikolia Lobachevsky.

[hollow shore]

I know of Ghoparde & Limaye, Apostol and Courant which seems to fit the bill here

[soft drift]

Does anyone know of a "statistics for science for dummies" type book? Just for personal reading. I wanted it for psychology but there is no psychometrics for dummies book (there is a psychometric tests for dummies book, but that's for people trying to understand psychometric tests in the context of job applications [according to the description])

[gray gazelle]

There's Statistics: An Introduction by Roger Kirk, pretty good read

[rose heron]

Stephen Abbott?

[past ridge]

What are some book recommendations for Mathematical Geometry or just Geometry in general?

Could be either High School, College/University or above. Just looking for any.

[past ridge]

Off-topic but how do you have nitro emojis with no nitro?

[queen sand]

"the art of problem solving" books

[fickle bough]

I don't rely on them I only use them when I'm convinced I have the right answer if I can't come up with something I think is right and use the solutions it's just a waste of a problem, but having them to be able to check yourself after is good when you have no one to check your work

but I get what you're saying

if it ends up being another method I didn't think of that's always good to learn about too even if I end up not being able to use it to correct myself

but used wrong it definitely does more harm than good

like people who just open them up as soon as they can't come up with something that's a horrible way to go on about using them

[narrow relic]

I agree with this point!

[rose heron]

Would Schaum’s be good for Real Analysis? (I’m looking at the Advanced Calculus version for sequences, series, and eventually Multivariable)

[narrow relic]

I wouldn't recommend that kind of book to study real analysis especially at the start, I'd recommend something with more of a narrative. I used Introduction to Real Analysis by Bartle and Sherbert (https://www.amazon.com/Introduction-Real-Analysis-Robert-Bartle/dp/0471433314)

[rose heron]

This is a description of the course by the way. Would you say this book is appropriate?

Formal treatment of limits of functions and sequences of continuity, including a thorough training in constructing rigorous proofs of the epsilon-delta type. Convergence tests for infinite series. Radius of convergence, differentiation, and integration of Taylor series.

[narrow relic]

Yes. You can see the table of contents here: https://www.wiley.com/en-us/Introduction+to+Real+Analysis%2C+4th+Edition-p-9780471433316

(the series stuff is in Chapter 9)

[rose heron]

This class is kicking my ass so I need as much help as I can get

[narrow relic]

I'm not sure if it covers integration of Taylor series

[rose heron]

We have yet to cover Taylor Series integration even though we just covered the Integral Test

[narrow relic]

I recommend you try Chapter Two and see what you think about it

The integral test was in Chapter 9 of Bartle and Sherbert

(by the way, you can skip the stuff about "gauges" in section 5.5)

(side note, I just noticed this publisher, Wiley, is charging $194.95 for this book, which is ridiculous)

[rose heron]

I'm reading through Chapter 2 right now and its making sense

[rose heron]

I have traveled the high seas

[dapper root]

Ewww…… Wiley for a real analysis book…

[narrow relic]

Awesome, that's good to hear, their description of the equivalent facts about supremums really clicked for me

[dapper root]

Wiley is like, in the business of making those crap books with 17 editions

[narrow relic]

I still remember it clicking even though it was a while ago

[dapper root]

That just shuffle the problems around so you’re forced to buy a new one

[narrow relic]

This isn't a crap book, but I know what you mean

[rose heron]

I read through his description of the nth term test and it was the same as my Prof described it. It is nice however, to see a description given in paragraph form

[rose heron]

It is only third edition which I don't think really matters

[narrow relic]

Cool, yeah I really like the writing style

[narrow relic]

Probably very little difference

One of the authors has passed away and I'm not even sure he had input into the 4th edition

[rose heron]

And this book also uses rigorous proofs for evaluating divergence and convergence and so on?

Not just those topics but rigorous proofs no less

[narrow relic]

Yes I think so, Chapters 3 and 9 are the ones for sequences and series respectively (I'm not quite sure why series doesn't just come after sequences, I don't remember, but I think I read Chapter 9 out of order, like, closer to when I read Chapter 4 probably)

[orchid mortar]

On the topic of publishers the least worst publisher seems to be CUP, or perhaps at least authors of CUP somehow easily have other easy available copies. MIT P, OUP, PUP, etc I think don't. My uni has a Springer subscription, but otherwise it's the same, and Elsevier is just lolno.

[narrow relic]

What is CUP?

[orchid mortar]

Cambridge

[rose heron]

I found the textbook through the same site that my Probability teacher linked to me last quarter FUCKIN LOL

[narrow relic]

Oh interesting. You mean least worst in terms of the prices?

[orchid mortar]

In terms of allowing easy digital copies

[narrow relic]

What is "Cambridge Core"?

[rose heron]

I know for Calc II at my Uni you had to opt out of the textbook or you would have to pay a fee

[orchid mortar]

It's just a single website to host both books and journals I think

[narrow relic]

Okay I see.

[rose heron]

So does Real Analysis fall under Calculus or its own branch of Mathematics? I wonder because whenever I look through the TOC of some of these books they have a lot of stuff relating back to Integrals, Surface Area, Theorems like Stokes and Greens...

[orchid mortar]

Calculus translates to 'calculation' - it's just associated with math at a higher level.
Real analysis is an actual descriptive topic telling you that it deals with real-valued functions and how they must act

[rose heron]

I love learning new stuff

[fickle bough]

Whatever you do don't listen to people telling you to use Rudin as your first book with no other reference, I don't know about that specific one, but as an introduction you can use Abott alongside Cumming's book, then later on you can use Rudin with Pugh's book

I think Rudin is really good but you need another reference to use with it otherwise you'll drive yourself mad unless you have alotttt of experience

[rose heron]

Bartle and Sherbert has been making sense so far

[fickle bough]

I don't own that one but I heard good things about it

[rose heron]

My Probability textbook by Hogg from last quarter was eh to complete garbage

[fickle bough]

I want to learn probability theory eventually when I get to measure theory but that's still far away so

I feel it'll be much more interesting from that point of view

[sage python]

Measure theoretic probability is chef's kiss

[fickle bough]

yeah that's my goal eventually, atm I need to get better foundations in analysis, then learn more topology then I'll move on to measure theory

it seems interesting

[sage python]

How's your analysis rn?

[narrow relic]

I wouldn't bother with the Rudin book, it doesn't seem to cover anything you can't get elsewhere better

But what do I know

[fickle bough]

it'd be at the level of finishing abott, now I'm reading through Rudin with pugh as a side reference

[sage python]

Rudin's alright, definitely better as a course book than as self-study

And I don't like some aspects of how it handles topology

[gray gazelle]

hello. i hope this is the right channel to ask this:
does anyone know where I can find a booklet/book of derivatives of trigonometric funct, integrals of trigonometric funct, identities, and everything for trigonometry?

[fickle bough]

for topology I'm definitely using pugh not rudin

[sage python]

Pugh is even worse

[narrow relic]

The fact that everyone needs another book to help them understand it is evidence that it isn't very good IMO

[sage python]

Rudin gets it 80% right with the topology lol

Pugh chapter 2 is awkward af

[fickle bough]

as a book for learning from I agree but everyone says the exercices are really worth doing

rudin alone as self study is like actual hell

[fickle bough]

do you have any book in mind then? I'm planning either way to move onto an actual topology book when I'm sure of my analysis

[sage python]

So you can do point-set topology from an analysis book tbh

[coral prawn]

Finding an actually good topology book be like

[fickle bough]

that'd be enough for measure theory later?

or would I need more

[sage python]

Folland Real Analysis has chapter 4 on topology

If you want a dedicated one use Lee Topological Manifolds

[fickle bough]

I will check them out probably not getting more physical copies since the costs are racking up lol

[sage python]

Or you can read chapter 1 of Bredon's Topology and Geometry

Fair enough lol

But yeah as for analysis... idk I sorta used a few different things

I would say most of my metric topology did come from Rudin, and then I just kinda figured out certain pieces that weren't explained as well (mostly centered around subspace topology) elsewhere

A bit of Kolmogorov-Fomin

[fickle bough]

one sec give me your thoughts on this

[sturdy shore]

I'd recommend stephen willard - general topology especially for someone that is analysis oriented, it is a difficult book but well worth it

[sage python]

Willard is way too long

[sturdy shore]

you def don't need a specific text early on though

[fickle bough]

this is singh's book table of contents which I'm considering

[sturdy shore]

yeah but eventually you'll wanna learn absolutely everything in willard

[sage python]

Looks fine at a glance just a bit excessive

[sage python]

Hard disagree

[fickle bough]

it definitely looks like more than I'll need but whatever not really a bad thing

[sage python]

Point set is very wingable and spending God knows how long trying to really learn all the details is mostly a waste of time

[fickle bough]

so I should just pick up what I can from other analysis books

for point set

[sage python]

If it's not in Folland chapter 4/Bredon chapter 1

[sturdy shore]

well I disagree with that, reading a dedicated topology book has helped me a lot in analysis (and other places)

[foggy relic]

munkres is good

[sage python]

It can be picked up on an as need basis

[foggy relic]

fast and easy

[sage python]

I also think Munkres drags too long and its examples are too dumb

[foggy relic]

it has everything though

and a nice head start on algtop

[sage python]

Dictionary order on [0,1]x[0,1] induces a topology like

[sturdy shore]

I also don't like some of the parts of munkres I've read, but I'm no topology expert

[foggy relic]

lol

[sage python]

Why don't you induce some bitches instead

Okay joking but you get the point

[fickle bough]

actually made me laugh lol

but yeah now that you mention it I'll check out the topology section in Folland I've never thought about just getting the topology I need from analysis books

[sage python]

Yeah CT I'd say for real analysis, measure theory I'd use Folland or Bass

[sturdy shore]

what knapp does in basic real analysis is cover only metric space topology in its 2nd chapter and cover general topology in its 10th chapter

it has its ups and downs

[sage python]

If you wanna jump in soon and you like doing Lebesgue measure on R first and then repeating for abstract measures later, you can also use Royden

Royden you can read as long as you've had proof based calculus

[fickle bough]

yeah Royden will probably be what I'll use I don't think I can take another Rudin book when I'm done with this without getting an heart attack

[sage python]

Maybe with Folland you'll want a bit of metric topology going in

[fickle bough]

I'm debating if I should go for measure theory or complex analysis when I'm done complex analysis also seems cool but it won't really be of any use for what I'm trying to get to

[sage python]

lems how do you like Knapp

[sturdy shore]

I am currently going through its 3rd chapter on basic real analysis, about to finish chap 4 on basic algebra

[foggy relic]

for undergrad analysis browder is really really nice

covers stokes at the end

[sage python]

I feel like on some level I have no idea why the fucker wastes his time doing Riemann integration on R^n

When he's gonna do measure theory anyway lol

Browder and Schroder are my picks for undergrad analysis. I hadn't known of them when I was learning and mostly bounced off Kolmogorov-Fomin, Rudin, a bit of this dogshit book called Sally

[fickle bough]

I'm not going to learn multivariable analysis

It'd be pointless for what I want

[sturdy shore]

I'd summarize him by saying that he truly cares about pedagogy, so he will be as chatty as he feels like he needs to be (which can be like 2 pages he spends on one row reduction example he does for finitely generated abelian groups)
on the other hand, his proofs can be very mystical. Like, he pulls random upper bounds out of his ass considerably more than the average author, and in general his proofs are terse
this is very much to my taste since my favorite "exercises" are going through proofs written by others, knapp gives me the active reading that I crave

[sturdy shore]

tbh I find this a positive because I can't escape riemann integration in my day to day life even if I want to

[sage python]

Well the problem is the R^n bit

Like... proofs of multivariable calculus theorems are obnoxious with Riemann integral

Just say product measure lol

[sturdy shore]

I haven't done the section on R^n yet, but I assume most of the theory would carry over as it does
like yeah some of the theorems can be obnoxious like fubini and change of variables but I think you can safely skip them and get to measure theory without loss of continuity

so can just treat their existence as there for completion

[sage python]

Esp because on some level I don't like the whole shtick about oh Lebesgue integral is about partitioning the range

It's just Riemann but you allow yourself to take linear combinations of characteristic functions of measurable sets

Rather than just intervals

[fickle bough]

are the measure theory bits in rudin/pugh worth even going over I assume they won't be that good since they're not really the point of the books

[sage python]

And then you just rework the Riemann bit in by saying hey, it suffices to consider step functions instead of general simple functions iff you're continuous almost everywhere

[sturdy shore]

well, I disagree on this, I like the analogy of partitioning the range, it actually motivates measurable functions really well since the difference when you partition the range is that the "width" of your "rectangles" won't really be a rectangle as in the Riemann case, but the preimage of the function you are integrating at some interval

[rancid hollow]

We're using royden in my measure theory class and I can say it is certainly one of the books of all time

[sturdy shore]

so the heuristic is that we want those preimages to be nice enough

[rancid hollow]

I. E. I don't read the book

[sturdy shore]

ofc your perspective is also valid, and there are many others and they all deserve a mention to build up intuition

[fickle bough]

I one day decided to open an algebraic topology book despite not having any of the prequisites to learning it scarier than any horror movie that I've seen

[sage python]

Spectral sequences

[sturdy shore]

don't worry it's still scary after you know the prereqs

[fickle bough]

good to know

[coral prawn]

I'm scared

[sage python]

Don't be scared it's so much fun tho

[coral prawn]

I hope

[rancid hollow]

Alg topology is hard if you have aphantasia

[sturdy shore]

yeh that's me

[coral prawn]

Aphantasia?

[sage python]

Eh you can read a non-Hatcher book then

Rotman or tom Dieck

Rely less on your ability to visualize

[rancid hollow]

Inability to create images in your mind

[coral prawn]

Ic, so basically, if u can make a 3D model in your head topology would be easier?

[sturdy shore]

actually opened up rotman for the first time today, wanna learn alg top

his chap 0 definitely resonated better with me

[sage python]

So, a lot of arguments in topology are visual. Some people have a high propensity to lean heavily on the visuals

[sturdy shore]

well, algebraic topology specifically

[sage python]

And certain situations call for it

[sturdy shore]

is like this

[coral prawn]

Icic

is topology important in quantum physics tho? Just curious

[sage python]

I mean, geometric topology, knot theory, etc

[fickle bough]

Opening an algebraic topology book at 3AM, what happens next will surprise you

[sturdy shore]

oh I was just distinguishing between point-set, u r right

[fickle bough]

but yeah I've never seen that much notation I can't recognize in so little sentences

[sage python]

Ah, at some level when someone says "topology" you assume by default they mean algebraic/differential/geometric topology

[coral prawn]

Differential topology-

[fickle bough]

which is to be expected since I'm not anywhere near the level I'd need to be able to learn such a subject but damn

[coral prawn]

[sage python]

Differential topology is fuckin based

[coral prawn]

Time to learn differential equations 1st 💀

[sage python]

Lmao nerd

[rancid hollow]

Neeeerd

[coral prawn]

coming from you guys who alr know it

[sage python]

Tbh I don't know much lol

[dapper root]

I knew it a blue moon ago

[sage python]

Never took a class on it

My analysis class did a bit for a couple weeks, then some Sobolev spaces in functional

And I know some people in PDE who I just talk to about random shit

[coral prawn]

All I know is that I slap it in wolfram and it works

[rancid hollow]

I hated my diff eq class it was all applied no theory ;-;

So I don't feel like I know it tbh can't prove existence/uniqueness theorems, etc

[sturdy shore]

knapp actually dedicates one chapter in his book to a theoretical study of ODE's, I'll hopefully be getting to that soon

[rose heron]

I’m excited for ODE’s

[finite crane]

there is really a big divide between measure theory knowers and non-knowers
and a lot of times teachers can't really do anything about it
so multivariable calc with Riemann is an unfortunate area one has to teach, especially for short courses

if the course is allowed to be longer, then sure you can fit in measure theory

[sturdy shore]

riemann sum fans vs lebesgue measure enjoyers

[loud cradle]

don't forget about gauge integral weirdos

[sage python]

Lol I have this vague idea of how I'd want to teach the first couple years of the math major

Someone should write a book based on that tbh

[narrow relic]

Your knowledge is very impressive to a person at my level

[sage python]

So I should tell you, and would be correct in telling you, that this is mostly because I'm further along

Obv I part me wants to just be like "Yeah I have an abundance of skill tru" but by sending the previous message I've taken that option away

[narrow relic]

Well thanks! But it's still impressive and I appreciate the fact you try to share your insights on a good path with others

[sage python]

Sure thing fam

[grave thorn]

[grim silo]

what kind of books do you recommend to learn function and logarithmic equation

[undone finch]

it'd help if we could know what the full syllabus is, because "discrete math" can be many things. kenneth rosen's book covers a very wide range but i personally think it's a bit of a boring book, so maybe getting two or three diff books may be the best course of action instead

usually discrete math courses cover sets, relations and proofs such as mathematical induction which is covered by How To Prove It

yeah rosen covers like everything in the list

sagan's the art of counting cover a fair amount of combinatorics and the author himself has a pre print of the book free on the internet

how to prove it covers induction, sets, functions and relations

that's all in case you want to escape from rosen eventually

i just found it boring, like, for me it's not written in a way that makes me want to keep reading. maybe for you it's different

in the end i just did the exercises and checked what i needed on demand

yes, rosen actually has a ton of exerrcises

that's a plus for the book

by a ton i mean like, 40-60 per section

discrete mathematics and its applications

np!

thanks

[fierce hedge]

How is Rudin with the supplement by Bergman, I'm currently using it and it seems decent enough

[undone finch]

what do you all think about proofs from The Book? i started to read it and the first section (six proofs on the infinitude of primes) struck me as kinda badly written. does it get any better or should i drop?

badly written as in, i read goldbach's proof in a random math exchange post and it was a lot clearer

[upbeat finch]

any good textbook for learning mathematical physics?

[gray gazelle]

does anyone have a good book/booklet for trigonometry in calculus? all the trig derivatives/antiderivatives, inverse trig functions and so on

i have looked, but i cant find anything because its just low resolution images and nothing that includes what i am looking for

[bright quail]

That question might be posed a tad too broadly. From my own searches, I can say that it really depends on whether you're a mathematician or physicist. Also it's always better to look for "mathematical physics literature" in a specific context. There's a book by Hamilton "Mathematical Gauge Theory" which goes to town on principle bundles and moves on to applications of it in Standard Model Physics. There's Abraham/Marsden's "Foundations of classical mechanics" (I think it is called) which is classical mechanics in differential geometry language and they also do a lot concerning non-linear dynamics judging from the table of contents. There's the two part book "Quantum Fields and Strings: A course for mathematicians".... and a whole plethora of others. Perhaps if you can be more specific about what your level is and what you look for someone (maybe even I) can suggest something more concrete.

[upbeat finch]

i'm definitely a mathematician lol, which is why i'm interested in mathematical physics. i'd say i have quite good understanding on calculus, now i'm doing multivar calc

[bright quail]

Do you have any prior physics knowledge? This isn't strictly necessary for mathematical physics in my opinion, but it can help with understanding why things are interesting to consider. Do you have some subject in physics you are interested it?

[sage python]

I mean yeah Rudin works nicely. Around chapter 7 or 8 is where you wanna switch gears a bit

[teal orbit]

Does anyone have any recommendation on basic math knowledge that no one teaches you because ppl teach other things?

Lemme explain

Yesterday i just freaking learnt something very important and basic, the general cancelation rule for fractions

Everyone knows how to cancel variables when it comes to fractions but it seems like there are a lot of basic rules that ppl don’t teach you, they just tell you how you do it and thats it

Even if you know things that are more “difficult”, lets say how to solve integrals

I still feel like i lack a lot of basic stuff that are not taught 😭

[mossy flume]

Khan Academy is my go to rec for basic math

Rather than a text

[remote sparrow]

while written for pre-service teachers, you may get a bit of mileage out of reading hung-hsi wu's six volumes on k-12 math

[narrow relic]

This might not be basic enough but this is a possibility (I haven't read these particular notes myself): https://tutorial.math.lamar.edu/Classes/Alg/Alg.aspx

[atomic hound]

a books that teachs everything about set theory

[heady ember]

Idt there is a book that teaches "everything" about set theory

Set theory is a diverse and deep subject

[narrow flax]

Hello I am in high school right now and I have about three years left, I would like to get ahead of me and read some good books that could cover these three years. I would want to do that because I need it for thertain things I am programing and out of pure curiosity and fun!

[heady ember]

Specify what you want to learn

[whole cove]

anyone have a recommendations for a book on

measure theory

like undergrad level with a good amount of problems to work through?

[heady ember]

Look in pinned

[gray jungle]

"Measures , integrals and martingales" by schilling is a good book with plenty examples and exercises , feels a bit probability flavored sometimes but its good nonetheless.

Folland is good too if you want something faster and more analytic in flavor

[sturdy shore]

folland might be a bit difficult to someone asking for undergrad level

schilling is good, I'd also recommend axler's book those two are the gentlest measure theory books I've seen so far

(gentle =/= easy)

[sage python]

I'm skeptical of Axler given his dogshit take on linear algebra lol

But to be fair that might just be a function of him being a functional analyst

[sturdy shore]

I think his take is reasonable given his background yeah, and the book gets too much hate imo

but well, that's not really related to his measure theory book

even if you hate his take on determinants, it is undeniable that axler is an author that actually cares about pedagogy, following in his advisor and the advisor of his advisor's footsteps

[narrow relic]

Did you go through this book chapter-by-chapter?

[sturdy shore]

ofc, caring doesn't mean succeeding in being good at it, but imo his measure theory book succeeds (based on the parts I've read)

[whole cove]

thats not a problem tbh itll be good for the probability module im doing as well

[narrow relic]

I'm asking because I read a lot of it about a year ago but I found some of it to be difficult going

[gray jungle]

Im using it as a main reference alongside folland , it was great all the way to integration (where i am rn)

Good exercises and detailed proofs

[narrow relic]

Can I ask what Chapter you're on? And are you using the first or second edition?

(I never did any of the exercises by the way, I was just trying to understand the proofs and definitions)

I have the first edition, published in 2005.

[gray jungle]

I would be on chapter 12 rn ( L^p spaces ) and i think i have the first edition

[narrow relic]

Okay wow, nice progress!

[gray jungle]

I didnt use all the chapters in schilling btw as im following folland with it as a reference , but its my go to for clear explanation and neat proofs + exercises

[narrow relic]

I want to learn that material properly when I'm done with some of this Carothers book, and I'm debating returning to Schilling or going with this neat functional analysis book I found from Springer

[gray jungle]

Exercises are part of understanding the material ! Sometimes even containing crucial result

[narrow relic]

Okay that's good to hear. I couldn't tell if it was clear or not since I'm not super-skilled at this stuff

[narrow relic]

Yes I was being dumb by not doing them

I will definitely do some of them when I approach the book next time.

[narrow flax]

well everything and anything really, for example derivatives complex numbers and do not know what else some high school stuff

[narrow relic]

Thanks for sharing your thoughts 😀

[gray jungle]

Np and gl

[narrow relic]

You too.

[narrow flax]

I still apprecciate recomendations^-^

[sage python]

Eh, I mean to me it's one of those things where

His view is narrow enough that I feel like he should know better than to market them as like, "the way to do it"

And frankly this take is not just a matter of taste it's genuinely fucking stupid

Like "if I were giving an oral exam and a student tells me that this is how they understand determinants they are dropping a letter grade"

[blissful pike]

Determiants are important topic tho, at the basic level tho they tell about the nature of a linear transformation

[austere zephyr]

Woah it's Rei Ayanami

[finite gale]

I think you'll need to at least specify what you already know for anyone to give any meaningful recommendations

If not what you're interested in learning

[sturdy shore]

I agree that the name is stupid, and it is a terrible book to use for a one semester course, but it does by the end cover pretty much everything you need to know about determinants (in the context of linalg) so yeah I do think the book is a bit overhated

[sage python]

If someone thinks that characteristic polynomials over R are given by complexifying, upper triangularizing, and taking product of (t-lambda I)

And thank the lord the coefficients are real

Then like I'm sorry but no

Teaching someone to think that badly is immediate DQ to me lol

[rose heron]

What are some good books on Set Theory that are kind of hand holdy and do a really good job of simplifying terminology (preferably from an Engineering Perspective)

[thin dock]

Is the first edition of abbott's book good for self studying analysis? I've heard good things about the 2nd edition but wondering if theres a big difference

[rose heron]

How good is Anton as a resource for Linear Algebra?

[mystic orbit]

measure theory isn't an undergrad topic lel

[finite gale]

I think measure theory is fairly often at least offered as an undergrad upper level class if not covered in an analysis class

[oblique hatch]

The US isn’t the only place in the world

[finite gale]

Speaking about us universities

[stray veldt]

skill issue

[mystic orbit]

I'm not in the us but ok

[stray veldt]

measure theory is required for math majors in most european universities, usually in 3rd/4th semester

[mystic orbit]

Oh?

[stray veldt]

traditionally math in europe is more analysis heavy and analysis 1-3/4 (3 being measure theory, 4 being functional) is usually still obligatory

[mystic orbit]

based

[mystic orbit]

BASED

[mystic orbit]

For the record, I said that coz folland says his intro measure theory book is grad

[lapis heart]

the scope of what he covers may be?

[mystic orbit]

¯_(ツ)_/¯

[dusk tapir]

Do you have book recommendations for analysis 2? For analysis 1 I only followed the lecture script and didnt really work with a book, so I really dont know which ones are good candidates for self studying analysis 2 for the first time.
German or english is fine, if it helps I can post a list of keywords of topics the professor wants to go over.

[indigo mesa]

Amann Escher analysis books

[dusk tapir]

Hmm I can try, especially since I dont have time pressure now, but arent they supposed to be rather hard?

[indigo mesa]

They’re not easy yeah

Check out the end of the analysis 1 book, the stuff usually covered in analysis 2 starts there

[hollow shore]

I have heard people calling it the German Rudin

[indigo mesa]

I never read rudin

So I can’t comment on that

[dusk tapir]

Okay thanks, Ill check out the first book and use it to review analysis 1 and If I am able to work through it, Ill just go with the second volume.

[dusk tapir]

Did you do the practice Problems from the book even though they dont seem to have solutions or did you use another source?

[karmic thorn]

I have physical copies of AE 1 and 2

They're excellent books to learn from on your own but jumping in the middle can be difficult because they use a very linear narrative for their book design, so you can miss out on notation, ideas and examples very easily

I tried reading something straight from V2 chapter 1 and I was baffled by the notation and the setup

Because AE tries to do things a bit generally where it can

[indigo mesa]

Same

[karmic thorn]

[indigo mesa]

I mean it’s pretty rare that books do have solutions isn’t it

I did do the problems

[dusk tapir]

I'll Just start from chapter 1 v1

[karmic thorn]

[prime raft]

Lol sounds like you're obsessed with the US. No one even brought up anything about the US 😂

[oblique hatch]

When someone says [insert common undergrad topic in Europe] isn’t taught at undergrad, especially in English speaking places, it’s a decently high chance they’re American

[indigo mesa]

fair

[prime raft]

Again, sounds like you're obsessed with the US. That sounds like a really bad assumption imo

[indigo mesa]

🦅

[prime raft]

Whatever floats your boat

[gray gazelle]

Guys, does anyone know any good books on non-Euclidean geometry and/or about the works of Nikolai Ivanovich Lobachevsky.

[karmic thorn]

Will references on hyperbolic geometry do?

Or are you looking for historic accounts centred around Lobachevsky's works?

[fierce hedge]

Are those printed or purchased, if yes where from?

[karmic thorn]

Printed and you know where 😛

[fierce hedge]

Ohh, I thought you got from Amazon cause I saw like a cheap copy for 1.5k - https://www.amazon.in/Analysis-Herbert-Escher-Joachim-Amann/dp/8132231236/

But it's so cheap that it feels fake, idk

[karmic thorn]

No this must be an original

Paperback+international editions in subcontinent help with reducing costs

[fierce hedge]

There's another one, same stuff but for 6k

ah, I see

[karmic thorn]

I just got a GTM today

~500 for paperback

[fierce hedge]

which book?

[karmic thorn]

MacCluer's Elementary Functional Analysis

[fierce hedge]

never heard of it but noice

btw what book did you use for abstract algebra @karmic thorn

[karmic thorn]

Gallian was my primary text for a long time

I have also used Judson in places

And a bit of Artin

[heady ember]

500 dollars for one paperback book?

[fierce hedge]

500 rupees, that's around 6 dollars

[heady ember]

Oh

Nice

[fierce hedge]

Nice, what's your opinion on Judson, say better than Gallian?

Also, have you tried Herstein?

[karmic thorn]

I have never read Herstein

I think Judson and Gallian are both good at what they do

Judson might make sense as a primary text

Gallian for boatload of problems to work with

Stick to older editions

[gray gazelle]

Does anyone know if the book "3d math primer for graphics and game development" is worth the money?

Or am I better off trying to learn using freely available material on the internet

[fierce hedge]

any particular reason for this?

Like do you mean older editions are preferable for buying the book or older editions are better in general?

[karmic thorn]

I had the 8th edition which had comprehensive supplementary exercises after every 3-4 chapters

They were relatively challenging and good to be included

Newer editions have killed that (or possibly assimilated them in end chapter exercises)

Either way I think it was convenient to have them seperate for review or whatever

[fierce hedge]

I searched for the 8th edition supple problems but couldn't find them.

It's kinda weird that they would remove questions from later editions

[karmic thorn]

It's likely that they assimilated them in end of chapter exercises

Maybe

I'm not sure, I always find having so many "new editions" as a money making ploy

[rose heron]

The closest I ever saw to a $500 textbook was a $300+ O Chem book

[remote sparrow]

https://www.youtube.com/watch?v=RQlB8JsAI8U

https://www.youtube.com/watch?v=Ba97cRIzmjc

just found this channel from youtube recommendations

[sturdy sail]

Any recommendations for short introductions to monoidal categories and higher category theory?

i am mainly interested in applications to tqft and cobordism rn

so maybe some references that focus on these topics would be really useful

[fierce hedge]

@narrow relic did you tag me for abstract algebra book recommendation?

[gray jungle]

me too lmao , cool channel

[static prism]

anyone have any suggestions for intros to cryptography? i have a relatively good foundation in abstract algebra and number theory already, and i'm pretty familiar with stuff like polynomial interpolation. are there any other subjects/fields i should look into first or do i have pretty much all i need to start learning cryptography?

[frail pendant]

i have a pdf we used for our course if you'd like to see

[static prism]

yes please!

[frail pendant]

@static prism

lmk if it has what you were looking for

[gusty smelt]

average day in math server...

<@&268886789983436800>

[quick hornet]

i believe this book is freely available?

[wispy pebble]

there was acadishon

[quick hornet]

oh referring to another thing

whoops

[frail pendant]

yes i wouldnt dare share it otherwise

[gusty smelt]

smh you should know me better than to report piracy kek

[narrow relic]

I was going to recommend you a book, but the e-book store that sells it seems to be having a problem, so I deleted the message.

[narrow relic]

I found it, it's back online with a different domain name: https://centerofmath.com/textbooks/post/p_2398394

[foggy relic]

a really nice algebra book is Lang

[molten mason]

This is amazing, thanks

[fierce hedge]

Is this book only available on this site? I can't seem to find this anywhere else

Especially on a particular biblical library

[remote sparrow]

https://www.reddit.com/r/math/comments/119gkvy/physics_and_mathematics_selfstudy_project/

[fierce hedge]

Daaaamn, I don't think I would be able to even revise all of that in an year

[still nebula]

Can someone suggest a textbook for complex variables with these topics

[gray gazelle]

Real and Complex Analysis by Walter Rudin and Complex Analysis by Lars Ahlfors

[orchid mortar]

Is there a reason you're recommending Papa Rudin

[gray gazelle]

It's awesome. It begins with him comparing a topology with a sigma algebra and then building borel sets from a topology induced by continuous function. The book goes over analytic continuation and banach algebras and holomorphic Fourier transforms. Tbh idk how much a different book covers but I really enjoy that book.

[orchid mortar]

Rudin is not a typical first-recommendation, but I don't think there's any issue if the reader likes it

[vital bane]

same

[teal orbit]

I checked it and it is basically linear algebra

Tysm anyway tho!!!

[teal orbit]

Mmmh 6 volumes

[gray gazelle]

Yeah

[karmic thorn]

I have been using these lecture notes, they're quite nice.
https://personalpages.manchester.ac.uk/staff/charles.walkden/hyperbolic-geometry/hyperbolic_geometry_1920.pdf
Other resources recommended by my course include Katok's Fuchsian Groups, Bridson/Haefliger's Metric Spaces of Non-Positive Curvature, and Bowditch's lecture notes on geometric group theory (which are more of an addition to the end of the course, probably not directly related to what you're seeking).

[gray gazelle]

Thanks

[gray gazelle]

Jech the 3rd Millennium Edition has basically everything in set theory.

[kindred shale]

There Was Once A King
By Sayyid Fayyaz Mahmud

[gray gazelle]

I'm not pretentious. Ppl here have told me that I "like Rudin for the wrong reasons." But I hated Abbott for self study because I didn't understand fundamental concepts that were assumed in calculus classes and they were not explained in Abbott. For instance I didn't understand that the set of natural numbers as constructed from the peano axioms are not a subset of R as constructed from equivalence classes of dedekind cuts, rather they are naturally embedded into R (as equivalence classes of cuts). I loved Rudin for self study. It was a breath of fresh air compared to calculus classes, applied math classes, and even abbott for me.

[kindred shale]

Oh like math related books..... Opps

[narrow relic]

Yes, it's only $15 and it's basically self-published. The whole point of that Center of Mathematics project is to provide high-quality low-cost books to people wanting to learn serious math around the world.

[narrow relic]

You're welcome.

[wind trail]

ikrrrr

rudin is absolutely op

idk why ppl say it's a hard read and stuff

it's not THAT hard if you do it systematically

at least baby rudin isn't

[gray jungle]

rudin debate nb 3000 incoming

[hazy elk]

Am I the only one who finds Ahlfors' writing to be annoying at times, like he just does somethings without defining them coherently and expects us to just magically understand everything, I like the prose and the level of detail that is left to the reader as an excercise in most places but some sections are too confusing

Excercises are also quite interesting (but feel less analytic)

I think Stein Shakarchi's complex analysis book is cooler than Ahlfors

[real veldt]

yeah that book is fun, but why do the writers always say this is easy to see 😩

[hazy elk]

Standard math bs

Its always easy to see once you've seen it

[real veldt]

fr

It doesn’t add anything by saying it

[hazy elk]

Except possibly frustration lol

It's just one of those standard phrases I guess

[real veldt]

yee

[gray jungle]

I remember one auther said something about such terms once , let me try to find the book

A note to the reader found in "Introduction to topology and modern analysis" by George F. Simmons

[sturdy shore]

simmons

?