book-recommendations

[warm sinew]

I asked an AI for a book roadmap and it spit out this in order, it thinks y'all would agree with this. Perhaps we could insert the Dr. Seuss book as the 0th book lol

Is this a good roadmap of math books? Honestly I was just gonna send them a list and let them pick off of it, though it would be nice to have a checklist for myself too of what I'd like to eventually have, feel free to argue with it because the AI came up with the list ordering and selected books

1. How to Prove It by Daniel J. Velleman
2. Calculus by Michael Spivak
3. Linear Algebra Done Right by Sheldon Axler
4. A First Course in Abstract Algebra by John B. Fraleigh
5. Topology by James R. Munkres
6. Principles of Mathematical Analysis by Walter Rudin
7. Real Analysis by H.L. Royden and Patrick Fitzpatrick
8. Complex Variables and Applications by James Ward Brown and Ruel V. Churchill
9. Complex Analysis by Lars Ahlfors
10. Visual Complex Analysis by Tristan Needham
11. Complex Analysis by Elias M. Stein and Rami Shakarchi
12. Algebra by Serge Lang
13. Algebraic Topology by Allen Hatcher
14. Differential Geometry of Curves and Surfaces by Manfredo P. do Carmo
15. A Friendly Introduction to Number Theory by Joseph H. Silverman
16. A Course in Arithmetic by Jean-Pierre Serre
17. Quaternion Algebras by John Voight
18. Quaternions and Rotation Sequences by J.B. Kuipers
19. Functional Analysis by Walter Rudin
20. Representation Theory by William Fulton and Joe Harris
21. Algebraic Geometry by Robin Hartshorne
22. Category Theory for the Working Mathematician by Saunders Mac Lane
23. Homotopy Type Theory: Univalent Foundations of Mathematics by The Univalent Foundations Program

(it includes quaternions because I mentioned quaternions in the conversation, I can understand cutting one of those out if you think it's a bit much)

[near jewel]

The first question to ask is what your goal is. Do you think of doing pure mathematics, is it a hobby, or the math is for other subjects?

Sharpen your knowledge is more important than widen your knowledge.

[oblique hatch]

Lang is a bit of a tome
I wouldn’t learn from it
Topology before any analysis is weird
Four complex analysis/variables books is unnecessary
If you can read PMA you don’t need Royden

Tldr the longer I look the more wrong it looks
Aka average ai stuff

Also in general like
Don’t really think more than 1-2 books ahead in terms of what you’re learning
Because interests will shift

[wet sentinel]

along with the points made by others, i wouldnt recommend using a book solely for proofs, you learn these when you start with a proof based topic like proof based LA or intro real analysis etc..

[warm sinew]

I want to be a math major, though nothing super specific yet

I mostly just want some undergraduate books to help study as a hobby before I actually go to college for it

[oblique hatch]

Bleh I’m bored so I’m gonna see if I can critique this whole list (bearing in mind my caveat before about the whole concept of a list)

1. Sure, but I’m not that big on “how to prove it”
2. Yeah, good book
3. It’s a standard recommendation, and in a reasonable place in the timeline, but I think it suffers too much from its thesis statement (to avoid determinants as much as possible) compared to something like FIS
4. Sure
5. Topology before analysis is not the best choice, but munkres is good
6. PMA as intro analysis. It wants you dead
7. Royden after PMA is lol, but it’s good if you removed PMA from the list
   8-11. Just read ahlfors, it’s good, and the others probably cover basically the same
8. Algebra isn’t a book you learn from, and you probably don’t want it after #4
9. Yeah Hatcher is a standard recommendation, and this is a reasonable place for it
10. Never heard of it, but I don’t particularly like curves and surfaces courses. If you replaced this with one of Lee’s many books on DG, it would be good
11. Idk the book
12. There are better reqs for AlgNT, like Markus
    17-18. Quaternion stuff this early is weird, I wouldn’t do it until you’re more specialised
13. Sure, good book, good placement
14. See above
15. See above
16. See above
17. That’s a take and a half. Read iff you want to learn about HoTT

[graceful moon]

Planning this far ahead is just silly, go where your interests lie. Beyond that the order is just silly and the book recommendations are mid at best.

My advice, read the intro to proofs in the pins of #proofs-and-logic then pick up a book like “Understanding Analysis” or any linear algebra book, and go from there

[warm sinew]

Linear Algebra is definitely a topic I struggle with, so preferably a beginner book on that would be in my list of "books wanted"

AI says y'all would like these from the comments and as a "condensed essentials for undergraduates that 100% must be included"

• Book of Proof by Richard Hammack (y'all actually seem to hate this one tho?)
• Calculus by Michael Spivak
• Linear Algebra Done Right by Sheldon Axler
• Abstract Algebra by David S. Dummit and Richard M. Foote
• Understanding Analysis by Stephen Abbott
• Topology by James R. Munkres
• Complex Analysis by Lars Ahlfors

So in my list of "books I want" I should add these?

Any book I should go for first?

[oblique hatch]

I don’t doubt the first book does its job
I doubt the necessity of its job
(And also I don’t like LADR)

[graceful moon]

Agreed with mico here

People do like the book of proof, I think it’s pointless

[warm sinew]

Ok, so... as a replacement for LADR you suggested... Linear Algebra by Stephen Friedberg, Arnold Insel, and Lawrence Spence?

[graceful moon]

My recommendation for intro to proofs is also the notes in #proofs-and-logic

[graceful moon]

FIS is a very good linear algebra book, but I would read something more computational and grounded first then come back to FIS

So maybe Strang or Nicholson

[wet sentinel]

the thing imo is that you dont really need a book on proofs tbh (i am saying this again because it would probably be a waste of money to buy a book on proofs)

[wet sentinel]

yes personally i would recommend that

[warm sinew]

I'll definitely go through that, I downloaded it so I could go through it later today (hopefully), though I've spent a bit of time digesting the notation, so it should (again hopefully) be a quick read

[wet sentinel]

also others may disagree with me but i dont like D&F, its like talkative lmao

[graceful moon]

You shouldn’t expect to get through any maths book that “quickly” you don’t read it like a novel

[warm sinew]

It was like 30ish pages in the pdf, I was hoping to go through it over the course of a few hours tonight

(longer if I'm overestimating my ability to read the notation of math, though I don't think I am)

[molten gulch]

It's less how long it takes to read the maths and how long it takes to properly understand the maths

[warm sinew]

That is so real honestly

[wet sentinel]

you might do it, but if you havent done any proof based stuff then it will probably take more than that. More generally, you should expect to spend hours on a single section from a certain point onwards in math

the number of pages might trick you into thinking that it will be an easy/quick read

but thats certainly not the case (at least it often isnt)

[scenic sequoia]

Shilov for the win

[graceful moon]

30 pages of new maths would likely take me anywhere from 5~20 hours to get through

Like don’t expect to be able to just rush through stuff

[warm sinew]

Ok so y'all seem to like these books

• Calculus by Michael Spivak

• Abstract Algebra by David S. Dummit and Richard M. Foote

• Understanding Analysis by Stephen Abbott

• Topology by James R. Munkres

• Complex Analysis by Lars Ahlfors

• Linear Algebra Book by either Strand or Nicholson
  (y'all didn't pick one so I guess I'm putting both) (I'm also being told Shilov I guess? I have no idea what to pick for this, Linear Algebra is a weak area for me so I find this one in particular to be important, that's also why it's in its own spot)

Any issues with these? Any one I should pick first?

[wet sentinel]

shilov is a hard hitter. FIS is what people usually go with

i also think that you should try to check the books you are talking about before buying them and check if you like them or no

at the end of the day you are the one buying the books lol

[gray gazelle]

LADR not mentioned

[wet sentinel]

sorry but it just happened that the 3 people who responded hated LADR

[gray gazelle]

Coming from 0 linear algebra and reading LADR really really really helped so much lol

Just saying

[molten gulch]

FIS is my favorite

like by FAR

Don't ever mention LADR around me or my family again :3 /j

[gray gazelle]

[warm sinew]

I'll just put LADR and FIS in the list, this is for a Christmas list so both is fine in the list ig

[molten gulch]

Don't do spivak and then abbott, just do an analysis text

[gray gazelle]

Yeah lmao

[molten gulch]

LADR is free

[warm sinew]

Oh is it?

[molten gulch]

https://linear.axler.net/

[warm sinew]

Ohhh the PDF is free online oki

[gray gazelle]

Also hard copy can be ordered

If that’s what u want

[scenic sequoia]

LADR 🤮

[gray gazelle]

LADR hate is real

[warm sinew]

You confuse me

[warm sinew]

Like

[wide spruce]

What?! Why?!

Why hate LADR

[gray gazelle]

Right literally

[warm sinew]

Or is it like "wait that's real???"

[scenic sequoia]

Just trolling it’s good. Just pick up anything and start reading

[gray gazelle]

Like idek

[molten gulch]

Writing style, determinants pushed to the end (you can definitely introduce multilinear functions way earlier, hoffman and kunze does it fine), too much colour unironically (some colour is fine, but my eyes hurt after reading it and it feels like I'm reading a year 1 calculus text again), etc...

[gray gazelle]

Sarcasm

Not literally as in what I think

[gray gazelle]

Too much color? There is literally 2-3 colors used yellow, white and black

[warm sinew]

I'm just gonna put FIS on the list idek 😭

[scenic sequoia]

FIS is good

[molten gulch]

yes but it's used so profusely that I unironically feel like I'm reading a year one calculus text again

and I don't really like that

[gray gazelle]

Lmao I’m in year one

[molten gulch]

FIS is great

[gray gazelle]

May be that’s why

I feel oaky

[molten gulch]

I feel like as I go further, there should be less colour in my texts, some colour yes, but less

[gray gazelle]

Life be get colorless as we get older

[molten gulch]

Also I don't know how much I like that matrices are basically ignored for large parts of the text

[graceful moon]

I don’t agree with the sentiment that books should just be less colourful just because, but I do agree that I just dislike the way LADR looks

Along with the other writing and mathematical complaints

[remote sparrow]

fyi, there have been holiday coupon codes offered on springer's website in the past

[gray gazelle]

But we can invert the colors

They can be changed

lol

[molten gulch]

Fair, I think most of my dislike of colour in texts is because my eyes are sensitive as hell

at-least I know that's how Ryan feels about colour in books

[gray gazelle]

Well ngl I do feel like ladr is not rigorous enough at places lmao it’s kinda give engineering vibes

[molten gulch]

I also just...I don't like how overused colour is in introductory calculus or linear algebra or physics textbooks in general so-

[molten gulch]

Where?

I thought LADR was intended to be rigorous

[gray gazelle]

It is but the assumptions at places makes problem easier

[molten gulch]

That doesn't seem like a bad thing? Like broadly this doesn't seem that bad

Certain problems could be significantly more difficult without hints or assumptions that people reading the book may just not be ready for

[graceful moon]

The main assumptions are just working over R and C rather than general fields which like, I don’t agree with, but it’s still completely rigorous, it just makes some theorems slightly less annoying

[warm sinew]

I kinda wanna put a stats book in the list, just cuz I keep forgetting my time in elementary stats and I'd like a reminder and a bit, any stats books y'all would recommend?

[gray gazelle]

Yeah I mean it’s not bad enough to make me stop reading , for first read it’s fine better than doing calculation based linear algebra

[graceful moon]

I think you should do both tbh

[molten gulch]

Should still know how to calculate imho, reading off matrices is an important skill

[graceful moon]

It’s why I like a computational, geometric very intuitive pass first followed by a proper down and dirty general algebra text after

[gray gazelle]

I was gonna read this MIT guys linear algebra I forgot the name, it made me scared enough I didn’t touch linear algebra for months

[molten gulch]

I didn't like my computational linalg class much, the professor was great, but I didn't find the material to be too interesting, until I pulled open FIS and started proving everything we either only sketched in class or just didn't prove

[graceful moon]

Which I guess is possibly part of why I don’t love LADR

[molten gulch]

Strang?

[gray gazelle]

yeah

[scenic sequoia]

I hate compute with a passion

[gray gazelle]

Well I was thinking I can use notes or smth after the rigorous treatment to quickly get on speed with computations

[molten gulch]

We never did cayley hamilton in class, but I read the statement of it in FIS, I don't really get why it's supposed to be true (intuitively). I read the proof, but what does a polynomial with matrices even represent

[molten gulch]

It's not always that easy

[gray gazelle]

Also I was thinking about doing numerical analysis so I can just learn some from there I hope

lol

[molten gulch]

Numerical at-least for me was very very code heavy, not a lot of hand computation

[gray gazelle]

Yea

Is hand computations necessary

😭

Well what u guys recommend book for computation linear algebra?

Smth other than strang

Or if anyone got notes

I will take it

[molten gulch]

Yes, like YES

You see them quite frequently, also you should just know how to compute

[gray gazelle]

Is this like how integration is

[molten gulch]

I hope you learnt how to integrate too and didn't just learn them theoretically...

[gray gazelle]

I did

Learn them using hand computations

lol

[remote sparrow]

#book-recommendations message

good for both computations and proofs

[gray gazelle]

Yooo it’s free

As well

[warm sinew]

AI recommended

• All of Statistics by Larry Wasserman

Is that one bad?

[molten gulch]

It's not bad, it's insanely hard

(at your level)

Also please don't make giant lists of books to read

Go one at a time

[warm sinew]

Well I'm gonna go one at a time, this is just a list for the future

[gray gazelle]

You can also just ask them when you need to learn a subject

☠️

[molten gulch]

Bad idea

don't do that

[warm sinew]

✨ Christmas list ✨

[gray gazelle]

lmao

[old elk]

Undergraduate Commutative Algebra by Miles Reid

[molten gulch]

At this point just get rudin, jacobson 1 and 2, and munkres

[gray gazelle]

Jacobson?

What’s that

[molten gulch]

Nathaniel Jacobson Basic Algebra 1 and 2

[gray gazelle]

Abstract algebra

I see

Wait is this like good to learn undergrad

Stuff

[wet sentinel]

real ones do advanced linear algebra by roman from the get go

[molten gulch]

LMAOOOOO

[gray gazelle]

I didn’t get the reference

Is this insanely hard

[molten gulch]

...yes? Of-course you should learn some modern algebra in undergrad

[molten gulch]

yes

[gray gazelle]

Lmao

[gray gazelle]

That’s neat

Also Linux

User

[molten gulch]

yes

[gray gazelle]

What I find is hard studying multiple subjects same time

I always tend to spend more time on single

Anyone know what to do ?

[graceful moon]

I have literally never understood who this book is for

[warm sinew]

I do math like all the time as a hobby? I'm just a nerd at the beginning of their math career I guess 😞 only five notebooks of scribble (well I'm ON the fifth)
nun lernd big sad

[gray gazelle]

Do calculus

[warm sinew]

I've taken a calc course

[molten gulch]

Well then you should definitely learn in a structured manner, don't try to plan out every single book you want to read, that is a bad idea

[warm sinew]

I like to do old bee integrals they're fun

[warm sinew]

Yea everything I've done is unstructured and incomplete in an overall sense

[gray gazelle]

Doesn’t look so bad?

[molten gulch]

Then pick an analysis book, an algebra book,a nd just start reading

[warm sinew]

I'm going through Introductory Discrete Mathematics by VK Balakrishnan if that helps

[gray gazelle]

Start reading analysis and algebra

Along

[warm sinew]

I'm just thinking of what books I'm gonna want after, someone asked what gifts I'd want so I'm making a list

[gray gazelle]

Books as a gift 🗿 Chad

[warm sinew]

Yeeees

[gray gazelle]

Best gifts are books

[warm sinew]

I am math nerd

[molten gulch]

You do know there are ways to acquire books right? (I can't share methods because that's against rules)

[molten gulch]

Discrete maths has always felt like a random grab bag to me because every one of the subjects covered within a discrete coure can get several books of its own

[warm sinew]

Technically they said to write a Christmas list but I just want math books

[gray gazelle]

Maths sorcerer guy always recommends

Doing discrete

Before anything

[molten gulch]

yeah let's not talk about math sorcerer, he's just an AI book writing grifter who's fallen into giving out bad self help advice

[warm sinew]

I know right? The book I'm reading on it covers so much

[gray gazelle]

Most of the peeps studying mathematics never buying books lol they go digital or just 99% times jus read notes by prof

I know this guy who just never touched a single maths book and now is in grad school

Also was a maths Olympiad

[warm sinew]

I like books tho :(

[gray gazelle]

Buy one or 3 not too many

[wet sentinel]

for chads

[gray gazelle]

Costs too much but if you got the money go ahead

[remote sparrow]

[warm sinew]

All of mine are gifts from other people since I do math 24/7

I carry a notebook that I do math in, a leatherback diary-sized thing, I'm on the fifth one in the past 3-ish years

[gray gazelle]

Romantic

[tawny solstice]

wait can you share the list

[gray gazelle]

It’s above

[tawny solstice]

oh mb

[molten gulch]

Don't look at that list anyway

[gray gazelle]

This

[molten gulch]

As we've been trying to tell Zack for the last several minutes

Making a random list like this is not helpful

[warm sinew]

Rip 😔

[gray gazelle]

Many exists online too if that’s what needs to be done lma just saying

I got this one , it’s like every major subject with book for each

Here

[gray gazelle]

Lmao

[tawny solstice]

i was just curious, doubt id be able to comprehend them anyway lol

ty tho

[warm sinew]

Crunchy image

[molten gulch]

I mean, if you've done school algebra and trigonometry, then a text on analysis or modern algebra shouldn't be terrible

[gray gazelle]

Zoom

Enough

Well yeah it’s insane , just go one at a time

[warm sinew]

Had to download it cuz discord didn't fix when I zoomed sadly, this is a nice list I think

[tawny solstice]

don't think im there yet ngl

[gray gazelle]

Yea but don’t buy those books lmao

Alr peace out

[old elk]

Hello everyone, could anyone recommend an introductory book on commutative algebra?

[visual terrace]

I don't have a book, but I know that TabletClassMaths is extremely helpful.

I paid for all the courses and I've been using it for 7 years and I can tell you from experience that the price, though steep, is worth it.

[daring wolf]

atiyah is a standard choice

[visual terrace]

I have my entire education based upon it, and as far as I know, I'm learning 5 years ahead of my school (as was stated by my maths teacher)

[daring wolf]

altman is a somehow good choice if you want a book with solutions for free (legally)

[old elk]

That book gives me a headache because of the way it presents the topics.

[slow roost]

I went with Eisenbud.

It is very large and Im not prepared for it lol

seems awesome tho

[molten gulch]

what specifically about it?

[gray oracle]

i'd recommend working through the aops series

[old elk]

I'm not familiar with that type of writing

[tawny solstice]

looks quite nice, ty

[brisk basin]

didn't know where else to ask this - does anyone have any clue where I can purchase a copy of the extended set of Coordinate Geometry by SL Loney?

i only seem to find the first part ("cartesian coordinates") but out of curiosity I want to explore the other books too in that series

ive checked everywhere - amazon seems to have a book of the same name but the part isnt listed so is it all the books in 1 or a single unlabled part?

even libgen didn't have it

i don't even know how many parts there are to that series 😭 I just liked part 1 quite a bit (its theory seems good) and now i wanna check out the rest

if anyone could help i'd appreciate it thx

[gray oracle]

from my research, they seem to be published separately

what's in the second part tho?

[vast flame]

I got a book today and I'm regretting not getting a different book, has anyone here retaught themselves algebra and pre-algebra as an adult after many years of being out of school?

It's the big notebook of pre-algebra and algebra I can't remember it's title I don't have it handy, but I wish I got the algebra 1 for dummies instead

[foggy gorge]

I did

The Algebra book on OpenStax helped me quite a lot

[vast flame]

How are you now in your math journey?

[brisk basin]

Yes they are. I have the 1st part on Cartesian coordinates but the 2nd I don't

[brisk basin]

It's titled 'trilinear coordinates, etc.' But I haven't read it yet. Although I did manage to obtain a digital copy from Scribd. Turns out it was just a few results down on google, idk how i missed it.

It seems to be the more advanced topics in coordinate geometry. I havent studied any of the chapters in it at all yet so I really have no clue what its about 😔
Its available on scribd though and a review of it is on the cambridge website so you can check those out

[brisk basin]

You, being an undergrad would probably be better informed on the topics in it lol 😅 (im in high school)

[gray oracle]

well i'm studying maths for fun lol but geometry is not my forte

[prime tree]

Idk about being an adult but i had to retaught myself after going into high-school cuz the early years education here in Brazil kinda sucks, and I didn't start using books

I learned pre-hs things with courses and then I went to books

In this scenario Openstax books helped, as Pi said

And then going into high-school subjects like functions, set theory and etc I used a brazillian collection, but you can find very good books everywhere

It'll always work, you're 20 times more important than the book itself

[vast flame]

I see, I have personal goals but I'm needing to go over all the things I've since forgotten

[prime tree]

You just need time and patience then, nothing beats a patient man

[vast flame]

I agree 🙂‍↕️

[prime tree]

Find a book you're comfortable with and go deep

[gray oracle]

openstax is great but i've seen a lot of varied opinions for it, and a lot of the textbooks have not fully matured yet

from my usage, it's pretty computation-heavy for maths, there's tons of problems but not everyone needs that

@vast flame i would highly recommend the aops series

[vast flame]

What is this?

[gray oracle]

"art of problem solving"

[vast flame]

I'll check it out, are they physical books?

[gray oracle]

they do have them and also soft copies

[vast flame]

Nice I will definitely look into them

My current book doesn't have enough problems in it

Only a few per chapter

I regret not buying the more expensive book

[gray oracle]

check dms

but aside from that you can probably find more public domain/legal/whatever precalculus texts online

paul's online math notes is nice

[vast flame]

I'll look into what you told and sent me, thank you

I haven't heard of that before

[near jewel]

I would suggest to go top to bottom instead of bottom to top, since it’s stuff you’ve once learned.

[gray oracle]

i would honestly find that intimidating tbh if i weren't able to solve it

if something is too easy, only then would you rationally want to try something harder

[near jewel]

To me it’s intimidating to go over the stuff learned before. Not all formulas will be used, but the mindset that shaped through matters.

If you already have the first expression (you’ve learned before), then taking up things won’t be as difficult as learning it at first glance.

[gray oracle]

welp @vast flame you can try both approaches but if you can't do it, start from first principles again

[foggy gorge]

U not obligated to solve all of them tho

[gray oracle]

of course but they do get bland

the goal is to enhance appreciation for mathematics, after all

[vast flame]

My goal is to get better at math and have fun

[trail void]

yes

[vast flame]

And?

[trail void]

the approach ur doing is not good

from personal experience

[vast flame]

Reading books and doing videos?

[trail void]

are u solving 80% of the exercise questions?

or minimum 50-60%?

[vast flame]

I'm solving 100% but there isn't a lot of questions in my current work book

[trail void]

i noticed that getting an seperate elementary and intermediate algebra book is more helpful

i got one by Jerome E. Kaufmann

lovely author

he has both elementary and intermediate

u shld do geometry before intermediate algebra tho!

and trigonometry after, or well u can directly do precalculus instead of trig

[vast flame]

Should I do pre algebra, algebra, and then geometry?

And then algebra 2?

[trail void]

no need for pre alg tbh

[stiff lodge]

Hi, could you recommend me a book for Stochastic Processes? I’d like it to be a sort of introduction to get to know different types of processes etc. I already have a solid background in probability and measure theory, so the book doesnt have to contain any of this. A great plus would be if it was available in Europe

[remote sparrow]

@foggy quest @timber mesa

[trail void]

just do elementary algebra, geometry, then intermediate algebra, followed by precalculus

prealgebra is just basic arithmetic with 10 other chapters on statistics, probability, word problems etc that you dont need

[brisk basin]

i see
in that case i suppose i'll ask my teacher

[trail void]

u can use any coordinate geometry book btw

its mostly covered in algebra books, and also revised in calculus

and expanded upon too

so i dont think you'll need it for now sinc youre in hs

[timber mesa]

Durrett's is a great book, it does contain a preliminaries chapter like most books but it's for the case of being self-contained, I think the content is good for someone at your level

I also have been skimming https://people.math.wisc.edu/~roch/mdp/index.html which might be better for the purpose of knowing different processes like you say

[copper schooner]

Good morning ✨️😌

[ember arrow]

Is the book Real Mathematical Analysis by Charles C. Pugh something I can read when just starting with analysis or should I know some more advanced stuff beforehand?

[river kite]

The book starts from basics of real analysis, and there is no prior knowledge as such, although calculus background will be preferred. On a side note, I personally don’t recommend this book, it tries to explain analysis with a different and simplified approach but this results in some misleading concepts that will cause issues in further courses.

[wet sentinel]

you can start with it directly, tho its on the harder side from what i hear

from what i hear its comparable to rudin's PMA for example (in difficulty)

so its probably harder than books like understanding analysis by abbott

[river kite]

I have completed both pugh and rudin’s books. Pugh is way easier that baby rudin. Though the berkeley problems in pugh’s book are worth solving. Do solve those

[ember arrow]

i've heard that it contains a lot of visualization to help understand certain things better, thats why I'm interested in it, cause sometimes i feel like a nice visualization can help me quite a bit

[wet sentinel]

of course having calc background is very much recommended as pointed out by Om Bhartiya

[wet sentinel]

ohhh i see, i have only gone through rudin (up to and including chapter 7) so idk much about pugh. Thanks for the clarification

[ember arrow]

So what are some different books about analysis that maybe are easier to follow/understand that i could maybe read instead?

[wet sentinel]

#book-recommendations message

[wet sentinel]

here is a list of intro RA books

[ember arrow]

thanks :)

[river kite]

Baby rudin is not difficult in most part, you can refer to pugh when stuck. You can also find other recommendations in the server

[surreal heart]

looking for texts in control theory, from a background in undergrad (pure, not applied) math

[fervent bolt]

are adv math engineering books (like by erwin kreyszig) enough to learn stuff like fourier analysis, bernoulli's number, reimann integration, Laplace's method of approximating integrals of the form e^mf(x) ?

or there are some better alternatives?

[gray gazelle]

should be

[fervent bolt]

how about group theory, set theory etc?

[gray gazelle]

pretty sure he does not go into group theory

i think the set stuff is discussed tho

[gray gazelle]

that comes descrete maths

do u guys do linear algebra?

[fervent bolt]

i mean my uni course only touches basic engg mathematics (gamma function, convergence of series), so i just wanna learn stuff on my own because i find math interesting, hence looking for some resources to learn from.

[fervent bolt]

i mean if you mean at uni then what we do is some calculus, and then matrix in the 2nd sem. and then its all electronics

[gray gazelle]

pal das

[fervent bolt]

chapter 7 of?

oh, then i think i should complete it before looking any further.

thanks

!

[austere steppe]

Me wanna learn Algebraic Topology, what book shall I peek at

[noble lynx]

Good afternoon, everyone. Sorry to bother, but does anyone have a book recommendation that discusses the boundary-term/variation-of-endpoints in the derivation of the Euler–Lagrange equation? I’ve heard that it’s not always zero, so I got curious and would like to learn more...

I'm talking about this part, if I didn't get the name right

[wet sentinel]

I see, if you want to learn math topics for this purpose then it's probably good to pick up a textbook dedicated for each topic.

For example if you want to study linear algebra then pick up a textbook linear algebra like FIS or greub etc..

If you check the pinned messages and scroll down you will see several recommendations for many different topics

[gray gazelle]

Topology & Groupoids by Ronnie Brown is my personal rec!

[scenic sequoia]

A man of culture.

[gray gazelle]

indeed…

[wide spruce]

have bought Ordinary Differential Equations by Tenenbaum, Morris, Pollard, Harry. tell me I spent my scarce money wisely :/

[remote sparrow]

not very rigorously

[remote sparrow]

no

[remote sparrow]

you did spend your money well

[lost arch]

any recommendations for an intro book on functional analysis, please?

[molten gulch]

brezis

or rudin

are standard AFAIK

[cursive orbit]

buhler

[dark sierra]

I have self studied Understanding Analysis by Abbott. Is that enough of a prerequisite for this functional analysis textbook?

[cursive orbit]

I think that's fine for Kreyszig, but I would also recommend learning measure thoery before FA in general

[molten gulch]

It should be, you also want some linear algebra at the level of FIS or Axler

[crude sage]

Anyone know a source which proves Heine-Borel for the standard euclidean norm in Rn?

Ah well Rudin does it in PMA

[lost arch]

eth notes?

[remote sparrow]

conway

it's more on the challenging side. it was inspired by rudin after all

[old elk]

Indeed, it is more than enough, although I should have taken Linear Algebra I and II.

[surreal heart]

what is linear algebra II?

[remote sparrow]

second term of linear algebra. presumably the first term is more focused on computations with matrices, while the second term does more proofs. maybe linear algebra is a two-term course if the term is one quarter.

[surreal heart]

ah

[pliant comet]

Do step by step and organize them.

[unique grove]

alr ill try 😭

[naive lava]

eeeh

it only matters when you have a topological term or similar

so it's only relevant when you're doing field theory

for classical mechanics you can safely stop worrying about it

[lost arch]

thanks!

[deep moat]

Books for data science?
I plan on doing some advance work before I go to college

[brisk basin]

yeah ik was just checking out that book

[brisk basin]

part 2 of sl?

or coordinate in general?

because coordinate is part of our syllabus

lines (single and pair from general equation of conic) and conics (circle,ellipse,parabola,hyperbola and basic general equation of conic)

[trail void]

coordinate geometry is covered in pretty much every pre calculus book alongside conics

if not even in intermediate algebra, trigonometry books, or sometimes even in geometry books

[trail void]

i have no idea what youre saying by part 2 of sl

i am speaking of coordinate geometry in geenral

[brisk basin]

i see

[brisk basin]

i mean the second volume of SL Loney's Coordinate Geometry (that was what I came here for initally)

[brisk basin]

right

[trail void]

what topics do u want to read from it?

all topics from it needed for calculus are basically taught in pre calc books

[noble lynx]

Thx for the response 🙌

[bronze iris]

im a mathematic student and its my last year at high school before going to university so i would like some books suggestions that can help me

[wet sentinel]

do you know calculus?

[graceful moon]

Check out "A Concise Introduction to Pure Mathematics" by Liebeck

[bronze iris]

what makes it special?

[graceful moon]

Its a nice whistle stop tour of the things youll learn in uni, and itll give you an idea of what maths at uni looks like, its quite different to what you will have seen in highschool

and its just generally a very approachable book, its aimed at people who are in their final year of highschool/just started uni

[bronze iris]

since im in high school idk if what im studying is the same as others in america and other countries

[graceful moon]

I dont know if you are either. But id say have a look at Liebecks book and see how you feel about it

It is very approachable

[bronze iris]

ok

thanks for the help

hope i find it in the library

[graceful moon]

It is availible on online libraries, if you catch my drift

[bronze iris]

got it

will try to find one

[vast flame]

Are there books that could teach me things that are useful or fun that don't require me to know algebra yet?

Im relearning math, but a video recommended a book called "discreet mathematics and it's applications" and I might get it because he said I didn't need to know algebra for it

Nevermind it's 198 dollars haha

[graceful moon]

Abstract algebra or highschool algebra? Discrete maths would assume you know the latter but not the former

Discrete maths is a (slightly random) collection of university level topics

[vast flame]

I only know and remember some high school algebra but not a lot yet

I'm still relearning pre algebra

[graceful moon]

Ok yeah, discrete maths is not the book to go for then lol

[vast flame]

Haha okay thank you

[sage python]

I think high school algebra is crucial enough that you'll have to just learn that

[graceful moon]

Yeah it is in a sense, the langauge of mathematics, theres just really no avoiding it

[bronze iris]

what algebra u guys learn at high school

[molten gulch]

who is "he"?

[molten gulch]

https://openstax.org/details/books/elementary-algebra-2e

[vast flame]

A guy called the math sorcerer on YouTube

[molten gulch]

Oh that's a terrible channel to watch

[vast flame]

Really?

[molten gulch]

Yes

[vast flame]

Why?

I've only seen a video or two

The one about the books and then some other video

I can't recall

[molten gulch]

He uses AI to write his own books, gives soddy self help advice in his newer videos, and overall doesn't recommend books that are that good

though some of them are just standard texts for the field that he recommends

[vast flame]

Boo

That stinks

[molten gulch]

Some of his recs are good like Epp's discrete maths and rosen's discrete maths, I've seen both on his channel, used them duirng my discrete maths lectures at uni, they were fine

[lavish radish]

His face gets closer to the camera every video

[molten gulch]

Munkres is a good point set topo text, etc....

[vast flame]

I found him by trying to see if there was anyone who's made a video about being an adult and relearning math as a hobby but I couldn't find any and then his video popped up

It feels like once people get out of school they drop math forever after that

[molten gulch]

Ehh some people do, mainly because at-least in the US, school maths is taught so abysmally

[vast flame]

Are you in the US? My experience at school wasn't that good but I only really applied myself to the language arts

[molten gulch]

yeah

I live in the US

I didn't really like maths in school, or eevn when I got to uni

Only started liking it after a few friends really got me back into looking at maths

[vast flame]

Same, but yeah I want to get to the point I can do calculus one so when I try to go back to college I can do well on their placement test for math

Also it just seemed fun

[molten gulch]

Yeah calculus is quite fun, a lot of my current mathematical interests involve calculus in some way, but in a far more...advanced(?) way

[vast flame]

What do you mean?

[molten gulch]

Differential geometry

[vast flame]

I can't wait until I know what all this stuff means

I wonder how long it will take I only have 1 hour to study a day

[molten gulch]

Several years

It'd still take several years doing 3-4hrs a day

[vast flame]

Disheartening 😔

Hopefully I am not stricken down by the hand of God before I'm able to accomplish my goal

[gray gazelle]

🙏

[surreal heart]

nah don't let it get you down. you'll never know all of math or even close, so there's no point in being disappointed you may or may not make it to a particular field or concept.

if you're enjoying studying math that's all that matters, just keep up and you'll be very impressed with how much you're able to do over time if you're consistent

[bronze iris]

a wise man once said :

[shadow maple]

Hey everyone, could you recommend some resources for me to delve deeper into gauge theory?

[bronze iris]

what is gauge theory

[molten gulch]

Google it

[bronze iris]

didnt know i could do that

[molten gulch]

Obviously

[marsh egret]

can someone recommend me precalc books with proofs for each theorem/rule in it

can't find any

[willow merlin]

which book contains good info on taylor polynomials for multivariable, scalar and vector fields

I am looking for a simple form of the taylor series in multivariable case, for scalar and vector fields

is there any book that explains that with differentials, hessians, jacobians or something? I am looking for a compact notation for the taylor series just like the one from single variable case but in multiple dimensions

[slow roost]

Serge Lang, Basic Mathematics

[mortal iris]

You are looking for Mathematical Analysis 2 by Zorich. Has everything you listed and more in great detail but perhaps better read after Volume 1 first. It is quite a grind though.

[willow merlin]

will take a look at it, thanks dawg, time is the only thing I have

[mortal iris]

To put it in a layperson's terms, it is a study of a special kind of symmetry (called Gauge symmetry, duh), one that physically seems to manifest as redundancies in our current mathematical models. Yet, these redundancies are what allow us to exploit many of the nice mathematical properties that we like about our models.

Essentially, the core idea (gauge invariance) is that our way of modelling reality (using mathematics) or measuring (gauging) stuff should not change reality itself. As an example, what we measure or gauge (like a potential difference) may change under how we make our devices (choice of gauge), but the underlying cause (electric field) should not (gauge invariant). Gauge theory is basically an extension and generalisation of this example.

In a way, gauges are to physics as bases are to linear spaces (this one is for someone who is new to math and physics, not for the layperson).

[mortal iris]

Ik this flies at the face of some popular (oversimplified, much, like my above explanation) extensions of the idea behind contextuality in quantum foundations like the whole "reality does not exist until we observe it" garbage and what not but that is a whole different philosophical debate to be had that has nothing to do with the math.

[mortal iris]

Mathematical Gauge Theory by Hamilton if you have not already. Amazing stuff. Hated the physics presentation of the subject before coming across this.

[remote sparrow]

mathematical adventures (but he has a phd in physics)

[harsh agate]

Besides spivak, are there any alternative calculus book recs that are simliar? i am not sure which one i should read, i use my e-ink reader and spivak is just... not well suited to it due to how old it is.

[marble solar]

If you're looking for a readable introduction to Calculus Spivak is really good. If it's not gel-ing with you, then Apostol's Calculus is a go to alternative. Salas, Hille, and Etgen is another very good Calculus book, that's more of a hybrid between an honors book, and more traditional books like Stewart or Thomas

I'd say Salas, Hille, and Etgen is a very good book, now that I'm looking back at the PDF

[paper crescent]

Does anyone have a recommendation for a maths heavy machine learning book?

Lile the maths behind all the models

[naive lava]

ai theory has lots of different math these days

some people try to use manifolds, other try functional analysis

there is no way to fully describe everything

what i'd suggest is to just pick up a book on general ai models, somewhat mathematical, as you wanted, then use other maths to apply them to ai or read the original papers, they usually contain a basic intro to these topics

[mortal iris]

Take the leap and go for Zorich 1 or Cummings' Real Analysis. I personally feel that a first introduction should be pedagogically interesting and challenging at the same time. Spivak does this. Apostol sadly does not. It was the most boring drivel I have been through besides Rudin.

[paper crescent]

I don't really know anything about manifolds but I've only heard of them in like differential topology. They have applications in machine learning?

[naive lava]

is it being old a problem? calculus is, like 400 years old, you will not miss out, and spivak is kinda unique, it sits to make the bridge between real analysis and calculus

[naive lava]

yep

some ppl are trying to estimate how good ai's can theoretically scale with manifolds

imagining a parameter space and getting constraints and whatnot

you shouldn't need too much math knowledge tbh, even an intro course could potentially be overkill

[mortal iris]

Many introductory books on Real Analysis are doing it now and are being used in Calculus courses tbf so not unique. Spivak's real selling point today are the problems.

[naive lava]

unless you want to combine FA and manifolds to get a "smooth" approach you won't be needing very heavy machinery

[mortal iris]

https://www.cs.huji.ac.il/~shais/UnderstandingMachineLearning/understanding-machine-learning-theory-algorithms.pdf

Nice place to start.

For DL specifically, https://mjt.cs.illinois.edu/dlt/
Is pretty good.

[sleek python]

https://www.di.ens.fr/~fbach/ltfp_book.pdf

[harsh agate]

Old as in there is no proper modern typesetting available for it, everything is images, i do not like to use physical copies, and the pdf's available for it are just weirdly captured in general.

[harsh agate]

I dont think i wanna do that, i can always do analysis in a couple months later.

[mortal iris]

Spivak's Calculus is basically an Analysis text. In many European courses Calculus 1 is called Analysis 1 and has the same contents. Zorich may be a big leap but consider trying out Cummings. It is literally a text for someone who has some elementary knowledge on writing proofs wanting to study calculus. Very visual yet rigorous.

[remote sparrow]

cummings is great

[harsh agate]

Is cummings available as a ebook?

[remote sparrow]

no, but it's very affordable

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

actually it does have a kindle edition, but a lot of kindle editions have quality issues in my experience

[mortal iris]

Yes? It has a Kindle Edition. Unless you need it in a specific format

[remote sparrow]

i don't see any kindle edition files floating on the web, so i'm not able to see for myself

[remote sparrow]

i just mentioned that

[harsh agate]

If i want to dip my toes in calculus fairly soon and get to solving standard problem (say from i.a maron's book or whatever), would you still recommend that i make the leap of faith in an analysis book?

[azure pelican]

Is Apostle calculus like a thing?

[remote sparrow]

yeah?

[azure pelican]

I bought it thinking it was legit, but nobody talks about them

[mortal iris]

Missed that, my bad. Ig I should get some sleep soon lol

[remote sparrow]

it is legit?

[azure pelican]

It's always "Spivok"

that people bring up

[remote sparrow]

well i prefer spivak, but apostol is good too

[mortal iris]

Especially one with the pedagogical flair like Cummings. It is wonderful for beginners. An antithesis for those who shove Rudin onto ppl in Calc 1.

[remote sparrow]

it does suck that apostol is both exorbitantly expensive and new copies are very poorly bound (i saw a library copy that is likely from a newer print run)

[azure pelican]

Yeah... and it's even worse that it's just sitting unread in my bookshelf

[mortal iris]

I used Apostol Calc 1 in my undergrad. It helped me even in Analysis (nearly a third of the course) as opposed to Rudin was a stupid book to suggest or read. But while Apostol is a great reference to have I still find the presentation needlessly dry.

[harsh agate]

Does cummings cover the techniques many standard calc books go over though? Many problems require some funny shortcuts and insights which analysis books miss (because they fundamentally have calc 1 as pre-req), which is my main issue with making the leap of faith.

I am not sure there are any books that i could use on the side to aid with that.

[mortal iris]

What "techniques" do you speak of here?

Name one that is in Spivak for starters considering it is used as a supplment often to Bartle in reasonable Analysis courses.

Spivak is in itself far from your standard calculus textbook because most ppl looking into problem solving annoying integrals and differential equations would be looking at Piskunov, Stewart or Thomas.

[harsh agate]

Well i think this will be a bit difficult for me to answer, while obviously spivak is not a standard calculus text, i certainly think based on anecdotes after going over analysis texts that it tends to be more complete-ish.

IHere is a problem i was recently working on for example, now i was able to solve part (a) but it is a fairly decent representation of problems i tend to solve, but if you read cummings, do you think any student would be able to solve it after going over cummings? That gives a decent-ish explaination to me.

[mortal iris]

If you wanna learn things conceptually and know how to write proofs for all the standard theorems and their typical extensions then Cummings is your guy. He does have a sizeable number of problems outside of proofs for intuition.

But if the goal is the engineer or physicist trickery to solve shit then Piskunov is the nicest (and free) to get your hands on. Spivak itself was not quite for you in this case.

[queen lantern]

Anyone know any good books for preparing for the Putnam, I'm currently taking Algebra, Analysis, and Probability Theory, but thats as far as I have gotten in Math so far. I'm just wondering if anyone knows some books that has helped them prepare for the exam

[naive lava]

there's a book by titu andressaciu(butched the last name) called putnam and beyond

hard problems, doesn't beat around the bush

it's pretty great imo

[mortal iris]

Cummings is perfect for stuff like this imho. There were some very eager high school students who knew not more than elementary Euclidean geometry that started calculus using Cummings. You will be just fine, if not better if the problems are about constructions and simple proofs.

[queen lantern]

thank you, will check it out

[worn prism]

How much do mods get paid

[sage python]

If only

[bronze chasm]

Why are you asking here

[worn prism]

Because #discussion is all fools and extremists

[smoky meteor]

Hello everyone! Recently, I have been working on some topics in Information Theory for Neural Networks/Deep Learning, and although I'm pursuing a degree in physics, I'm looking forward to applying some of these concepts to complex systems (networks in general). Which books are good for learning Bayesian inference and/or complex systems from a mathematical perspective?

[cyan crescent]

lmao

[cyan crescent]

https://www.kaggle.com/datasets/pranavunni/maths-for-ml

i believe this would be apt

can't share the pdf directly cause fuckass discord doesn't allow more than 10 mb uploads

without nitro

[heavy brook]

Can someone recomend me books so that I can strengthen my maths for Machine Learning

[normal crystal]

how about you strengthen your ability to read a post directly above yours

[normal crystal]

also, idk why pranav shared some kaggle host of the PDF when the official site makes it free with supplements
https://mml-book.github.io

true!
it's kinda dumb though since it just redirects to what I posted

I guess it's in case they ever stop using a GitHub page
or maybe it wasn't originally on GitHub pages

[remote sparrow]

https://www.rxddit.com/r/math/comments/1oyblvt/hatcher_algebraic_topology_is_the_worst_textbook/

https://www.rxddit.com/r/math/comments/1oy23qu/textbooks_on_mathematical_physics/

[gray gazelle]

Lmfaooo

Chain of msgs above is so funny

[dawn crater]

I too would nbe doing from ia maron

[gray oracle]

it's legit and also a very rigorous option

it dabbles in linear algebra a bit as well

[mortal iris]

If I were you, I would get Zorich. Its richer in its content and rigorously develops applications too wherever useful.

[bronze chasm]

Is "Topology Through Inquiry" a good way to learn topology? It doesn't seem to require that much in terms of prerequisites.

[mortal iris]

The only pre-requisites formally to study topology is naive set theory and a foundation on logic and proofs. It is preferable if you know your calculus to some degree for intuition but it is not strictly required.

[valid harbor]

can someone recommend a textbook that is a good introduction to category theory?

[bronze chasm]

What courses have you taken so far

[valid harbor]

i'm self studying currently

[bronze chasm]

OK. What is the most advanced stuff you are currently acquainted with

(I want to get a sense of your abilities)

[valid harbor]

uh currently lie theory (lie groups and algebras and other stuff closely related to that, also topology of them)

[bronze chasm]

I liked "Category Theory for Computing Science" by Barr and Wells"

[rough umbra]

Is there a canonical intro text for graded rings/algebras? followup, is there one specifically for commutative rings?

[bronze chasm]

It's a pretty comprehensive book, even if you're not reading it for the computer science parts

[floral lantern]

you should be a relatively mature student and definitely have taken real analysis before

[bronze chasm]

Well I guess I'll do real analysis first, then

[valid harbor]

👍

[floral lantern]

you can learn topology without analysis

but an IBL course will frankly make topology seem pointless with zero motivation

unless you are able to generalize concepts you've already seen in analysis

[rough umbra]

Idt you need RA, intro analysis (like on R^n) is prolly enough for intuition

[bronze chasm]

But I'm split on whether to do Abbott or Tao

[rough umbra]

You’ll want group theory for some of the cooler stuff tho

[floral lantern]

I mean by real analysis I mean an undergraduate course

[rough umbra]

Yee Ik, idt it’s necessary

I took topology b4 undergrad RA

[bronze chasm]

Like I'm really not sure which book would be better to learn real-analysis from

[rough umbra]

Browder

Is my pick

[bronze chasm]

But given the choice between Abbott or Tao, which one would you choose

[floral lantern]

self-studying topology with nobody to answer "why do I care about these things" I feel ends poorly

[rough umbra]

but if you’re self studying you don’t have to get into a lot of the guts of point set, you can just pick up the basics and start doing stuff in other settings with it

[floral lantern]

this is true

[rough umbra]

And I think analysis on R^n motivated it enough for me

[floral lantern]

but like it's difficult to motivate why do I care about hausdorff/compactness

[rough umbra]

Like just knowing the Euclidean topology

[floral lantern]

if you can't say "sequences converge uniquely/guaranteed and this is great"

[rough umbra]

That’s fair ig

@bronze chasm I’ve only read the first few chapters of Abbott but I thought it was fine if that helps at all

[floral lantern]

abbott is fine

If you want to get to learning analysis as quick as possible

[rough umbra]

You’d probably save time by just going to a proper analysis book first tho

[floral lantern]

tao does a bunch of random stuff at the beginning which is good for understanding but

[rough umbra]

#book-recommendations message

Or well I mean one that does multivariable too

Bc I think that helped me a lot

[bronze chasm]

I love it when I know how to do induction but have somehow forgotten the laws of basic arithmetic

[bronze chasm]

Which ones?

[lost arch]

have you done analysis using browder?

[rough umbra]

#book-recommendations message

Just listen to this person they are way more informed than me lol

[rough umbra]

I read like half of browder and then took RA

Ik he does measure theory too but my friend told me to switch to folland

[lost arch]

im planning on doing it after linalg and people say it's quite.. dense? I've heard people describe it as Rudin-like. do you think it's optimal to read browder only given that im self studying and have the prerequisites? like i know linalg, some set theory, some point topology, just general math objects and proof techniques

[rough umbra]

I think you should probably be fine, you can pick and choose what parts to read (I did not go cover to cover, I just read the parts my course covered)

[fair fiber]

The Definitive Technical Interview Guide On Probability & Market Making For Aspiring Quants

anyone have this book ?

i wanted to ask some questions about how good and relevant the content is

[mortal iris]

For self study at that level I would recommend Zorich. It is far more comprehensive and spends more time on developing things properly before diving into more sophisticated abstractions.

[lost arch]

developing things like what? i happen to have it, and i appreciate all the physics motivation and all, but it's thrice the size of browders and i dont have much time. not that it was necessary of me to tell all this, but i just would like to know if you might reveal some cool features of zorich i dont know about

besides, browder is more of an intermediate step as i then plan on reading amann-eschers books

[mortal iris]

Well. The size is the biggest downside to using it but it is mostly because of a much larger number of worked examples, some plain, some applied. Gives you a much better sense of what is going on as opposed to a blind grind. Nearly all the exercises are dedicated towards results that may not have been covered in full detail.

The other downside is that the goals you may have might vary. Zorich is more suited to someone taking analysis but has an interest in geometry and he does go into differential forms and a bunch of formal vector calculus in the second volume but he does not cover the Lebesgue integral. That said he does go pretty deep into Fourier analysis, Uniform convergence and a couple other non standard things.

In the end its a matter of taste but it is written in a way where self study is easy and aside from some minor notational idiosyncrasies it is easy to skip through a lot of the worked out stuff if you need to.

[tiny dagger]

Opinions on this book?

[shut geode]

nice intro book provides good intuition

very conversational

[mortal iris]

Nice for beginners. It used to be my go-to suggestion before Cummings came along. Very intuitive and eases you into it.

[tiny dagger]

This is great because im a beginner

my pre reqs are:

Linalg
Cal 3
Discrete mathematics

[old elk]

Topology by Stefan Friedl

[hybrid bison]

Does anyone know book recommendations for learning trigonometry

[old elk]

It's fine if it's ripe, but I think Jay is better.

[tiny dagger]

Stewart Precalculus is pretty good

it has massive coverage and a ton of examples

[tiny dagger]

for beginners?

[lapis beacon]

You should be fine, I liked it

[hybrid bison]

Thx

[old elk]

yep

[mortal iris]

Stitz and Zeager have a great book that is open source. Axler also has a good one.

[mortal iris]

Would recommend Cummings over Abbott because of the visual style and student-like explanations. That said Abbott is very nice indeed.

[remote sparrow]

Category Theory in Context by riehl

[foggy quiver]

Chess novel by idk who but its peak

[floral lantern]

Leistner is a good very short intro

[fair fiber]

may i remind you this server is 13+

How did your TCS thingy go ?

[manic cairn]

yes, but topology books mention this in my experience

also, topology doesn’t have to be a slave to analysis

there are a bunch of things in topology that are intrinsically interesting for their own sake

[exotic comet]

can I get recs for physics books up to quantum/pertubation theory?

I have not taken a physics course but I'm good at math

calc 3, prob theory and analysis

[naive lava]

I'd go with shankar in your case

starts up with a brief chapter on classical mechanics

than introduces quantum mech through axioms

it is in no way very rigorous but rigorous qm is a drag anyways

[exotic comet]

fund of phys mech rel and thermo?

[naive lava]

for cm, you can use taylor's book, which is the standard in physics, it starts out with newton and then introduces basics of lagrangian and hamiltonian

you can also use goldstein if you wanna skip newton and go for the lagrangian directly

it's also quite a bit more advanced

for EM, griffiths is your best friend

by rel, do you mean GR or SR?

and thermo is a huge thing with various approaches

[exotic comet]

oh sorry I meant is that the title of the shankar book @naive lava

[naive lava]

no it's just quantum mechanics

[molten gulch]

Isn't there also Jackson for EM

[floral lantern]

Jackson is a book for which you need to know E&M at the level of Griffiths to actually have any hope of going anywhere

[naive lava]

yeah but that sucks

it's obviously true that: and than you can't derive it, spend 3 hours looking it up to actually see that it's not obvious at all, it's a huge 3 page derivation

I'd prefer Zangwill tbh

also wald has a new book on EM

I heard it's very good too

[molten gulch]

https://www.amazon.com/Advanced-Classical-Electromagnetism-Robert-Wald/dp/0691220395 this one?

[shadow vector]

Has anyone here read this book and knows if its good/can maybe see from the chapters if its good? https://www.amazon.de/-/en/First-Steps-Differential-Geometry-Undergraduate/dp/146147731X

[naive lava]

yeah

[exotic comet]

what is a good order to read all of these?

or order for the topics?

[naive lava]

usual way is to go classical mech, then EM and then quantum, statistical mechanic sits somewhere between

depends on what you're interested in tbh

I'm doing my phd and i still don't know half of the stuff in stat mech for example

but the other 3 are essential

[exotic comet]

lol, I'm also interested in stat mech and qfd

I'm mainly trying to learn for math modeling

bc I'm interested in economics

and qfd in economics/econophysics is interesting

[naive lava]

why do you want to learn physics then?

[exotic comet]

i also think it's interesting

[willow merlin]

where can I read more about Gn groups

also for Zp cyclic rings

[graceful moon]

I’m not sure what G_n groups are, but Z/pZ can be found in any intro algebra book, so I’d guess you’ll find G_n groups (though maybe with different notation) too. Try Dummit and Foote

[willow merlin]

the group of nth roots of unity

[floral lantern]

This is isomorphic to Z/nZ as groups

[willow merlin]

care to elaborate?

[floral lantern]

Choose a primitive nth root of unity zeta_n. All nth roots are then zeta_n^k, and multiplication corresponds to addition mod n in the exponent.

[vital chasm]

e^(2pi j n)*e^(2pi k n) = e^(2pi (j+k) n)

[floral lantern]

You can check for yourself this is a group isomorphism

[orchid vortex]

Is anyone familar with Real and Functional Analysis book by Oleg G. Smolyanov and Vladimir Bogachev, I would like to know whether the book is suitable for a first time learner of the subject ?

[scarlet narwhal]

anyone got a book recomendation for AP calculus AB? potentilly BC too since ill be taking that in 2 months

[remote sparrow]

any mainstream calculus book covers all that and more

[cunning elk]

AP calc questions especially are so braindead copypasted that drilling lots of past test questions is also a viable study strategy

[marble solar]

There are lectures on youtube MIT OCW for 8.04, 8.05, and 8.06. There's a corresponding book for it. I'd say the greatest strength of using this book are the lectures online explaning the steps

[mortal iris]

I quite like Einseidler and Ward for its exposition but to begin I would say Hunter and Nachtergaele's Applied Analysis is better.

[orchid vortex]

I'm heard a lot of good things about Einsiedler and Ward book, but I'm new to the subject and currently studying on my own, I'm not sure which topics in the book I should focus on.

I'm particularly interested in stochastic processes, differential equation, dynamical systems, and mathematical physics.

[mortal iris]

Then I would recommend going through the latter book. It focuses on the applied matters that are of interest to you without sacrificing rigour but at an introductory level.

[fickle dock]

ideas for books to expose me more to all the differernt topics in math and what it is like to get a degree in it? im a chem major right now and had been commited to that all of my life but recently higher level math has seemed pretty interesting to me so i want to explore it. im in calc 2 rn

i also am wanting to self study a topic in math that isnt calculus so i was wondering if you guys had any ideas for texts assessible to someone that hasnt had a proofs class

or ideas for books to supplement what im learning in calc right now, we're stewert but i feel like the text and professor focus more on solving a given problem than the reasoning behind the methods used and that kinda stuff

[graceful moon]

I think "A Concise Introduction to Pure Mathematics" by Liebeck might be up your alley

It takes a whistle stop tour of some areas in pure maths, and teaches you proofs. It should give you a taste of what maths is like

[mortal iris]

You could pick up either Axler's Linear Algebra or Judson's Abstract Algebra since they are invaluable to analytical chemistry, particularly when you get to the quantum stuff. Of course they both involve a ton of proofs but they are gentle enough that many people can pickup without already doing a formal proofs course.

[graceful moon]

I would say those are good, if you decide you like maths. I think if youre still undecided and want to know specifically what a degree is like, Liebecks book may be better. If you find you enjoy that 100% do one of those books, all killuminati says, Linear algebra will be hugely helpful to you if you go on to do anything QM related in chemistry

[fickle dock]

i see thank you for the recommendations

[mortal iris]

I would suggest going through material for a proofs course by yourself. Hammack's book is a classic and pretty nice but if you need a slightly gentler and more conversational text you may take a look at Cummings. Piskunov 1 is likely a more provocative alternative to Stewart to go deeper.

[graceful moon]

The book of proof, while well written, is I think about 200 pages longer than it needs to be

[mortal iris]

Agreed.

[mortal iris]

This is in fact a wonderful book for anyone fresh out of high school exploring math.

[graceful moon]

This is why its my go to reccomendation. I think its great to give people an idea of what maths is, and teach them proofs and logic along the way

Perfect for anyone considering maths

[gray gazelle]

Any book reccos for somebody going back to the basics? I feel like I forgot all the basics already, I was really good at math back then🫩

[near jewel]

What do you mean with “basics”?

[grim ore]

I also agree, are we talking about like calculus level, precalc, or maybe even college algebra?

[ashen flax]

pre uni role so probably precalc / early computational calc maybe

[normal crystal]

Openstax has from Prealgebra to Calc

[humble spire]

Any trig book with objectively hard problems? A precalc book with trig is fine.

[cunning elk]

aops precalc

their starred exercises and challenge problems far outstrip anything you'd find in a standard trig book

[gray gazelle]

Hehe all

[molten gulch]

That is not a specific-enough answer, what is the highest level of maths you've studied

[grim ore]

I cant just recommend a calc text without knowing if you know algebra or precalc

But yes I was going to suggest openstax for those areas as well

[gray gazelle]

So far I'm in 10th grade currently so we're learning Algebra 2 (Yes we are behind sm despite being the highest class)

Algebra 2

[grim ore]

behind? if you are in the US, thats honestly pretty standard

Most highschools only teach up to precalc in hs, and some not even that, that is why there are remedial courses in most unis including ivys

Its getting to become a bit more standard, but more schools are now implementing APs, IBs, and allowing accelerated pathways to achieve such ambitions for students; but i wouldnt downplay your education

[grim ore]

for context, college algebra is a remedial course jsyk

[gray gazelle]

Oh I see thank you

[static linden]

Does anyone know where I can find hard vector questions?

[south compass]

Here's a good one, see if you can find some new unitary solutions: https://en.wikipedia.org/wiki/Yang–Baxter_equation

[slow roost]

Shilov - Linear Algebra is nicely challenging

it depends what you mean by hard vector problems, though

that book takes a pretty high brow approach and is heavy with the theorem-proof style

if you mean more like hard computational problems, that may not be the one

[slim pewter]

Can someone guide me with a book about calculus problems (specifically integrals) getting harder and harder? I am trying to get ready for a math competition, but I am not finding a lot of problems on the level that I need.

[cunning elk]

no math contests at the precollege level require calculus

the only college competitions that explicitly test integration are integration bees

[mortal iris]

Lets not resort to some regional defaultism.

[cunning elk]

for those i'd recommend a mix of working through past integration bee problems and then there are some books specifically dedicated to crazy integrals

unfortunately i dont remember their titles off the top of my head

[static linden]

Nevermind way to difficult I'm like studying for an exam on vectors for like a year 12 hsc level, so it's like geometric proofs and like dot products or somthings like that

[kind hamlet]

book for calc and linear algebra?

single variable calc + multivariable calc

[lost hull]

stewart

/lh

[opal vessel]

book for 3 & 2 dimensional integrals.

[remote sparrow]

#book-recommendations message

[kind hamlet]

Thanks!

[kind hamlet]

Is this a tone indicator?

What do you mean by "light-hearted?"

[glacial pilot]

any recommendations for Stochastic Processes, optimization, and decision theory?

im reading from wiki and papers rn

[kind hamlet]

This?

[mortal iris]

Depends on what you need. I typically recommend Spivak for Single Variable Calculus but if you want an alternative that is less heavy on proving results then you can try Piskunov's two volume set which covers Multivariable Calculus as well.

However if you want a really nice beginning resource that is fairly modern and teaches you all of this then look no further than Hubbard and Hubbard's Vector Calculus, Linear Algebra and Differential Forms.

[gray gazelle]

[molten gulch]

<@&268886789983436800> inappropriate level of brashness

[remote sparrow]

i don't think hubbard and hubbard does single variable calculus

but it's great for multivariable and vector calc + linalg

[molten gulch]

it does not

[kind hamlet]

Thanks! I'll check them all out and see how it goes

[warped herald]

Hi, I was wondering if anyone had any book recommendations for self-studying discrete time dynamical systems. On math stackexchange, I've seen people mention Delaney's introduction to chaotic dynamical systems and Holmgren's a first course in discrete dynamical systems. Any thoughts on these?

[worn prism]

What was the conversation that made mods ban discussion about a certain type of popular test

Which is a wise move to be fair

[graceful moon]

No specific conversation, it’s just never productive, and general descends into eugenics or other pretty horrible conversation quickly

[mortal iris]

It does not, not explicitly but it does not assume it very strongly either. The exposition on multivariable calc it has goes into single variable examples first to make things make sense and it covers most of the major theorems. It is the areas such as sequences and series which would be lacking.

[toxic nacelle]

I want to learn real analysis but i don't know from which book to start what book would you guys recommend

[merry sphinx]

probably abbott or cummings

[toxic nacelle]

thanks

[molten gulch]

rudin

[toxic nacelle]

how should I choose the book I will read

[merry sphinx]

abbott and cummings are pretty gentle intros to the subject and dont assume familiarity with proofs, and they also talk to you about the ideas/concepts of the subject

[merry sphinx]

find pdfs of the books and skim a bit to see how you like the feel

idt rudin is a good choice as a first book btw

[toxic nacelle]

i don't have familiarity with proofs

should i learn them first

[molten gulch]

No you learn proofs while doing analysis

[toxic nacelle]

ok thanks

[mortal iris]

Hell no. Rudin is a pedagogical nightmare. Avoid it at all costs. Nothing to be gained by putting yourself through it. If you ever feel the need to revisit analysis later is when you should pick up Rudin because of its brevity.

[mortal iris]

Spend some time going through elementary proofs and logic first (consider either Cummings or Hammack) before jumping into analysis. While it is entirely possible to pick it up on the go, I do not recommend it. Deciding what kind of proof is best to write and when to make new constructions can seem very arbitrary if you learned this stuff on the go.

[toxic nacelle]

after i spend some time in proofs can i start analysis

[toxic nacelle]

should i finish a proof book or do i just need to learn a couple of concepts from them

[mortal iris]

It depends. If you are doing self study then I recommend completing one. Most proofs texts end in proofs associated to relations and functions and countability so they can be a good transition into a rigorous text on Analysis. Best bet imho, stick to Cummings for both since its the same author so the style would mesh.

[mortal iris]

Yeah. You are more than ready to after that.

[short cloak]

I need portuguese books recomendations

[south compass]

Looking for a proof of the Ruelle-Perron-Frobenius theorem that allows for countably infinite branches

[near jewel]

For what?

Math or novels?

[remote vortex]

I agree, there are some Rudin success stories, but for the most part it's not a great recommendation for first-time learners that don't have mathematical experience already.

It is, however, an excellent second read

[urban hemlock]

Does anyone have a book about how the Universe was created from nothing? I heard it's trivial

[mortal ore]

how could a result like that possibly be trivial

[urban hemlock]

It's a joke

[mortal ore]

youd be surprised how many people come in and say silly stuff like that

though theyre also probably just trolling

[normal crystal]

trolling so deep they don't even know themselves

[foggy gorge]

what's been the best book on logic youve read

[remote sparrow]

@timber mesa

[scenic sequoia]

Any recommendations on stochastic processes ? I hear Ross is standard but wanted to know any other texts anybody finds decent

[worn prism]

There is a book by physicist Lawrence Krauss called “a universe from nothing”, but he admits ad nauseam therein that what he means by “nothing” isn’t actually “nothing”. So it’s just a scam

[hidden leaf]

im currently taking mv calc and im super invested in math and want a book that could talk about a mathematical concept, course, idea, etc. I want nothing that requires a prerequeisite above calc as I am currently not above that
IF anyone has any reccomendations id love that!
Any math book is well enough

[naive lava]

maybe try linear algebra? It's the 2nd most useful math topic right behind calculus

and almost anything else you'll learn will have linear alg as a prereq

[hidden leaf]

well ill be taking that class next semester

so i feel little point in going over it a bit before

i want something thats like

a bit more random

than just a standard math class

if that makes any sense

[naive lava]

well personally, one step above calculus/lin alg is either abstract algebra or analysis

hmm

maybe you can try learning some number theory

[mortal ore]

only if theyve done proofs before

[hidden leaf]

hmm ill try that!

not specifically looking for something above the clasess im taking but maybe an application or something that doesnt require prerequisites to do

[mortal ore]

have you done proofs before

like do you know direct proof, proof by contradiction, by induction, etc

[hidden leaf]

well of course

nothing ridiculously complex but you know

all of those yes

theyr all elemntary in principle, but applied to a har dproblem can be a FORCE

induction 👅

[mortal ore]

well yeah proofs arent easy

but without having learned about proofs, learning algebra or analysis is gonna be impossible

bc all the problems are proofs

[hidden leaf]

sounds interesting

any books you know off the top of your head or know to be good?

[mortal ore]

dummit and foote is the standard algebra text

tho theres others if it ends up not feeling too good for you

if anything its a good second read

analysis doesnt really have a standard text, but i use tao for analysis 2 and its good

even though i dont really care about calculus/analysis

at least not yet

tao also has an analysis 1 book so that could be good

once you do analysis though you can start with topology, for that i recommend munkres starting at page 70

[hidden leaf]

dummit the northeastern guy?

[mortal ore]

you dont 100% need analysis but itll be a good reference for topology

[mortal ore]

nah different guy

[hidden leaf]

ive heard analysis is one of the most useful classes you can take

can you dm me a link? i seem to be incapable of finding the books youre talking abt

[mortal ore]

id get in trouble if i did

for 🏴‍☠️ reasons

true

[mortal ore]

check dms

[agile kite]

Recommend Envision Algebra

[fair fiber]

Mybe he already did but is saying that to be safe

https://tenor.com/view/feel-me-think-about-it-meme-gif-7715402

[wintry quartz]

Does anyone have a recommendation on geometric quantization?

[misty frigate]

hey can anyone suggest me a book for number theory

[remote sparrow]

math sorcerer is a passport bro now??? 💀 💀 💀

[echo elm]

What went downhill with sorcerer😭
He was good before

[gray oracle]

this guy has been sketch ever since he published those ai slop textbooks

which has been years btw:
https://www.youtube.com/watch?v=41nJz-rYFYA

[fair fiber]

what a sigma

im so proud of him

[mortal iris]

Probably Richard Epstein's Classical Mathematical Logic.

[mortal iris]

Nope. He was not.

[mortal iris]

Not necessarily but in a math course, mostly yes.

[mortal iris]

Burton's Elementary Number Theory is great for beginners.

[mortal ore]

Not sure what algebra and analysis courses arent math courses

[mortal iris]

http://ncatlab.org/nlab/show/geometric+quantization#References

Take a loot at this. I personally used Ritter's notes at one point but I cannot really comment on the quality of these things pedagogically. Best see what fits for you.

[mortal iris]

Plenty of physics courses have their versions of analysis and algebra which are fairly light on the proofs and more calculational. This is also true of some applied math courses. Unfortunately this is also the case with general math curricula in your run of the mill undergrad programme in most of South Asia.

[mortal ore]

Oh I see

In the US physics students just tend to do the math courses for those topics

There arent really any physics algebra or analysis

[remote sparrow]

https://milneopentextbooks.org/a-friendly-introduction-to-mathematical-logic/

[gray gazelle]

BRO WHAT IS THUS

OMG

HELL NAW

Downfall is fucking nuts

Nah man I feel shocked

[remote vortex]

I can see your YouTube reaction video already; title "Math sorcerer's downfall: a deep dive", and thumbnail with shocked face and the text "He's doing what?!"

[summer birch]

what's a good analysis book if im taking analysis for the first time

[mortal iris]

Cummings. Alternatively Abbott. I prefer Cummings but Abbott is amazing in its own right.

[gray gazelle]

Hey guys, I'm a high schooler, looking for suggestions on books for graph theory for problem solving in pure math.

[fair fiber]

the ones for engineers

[desert oriole]

always seemed like he didnt read most of the books he touched/it didnt make much sense why he recommened 10 different books on the same topic without really explaining why one would choose x over y

[desert oriole]

diestel

no prereqs

[misty frigate]

hey can anyone suggest me a book for number theory

[fickle umbra]

david burton - Elementary Number Theory

[supple ferry]

Have you read parts of Shao or Keener? I've seen comments like that they "bury the subject in measure theory". It feels like a very applied subject (I say that from a point-of-view where I haven't really studied it ... I did take one course on the subject though!), and currently I don't know if it's better to pick a book that avoids measure theory, like Casella and Berger.

[summer birch]

wdym by "in it's own right", what's the difference in what you learn

[mortal iris]

In terms of presentation style (Cummings is a tad more visual) for the most part. Also, Cummings has a gentler pace imo. Otherwise, contents are not so different.

[summer birch]

oh ok, i think I'll get Cummings then. thanks!

[mortal iris]

Always seemed to me like he would look at the toc, read the preface and then put his spin on things for content. I once knew a guy in my physics dept who did that. Every time there was any kind of discussion he would throw jargon and when asked for an explanation he would cite sources. Idk why these ppl like to pretend they are smart. Like what are they gaining from it?

[hybrid sigil]

prestige! 🙂

often enough no one will challenge those people and they will achieve their goal (i.e. looking smart)

[shadow vector]

is there a book/lecture notes (something really small/compact) that goes over the absolute basics of point set topology that I might need for an intro to manifolds?

[daring wolf]

i mean if you want a book for an introduction to manifolds then it's time to get a book on manifolds

something like Lee's ITM

[tender river]

https://link.springer.com/book/10.1007/978-3-662-70602-2

[shadow vector]

yeah I don't have the background for that yet. I haven't done real anal and point set topology yet. I had a pretty physics-ish intro to diff geo so far

[tender river]

hatchers notes are popular too https://pi.math.cornell.edu/~hatcher/Top/TopNotes.pdf

[shadow vector]

hey thanks! This looks amazing

think ill be fine without knowing real anal? I've done other proof based stuff like lin alg, just not real anal yet

[full cairn]

Lee's Introduction to Topological Manifolds requires no previous topology - it teaches all the topology you need for manifolds

[daring wolf]

the point-set topology doesn't require real analysis explicitly

they just sometimes use real analysis to motivate topology

[full cairn]

I highly recommend Lee's ITM, I liked it better than Munkres for example

[shadow vector]

you think it would be accessible with having taken no real analysis or topology courses at all yet? I guess it doesnt hurt to take a look at it

[full cairn]

you don't need to know any topology for ITM, it is an introduction to topology

[shadow vector]

alrighty, thanks

Ohhh wait, I always thought there is just Lee's intro to smooth manifolds

Okay yeah nvm

[full cairn]

Here is what Lee himself says the prerequisites for ITM are:

IMO I don't think you need to know real analysis at the level of PMA for example; I think it's enough to look at the appendix to briefly learn what a metric space is. And the recommendation to know group theory at the level of Hungerford is completely unnecessary, you need to know just a tiny bit of group theory for chapter 7 and onwards

[shadow vector]

thanks! Ill just do this and see how far it get's me. Cause outside of that, the book looks perfect

[hybrid sigil]

those lecture notes on Topology are nice: https://www.math.toronto.edu/ivan/mat327/?resources -- plus there is also a "Big List of Problems" included there too. And "Things you should know"

[cunning elk]

"IT'S

OVER"

[sonic ocean]

Alternatives to the first chapter on maths foundation for machine learning in the text book ‘Deep Learning’ ?

[near jewel]

Do you mean Part I, if there are other books that covers the math part?

[near jewel]

If so, I think using the Part I is fine. Most of the more "theoretical books" covers this as appendix or parts (as in "Deep learning"). For chapter 2 "linear algebra", any good linear algebra books will cover the most, or even more.

[fair fiber]

you will succeed him aint that right ?

[cunning elk]

what 😭 all I upload rn is shitty gaming videos that don’t get views LMAO

[remote vortex]

I'm not sure how reliable that is because YouTube is famously opaque about these things, but apparently the median view count of a YouTube video is around 35

[cunning elk]

ig that tracks

[remote sparrow]

applied doesn't mean no theory. these are still commonly assigned for stats phds (but not for masters programs)

it really depends on why you want to learn statistics

[pale gale]

Someone give me a good book to learn 10th grade math

[sullen wigeon]

What exactly does that entail? High school math classes are generally divided by specific field, not grade level

[gray gazelle]

chat recommend me a book for an absolute bumahh who is a math enthusiast

[mortal ore]

Read Lang's undergrad algebra textbook and if u don't get bored then ur a certified bum

[gray gazelle]

aight smart ahh papi

[surreal heart]

hey so I have a lot of rigorous background from undergrad (and some grad) pure math, but I'm trying to study more applied math, and I need to do differential equations (which I've done literally none of). I want to learn the basics as quickly as possible. how should I tackle it? is Khan Academy decent for ODEs or is there a particular book I should run?

[slow roost]

that’s Hungerford’s undergrad level book, so I think it’s a reasonable choice to represent that topic

[cunning elk]

KA is woefully insufficient for anything beyond the high school level

go find yourself a book like simmons or smth and work through that

[surreal heart]

thanks!

[cunning elk]

np

[visual delta]

What book can help me understand the math in here?

[slow roost]

most any group theory book combined with whatever paper by Wagon (1994) that is referencing

[gusty musk]

I guess you would need groups and a bit of probabilistic measure theory, any book on group theory or abstract algebra will do . For probabilistic measure theory I am not sure

[visual delta]

https://www.cambridge.org/core/books/banachtarski-paradox/9C1FEAACF5EF6EB51C99F67136C8FCCB It's this book. I just realized I have access to this book through my university, which is nice.

[slow roost]

oh neat

[visual delta]

https://www.amazon.com/Banach-Tarski-Encyclopedia-Mathematics-Applications-2016-06-14/dp/B01JXNXKVA/ The author actually left a review for the book on Amazon.

[mortal iris]

You can use Paul's Online Notes to start with ig.

[pale gale]

ok give me a good one then

[remote sparrow]

you still didn't answer her question

what topics have you already learned? is there a set year-by-year curriculum your school goes through?

maybe you already took, say, algebra and plane geometry, so the next thing you'll learn is trigonometry

[mortal iris]

Well, it is not necessarily ideal, especially for a rigorous course, but if its quick and dirty you want then, Paul's notes are exactly what he asked for imo. Its a fairly quick introduction to the basics. I would also add Arnold's ODE book to this if @surreal heart wants to spend more time on the subject. For a comprehensive exposure I would suggest something else entirely.

[undone ermine]

What about for reviewing ODEs for a final

[mortal iris]

Again, it would depend on what your course entails. If what you care about is different methods to solve different kinds of (mostly linear) ODEs then Paul's notes are an amazing resource. But if you care about the geometry and proofs therein, then its probably not ideal.

[undone ermine]

We don’t do many proofs so I’ll check out Paul’s notes. Ty

[orchid vortex]

I like ordinary differential equations basics and beyond by David G. Schaeffer and John W. Cain

[jolly pivot]

What books should I buy if I want to learn Algebra and Trigonometry and everything else I need before doing Pre-Calculus/Calculus? Based on the fact that I know only linear equations/inequalities (and want to self learn math), and it is preferable if the book starts with a review of arithmetic’s and basic operations while teaching everything needed as said for Pre - Calculus/Calculus. Also can be one book or more books, I don’t mind. But it should explain each subject extensively: in terms of content I’m looking for something like OpenStax books or even more, but I want to buy an actually good physical book

[cunning elk]

try lang, basic mathematics

and supplement with various online resources (KA, openstax textbooks, etc)

[normal crystal]

most of the publisher precalc books are the same as the algebra + trig books, give or take a chapter
If you want to start at arithmetic you need a Prealgebra book

[gray gazelle]

this is true

literally every single pre calc book is same

unless you get a book from 1900s

(but basic mathematics by serge lang is one of my fav of all times)

[jolly pivot]

True, I was looking at the table of contents of Stewart’s Pre Calculus, the only thing that prevented me from buying it was that the first chapter was a review some really basic algebra and I just thought that, since I didn’t know most of it, learning it from just that small chapter wouldn’t be ideal.

[gray gazelle]

Okay here is my take

On this

That small chapters are enough to learn all that stuff

they not that small either

They are quite sufficient!

It was the book I used to learn

[jolly pivot]

Alright, you convinced me, thanks for the advice 😄

[gray gazelle]

Book is enough to learn all the stuff one need for calculus

[humble spire]

I saw this very late, but tysm!

[cunning elk]

np

[fair fiber]

Bro is so mean

[cunning elk]

am I wrong? 😭

[fair fiber]

No when i did ap calc o discovered they alternate pasted 3 types of questions every year

I created a google doc of each question type

[gray gazelle]

That’s why you are one of smartest in my eyes

Bro I swear every person big on smth always have a google doc

[vital bane]

Bro is so neam

[fair fiber]

Neamesis when he meets nemesis

[knotty topaz]

Hello! I got recommended Mukres's Topology, but i am finding two books: 'topology" and "topology; a first course". Which one should i try and use? I am attempting to study before taking my universities Topology course(However i have taken a real analysis course, so i atleast know what stuff like open,closed and compact sets are). Any key differences between the books?

[remote sparrow]

think munkres dropped the "a first course" subheading for the second edition for whatever reason

[knotty topaz]

See, i initially thought so too, but it appears they cover different topics. Attached are the contents pages of each book.

Here is FirstCourse

And here is Topology

Unless maybe it was a huge rework, that could be it actually

[remote sparrow]

yeah, he added more stuff in the second edition

you can read the preface

[knotty topaz]

Ahhh, alright, thank you!