book-recommendations

[small cobalt]

if you've covered the essentials and can demonstrate that I'd guess you'd have a fair shot there'd be no harm in getting in touch with the department and asking at least

[rustic grove]

I probably will nearer the time 🙂

[small cobalt]

good luck

[rustic grove]

thank you, and you too!

[remote sparrow]

for pure math, FIS is a good choice. it's not a great choice for those who need matrix theory more (i'm not saying people wouldn't benefit from the conceptual insights an abstract vector space approach gives). horn and garcia has a book which suits this purpose: https://www.amazon.com/Matrix-Mathematics-Cambridge-Mathematical-Textbooks/dp/1108837107. there is also the reference work by horn and johnson: https://www.amazon.com/Matrix-Analysis-Second-Roger-Horn/dp/0521548233.

[small cobalt]

agreed, not personally familiar with the book by Horn and Garcia though. I read some of Meyer's book and liked that

Sutherland, it's decent but not inspiring lol

[rustic grove]

I am using sutherland, but Idk if you used another one

[rustic grove]

Ye, it is so dry

[small cobalt]

I don't know of many books pitched around the level of that course tbh

[rustic grove]

What about the Norms part?

[small cobalt]

just the lecture notes for norms

it wasn't emphasised too much so they were sufficient to get by

[rustic grove]

I see

[small cobalt]

working Sutherland did help a lot even if it's not the most fun

[rustic grove]

Ye I plan to cover it's contents, atleast C5 - finish

[remote sparrow]

https://www.amazon.com/Metric-Spaces-Companion-Undergraduate-Mathematics/dp/3030949451

i recently found out about this book

seems good

gamelin and greene's topology textbook isn't precisely what you're after, but it focuses a lot on metric spaces

carothers' Real Analysis is worth looking into too

[small cobalt]

I like carothers a lot but it's written at a higher level than the NMT course and only covers the metric spaces content iirc

when I took it the majority of the course was really on topological spaces

[rustic grove]

Ill have a look at them thanks, I think for topology I am going to supplement sutherland with Munkres

[manic cairn]

Re-reading Lang Part I and Munkres, so I have my basics down before I hopefully go to undergrad next year:

(Also adding the analysis book that I never finished, because that seems really important)

[magic moth]

which analysis book?

[magic moth]

lang

mm

[mellow wren]

you're gonna read lang's algebra before UG

that's a new one

[dusk wind]

what are the thoughts on the open logic project?

[manic cairn]

Not all of it.

I’ve gone through part 1 and done most of the problems

And I’m going back through it and writing the proofs up again

Because I’m rusty

same thing with munkres

[mellow wren]

you don't remember the proof of some kummer theory result ofc I would do the same

[manic cairn]

The kummer theory stuff is later

[tawny copper]

Are you in high school?

Reading Lang to prepare for ug sounds so weird to me, since Lang is core undergrad material and also has graduate material

[dusk wind]

biased comment incoming

[manic cairn]

That’s the idea. I want to go into undergrad with a strong basic understanding of algebra, topology, and analysis.

[rare estuary]

You may be bored when you take calc 1

[dusk wind]

they might be bored now

[manic cairn]

And I haven’t sat down and ground out, say, Sylow group calculations in a while

[tawny copper]

I dont think you will like to be in a class where you know every single aspect of and you find the exercises easy

Unless you go to a good university where the courses are intense and with hard problems

Otherwise, the stuff you are doing is probably more than you will be doing in first year lol. Even later years

[small cobalt]

this, I know someone who went into undergrad at an extremely good university with this kind of prep and they were very bored

especially if you go to uni in a country where it is hard to place out of classes

[tawny copper]

I mean, I experienced that myself, but the uni I go to is low tier, so would have probably been bored anyway

[small cobalt]

my recommendation would be to go broader and explore stuff you might not get a chance to cover in your undergrad

you can develop a lot of mathematical maturity doing that which will still transfer anyway

[heady ember]

Set theory

[tawny copper]

I am not giving advice, but Im saying that their situation kind of sucks, they should be doing math courses already. When they finally take Lang level algebra courses, they will know the msterial already having had to struggle twice as much to learn it, but it is likely that no one will care

[dire gorge]

Hello everyone,

As I am in grade 10, I'm determined to elevate my math skills to new heights. While I currently don't feel entirely confident in my math abilities, I'm eager to change that. My aim is to become adept at mental math, tackle challenging problems well above my current level, and build a solid foundation for advanced learning.

I'm reaching out to this community for guides, resources, and tips that can help me achieve my goal. I'm particularly interested in eventually delving into calculus ahead of schedule. If you have any recommendations – whether it's strategies for enhancing mental math, book suggestions, online courses, or other resources – I'd be grateful for your insights.

My aspiration is to not just catch up but to forge ahead, and excel in math beyond what's expected at my level. Thank you for your time and any support you can provide. I'm excited to learn from your experiences and knowledge as I work towards my goal.

These are also 2 books I found after research. Would they be good?

• "Discrete Mathematics with Applications" by Susanna Epp

• "Concrete Mathematics" by Donald Knu

Also to add, the cut off for my knowledge is algebra, my math teacher last year did not teach us much, so I am even not that good at algebra ok my question was anwsred any good textbooks i should please tell me Finish learning algebra
Learn calculus 1/2
Learn any of Linear algebra, calc3, diff eq

Use khanacademy or a textbook, or whatever helps you learn and keeps a structured course

[dire gorge]

@gray gazelle will that help with the stuff in that step i will only start reading sussan epp once i get algerba one and two down

so the basically the books i already have are good and help get me what i need

these a parts to be spefic

Learn calculus 1/2
Learn any of Linear algebra, calc3, diff eq

what i reading lang?

What is is reading lang

good god

i cant type today

ok

so just to make sure

the books i have are already good

and i thought start reading susasn epp when start calc 3

and then the other book when i do or do lin alg and calc 3 simultaneously

i just want to know what should i start reading when i learning calcul;aus one and 2

ok

how about

with

ah

lin alg and diff eq?

Ok, let me start fresh

So, after I do Alg 1 & 2.

I'll move on, to Calc 3 & Lin Alg simutaleonsly

i want to know whats a good text book

i should get to study and learn it

and get grasp on it

ok

so an all in one book thats even better

and i presume each topic is sepaerted even ebtter

Apostol's 2-volume Calculus

thank you spin now i need to find the book

what is the latest edtion so i know

cause yk what im bout to do 💀

yar ye maties

ok shit

oh shit really?

dang

thats even better

where do i find it online?

i did serch

and came up with nothingg a link?

wow looks overwhealming but it all be worth knowing calcualus and other subjects and young and early age 🤣

also i got time to kill

so ya ya ya

yes ty

first alg bera one and 2

now im ready

@gray gazelle

wait one more question

when does trimontry happen

oh god that looks scary

i guess ill take trig after algbera 2

well simple enough wish me luck!

@gray gazelle one last thing the booj has all that i need to study and practise it

ok sorry i gotta stop overthinking

i dont why i keep overthinking things

I JUST GOTTA DO IT

JUST DO IT

@gray gazelle oh shit

i missworded smth

i said, once i do alg 1 and 2

ill move to calc 3

i meant ill move on to calc 1 and 2

the book covers it right

or you understood what i meant right

so book has everything i need 5 in one package

all in one crazy link

i dont need pull 150 outta my ass now

oh sick so its orginzaed 2

i just gotta read a book and follow along with it, cause it pakced full of practise questions and other things

so i dont even gotta look online for tests and practise

just read the book from my understanding

and ill be good?

after alg 2 then ill do khan trigmontery coruse

and ill be golden

well im set

thank for time, and dealing with my rabbit hole of overthinking

im going to shot myself if i overthink something

[glass badger]

Apologies if the following questions are ignorant or if I'm speaking out of my ass, but:

• Is there a list of book recommendations (arranged by topics) that has been compiled somewhere (e.g., maybe a collaborative project of sorts that a community of people have worked on)? Or some book recommendation site that math peeps use?
  If not are there thoughts about putting one together? (Not a site, maybe just a doc with a shareable link with recommended titles; no idea how much effort/time/work this would require and I can imagine there might be conflicting opinions, so again, apologies if I'm asking the impossible).
  I'm aware that certain recommendations have been pinned, but for people looking to self study I think it'd be neat to have a list of recommendations which one could quickly and easily access or be referred to while using this channel to ask for more in-depth opinions/guidance. If listed by topics, it might also help to give newbies like me an idea of the breadth of mathematics.
• Is there a list of recommended topics that should be covered first? While reading some of the posts here I've seen, for instance, topology, linear algebra, analysis, algebra, set theory; I'd imagine it varies depending on mathematical maturity e.g., I mainly see people classified as pre-uni, uni, and grad, so apologies if this is yet another ignorant question.

[magic spade]

@glass badger i have a huge personal list, so if you ever have any questions, feel free to message me

[small cobalt]

Some lists do exist, but they often contained oudated or inferior choices (at least in many people's opinion) for some topics. I could link some if you would like but I don't personally hold any as gospel or even close. There are a lot of textbooks out there and personal taste plays a not insignificant role in which people favour (if they're not just recommending the texts they were assigned in undergrad). There are sites which review books like the MAA and communities where users will discuss and opine on books like stackexchange and reddit. Another possible issue with putting together a sheet is simply that currently recommendations are often tailored to the user asking for them and adapted to information and requirements they provide.

As for a list of topics to cover first, then beyond the highschool level you can basically just look at any Uni's curriculum, many of which are online.

[fierce hedge]

A decent one I've seen is the book list maintained by UChicago Maths

[magic spade]

its really good but some of the recommendations are pretty dated, overall good though

[remote sparrow]

4chan /sci/ wiki

[fierce hedge]

I mean maths is a pretty slow field so usually not much will be changed in like few decades.
I am curious as to what book you found that you felt was dated?

[magic spade]

it doesn't really have a good suggestion for multivariable calculus in my opinion. i mean dated in the pedagogical sense

[manic cairn]

Unironcially this

[manic cairn]

Also, the Chris Jeris “Undergraduate Math Bibliography” is really good too

[remote sparrow]

https://link.springer.com/book/10.1007/978-3-030-03255-5

recently found out about this book, seems good

nice thing is that it seems to have solutions to most, if not all (haven't checked the entire book yet) the problems at the end of each chapter

[glass badger]

I appreciate the responses.
Many thanks to all of you!
And if y'all have or come across more feel free to @ me or drop 'em in here. I'll probably be going through more of this channel's past anyhow.

[atomic hemlock]

I'm reading Logical Methods - The Art of Thinking Abstractly and Mathematically linked here (https://link.springer.com/book/10.1007/978-3-030-63777-4). Does anyone know where can find solutions to the exercises? I like the book but the inability to check my answers is killing it.

[fierce hedge]

Those are the same thing right?

At least this is what I was referring to when I meant UChicago list

[manic cairn]

They are.

[pseudo dust]

Any recommendations for algebra 1 and analysis 1?

[heady ember]

Look in pinned

For alg

For anal, dami recs either Schroder for a gentle intro or browder (rudin but better)

[vital bane]

abbott

absolutely beautiful book

[rustic grove]

'Introduction to Real Analysis' by Bartle is excellent

[maiden heart]

has anyone suggestions the physical math book

[balmy lance]

Can’t find a recommendation for an Intro to Probability book anywhere in the channels. Any help?

Context: University student in a pretty competitive environment

[covert zealot]

I found "A first course in probability" by Sheldon Ross was very good some decades ago. Typically, it's best to use the course texts and references therein.

[balmy lance]

Can’t find any references

emailed the professor - no response

Go figure

[rustic grove]

Narrow that down, what field?

[covert zealot]

Your recommended text or texts has no bibliography? Or your course/module has no recommended text? Are your classmates aware of any recommended text or are they also reading nothing?

[maiden heart]

astrophysics

[balmy lance]

Theres a pretty messy syllabus. Nothing beyond that. No contact with classmates as I’m a transfer student at the semester hasn’t started yet

[rustic grove]

mmm, astrophysics isn't very mathsy* early on, and I am not an astrophysicist, but I have heard 'An introduction to Modern astrophysics' by Bradley W.carrol .... is quite good.

[maiden heart]

thanks for ur suggestions

[tired smelt]

Hi, does anybody know good books for numerical topology? I have advanced in topology and also want to start algebraic topology but my goal is to try and understand numerical topology

[vagrant hamlet]

Hello! Does anyone have opinions on Jürgen Elstrodt - Maß- und Integrationstheorie?

All reviews seem to be praising it as one of the best books ever, but there are few reviews because it's in german

[balmy lance]

Anyone?

[hearty steppe]

Looking to start working through Tapp’s Matrix Groups for Undergrads book today.

I was disappointed in the other book I was going through… A. Zee’s Group theory in a nutshell for physicists

[rare estuary]

I used A First Course in Probability by Ross

I haven't looked at many alternatives, but I found that book pretty readable

[crisp geode]

Fine if I skip algebra 2 and jump right to it, and then come back to alg 2 later?

[vital bane]

what is numerical topology?

[tired smelt]

Well this topic doesn't have a clear name, but it's somewhat topological ways of optimization. We have this theme in our university, so I wanted to research about "applied" topology

[vital bane]

something like topological data analysis?

[tired smelt]

yes!

[manic tendon]

Suggest me a Book for calculus of variations

Im a Beginner

[small cobalt]

Blitzstein and Hwang is highly recommended and has lectures online

[dusk wind]

+1 to Blitzstein, full youtube with curriculum and everything

but there are plenty of good ones for it

[magic spade]

What is your math background?

[manic tendon]

Im a recent graduate, i want to work in Geometric measure theory

I have read apostol's analysis book, and i have read in gareipy and evans book ... But i want to start with the calculus of variations way

[pale pecan]

thank you soo much, i just bought it

[magic spade]

Have you looked at Maggi's book? It has geometric measure theory and variational stuff. Or do you want a book only on calculus of variations?

https://doi.org/10.1017/CBO9781139108133

[manic tendon]

If there is any book introdues the subject for someone who has no knowledge about it

[magic spade]

Check out "Calculus of Variations" by Rindler

[manic tendon]

Thank you😃

[gray jungle]

<@&268886789983436800> ?

[upbeat vine]

Billingsleys probability and measure

[remote sparrow]

https://www.stat110.net

[dusk wind]

need to fix a PDF is there a server for that

[glass badger]

Fix? Aren't there tools for that? Why a server?

[dusk wind]

there are others that can do it more efficiently

for example people that scan tomes better than some publishers and distribute them for free

[glass badger]

Ooohh, okay. I was assuming minor fixes, but this sounds like an endeavour.
Good luck!

[storm fossil]

Are any of Euler's books approachable for a 1st year in college? Not necessarily as a textbook, but just for the interest of reading something by Euler.

[median saffron]

Nice! I hope you enjoy the book

[glass adder]

water beam

i think you forgot something

[maiden halo]

Blitzstein & Hwang is good

[fierce hedge]

Use pdftk for editing PDFs

[spring sequoia]

does anyone recommend the saxon math textbooks for self study

[remote sparrow]

there are ways to get adobe acrobat pro for free

[orchid mortar]

pdftk does work tho

[wise bobcat]

want to be smart like professor phd 70 yrs old ?

ask professor , hey can you look up the names of the textbooks you used to learn math ? id like to read what you used to learn math ... 45 years ago in the 1970/1980s

[gray jungle]

Bad advice considering some books have better modern/padagogicaly-better versions than what your professor used , not saying books from the 70s are all bad (some are incredible) but sometimes there is better alternatives

[mystic orbit]

What kind?

Measure theoretic, discrete, ...?

[wispy bison]

What is the asterisk

[rustic grove]

I was emphasising the fact that whilst it is a good book on astrophys, I wouldn't class it as a maths book. At least considering the sort of maths people are looking at on this discord...

[cyan valve]

Anyone have any opinions on Shafarevich's two volume "Basic Algebraic Geometry" series and Bosch's "Algebraic Geometry and Commutative Algebra"?

[olive bloom]

If someone has an analysis reading group I'd like to join

[dusk wind]

yea just learned this might be the way

it specfically has what I need rip PDF software monopoly

[dusk wind]

there is no way you will ever catch me using a book pre 2000's unless its some specific material only found there or part of some chain of logic

most modern sources have already done the research for you

[rare estuary]

No Spivak's Calculus? Baby Rudin?

[dusk wind]

thats different

but average academic books from the 80s are just that

think about it, if the books assigned to your class suck today, they probably sucked back then too

[sturdy shore]

there are so many good math books written in the 90s or before, that is just an ignorant thing to say

(so is the other statement, that you should look up what people used in the 70s as if that is going to give you better books on average)

[dusk wind]

yeah but there are good books written today which is more important and relevant

[rustic grove]

From what I have gathered so far, new books tend to 'dumb things down' a bit; where as old books just give it to you how it is 🤣. Maybe I am wrong tho...

[dusk wind]

thats true if you want to go on a serious study hunting after chains of logic by all means dig into the past but you might see things differently from those who were spoonfed

of course you could just filter out such books written today as well and hope the nuggets of knowledge are enough for your crusade

[rustic grove]

I guess so 🙂

[sturdy shore]

but that is not necessarily true? there are many subjects where the textbooks that get the highest praise are older, and it's not like the praise is unwarranted either
willard is imo the best book on topology. which point set topology book today is "more important and relevant"?
what is a book "more important and relevant" than hoffman & kunze?
heck, folland was first released in 1984 and second edition in 1999
rudin RCA was also released in 1986, rudin and folland together are pretty much the standard references on grad level measure theory/analysis, which books are more important and relevant than those?

it's not like these subjects have evolved at any meaningful level to change what textbooks would look like for them
I'm not sure where this expectation of linear-esque improvements for textbooks comes from

[dusk wind]

linguistics and the internet

[dusk wind]

wonder why this is

[fierce hedge]

Cause progress is very slow in mathematics and even then the fundamentals do not change much if any at all. On top of that most of the new research is not within the grasp of a ug student and it remains to see if such things might be too useful to not know.
For example calculus was considered very advanced few decades ago before few people found the pedagogical way to teach them to ug students.

[dusk wind]

thats not the same in other fields and I wouldn't say topology is reason to jump into older books
for example you can't use Python 2 anymore nor all things associated with it

of course the more difficult or niche something is the chances of it changing are lower, that has nothing to do with progression or linear improvement
given enough time all errors are eventually and hopefully found and corrected, what was true once before simply isn't depending on how much later you want to go

[ancient sand]

is there anything i need to know for that popular book on real analysis

or do you know what you need if you've just taken basic calculus

[rustic grove]

which book? Rudin?

[ancient sand]

abbott

[livid lichen]

after the book algebra: structure and method method I move on to intermediate algebra

[rustic grove]

You don't need much so feel free to dive into it 🙂

[ancient sand]

thank you

[vivid zephyr]

I doesnt seem like abbot's book covers proper and improper limits any reccomendations on handouts or books that might

[mellow wren]

have you considered the fact that maybe modern authors don't feel the need to write a book on a subject if there's already a great book on it pre 2000?
like almost all the math books I read on a daily basis were written pre 2000 lol

[mellow wren]

maybe try chapman pugh's book
It goes quite a bit deeper than abbot but I don't think improper limits are a super important concept so idk if there's any book that goes into them that much

[vivid zephyr]

@mellow wren thanks

[livid lichen]

Is the revised edition or the student edition better?

[rose lynx]

Does anyone have recommendations for reading material on hyperbolic manifolds?

[magic spade]

What's your background?

Have you looked at "Foundations of Hyperbolic Manifolds" by Ratcliffe?

[rose lynx]

I'd heard about Ratcliffe and Janich. I thought best to ask for recs before starting since I'll be doing this in my hobby time
I have very limited background in advanced topology mostly from some reading on relativity.
Here I'm looking to study hyperbolic manifolds and preferably it's connections with information theory, which is also why I'm asking for recs xd

[rose lynx]

Thanks I'll have a look!
Any recs for papers on representation of high-dimensional spaces with hyperbolic geometry?

[magic spade]

No I don't, sorry. If you find some good ones let me know, I'm interested too

[rose lynx]

Sure. And thanks!

[low condor]

TN Reveal Math (for students living in Tennessee), this is what my school uses and it is what I recommend, I even got ahead a few lessons in First Quarter before the teacher taught

[gray gazelle]

Hey guys is there any book to improve my geometric proofs

that only focuses on geometric proofs

[vital bane]

complex analysis by gamelin seems really good

[turbid mural]

any book recommendations for Lie theory?

[dreamy matrix]

any book recoms for diff equations & pde?

[maiden heart]

ohh man, it's so expensive, I'm living Turkey therefore that book so expensive here, 2,700 lira

[graceful moon]

People seem to like boyce di prima and meede, it’s a pretty comprehensive introductory text.

It’s not my favourite book in all honesty but I do seem to be an outlier, there’s copies of it online so you can have a look and see if it’s to your taste

[spice finch]

[sick lark]

Any book recommendations for brownian and martingale stochastic Procesee?

[magic spade]

Do you want an introductory book, an advanced book, an applied book, a theoretical book, or something that does a bit of everything?

[dreamy matrix]

applied

[magic spade]

mainly on pdes? or odes with a little bit of pde?

[dreamy matrix]

pdes

[magic spade]

@dreamy matrix Applied Partial Differential Equations with Fourier Series and Boundary Value Problems by haberman

[magic spade]

Lie Groups, Lie Algebras, and Representations by Hall for the real deal or Naive Lie Theory by Stillwell for a nice intro

[hearty steppe]

Do you guys think Devaney’s books on chaos theory and dynamical systems are worth reading? Also what about this book?

https://books.google.com/books/about/Chaos_Theory_Tamed.html?id=I01ZDwAAQBAJ&printsec=frontcover&source=kp_read_button&hl=en&newbks=1&newbks_redir=0&gboemv=1&ovdme=1#v=onepage&q&f=false

[magic spade]

Do you want to study dynamical systems for applications or for pure math? And what is your math background?

[magic spade]

Also which devaney books are you referring to? He has at least 4

[hearty steppe]

I was looking at his whole publication history.

I don’t study pure math. I work on publishing meta-analysis papers but my area of interest that helps guide me is dynamical systems

So applications would be the appropriate route*

[magic spade]

My favorite is "Chaos" by Alligood et al. Take a look at the beginning contents and let me know what you think

[hearty steppe]

I’ve went through a couple dynamical systems books and a introductory complex systems book already. But it seems like Brin and stuck came out around the time Devaney published his earlier works. Seems worth reading

I haven’t found a dynamical systems book I haven’t enjoyed yet. Although I found Strogatz to be the most underwhelming even though it is very broken down for people with not so great maths background

But Strogatz does not give you a comprehensive picture… it is quite an underwhelming read

Strogatz I definitely would recommend as a first read if your math isn’t great

I consider mine to be good enough. I can get through some challenging books even grad level books but I am not like totally committed to studying maths. I am not so good with proof writing and really obscure rigor.

I couldn’t work through texts like Stein and Shackarchi

[magic spade]

Are you recommending me a book or I'm recommending you a book? XD

[magic spade]

If you want something serious try Wiggins dynamical systems book

[hearty steppe]

I am totally gona check out the recommendation you suggested

I think I am just about ready to explore Ergodic theory though so I’ll consider these texts for when I want to take a step back and refine my understanding of dynamical systems

I worked through Brin and stuck many months ago. Which is probably just as hard as Wiggins or harder

[magic spade]

Hmm I guess I'm pretty confused what you want

[hearty steppe]

Actually at the moment I’m focusing on some algebra texts for a better understanding of representations and spectral theory

[magic spade]

You could read about the Conley index and the fundamental theorem of dynamical systems?

[hearty steppe]

There’s so many books on my reading list that at this point I’m just trying to make a map for to figure out which I should prioritize

And I think within the next couple months I ought to start learning Ergodic theory in better depth

[magic spade]

Can you be more specific what your goal is? If you know the basics then what you should study next depends on your goal

[hearty steppe]

I tried going the Fourier series route and my brain just tapped out. Maybe because Fourier series is not as fundamental as Ergodic theory and ergodicity really gets into patterns and pattern breaking more intuitively

But the Fourier texts I tried checking out seemed too vague

Stein and Shackarchi is too rigid. I also tried Tolstov which was jumping around all over the place in exposition

[hearty steppe]

So the reason as to why I am curious about Fourier series is because I have an interest in understanding harmonics, resonance, and frequency decompositions

[hearty steppe]

But I am also realizing that maybe just going the Ergodic theory route for now can align my intuition for that better than just jumping straight into Fourier series more deeply if I’m struggling with it

[sage python]

They can intersect!

[hearty steppe]

That’s precisely what I was thinking 🙂

There are a good chunk of Fourier series books I haven’t tried working through yet so I haven’t given up on that journey. I just figured I’d try an alternative path to getting there than just jumping directly into Fourier series

It’s kinda like how much trouble I have jumping directly into spectral theory

When I realize I got to find the right algebra books that cover matrix groups and representations

[remote sparrow]

https://www.amazon.com/Partial-Differential-Equations-Completely-Problems/dp/152555025X

[dreamy matrix]

thx bbg

[narrow relic]

I'm not sure, I'm sorry.

[livid lichen]

Oh its fine

Np

[timber holly]

Any measure theory books

[remote sparrow]

many

there are some suggestions in pins

https://measure.axler.net

here is another

[timber holly]

Love the cat in the website

Ty

[remote sparrow]

https://web.archive.org/web/20150712180839/https://www.math.ucla.edu/~hbe/amil/

Enderton once had a companion website for his logic textbook. The link to that website is dead. In lieu of that link, I have linked an archived copy.

[gray gazelle]

Do you guys Have any book to improve my geometry pls

Or any book to improve my problem solving skills

[waxen tundra]

Hello, I have a book on Discrete Mathematics by Susanna Epp that introduces set theory, logic, and number theory. Do these topics prepare me for a book of proof like Chartrand's and Spivak's calculus, or should I get books like set theory and logic to be more in-depth with the subject?

[narrow relic]

That sort of does, but the logic covered there doesn't tell you how to actually prove things. I recommend you read something that teaches natural deduction like Ch 1-5 (they're short) of http://intrologic.stanford.edu/public/chapters.php

[waxen tundra]

So, should I skip the logic chapter and read this instead?

[remote sparrow]

You do not need to study logic in any depth beyond the snippet offered in any discrete math or intro to proof book. You do not need to know the specificities of what natural deduction, Hilbert-style deductive calculi, sequent calculi, or any other proof system are in order to do mathematics. In fact, the previously mentioned proof systems are models (not to be confused with model in the model-theoretic sense) of logic that we informally reason about in basically the same way we reason about things in the rest of mathematics.

[swift blaze]

is dummit and foote a bad idea for first time learners in abstract algebra?

i'm currently studying gallian but have heard very good things about d&f

[remote sparrow]

It is generally considered, at minimum, an honors undergraduate textbook. It is a graduate textbook for my college's master's program.

[swift blaze]

so though it technically is possible, it isn't really recommended right?

maybe i should leave it for later

[dim sierra]

i think you could do it, thats personally what i did

[formal bronze]

I'd say it is a great book for first time learners. Don't expect to be able to get through the whole book quickly though.

[vital bane]

almost 1000 pages

[peak ledge]

I want to learn group theory on my own, can someone please recommend a book regarding this topic?

[finite gale]

rotman

or check out #book-recommendations message

[gray jungle]

Artin , very fun book accompanied with benedict gross videos

[peak ledge]

ty

[fierce hedge]

How much do the videos cover btw since Artin does Groups, Rings, Fields, Galois theory as well as Linear algebra

[gray jungle]

groups linear algebra and rings ,mostly following the first edition

he covers everything you will need from the basics

[fierce hedge]

That's the thing, I don't want the basics, there's Borechards video but it's straight grad level. Is there some a bit intermediate?

[gray jungle]

not that im familiar with , but gross covers a fair bit of groups , he only misses on stuff like solvability/extensions/decomp of finite abelian groups/linear groups
and by the time you finish the rings he cover you are just better off picking up a comm alg book and using borechards videos

[tawny copper]

I dont think there is anything susbtantial between Artin and Borcherds tbh

[remote sparrow]

https://www.youtube.com/playlist?list=PLPW2keNyw-utXOOzLR-Wp1p0eE5LEtv3N

This lecture playlist has Enderton as a suggested text. The book is not required. The lectures may be useful to those studying from Enderton, though.

A notable aspect is that it gets to Godel's incompleteness theorems, which I haven't found in other lecture playlists.

[narrow relic]

I was never able to understand proofs in say analysis before learning Fitch natural deduction

[narrow relic]

You can read the logic chapter in Epp too but you could also try the Stanford thing first

[narrow relic]

I also should have said Ch 1-5 instead of 1-12, sorry about that mistake. I forgot that Fitch natural deduction gets introduced in Ch 5, and that's as far as you need to know.

[narrow relic]

5 chapters is a lot less than 12! 😀

[valid dawn]

hi, i want to teach myself algebraic geometry from ground up. i'm fascinated by the field and want to at least get a somewhat confident grasp of it. i'm looking for a book that can start from basics and slowly build knowledge, preferably with a lot of exercises, but not too terse.

i have some basic group, ring and field theory covered, but not much linear algebra (will that be an issue?). additionally, are there any recommendations experienced math people have for picking up this subject in math?

(ping when replying)

one source recommended Ideals, Varieties, and Algorithms and from the preview it looks very nice but i wonder if there's any better resource

(if this helps: i am also good with code and i have experience using Sage already)

[magic spade]

Ideals, Varieties, and Algorithms is a good book. you could also check out "Algebraic Geometry: A Problem Solving Approach" by Garrity et al.

[graceful moon]

A totally introductory book could be Reid algebraic geometry, that’s the book my uni uses for its undergrad course (I’m taking it next semester so Ive not personally read it yet)

Knowledge of rings groups and fields is all my uni requires to take it too so I’m guessing that should be appropriate

[valid dawn]

thank you!

[crisp geode]

Need a book that's specifically there for proofs in plane geometry, It makes me anxious to study something without knowing where it came from

[green dagger]

I recommend Horrid Henry specifically the one about knickers (forgot the name). Perfect Peter is surprisingly useful

[waxen tundra]

Thank you

[stuck zephyr]

what

[trail hemlock]

hi yall. Im a HS student currently studying proofs (for linear algebra). I have this book "proofs: a long-form mathematics textbook" by Jay Cummings because people say you need to know how to write proofs for linear algebra.
What linear algebra books do yall recommend for purely self studt (I will take a Uni class on it next year) ?
sorry in advanced if this is the wrong type of question, please lmk

[dim sierra]

Friedberg Insel Spence

[remote sparrow]

#book-recommendations message

[trail hemlock]

thanks a lot!

[mossy flume]

FIS my beloved

[zinc lantern]

Does anyone have a good geometry book recommendation for honors geometry in highschool. Specifically ones that go over circumscribed and inscribed circles and polygons. Because I really don’t understand that topic

[fierce hedge]

I don't think Artin talks about spectral sequences and some other grad topics but that's just a guess since I haven't watched Artin videos.

[dusk wind]

Tim Hefferon

[unkempt gorge]

Any book recommendations that help with visualization & interpretation of word problems/real life problems into mathematical expressions or equations?
I find myself still struggling, though not completely failing, with word problems despite having absolutely zero difficulty with the same concept in an equation format 😕

[tawny copper]

No, but why would you want to learn spectral sequences to watch Borcherds videos? You are talking about this right https://youtu.be/RnqwFpyqJFw?si=YgnI6To8VdyyvsDq

[fierce hedge]

Huh? I meant that he covers some grad stuff also like spectral sequences

[tawny copper]

so why would you want to learn spectral sequences beforehand? doesn't look its something central in the course at all

oh maybe I expressed myself wrong, when I said "there is nothing in between" I didn't mean that they are the same, but that going from one to the other does not require like reading a book beforehand

you could read some book like Isaacs "Finite group theory", and whenever you need to brush some of the basics go to Lang or Dummit and Foote

[fierce hedge]

Idk if it's central or not, I merely meant that it feels like Borechards covers grad topics while Artin video probably doesn't

(Probably cause I haven't watched the videos)

[tawny copper]

yeah no Artin does not, but I thought you wanted to go further from the basics

[fierce hedge]

True, I think I got confused a bit. This clears it up.

[ancient sand]

which is better for an intro to real analysis: tao's or cummings'

(please @ me when/if answered)

[gray jungle]

Not familiar with cummings but tao analysis books are good , thats how i first learned the subject

@ancient sand

[timber holly]

I have cummings proofs book but I got bartles real analysis (rec cummings proofs book)

but uhh

tao is what I would choose ig

[ancient sand]

thank you both

[daring lake]

I liked Bartle the most. Cummings is nice, he is very verbose, has many memes, well illustrated, but he covers only the bare bones of an Analysis course. Tao felt like a novel, but covers a lot. Bartle felt like a nice in between spot, its not written in definition-theorem-proof format like Rudin (it gives pretty good coverage with many topics, although it completely avoids Topology over R), easier to read, has many examples and problems too.

[heady ember]

You probably can just jump straight into proof-based LA without an intro to proofs book. As long as you know what are conditionals/biconditionals/quantifiers, etc, you can probably just learn and improve along the way.

I never read anything in particular for those things, except like 50 pages of Rosen discrete math that was so boring I just moved on within a day or two lmao

[daring lake]

I think Axler starts from scratch

[heady ember]

Axler's treatment of dets is ass tho, fyi (to the rec requester)

FIS seems to be the common rec in this discord

Which I agree with as a person who has read the first 2 chapters of it.

[daring lake]

I only read Hoffman&kunze

i just have axler lying around

[heady ember]

One of my classmates is 'reading' that because he heard it was the hardest one
(Yeah he hasn't gotten very far)

[daring lake]

might just jump to roman tbh

[daring lake]

i thought hoffman&kunze was easy

[heady ember]

idk never tried it before

[daring lake]

well i did analysis before LA so maybe that's why

[heady ember]

I picked FIS because I didn't want to overestimate my own abilities lol

[heady ember]

Yeah ig

After I read Enderton, FIS has been quite a breeze tbh

When I start learning intro alg, I'll probably have my shit slapped outta me by Jacobson

That prepares me for more set theory tho

[pliant wadi]

FIS?

[heady ember]

Friedberg Insel Spence

[pliant wadi]

ah

I am reading H&F but I personally don't like it that much, idk why

hows FIS in comparision

[daring lake]

I have only read D&F

Although wasn't a fan of getting slapped by 50 problems every 4 pages

[pliant wadi]

I am looking for a more self-contained lin alg book which properly deals with quotient spaces, any recs?

[heady ember]

Like I said, FIS would be my rec.

But keep in mind that its the only LA book I have read

Though many here share the same opinion as me (FIS being an excellent resource for LA), such as Dami and tera

[fierce hedge]

H&K is kinda the honours maths standard for LA so if that is easy you might wanna try Roman or Greub

[fierce hedge]

Less comprehensive and slower but definitely dry

[trail hemlock]

Honestly I just love proofs lol.

[heady ember]

Objectively correct opinion

[heady ember]

Some ppl don't find it dry, though for me it definitely has been a bit.

But I mean, you can just skip the example they give, at your own risk

Without the bajillion examples provided, the book would be much shorter

[daring lake]

My learning curve is very weird. Group theory -> Rings -> Real Analysis (baby Rudin) -> Linear Algebra

I am currently reading papa rudin

[heady ember]

lol learning alg before lin alg

[daring lake]

i just intuited Lin alg when ever it was used

[heady ember]

idk if that's good or bad

[daring lake]

well all of this is self study

[fierce hedge]

Not too weird, in most Indian universities you'll be expected to learn Groups, LA and analysis all in the first year itself

[lapis sundial]

Same here in UK

[daring lake]

what about papa Rudin contents?

is it grad level?

[fierce hedge]

That's like analysis 4 I think, upper UG

[daring lake]

oh

[lapis sundial]

Though in America you can assume any textbook is grad level

:)

[fierce hedge]

General sequence is Real Analysis -> Metric spaces -> Multivariate analysis -> Functional

[daring lake]

I see

[heady ember]

Meanwhile in Singapore:

This is their 'special programme'

[fierce hedge]

Huuuuuh??? We took only 1 humanities course and one other department extra

[heady ember]

Singapore moment. You're forced to take some annoying number of GEMs (general elective mods)

[keen orbit]

https://discordapp.com/channels/268882317391429632/716264872018706443/959370522938974228 check this list maybe you can find what you are looking for there

[crisp geode]

Need a book about proofs relating to geometry

[spice finch]

Euclid's elements

[crisp geode]

Thank you

[gray gazelle]

Hello folks, I'm new here, I'm a programmer, looking to widen my knowledge on math for fun.
Uh, to start off, what are some fun introductory books to topics like Discrete Math and Linear Algebra?
I was wondering since I was planning on starting Kenneth Rosen's book and C Lay's on L ALG after finishing my current reads.
Any recommendations are welcome, I'd like to learn more and get a better understanding of these topics.

(context I come from a self-study background so)

[heady ember]

I got bored af the last time I tried using Rosen's book on discrete math so yeah. I wouldn't say its necessary imo

[gray gazelle]

It's quite the book.

[heady ember]

Drier than a desert

[gray gazelle]

It is

over what? 1k.

but then do you have any better recommendations for Discrete math?

@heady ember

[heady ember]

Haven't been interested in programming so idk. But for math idt there's a need to learn discrete math, in the sense of sitting down and reading a book on it or whatever. As long as you know the basics of what a conditional/bicondition/quantifiers, etc are you should be fine ig

[gray gazelle]

I"m more for it for the design and analysis of algorithms

part

[heady ember]

Idk about that

[gray gazelle]

since I"d like to touch upon some competitive programming more in depth

aside from my established interests.

But any books then on Linear/Calc that you'd recommend? I take anything honestly.

as I"d like to explore a bit of math so anything you give me will be a fun teaser

[heady ember]

I'm more interested in proof-based math so take what I say with a pinch of salt

For LA, FIS (Friedberg, Insel, Spence) has been good in my experience. And is also rec'd by Dami and tera, among others here.

Calc wise it depends on if you want it to be proof based or not. If you just want computations, Khan Academy / Pauls' Online Math Notes may suffice. If you're interested in proofs, Dami stans Schroder and it has been nice in my exp so far. Others like Abbott.

[hearty steppe]

Any good knot theory texts that aren’t too too rigid in the pure math sense? Trying to scratch my itch for dealing with protein folding and hyperbolic behavior

Doesn’t have to be directly talking about molecular biology applications

[gray gazelle]

alright I'll check them out and get back to you.

[remote sparrow]

#book-recommendations message

#book-recommendations message

https://www.amazon.com/Calculus-4th-Michael-Spivak/dp/0914098918

https://www.amazon.com/Calculus-Vol-One-Variable-Introduction-Algebra/dp/0471000051

https://www.amazon.com/Calculus-Vol-Multi-Variable-Applications-Differential/dp/0471000078/

https://www.amazon.com/Calculus-Variable-Dover-Books-Mathematics/dp/0486838064

https://www.amazon.com/Calculus-Rigorous-Course-Aurora-Originals/dp/0486809366

https://www.amazon.com/Calculus-Applications-Undergraduate-Texts-Mathematics/dp/1461479452

https://www.amazon.com/Multivariable-Calculus-Applications-Undergraduate-Mathematics/dp/3319740725

there are lots of choices for linear algebra and calculus

abbott and schroeder are not calculus books

they are real analysis textbooks

[gray gazelle]

thanks!

Hello

I was wondering what would be a good book to start 'Number Theory'?

Any recommendations for beginners?

[remote sparrow]

burton or dudley

https://www.amazon.com/Elementary-Number-Professor-Emeritus-Mathematics/dp/0073383147

https://www.amazon.com/Elementary-Number-Theory-Second-Mathematics/dp/048646931X/

[gray gazelle]

Thanks

[crimson leaf]

I like Niven and Zuckerman

[gray gazelle]

I'll check them out in the morning

[keen orbit]

if you want a computational book for calculus i recommend stewart's book and if you want a proof based you can try spivak's

[gray gazelle]

I'll most likely go through both

[keen orbit]

for linear algebra i am using linear algebra by werner greub rn

https://discordapp.com/channels/268882317391429632/716264872018706443/959370522938974228

[gray gazelle]

never heard of it.

[keen orbit]

this has linear algebra books with desriptions

[keen orbit]

me too the first time i heard about it was when i read this not long ago

but among the books that i tried it is the toughest tbh

i tried FIS and axler's

but i wanted a more rigorous and absract book

[keen orbit]

i went for this book when i saw its description from here

and i liked it thats why i am using it rn

[gray gazelle]

I'll have to see, right now I"m going to check with the recommendation lists above and compare them to what I have

I'll most likely read and do these books, but in which order I'll have to check for myself.

[keen orbit]

i am still in the beginning of it but i went to abstract algebra for a bit to understand quotient/factor spaces more

[keen orbit]

yes sure you have to decide yourself

[keen orbit]

when i am done ill move back to greub's book

[gray gazelle]

Most likely for engineering probably any basic book on LG will suffice

since I assume most of the scientific topics covered are more towards math majors.

But it'll be a fun brain teaser nonetheless for me.

[keen orbit]

if you dont want to go deep you can go for other books in LA other than greub's

[gray gazelle]

Oh, don't get me wrong. I'll go deep.

But as far as I'm concerned, for my interview I'll need to revise most of the basic LG stuff.

how do you abbreviate linear algebra?

LA?

VM ? - Vector math?

[keen orbit]

do it as you wish i write as LA 😂

[gray gazelle]

Oh, I see 😆.

Guess there isn't a good book on Discrete math other than Rosens it seems

or no one here atcually does it 🤣

[keen orbit]

i am not the right person to ask this question to 😂

[gray gazelle]

don't worry I don't think I'll find a single person here who does it 😂

Anyways, I have to go to sleep and work so good night!

Thanks for the recommendations

[keen orbit]

np gn

[tame tree]

#discrete-math

[fierce hedge]

There's Knuth's Concrete Mathematics but I think it's harder than Rosen's book and a bit more on the applied side.

[hearty steppe]

Knuth is quite nice

#book-recommendations message Still curious about this 🧐

[distant spear]

My friend said good things about elements of discrete math by chung laung liu

[storm fossil]

What I'm asking for might be a bit silly.

Just for fun, I'd like to do some of the calculations that the Ancient Greeks did for measuring the Earth, the distance to the Sun, the Moon, etc. If I'm not mistaken, they had gotten the size and/or distance of the sun wrong, but were very close (given such limited information) to the size of the Earth and the distance to the moon.

They did this with Trigonometry.

Is there any book (or maybe just a section of a book) that goes into showing how to work through these problems the way they would have? (Just trig, nothing else)?

[granite breach]

does anyone have any recommendations for intro to logic book, with medium to advance difficulty and depth

[torn hawk]

Recommendation for linalg book?

[final swallow]

How good is Elementary Number Theory by Rosen?

[quick hornet]

fine

if you're a bit more familiar with abstract algebra i'd recommend his other intro NT text, a classical introduction to modern number theory by ireland and rosen

but if you're not super comfortable with terms like "ideal of a ring", then rosen is good

[final swallow]

I know some basic group theory but it’s not enough though

[final swallow]

Is it true that the book is riddled with errors?

[quick hornet]

i do not think theres any conceptual errors but yeah theres a lot of errata

https://math.dartmouth.edu/~jvoight/Su2004-115/2004-115-Typos.pdf

[remote sparrow]

different rosens

one is michael h. rosen and the other is kenneth rosen

[remote sparrow]

what does "intro to logic" mean here

are you interested in a metalogic textbook?

[tawny copper]

The other author is Kenneth Ireland lol

[remote sparrow]

i know

but namington said both number theory books were written by the same rosens

that's not true

[tawny copper]

I was just pointing out that the names are similar, which I found funny

[gray gazelle]

hey guys ..... can you guys tell me any resources to better understand calculas 3, i was ok with single variable calculas but i think multivariable calc is gonna be big headache

[granite breach]

i was thinking more something stemming from the stuff like "p implies q is equivalent to not p or q"

[granite breach]

are you doing analysis or just application

[gray gazelle]

i dont know. i havent started it yet, basically i just completed cal1,2 , i think just the basic knowledge would be okay

i have an interview in december probally. they wont be asking many questions on cal3.. but i was gonna read it just in case

[remote sparrow]

not sure why this needs a whole textbook

[granite breach]

im saying more stuff following on from this

i wanna see more

we did that kinda thing in discrete maths, and i enjoyed it way more than group theory or number theory

[remote sparrow]

well the continuation is to do metalogic

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

you want a book like enderton, mendelson, van dalen, leary and kristiansen, etc.

[sweet stirrup]

Hii everyone, Is there a good alternative for z library or libgen?

[fierce hedge]

Piracy discussion is not allow here

[gray jungle]

As numbpy said piracy is not allowed so we cant discuss alternatives like anna's archive

[spring spoke]

Hi everyone, I have read (if I remember correctly in this server) a review of a physicist student about "Quantum Theory, Groups and Representations" of Peter Woit, but he wasn't very happy about it. Does anyone else can give me other information about this book?

[manic tendon]

Anyone knows a book in combinatorics that contains treatment of sterling numbers?

[hearty steppe]

So would you guys say that there is a connection between causal set theory (from the perspective of Fay Dowker for instance) and the concept of term rewriting as discussed in this book? https://www21.in.tum.de/~nipkow/TRaAT/

What do you recommend I check out going forward?

[old elk]

Hi guys, I would like to know which book do you recommend to study differential geometry for the first time?
It is worth mentioning that I am returning to study linear algebra, real analysis and I am studying a bit of topology.

I would like to prepare myself soon to study Differential Geometry, but I've seen some that are quite complex and I'm a little scared.

[heady ember]

I seen people here rec

1. Toring Lu's, and (or was it Loring Tu, idk always get mixed up lol)
2. Lee's (john m lee) books
   for diff geo

[old elk]

Loring W. Tu

[magic spade]

Which kind of diff geo are you wanting to start with? Curves and surfaces or manifolds?

[haughty patrol]

guys u should read moby dick

[old elk]

Curves and surfaces

[magic spade]

In that case, I recommend Tapp's book

Differential Geometry of Curves and Surfaces https://g.co/kgs/U4G1G9

[gray gazelle]

I might sound dumb but whats the difference between the two?

[cobalt arch]

I guess manifolds are of higher dimension than two or three (curves or surfaces respectively)

[gray gazelle]

what's the content of a usual undergrad diffgeo course?

[scenic matrix]

Any book to learn about mathematics from beginner to advanced?

[old elk]

x2

[finite gale]

both of those are very relative, and for different topics, you'll want different books

so you'll need to specify a bit on what you're interested in learning

[scenic matrix]

I want to start from scratch to have a solid foundation

[finite gale]

how from scratch do you want

if for pre-uni stuff, generally khan academy is the default resource

[cobalt arch]

Maybe specify what your strengths/weaknesses are so that we can give you proper advice

[scenic matrix]

Okay, thank you very much

[cobalt arch]

Is your elementary algebra good? What about plane trigonometry? Plane and solid geometry? If you answered yes to all of these questions then a calculus book would be a good next point. If you answered no then depending on your weaknesses you can find the corresponding resources to help you out.

For calculus spivak is a good choice if you want to get good at proofs otherwise a more computationally oriented book would be stewart or thomas or velleman

Start with calculus by stewart or thomas or velleman and see if you can do the exercises. If not then you are lacking something in your fundamentals of algebra/trigonometry and maybe geometry (although not as likely due to geometry not being a requirement for getting to calculus)

[rigid shale]

Can anyone recommend a well done graph theory book?

Since I'll be doing my preliminary reading for my puzzle game about graph theory

[magic spade]

Graph Theory by Diestel

[rigid shale]

How about a more introductionary text?

Seems im not yet proficient in decoding symbols that fast

[magic spade]

A First Course in Graph Theory by Chartrand

[velvet briar]

@lilac surge
Imo, worth getting better at linear algebra. It is bae.

Linear algebra done right is an easy to recommend book, if you're looking for a more rigorous treatment

I wish I had a good probability source. But I have read some of "all of statistics" recently and it added a lot for me

[fierce hedge]

"Probability and Statistical Inference" is a very good for both probability and statistics as recommended by my stat proff

[hollow shore]

author?

[fierce hedge]

Nitis Mukhopadhyay

[thick quarry]

Of mice and men John Stinebeck

[gray gazelle]

can never go wrong with the classic "Introduction to graph theory" by Douglas West, there's also a separate file with all of the solutions of the problems

[manic tendon]

Hey guys, i want a combinatorics book contains a treatment of sterling numbers

[gray gazelle]

check out "how to count" by Allenby and Slomson

[manic tendon]

Thanks

[misty mason]

hey guys, I am going into college (UK) at the end of the year so I was wondering if you had any recommendations on books so I could start learning sooner. Subjects like proof, complex numbers, matrices, further algebra and functions, further calculus, further vectors, polar coordinates, hyperbolic functions, differential equations, further numerical methods, further mechanics, and further statistics. Really anything to help me get a head start in maths.

[manic cairn]

“Further?”

Is that a UK thing?

I’d pick up Lang’s Basic Mathematics for most of the non-calculus stuff

[misty mason]

ye its just a more advanced version of each topic, its like taking maths for 2 subjects

idk how to describe it really

uh

instead of doing 3 lessons of math a week over 2 years you do 6 lessons over 1 year and then the second year is just higher math

[manic cairn]

Oh, in America every class is every day for an hour

and you get one math class a year

at least where I was from

[misty mason]

for college in uk you pick 3 subjects that you do for like 3 or 4 hours a week each, but further maths is a 4th subject that is literally just extra math. you do your math exam a year early then the second year is further.

[manic cairn]

is college not university?

[misty mason]

its not the same as uni though

no

college is 17-18

[manic cairn]

ah okay

Let’s move to #serious-discussion

[misty mason]

okie dokie

[gray jungle]

checkout andrew pressly full book elementary differential geometry, its what was used in my undergrad diff geo (curves and surfaces) altho idk if its "usual" , probably a good amount of places jump straight to manifolds instead

[lyric gate]

not really math but anyone know a good intro chemistry book?

[rustic grove]

Would anyone mind telling me if they have read Gamits' Topology, and is it any good. I plan on reading it as Sutherland is a bit dry (although I will keep it as a reference).

[rustic grove]

Ask here #old-network message

[graceful moon]

My school offers 2, the first one is essentially just an introduction and it covers
The Frenet-Serret frame
K forms and exterior algebra
Fundamental forms
Curvature
Geodesics
Integration
Guass-Bonnet and (briefly) generalised stokes theorem

The follow on full differential geometry course covers
Manifolds and bundles
Submersions
a fuller treatment of tensors
De Rham cohomolgy
A much fuller treatment of integration and stokes theorem

[gray gazelle]

that's a lot of content

[gray gazelle]

where should I start if I want to gain some basic diffgeo knowledge?

(before I apply for masters)

[graceful moon]

I mean it’s not so bad, the introductory course does essentially take about 6 weeks to start because you spend about 6 weeks just defining things. The class doesn’t follow a textbook however the professor reccomended, as a secondary source, Kobayashi “differential geometry of curves and surfaces”

The follow on course uses Lee “Introduction to smooth manifolds” but skips a few chapters

[gray gazelle]

I hear ppl talk about this book a lot, should I just read it from the beginning?

[graceful moon]

I mean it’s free online so it’s worth at least having a look and seeing if you follow, assuming you’ve taken the normal undergrad pure maths classes you should get on fine with it

[heady ember]

Everything is free online if you look in the right place

[gray gazelle]

which undergrad courses u mean?

[graceful moon]

Some basic topology and some abstract algebra (groups, rings and ideally a more abstract look at linear algebra) should be enough

[remote sparrow]

i could not find a book written by gamits. do you mean gamelin?

[remote sparrow]

when i took AP chemistry, we used brown, lemay, and bursten for part of the semester until we switched over to zumdahl and zumdahl. dunno if one is really better than the other, but the former was older.

https://www.amazon.com/Chemistry-Central-Science-Theodore-Brown/dp/0134414233

https://www.amazon.com/Chemistry-Steven-S-Zumdahl/dp/1133611095

[gray gazelle]

Is this worth buying? https://www.amazon.de/Maths-Book-Ideas-Simply-Explained/dp/0241350360/ref=sr_1_5?__mk_de_DE=%25C3%2585M%25C3%2585%25C5%25BD%25C3%2595%25C3%2591&amp;crid=18DKFOU5E6LAI&amp;keywords=math+book+english&amp;qid=1698342575&amp;sprefix=math+book+englisch%252Caps%252C125&amp;sr=8-5&_encoding=UTF8&tag=goodprodukt08-21&linkCode=ur2&linkId=36fdab5106e44c78e77f7ce5d0f8c96a&camp=1638&creative=6742">math

[rustic grove]

Ye, I must have been having a stroke when I wrote it -_-

[languid fossil]

does anyone know how to check if a book as an edition in another language ?

for example stewart's calculus : early transcendentals has an english and a spanish version

but I can't see other than the english version on the webpage or when I google it

I want to know if it has more versions

[halcyon zephyr]

Question: If I'm already familiar with competition math to a certian degree (as in, participated since a young age but never got exceptional results) would it be wise to skip most of the 1st volume of the AOPS book and go to the 2nd one, since it's theoretical contents are more relevant to me right now?

[finite gale]

Or you could just jump around

No one is forcing you to go in order of volume lol

Read whatever you feel you need

[halcyon zephyr]

Eh, sure, if I miss anything relevant I'll just flip through the book until I find it

[magic spade]

What is your opinion of Stewart's Calculus?

[charred osprey]

I recommend Thomas' Calculus over Stewart's

If it's your first run through Calculus, then Stewart is okay

[young light]

Sirs what is good measure theory book, Axler or Folland.

[charred osprey]

I'm biased towards Axler bc of his Linear Alg book so my vote is for Axler lol
New to Folland so I'll check that out too

Doesn't matter, it's all Calculus just start somewhere

It might be helpful to have both Stewart and Thomas as a reference while you move forward if one explains it worse than the other

[young light]

I also like LADR :)

good book

[charred osprey]

Thomas' later version for you though

[charred osprey]

Me too, not finished with it though

Newish

[young light]

I read it all it was good book and nice to read

[charred osprey]

Imo opinion, Steward gives you a view of Calculus that involves solving questions but not the why, and Thomas' gets closer to the why. Make whichever one that is your priority as the primary one

now to verify my opinion im going to double check my stewart book

[magic moth]

thomas apostol everyday anyday

then spivak

then baby rudin

[charred osprey]

yes, closer to it

[charred osprey]

p much what he said @young light

though take it step by step

[magic moth]

bartle and sherbert is nice too

less of a steep learning curve

[young light]

I see

[charred osprey]

Early versions of Thomas are good too

[magic moth]

apostol is really lightweight analysis

assuming u have taken trig and some shit

i forgot trig so i have not given it a chance but its only needed for understanding some stuff about the archimedian aproximation

or so i was told

[charred osprey]

trig

[sturdy shore]

folland is more advanced, make of that what you will

[charred osprey]

also need to patch up my trig

[sturdy shore]

both are great

[young light]

I see

[charred osprey]

lol wrong person

[sturdy shore]

if you aren't all that confident in your math maturity/analysis, go for axler

[charred osprey]

@gray gazelle

[magic moth]

this is probably a safe bet

[young light]

ye makes sense

[magic moth]

also

once ur done with axler or as ur going through it

pick any of the other books

[charred osprey]

which ones

[magic moth]

axler is considered really ez

spivak apostol

baby rudin

sherbert

[charred osprey]

for LinAlg?

[magic moth]

for analysis

lol

[sturdy shore]

huh

[charred osprey]

im going thru Axler for LinAlg

[magic moth]

ahh

[sturdy shore]

axler is meant to be read after books like spivak/baby rudin

[magic moth]

u can do lin algebra with apostol though

[sturdy shore]

oh this is a different discussion

[charred osprey]

two diff discussions happening rn

[sturdy shore]

I was talking about axler/folland measure theory

[magic moth]

lol

i remember apostol bringing up measurable sets in chapter 2

@gray gazelle thomas apostol

[charred osprey]

One was for Measure Theory as @young light was talking about and the other convo was @gray gazelle Is talking about Calc recommendations

[young light]

I see ye, I will probably look more into it, but if I don't think I can handle folland i'll go with axler

[charred osprey]

So which one for Measure theory?

I was referring to George Thomas, but I think @magic moth was talking about Tom. Apostol as referenced a second ago

[cursive orbit]

folland has more topics

[young light]

hi alphyte :)

[magic moth]

yes

what do u want to do?

[cursive orbit]

that being said, it's debatable whether it's worth learning those topics in folland vs picking up another reference for those topics

[magic moth]

try apostol imo

[charred osprey]

I can't vouch for Apostol but I trust @magic moth's opinion, so go for that. I've heard good things about the book as well

[sturdy shore]

yeah, like there's haar measure on folland but you can learn that from a harmonic analysis book eg
it has a section on topology, but you can just read a topology book for that

everything I've read of folland has been good though

[magic moth]

yeah

i have it physical

volume two is light blue

[cursive orbit]

also, axler's book has the advantage of being legally freely accessible

[young light]

I see

[cursive orbit]

what's up

[magic moth]

is calc 1 and linear algebra

[young light]

totally legal pdf

[cursive orbit]

the PDF of folland that you can get online is of worse quality than the PDF for axler

[sturdy shore]

well, axler's actually is legal

that too

[young light]

Ye that's true

[charred osprey]

Is this for the Measure theory book

[sturdy shore]

yes

[cursive orbit]

and arguably axler has a better choice of font than folland

[sturdy shore]

though I believe the latest version of LADR will be free when it drops?

[charred osprey]

yes

[young light]

I heard so

[charred osprey]

Next month

[sturdy shore]

imo axler measure theory is the gentlest measure theory book I've read

[fierce hedge]

Which would have a proper treatment of determinants using multilinear algebra

[sturdy shore]

just very good exposition for an introduction

[magic moth]

mmm

let me check volume 2 of apostol

[cursive orbit]

as of a semester ago I'm pretty sure the multilinear algebra section wasn't finished

[sturdy shore]

gentlest doesn't mean it doesn't cover a fair bit of ground though

and measure theory is inherently not easy ofc

[young light]

ye I imagine lol

[sturdy shore]

(from a ug background)

[young light]

nothing much, hbu

[charred osprey]

measure theory very exciting

You might enjoy Thomas' Calculus more then, that one has a lot more visualizations

[charred osprey]

Transcendentals are pretty helpful in general so my recommendation is early
It'll give you more examples to refer to during the calculus journey
I don't think this choice makes a major difference, but if you're struggling with stuff like logs and exponentials then switch to late

[coarse arrow]

Best books on introduction to proofs and logic also something that is not too long

[broken meadow]

hammack book of proof might be good

[dire torrent]

I've read Hammack's(and only that) and it's damn good.

[dire torrent]

plus it's free.

[trim estuary]

A bit out of the blue for a recommendation, but for anyone interested in developing some elementary mathematical thinking, I highly recommend that you read A View From the Top by Alex Iosevich. Iosevich is one of the most charismatic people I’ve met in the math world, and his ability to teach is unparalleled. Unlike a lot of other math books, this one deliberately goes through the process of developing the methods and techniques taught as though you were the first to prove them.
https://archive.org/details/viewfromtopanaly0000iose/mode/1up

[graceful moon]

Liebecks “A concise introduction to pure mathematics” would be good, it’s short, enjoyable to read and gives you a taste of lots of different areas of maths but all just to serve improving your proof writing and problem solving

[misty geyser]

Any nice books/papers that explain fractal geometry (especially with its applications in Biology)? Thanks.

[timber holly]

I would say Jay cummings and How to Prove It: A Structured Approach by daniel J

Love how to prove it

[stray veldt]

if you want something that is short, i have written a ~30 page introduction, that is pinned in #proofs-and-logic

[timber holly]

also yeah pins has amazing suggestions I own some of them

[coarse arrow]

Thanks for all the suggestions 🙂

[gray gazelle]

Can someone pls recommended me a good pre calculus book that I can buy?

[slender night]

I’m looking for a book that can be used as a refresher of foundational rules/formulas/etc. I’m currently in cal 1 and find myself forgetting what should be simple algebra rules.

[hybrid torrent]

i needed this and ended up getting a few schaums outlines and some older books on ebay. I like the content of the schaums but damn is the paper quality crappy. I would probably get some schaums outlines off ebay or half price books and throw them in the trash when you're done

[slender night]

Thank you! My gf and I love half priced and I just grabbed 2 books for math the other day.

I am excited to be so into math and reading again

[narrow relic]

Thanks!

[crimson ravine]

what book would you guys reccomend for abstract algebra? im an undergrad and have very little experience with abstract algebra but am comfortable with abstraction, the axiomatic method, etc.

[crimson ravine]

ive heard that it's a bit too tough and i did look at the pdf and didnt like what i saw in the first chapter

[formal bronze]

No, it isn't 'too tough'

It is an introductory text

[crimson ravine]

ok then im just dumb then

[rare estuary]

How is it compared to Artin?

[hollow shore]

gallian is a good gentle text for algebra

[crimson ravine]

ive done the first chapter of artin fully and i seem to prefer it to dummit and foote

[formal bronze]

I'd say Artin is more terse than Dummit and Foote. I found it a bit harder to learn from

[hollow shore]

no lmao

[rare estuary]

I was kinda leaning towards it because I wanted something with more LA

[formal bronze]

If you're already studying from Artin then I don't think you need to switch books

[crimson ravine]

yes unfortunately my library does not have gallian (it does, but someone has it on hold or something so i cant borrow it)

[crimson ravine]

i see

so i continue with artin?

[formal bronze]

Yeah, no reason not to

[hollow shore]

there is always that library

[daring lake]

artin is good too

[finite gale]

rotman is nice

d&f is very wordy

[daring lake]

i have read a good chunk of both d&f and artin, i like them

[daring lake]

true, also a huge problem set after like every 4 pages

[hollow shore]

https://youtube.com/playlist?list=PLelIK3uylPMGzHBuR3hLMHrYfMqWWsmx5&si=8lDR1YVmtd6UE8zI

this video series follows artin

[crimson ravine]

oh ive never come across this surprisingly

ill check it out

[crimson ravine]

i suppose ill stick with artin and refer to that video series then

thanks

[fierce hedge]

I have been following them and can vouch for the quality of the videos. By quality I mean quality of the contents cause video quality is garbage asf

[hollow shore]

I have a thing for old quality videos

[lilac yew]

Hello world, can I have some recommendations on integrals calculus theory ?

[sage python]

Are you just saying theory to mean the subject? Or do you want to see stuff with proofs?

[copper axle]

Hi! Can anyone recommend some learning resources that cover conic sections/hyperbolic functions in depth? Thx!

[dense copper]

Hello everyone

I need to improve my non-rational maths like number theory, geometry blah blah blah... for advance. Some book recommendations?

Please reply

Pin me if you answer

[rain wren]

wtf is non-rational math

I thought all math was rational

[graceful moon]

$$\pi$$

[hasty eagle]

Nope

[marsh pine]

Math with irrational numbers

[velvet rose]

Hi, I'm in my first year of linear algebra. I'm looking for a good book to study that is beginner friendly and that as answers for the exercises

[remote sparrow]

#book-recommendations message

[velvet rose]

thanks

[hearty steppe]

Linear Algebra and it’s Applications by Lay is probably my favorite for the most part when it comes to most broken down linear algebra books

And you only need to go through barely half the book to get the gist of the generalities you need to understand for matrices and systems of equations

[remote sparrow]

I recently found this book on mathematical logic while browsing through my library; it seems pretty good.

[orchid mortar]

@remote sparrow IDK if I asked you before, but how do you organise your digital library?

[remote sparrow]

i don't. it's all in a single folder

for the majority of the books anyway

[orchid mortar]

so you grep or sed or ls + regex?

[remote sparrow]

some light novels i download from the internet come in folders already so i just leave them there

[remote sparrow]

what are those

[orchid mortar]

linux stuff

[remote sparrow]

i use windows

[orchid mortar]

same but 1 massive folder is not searchable tho

[remote sparrow]

idk windows search is a tad slow but i remember what i'm looking for

[orchid mortar]

This is my 'matrices' folder
The problem with subfolders is basically there's going to be topic-overlap and then trying to find a primary topic is not always easy or possible

I'm also worried about eventually having multiple copies of one book

[remote sparrow]

i have never run into this problem

and i have several thousand ebooks

[orchid mortar]

several thousand

omg

mine is 1,473 Files, 161 Folders

[remote sparrow]

yeah it's like 35.8 GB of files

[orchid mortar]

Looks like I'm far behind :P

I'm much more picky on fiction stuff/non-educational books tho

[remote sparrow]

btw garcia and horn have a recently released second edition. a pdf doesn't exist for it yet.

https://www.amazon.com/Matrix-Mathematics-Cambridge-Mathematical-Textbooks/dp/1108837107

[orchid mortar]

[dusk wind]

This exchange is quality, it's fine though linux isn't used that much anyway

Only other way you could organize it is by being a keyword God or having some software that categorizes automatically for you somehow but that might be worse than the 1 folder solution. Name and year is enough in most cases

[dire torrent]

Are MirBooks legit? like are they actually giving e-versions of their books for free? is it their actual website?

[magic moth]

u mean mir editorial?

theres a editorial from the ancient USSR called MIR with really old books that u can find on ur own (and its pretty much the only way to get them)

[white pilot]

I just found this textbooks website: https://math.libretexts.org/. You can view the contents as websites or download them as (beautifuly) formatted books.

[trail hemlock]

omy i loooove libretexts they have so much not just for math

quick question: are there any books for linear algebra, calc3+ that are similar to how the AOPS books teach u stuff. not really contest prep, just a very intuitive book. im a novice so mb if this question is dumb.

[dusk wind]

This was posted a few posts up, but yeah the quality of the books are usually pretty good. Not a fan of their strange pdf backlink system, they take open books and point them back to their site

[dusk wind]

Try Jim Hefferon and mecmath.net/vectorcalculus

[trail hemlock]

ty 🙏

[remote sparrow]

https://mirtitles.org/

?

are you talking about this website

you need to link the website

[gray jungle]

kreyzig book introductory functional analysis should cover normed spaces in a friendly way @lilac yew

and in terms of integration calculus just any calculus book , altho i have to say what a weird request you ask about a advanced topic like topology on normed spaces then integral calculus ? what gives

are you asking about integration in normed vector spaces?

aka vector integration

[lilac yew]

Yes

[magic moth]

forget rudin

mir books are hardcore

[gray jungle]

do you know measure theory?

[lilac yew]

No

[gray jungle]

im asking because i want to know if you mean the calc 3 vector valued integration or the functional analysis vector valued integrals fron measure spaces to TVS

any calc 3 book should cover integration you need on R^n

beyond that its a bit messy

[lilac yew]

Ok

[lilac yew]

I don’t understand please

[old elk]

How can you send a screenshot?

[manic cairn]

What books on formal logic would be good for a layperson?

Where they would come out being able to prove trivial statements about first-order theories, knowing the difference between syntax and semantics, understanding goedel’s completeness theorem, etc.

[hearty steppe]

Can someone recommend a representation theory book that doesn’t get too weird or formal with exposition? Something with the flavor of Folland’s real analysis?

It’s like I went thru two books feeling kinda meh about the exposition.

I started going thru Tapp’s matrix groups for undergraduates and the first chapter was a great review of linear algebra concepts but my ass is getting handed to me in the second chapter

[remote sparrow]

a person interested in this material is not likely to be a layperson, if this layperson is, broadly defined, someone who has little to no experience with proof-based mathematics

[dire torrent]

yes and thanks.

[manic cairn]

interested while reading or interested to start reading

[narrow relic]

You might check out Chapters 1-5 of this: http://logic.stanford.edu/intrologic/public/chapters.php

[narrow relic]

That book is for a course described as "Appropriate for secondary school students, college undergraduates, and graduate students"

[dim sierra]

Ok that’s not true, Stewart doesn’t for example

And that’s one of the most popular ones

[mighty anchor]

any engineerring math book recs?

[vital bane]

sky

[mighty anchor]

Ye

[vital bane]

"mathematical methods for physicists and engineers"

famous book

[mighty anchor]

Hmmm

[vital bane]

very good

covers lots of topics

[mighty anchor]

I’ll check that

[narrow relic]

I just checked this book out today and it looks great. I'm actually probably going to switch to it from Carothers

[small cobalt]

Content is good and well treated but the exposition is dry

[fierce hedge]

How dry are we talking about, Rudin dry or Lang dry

[small cobalt]

Closer to rudin than lang

[gray gazelle]

y'all heard of Neural Networks From Scratch?

https://nnfs.io/

that's the only math book I got

[gray gazelle]

I saw the video series is also quite helpful! :0

[lean nebula]

@stuck zephyr

help

i cant message there anymore

what did i do

how do i stop studying role

,iamnot studying

[stuck zephyr]

do ,iamnot studying

[hasty eagle]

Removed the studying! role from you.

[lean nebula]

too easy

[stuck zephyr]

ye

[gray gazelle]

I loved it

[gray gazelle]

Such a shame the video series was discontinued, though, since it's so well done...

[hearty steppe]

I don’t mean to be annoying about asking for recs as I can understand other people are getting helped but… when anyone gets around to it… I need recs for these

#book-recommendations message

#book-recommendations message

#book-recommendations message

[gray gazelle]

yup but I decided to follow its trail

u knw like went hunting for research papers

and tried to understand them

but exams came so not been able to continue that passion of mine

[gray gazelle]

Ahh, that's unfortunate. Hm...

[gray gazelle]

man It's my finals tomo

first math paper

day after math is done

by nov 7th all my finals are over so I can resume that

🤓

[gray gazelle]

Ooh, I could recommend some articles I found very helpful on deep learning, for when so!

[remote sparrow]

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

https://www.amazon.com/Classical-Mathematical-Logic-Semantic-Foundations/dp/0691123004

[gray gazelle]

yes pls

[gray gazelle]

good book?

[remote sparrow]

it's not a link to a book

[gray gazelle]

This isn't really an article, but the series from which this lecture was from was up there with the most helpful resources I've come across:
https://www.youtube.com/watch?v=dB-u77Y5a6A
There's also this that I found to be nifty:
https://ai.plainenglish.io/calculus-for-backpropagation-doesnt-have-to-be-scary-16595d76e744

[hearty steppe]

Maybe I need to spend more time in algebra land… could explain my difficulty with representation theory/spectral theory

I admit I guess I became overconfident going mostly the dynamical systems route and a bit of analysis but did not really take a step back to finish working through some linear algebra and algebra focused books I felt overconfident about

[ionic portal]

is basic algebra by knapp good

[fierce hedge]

#book-recommendations message

[gray gazelle]

does anyone have recommendations for a problem book in abstract algebra?

preferably graduate level

[sturdy shore]

seems like the latest edition of LADR is finally here, available here online
https://linear.axler.net/

the new section 9 looks good

[remote sparrow]

@sage python revised treatment of determinants in LADR

[remote sparrow]

dummit and foote has a lot of problems in it

https://4chan-science.fandom.com/wiki/Mathematics#Problem_books

also check here

also feel free to google qualifying/comprehensive exams in algebra at various graduate institutions

[sage python]

Okay Axler has gotten rid of one half of the brainworms

The other half is characteristic polynomials

[remote sparrow]

so is ladr just the best book on linear algebra now? i mean, its price is definitely better than friedberg.

[sturdy shore]

I don't think Dami's criticism about char polys on LADR was about him not talking about it, because they were obviously in the prev edition also

[remote sparrow]

yeah i know

he said it was weird

and very nonstandard

paraphrasing

[sturdy shore]

Both the third and fourth edition initially define the char poly for complex vector spaces in the same way

[sage python]

Yeah

[sturdy shore]

here

this is fourth edition

[sage python]

I guess the question becomes, does he attempt to do it in the real case by reducing to the complex case?

[sturdy shore]

to be clear I don't think there is anything wrong with this definition, but the third edition did some dumb shit to define it in the real case

[sage python]

Because that's the probably the most moronic choice

[sturdy shore]

I think this edition waits until the determinant to define it for real vector spaces

[finite gale]

why does header look like it was pulled out of google translate

[sturdy shore]

yeah, so new edition defines the determinant and then char poly for real spaces

[sage python]

Okay wait maybe this book is now largely fixed

I wouldn't quite call it the best because it focuses on R and C, and I do think the best book would talk about general fields and give CS applications to stuff over finite fields

Also I do think the characteristic polynomial being product of (t-lambda_i)^{dim generalized eigenspace of lambda_i} conceptually should be a theorem rather than a definition

But this is no longer egregious

[gentle arrow]

did axler add a cat with a revision

[remote sparrow]

one of his cats died

moon

[gentle arrow]

WAIT MOON DIED?

[remote sparrow]

from a sudden blood clot

yeah

[gentle arrow]