book-recommendations

[gray gazelle]

though khan academy is good for intuition

[hearty jetty]

@gray gazelle can you suggest any online courses?

[gray gazelle]

If you’ve not had exposure to pure mathematics before, Khan Academy is fine to teach you how to use linear algebra

i self-studied so i don't know about online courses, but you can use the MIT OCW

If you want to do physics or engineering, that’s all you really need (for the most part)

but remember to find exercises and actually do them, that's how i self studied LA in eight grade

[hearty jetty]

@gray gazelle I'll be starting college in feb 2022, Bachelor's in Mathematics.
Meanwhile I figured, heck why not

[cursive orbit]

Axler is also an option

[gray gazelle]

If you want to learn it proper-like, Ive heard good things about Axler, even if he wages war against determinants

trust me, friedberg insel spence's book is better

[cursive orbit]

You should probably supplement axler with something that teaches you how to compute things though

[gray gazelle]

i've read axler's and it's not that good compared to friedberg insel and spence

[cursive orbit]

Because he doesn't go over row-reduction or anything like thaf

[gray gazelle]

Hoffman and Kunze is great computational based book

but trust me when i say that doing the exercises and correcting mistakes is extremely important if you want to self study

i didn't do it in eighth grade and it was a nightmare trying to remember key points

[hearty jetty]

I got a book called 3000 solved problem for seymour lipschutz

[hearty jetty]

I use it specifically for problem solving

[gray gazelle]

anybody have a good book on theory of equaitons

[valid moth]

It's worse

[hearty jetty]

@valid moth about 3k problems?

[valid moth]

I got 3000 problems but a b aint one

[hearty jetty]

Whattt!!!

[sinful crag]

My recommendation is to do it twice, basically. Once with a matrix theory approach and once with something proof heavy and more abstract like Axler's LA Done Right (probably my favorite math text). If you want some accompanying lectures, the MIT OCW Gilbert Strang ones are great for the former: https://www.youtube.com/playlist?list=PL49CF3715CB9EF31D . And https://www.youtube.com/playlist?list=PLflMyS1QOtxwiN5oOuyY4W_8fZlTTnRcF follows Axler.

[analog pollen]

Strang is really good

Axler is for a second look into Lin alg

[sinful crag]

I don't like Strang's book but I love his lectures

[analog pollen]

No point of learning Lin alg without determinants

Yea strang’s lectures are great

[sinful crag]

My first community college LA course used David Lay's LA book which I found to be pretty good for a matrix heavy approach. I like it more than a couple other texts I've read.

[analog pollen]

Never heard of it

Still formally have to learn Lin alg lmao

[sinful crag]

If you're really good at proofs/higher math, Steven Roman has a channel of free lectures as well, although it's very set and abstract algebra heavy because it's intended for advanced undergrads and beginning grad students https://www.youtube.com/playlist?list=PLiyVurqwtq0ZPlwaAojwrWLjPP9ZKlJ_N

My goto LA references are Axler's LA Done Right and Roman's Advanced LA but that's from the perspective of a pure mathematician because they are sparse (pun intended) on applications

[hearty jetty]

You guys are so helpful.
Thankyou All

[gray gazelle]

^^

[narrow talon]

Lmao based

[cursive orbit]

Is that a meme or actually good?

[narrow talon]

Meme mostly

But none of the books are bad picks mind you, just that things get a lot more sophisticated than you’d reach with those 3 books

[marble solar]

It could be the case that the /sci/ guide to riches is the pre-requisite mathematics to doing quantative finance

Or what they'd expect you to know and be familiar with when you interview

[narrow talon]

The third one is also just super hard, at least in my experience it would be a bizarre read without any prior finance knowledge, a standard book on options/derivatives then maybe Joshi would be good background for KS

[queen copper]

Do you have one like this but for statistics?

Hi, could anybody recommend me good introductory books for probability and statistics?

[narrow talon]

How elementary and to what end?

@queen copper

[queen copper]

I'm starting my first semester of cs, and I want to have a good foundation for data science. And also, just curiosity.

I also did 2 semesters of physics before I switched majors, but I didn't put too much attention to that subject.

[narrow talon]

I believe Ross has a book called "a first course in probability" which may be good. I like the book by Severini "Elements of Distribution Theory" for probability geared specifically towards stats, though it's probably best as a second read.

As for stats aimed at data science, I would say not to go looking for traditional stats books as much. There is a lot of overlap between stats and ds of course, but the language and concerns between the two fields are very different. The book by Provost called "Data Science for Business" is perhaps the best intro to the subject I've seen. Don't be fooled by the title, everyone interested in data science should read it

From there, if you're interested in ML the classic text is "Introduction to Statistical Learning," as well as its big brother "Elements of Statistical Learning." ISL is a more enjoyable book, ESL is a better reference and not a book to really read all the way through. "Understanding Machine Learning: From Theory to Algorithms" by Shalev-Shwartz is maybe the most popular reference I see for ML nowadays

Hopefully that's what you were looking for
I know some traditional stats books if that's what you want, and can point you towards some deep learning resources (though there's no good textbook I like for that)

[queen copper]

Thanks!

[gray gazelle]

guys I am looking for a calc book

[queen copper]

So, should I focus more on books for DS?

[gray gazelle]

I am thinking of doing Simmons

Any recs?

[queen copper]

I just want to have a good foundation, not just some random python course, lmao

[sinful crag]

Ross is what my probability theory course used and I think it's a pretty good text

https://faculty.math.illinois.edu/~kkirkpat/461-2019.html

My professor had excellent notes and hw with solutions for accompanying Ross as well

[narrow talon]

Yeah probably, at least the book by Provost which I mentioned.

A bit of parametric statistics is useful for sure, perhaps the book by Wasserman (?)

Unfortunately there's no book on statistics which I really like, and there's a pretty large gap between what you may find recommended here (Casella-Berger) and what's used in practice in applied or research-level stats.

Not to say that CB is bad mind you! There's some good stuff in there

[cloud trench]

What's a good book on groups, rings and fields? + in relation to cryptography

[analog pollen]

What kind of calc book are you looking for?

Advanced or more beginner friendly

[stark creek]

Any opinions on Bredons topology and geometry book

[tepid ravine]

goodfellow et al not up to par?

also you're missing bishop's book

[narrow talon]

Lmao, Goodfellow is sitting 2 feet away on my desk rn.

I like Goodfellow for sure, but it's starting to show its age. The covering of CNNs and RNNs is pretty good, the regularization, optimization, and practical methodology sections are also quite good. Everything that is included is good, but also it misses a lot of stuff that's totally standard now. Multiplicative modules are totally shortchanged, and by extension transformers aren't talked about at all. It's also a pretty classical outlook and doesn't cover much from the energy-based perspective (though the inclusion of chapter 18 on the partition function was quite nice, it's not devoid of EBMs but they're not as present as I think they justify nowadays)
Overall I'd it's the best deep learning book currently out there, but it's due for an update. I also think the target audience is a little unclear, why include linear algebra lmao

Bishop is nice, especially for the time series stuff at the end imo. Murphey is also a classic. Just didn't want to deal with the probabilistic perspective.

[gray gazelle]

does anybody have pdf of Euclidean Geometry in Mathematical Olympiads by evan chen

wait i have it

[crystal lion]

lol what was the point of this

[gray gazelle]

i couldn't find electronic version but it accidentally did

[crystal lion]

🍪 🏅

[gray gazelle]

a good starting point to learn

[brisk ice]

like calc 1, 2, 3?

like single variable?

or multivariable?

i mean for not proofy calc stuff , khan academy has their ap calc bc which was fine

[gray gazelle]

yeah

anything besides stewart and thomas lmao

[brisk ice]

I mean if it's just cal 1/2 I thought Khan academy did okay job. There are also online lectures by mit for both single variable and multiple variable calc with notes, lectures, problem sets, exam

Basically a full complete course available online

And there are plenty of YouTube playlist I assume of various people teaching it

[gray gazelle]

Okay

I will go with the MIT playlist

@brisk ice MIT has these calculus with theory courses which seem more rigorous. Should I do follow that up with Khan Academy's AP Calc BC videos?

[brisk ice]

Might better just to follow it with their own single variable could but those are kinda different?

One is more proof based so I assume you need to understand proofs also

[brisk ice]

Says "The course assumes knowledge of elementary calculus." So idk if maybe it would be better to just do calculus without the proofs or not If you are completely new to it

[past ice]

Velleman would be the standard intro calc book in my fantasy utopia land. It's easier than Spivak and more compatible with what general audiences might expect, but it's a rigorous book that a pure math student would still benefit from (unlike the usual Stewart/Larson fare).

[gray gazelle]

this sounds like what I need. would give it a shot!

[sage kelp]

Larson or Stewart are pretty standard

[polar pasture]

is that book enough to master euclidean geometry ?

[analog pollen]

Stewart is also decent

Don’t recommend the mit lectures,cuz they skip over a lot of things

[gray gazelle]

yeah

this book talks about feynman's trick

[cursive orbit]

Like what?

[eager stump]

i mean as long as you have a table of contents the mit lectures are not bad

for what they cover

[frosty wyvern]

Does anyone know where I can get a copy of McOwen's PDE book? Thanks!

found one.

[analog pollen]

There not bad, they just don’t cover everything what’s in a normal calc textbook

Also it’s in a kind of weird order

[analog pollen]

Epsilon delta stuff, limits weren’t covered much (only the concepts, not how to), Riemann sums where also barely touched. Etc.

Imo its a lecture series for someone who already has some experience in calc

[gray gazelle]

God I effing love meditating.

sorry, just had a really good session that's not what I came here to say.

So, I just ordered Calculus by Spivak.

Any tips if I get stuck?

[analog pollen]

I’m seeing now the course went over integrals first and then Riemann sums lmao

[analog pollen]

This discord

[gray gazelle]

lol.

Sure, but I don't wanna overuse the help section, yknow?

[analog pollen]

Just ask if you have a question

[gray gazelle]

Aight.

[analog pollen]

Bro that’s what the help section is for

Don’t worry about spamming haha

Just ask when the channel is not occupied

[gray gazelle]

Well dude, you got to bare in mind....At my university's discord I used the help section a LOT , the TA's basically labelled me as a moocher who never does his own work and wanted to be spoonfed.

I really don't wanna go through that again.

Feel me?

[analog pollen]

This is not your university’s discord haha

I think no one will mind

[gray gazelle]

I'm just saying, it would hurt me on a very deep level if people at Stanford got sick of me asking for help.

[analog pollen]

Bro don’t worry

What do you care about what other people think lol

[gray gazelle]

Like a lot, lol.

[analog pollen]

If they have a problem with you, it’s their problem

[gray gazelle]

Dems da breaks of bein a social creature.

[analog pollen]

Don’t worry about it to much

[gray gazelle]

Well, that's what the 50 minutes of meditation and self help books help with so you're mostly right.

[pale sand]

does anyone know a good book for geometry

[maiden slate]

the elements is a classic

[pale sand]

thank you me and my friend were getting stuck in geometry alot

[quick hornet]

i feel like the elements probably isnt appropriate for a modern high school class lmao

[gray gazelle]

not with that attitude

[sharp latch]

It’s where my high school taught geometry from. First semester was elements book 1 and parts of 2/3/4, then the second semester was a more standard high school geometry curriculum. Helped me fall in love with proofs, but I would take a look at the book as a curiosity rather than use it as a supplement

[analog pollen]

Damn getting real textbooks in high school

[maiden slate]

it was good enough for centuries

[whole rain]

yeah and people still consider Rudin good enough

so I don't think what people consider good enough is a good way to measure how appropriate is a book

[quick hornet]

sure, and high school geometry classes are not built like the classes of centuries past.

the elements never talk about, say, surface area

if all you want to learn is proofs, then sure, its sufficient at that

[eager stump]

i think the elements can be great to have for inspiration at minimum

just the idea of people coming up with great ideas with a limited tool set

[dapper root]

If my teacher brought out the Elements to teach me I’d do a flying knee on them

[eager stump]

that's impressive that you have that move in your rep

[quick hornet]

do you gain 1 energy at the start of the next class?

[wraith oracle]

hey guys how is mathematical methods for physics and engineering by riley, hobson and bence

is it good for self studying

[analog pollen]

Depends

It’s good if you are using it with studying physics

But for learning something completely new it’s not so great

It’s a reference

@wraith oracle

[lapis sundial]

I had it for first year physics and found it a decent reference - mostly used it for the problem sets/exercises - and I think you could use it for self-studying if you wanted to (I did a bit when I was into physics more)

But it's very much aimed towards physicists/engineers, focusing on results rather than rigour/abstraction

[analog pollen]

Tbh you shouldn’t learn new stuff like for example calculus from that book

Or Lin Alf

Alg

It just lacks

But a great reference for something you already learned in the past

[wraith oracle]

what math book do u suggest then for self studying for a physics major

cuz im going to physics major next year

so i need to prepare myself

[flint forge]

Khan academy

[gray gazelle]

Isn't Khan academy basically high school math?

[flint forge]

that is what i would suggest reviewing before starting a major, yes

[velvet briar]

Nah Khan covers calc and linear algebra as well

You've got a lot of choices for those, though

[gray gazelle]

Preparation for doing a physics major: meditate and come to grips with the reality that you may be stuck doing dumb calculations for the next 4 years

[static crest]

the real preparation is to come to terms with the fact that you will unironically have to write

[hasty eagle]

Dance of the Jade Demon God

[static crest]

and not throw up

[cursive orbit]

[halcyon garden]

Hey is there a functional analysis book that focuses on foundations of qm and applications in numerical analysis that is accessible to someone with just real analysis and linear algebra under their belt?

[gray gazelle]

i suggest granddaddy rudin

[gray gazelle]

a book on multivar calc?

from partial derivatives to greens theorem idk

maybe a book isnt really needed at all

[solemn rover]

stewart's calculus

[broken meadow]

anyone know any good texts on calculus of variations

[solemn rover]

someone already answered your question btw idk if you saw

gelfand and fomin

[broken meadow]

oh

i didn't see sorry

ty

[analog pollen]

Taylor has 2 solid chapters about it

If you are a physics major

[gray gazelle]

hah, i cannot let you shit on metal so easily

[analog pollen]

What

Lol

Is he a math major?

[gray gazelle]

at least, this is what i recalled

[analog pollen]

Oh my bad lmao

[sharp latch]

Does anyone know of a good book on enumeration/combinatorics that reviews the basics and goes into like basic graph theory, competition problems, etc? I took a discrete math course like a year ago and got a brief introduction

[eager stump]

a walk throught combinatorics (bóna)?

[whole rain]

Any recommendation for an intro book on diophantine approximation ? 👀

[buoyant flare]

Does anyone have favourite math books?
Non-textbook

[gray gazelle]

Mine is Fermat's Last Theorem by Simon Singh

[buoyant flare]

Thanks for the suggestion

Its reviews are so positive for a math book

[gray gazelle]

Also Polya's "How to solve it" is good

[buoyant flare]

That one i am familiar with

I never actually read it

But it is also something iv'e heard is worth a read often

[whole rain]

After some search, I found Approximation by algebraic numbers by Yann Bugeaud, any thoughts on this book ?

[tiny karma]

Quick question:

What's the difference between Elementary Analysis and Understanding Analysis by Abbot ?

[misty wyvern]

I never heard of the first one but know the second.

You really should be able to start with the latter.

[gray gazelle]

What would be the next logical step after finishing spivak calculus? Learning linear algebra from a separate book then multivariable/vector calculus or just going through this book Vector Calculus, Linear Algebra and Differential Forms: A Unified Approach

[eager stump]

not strang

good lectures but i'm not the only one who's down on that book

[ancient hull]

Anyone know a good differential equation book?

[marble solar]

Boyce and DiPrima for ODEs

[ancient hull]

Appreciate it, what makes it so good though?@marble solar

[marble solar]

Easy to read, good problems

[ancient hull]

Alright ill try it out

[gray gazelle]

Letters to a Young Mathematician by stewart

[fossil badge]

Gamma: Exploring Euler's Constant by Julian Havil

[marble solar]

I'm a big fan of Boyer's history of calculus

[pine iron]

What should I start with as a quick intro to advanced math (up to Calculus)? Currently comfortable with everything up to & including 2nd year Algebra.

[sharp latch]

Most people refer to Khan academy

[pine iron]

Oh, their material is awesome, completely forgot about them. Thanks!

[grave egret]

I am reading through Duistermaat and Kork's book. What book should I read next in order to be able to follow on with the book "Monopoles and Three-Manifolds"?

[still umbra]

I've done a differential equations + pdes course, I was wondering if there are any good books on modelling which someone could recommend

I don't really like physics applications (but willing to recognize that most modelling problems are physics based), so if there are any good books on modelling which aren't physics focused

that would be sweeet

ty

[lime sapphire]

Opions on knapp basic algebra?

[gray gazelle]

any good starter books for algebra?

[tulip blade]

What kind of algebra?

[gray gazelle]

I don't know. just basics and introductions.

Is Terrence Tao's book on Analysis good for like studying some basic calculus along with analysis?

I want to learn differential and integral calculus along with analysis

I don't really want a separate book on calculus

So yeah

I actually want to move from little knowledge of calculus (basic stuff, I haven't read a whole ass book on it or anything), to stuff like Real Analysis

[cursive orbit]

Why not learn them concurrently? Afaik, most anal books (including tao) won't teach you the computational technique that a calculus book will teach you.

[narrow talon]

Err, why learn math modeling in and of itself? It seems like numerical methods would be a better idea, or if you have an application in mind just look for modeling books focused on that application, like mathematical biological/chemical/financial/blah modeling

[gray gazelle]

Alright I guees cause Tao's analysis book seems like a more rigorous or pure math thing, doing calc will probably be a bit more useful, will do them concurrently thanks for the suggestion. Book recommendations for it?

Also I don't really want to watch lectures because I feel more comfortable with a book so one which is readable for a first course will be really appreciated.

[sharp latch]

What level of calculus are you exactly at to the best guess?

[past ice]

Zorich will teach you :)

[analog pollen]

Spivak

[gray gazelle]

have you done zorich before?

[past ice]

I went through a few select chapters after an analysis sequence (which used rudin) and learned a lot. Zorich's extensive treatment of multivariable is a particular highlight.

[fluid bay]

has anyone here heard of folland's real analysis. how is it?

[solemn rover]

folland's is a standard in a first course in graduate level real analysis

it is fine

I liked it

[gray gazelle]

maybe because i read lang's real and functional analysis, integration of real valued functions where you do all this fucky shit where you split it into a positive part and a negative part makes me cringe

[cursive orbit]

I think that's standard, not just Lang

[gray gazelle]

you are saying what is standard? i'm saying lang does not do the fucky shit

[cursive orbit]

oh

[gray gazelle]

folland does the fucky shit

[cursive orbit]

how does Lang do it then?

[gray gazelle]

you consider functions that you integrate generally as functions f: X -> B, where X is the measure space and B is a banach space, and you basically define the integral as the limit of integrals of simple functions that approximate f

then, you recover integration of real valued functions by taking B=R, and you didn't use the order structure of R, only its banach space structure

[fluid bay]

Don’t know any of that stuff yet but indeed that does sound better!

[cursive orbit]

I like it because you can just prove stuff for nonnegative functions without having to worry about any weird sign shit, and then you get it for all integrable functions automatically

[gray gazelle]

as much as I can learn but for now I guess I will do Tommy 1

[sharp latch]

If you’re really new and/or want an easy read that builds a nice foundation for the concepts, try Silvanus P. Thompson’s calculus made easy. I used it when teaching myself calculus and it just helped everything make sense

[sage python]

8da I guess Lang's treatment is probably cleaner but the "fucky shit" I think is largely standard so

[graceful lynx]

Thank you. I have also taken a great liking to 3 blue one brown YouTube channel to have concepts visualized. I will look into that book as I need to brush up on calc for my schooling

[gray gazelle]

looks like a good book, will probably do the first couple chapters from there just so you know I have some experience in rigorous math and mathematical proofs, not really a beginner, I am more of a MO student, so like a more rigorous thing is what I wanted. So I just hopped on to math overflow and Tommy 1 was mentioned there. Opinions?

I know functions, functional equations, limits and stuff

[gray gazelle]

No solutions to either of zorichs analysis texts 😨

[gray gazelle]

Really? One of my upcoming classes uses it.

Yeah

I couldn't find any

[distant stirrup]

Any book recommendations about linear algebra?

[candid obsidian]

gilbert strang

"linear algebra done right" - sheldon astler

intro to linear algebra - gilbert strang

[prime oak]

what books would you guys recommend for vector analysis

[analog pollen]

Use Spivak

[gray gazelle]

is A First Course in Abstract Algebra with applications by Joseph Rotman a good book?

or Contemporary Abstract Algebra by Gallian?

[cursive orbit]

.Here's a listing of common algebra books.

I seem to recall that you said you were in 9th grade, in which case I'd recommending learning linear algebra before abstract algebra

[gray gazelle]

how much linear algebra tho

i only learnt the necessary for multivariable calculus

and watched 3b1b linear algebra playlist

oh i think ill get artin

i recall reading that it guides you through linear algebra and abstract algebra

[cursive orbit]

I'd say learn linear algebra at least to the point where you're familiar with linear maps, surjectivity/injectivity/invertibility of linear maps, product + quotient spaces.

[gray gazelle]

i see

artin's algebra will guide me until that point right

[cursive orbit]

artin does a fair bit more than that

[gray gazelle]

awesome

[cursive orbit]

so yes

[gray gazelle]

thanks for ur help!!

appreciate it

[hallow lark]

Anyone know a good book for college algebra?

[cursive orbit]

I'd just use khanacademy

[hallow lark]

It has a college algebra course?

[cursive orbit]

no, but most, if not all, college algebra topics should be on there (depending on your specific course)

[hallow lark]

Oh ok ty

[gray gazelle]

should i get artins algebra first or second edition

first ed is from 1991 and the second edition is from 2013 or so

[cursive orbit]

unless the first is cheaper or smth, I don't see much reason to do so

[sage python]

^

[buoyant flare]

thanks

[buoyant flare]

and thanks

@sage pythondude what happened to sloth

[sage python]

He's an abelian pitbull rn

[gusty gorge]

Does anyone have some good recommendations for a book on Lie groups and Lie algebra? The book i'm currently using introducing the topic is skimming over and i'd like to get better knowledge of it

[stray veldt]

Stillwell for a nice and easy read, otherwise Godement

[gusty gorge]

My book is Stillwell lol, but not the specific Lie theory one

[stray veldt]

stillwell's naive lie theory book is one of my favorite math books

but its not too deep

[gusty gorge]

Yeah he recommends it in his Mathematics and its history, but I wanted a second opinion because conflict of interest y'know

[stray veldt]

are you learning this for a class or for fun? and what is your background?

i like stillwell because it basically only requires linear algebra as prereq

also he talks about the history of the subject which i like

[gusty gorge]

For fun, I already have a masters in maths, and this is just reading for leisure tbh, though I like academics still

[marble solar]

stillwell's Lie Theory is really good

There was a lot of hard things that stillwell makes look easy

I took a seminar course which was half grad, half upper division

It was hard for the prof to teach the class because 1/2 the class had grad algebra, real, comlex, and knew how to do things

and the other half were math ed people coming back to school after 2-3 years of teaching

[tranquil ocean]

Hall's book is pretty good. I also enjoyed Humphreys Lie Algebras book

[gusty gorge]

Cool, I'll check those out too

Thanks everyone @tranquil ocean @stray veldt @marble solar

[limpid widget]

Good day. wanna buy book for math calculus. Any recommendations?

Calculus: Early Transcendentals
by James Stewart . is it fine? 🙂

[gray gazelle]

Michael Spivak's is more helpful and more beginner-friendly than Stewart's

[limpid widget]

i Will 🙂

[gray gazelle]

please read it

and use Stewart's only for exercises

[limpid widget]

Calculus, 4th edition ?

[gray gazelle]

ye

[limpid widget]

thx for assist friend

[gray gazelle]

no problem, homie

[analog pollen]

How tf is spivak more beginner friendly than Stewart lol

[analog pollen]

It’s fine but if you are looking for going into more proof based courses later on spivak is better

[prime oak]

i tried using both, switched to spivak

its definitely not more beginner friendly but
more useful

[gray gazelle]

spivak is more helpful imo

[eager stump]

yea i guess it can be argued either way

[gray gazelle]

Are russian advanced problems books any good?

[gray gazelle]

Which one are you talking about?

[fiery bay]

hey guys! i wanted to ask about book recommendations to form a curriculum for myself. i want to study mathematics to an extremely high level as a hobby, and i dont care at all how many years it takes, i wanna be at a professional level. is there any book "pathway" that you can recommend to me, that starts at the undergraduate level, and progresses through to masters and then phd level?

thank you in advance

[quick hornet]

I'm not sure planning that far ahead in detail is prudent - it's good to have goals, but I wouldn't plan out far-future textbooks and whatnot until you have a better idea what you like and what you can handle

Especially since there's many paths you can branch off in your mathematics education, even in undergrad

But as an initial question: are you most interested in pure math? Applied? Not sure yet? (The last answer is totally fine, or perhaps even the most wise)

Also, what's your background? Just high school mathematics?

(btw I don't think self studying a mathematical PhD is possible except for wunderkinds, navigating the literature of your field is very difficult without an advisor)

[fiery bay]

yeah background is pretty weak, i'm done with my first semester of HS mathematics in the IB curriculum

which i've heard is sorta similar to first year undergrad stuff

[fiery bay]

i still plan to try. if i lose motivation and give up along the way, thats alright, but ill never be able to forgive myself if i dont start at all

[quick hornet]

It's not about motivation or anything, it's that when you do a PhD in mathematics, youre signing up to explore a super niche subsubsubfield of mathematics

Depending on the field, there might only be a few dozen people who can even give you recommendations at that level

(I mean in upper years of a PhD, first couple years aren't like this)

And many of the "recommendations" will be published papers and whatnot rather than textbooks

In my field, for example, it's basically mandatory to read Thomason-Trobaugh and then 10ish papers that make much of Thomason-Trobaugh almost irrelevant by modern standards

[fiery bay]

not sure yet

would it be too out there to say both are interesting? 😅

[fiery bay]

right i mean i dont want to have an official qualification - my understanding of a phd was that in the first few years you learn a little bit more, and then you undertake a large research project. im not looking to get in to the research side of things.

[quick hornet]

Sorry on mobile so giving good advice is hard right now

But if you're not sure, probably best to start with some proof based stuff and see how much it sticks

(applied math is proofsy as well but the emphasis is less on precision and definitional manipulation and more on justification of techniques and methods)

I'm not sure what exactly the first semester of the IB curriculum covers, but it probably covers enough algebra for you to learn at least basic proof-based linear algebra

You could consider Axler's Linear Algebra Done Right (though note that its anti-determinant ideology is a bit bizarre at times) or Halmos' Finite Dimensional Vector Spaces

Hoffman & Kunze is commonly recommended as well

I think proofs are best introduced in context of a linear algebra course, but if you struggle to keep pace with them, you could consider an intro-to-proofs-style textbook like Velleman as well

These texts are very slow and handholdy typically

But they can be a nice supplement

[fiery bay]

okay

i'll definitely check those out

ty for the suggestions!

[analog pollen]

Also spivak is great

It will prepare you for analysis

@fiery bay

[broken meadow]

@gray gazelleeezer

fuck sorry

thought there would be a freezer person

owell

[analog pollen]

Lmao

[gray gazelle]

metal banned for frivolous pinging arc

[broken meadow]

Yes

[gray gazelle]

What’s the go to book for an accessible introduction to differential geometry?

[tranquil ocean]

What background do you have? Have you studied smooth manifolds?

[gray gazelle]

Background is engineering education so Linear algebra, analysis and dynamical systems

No manifolds, so I guess it should cover them too

[tranquil ocean]

I guess it depends how rigorous of an approach you want. For math people, they'd probably learn some very basic point set topology, things like open sets and continuous maps between topologies, and then move on to learn smooth manifold theory, and then finally learn riemannian geometry

[gray gazelle]

Im looking for an introduction that makes me able to understand geometric control theory books

[tranquil ocean]

you might also want to ask in the physics server in #old-network , they might have a perspective that better fits what you want

Lee has a three book series on point set topology, smooth manifolds, and then riemannian manifolds, so that could be something you look into

But I feel like this is probably a lot more than you'd need, but I'm not really sure

[gray gazelle]

Yeah 3 books would probably be an overkill😄

[tranquil ocean]

Well, at least mathematically, there's a lot that goes into Riemannian manifolds, and I think physicists jump straight there, but mathematicians usually need more of a rigorous foundation I think

[lilac wedge]

I apologize if I missed it but i have looked in a few of the other channels and can't seem to find it.

I'm looking for a solid textbooks on probability as well as statistics (not together though). Additionally it would be really great if people could refer a great online class. Ideally one that is designed for beginners, has lots of practice problems and is pretty rigorous in it's teachings.

[gray gazelle]

recommendations on an elementary number theory book?

[tranquil ocean]

I enjoyed Silverman's A Friendly Introduction to Number Theory

[gray gazelle]

oo nice ill get it then

oh about math background

what do i need for it

im about to finish multivar calc and after that id like to go through analysis

[tranquil ocean]

Really not much for that book

On the other hand, if you plan to study abstract algebra eventually, it might be a better option to study algebra and then read a number theory book that uses algebraic ideas, like Ireland and Rosen's number theory book

[gray gazelle]

ooo yea im planning to to study abstract algebra

[tranquil ocean]

Yeah, I think I'd recommend doing that first and then looking into Ireland Rosen then

Abstract algebra can help frame some number theoretic ideas in a more general setting

[gray gazelle]

soo any recommendatinos on an abstract algebra book 😅?

i see i see

[tranquil ocean]

There's a pin in this channel that talks about algebra books I think

[gray gazelle]

OH right

i forgot that i downloaded artins algebra

i mean i forgot i bought it

awesome so

artins algebra and then ireland rosen

tysm!!!

[cursive orbit]

Lmao

"bought"

[gray gazelle]

yeahh i would never ilegally download a book🤨 🤨 🤨

lmao

eventually id like to dive deeper into abstract algebra

soo

oh nvm

[cursive orbit]

I mean there's always books you can do after Artin

Like Lang

[gray gazelle]

o awesome

[gray gazelle]

Hi there can anybody recommend me books on following topics for self study:-
book on calculus 1
book on calculus 2
book on calculus 3

michael spivak's calculus 4th ed

thanks

sure thing

[gray gazelle]

any books for trignometry

[gray gazelle]

Rational Trigonometry to Universal Geometry - Norman J Wildberger

thx

[primal summit]

wildberger

[analog pollen]

Just khan academy s fine

[gray gazelle]

k

[analog pollen]

If you also want spivak for calc 3 his book on that is called something like calculus of manifolds

[analog pollen]

He only covers calc 1,2 in his first book

[gray gazelle]

[gray gazelle]

thank you my guy

[narrow talon]

Algebra text for a second (ie. grad) course? Loring Tu’s tetralogy is really good, and had got me interested in algebraic topology/standard algebra. Lang seems like it may be most appropriate, but is quite large. Is there a concise grad algebra reference?

[cursive orbit]

Lang is large because it has a lot of material, not because it's not concise

[dapper root]

Do you want a genera algebra thing or do you want to focus on a specific topic?

I think depending on how much you know it’s pretty common to just focus on some specific sub field of algebra at this point

[narrow talon]

Primarily group and module theory I suppose, I’m just interested in getting more algebra to handle algebraic topology and any algebra I encounter working with graphs and potentially some basic Hodge theory

[dapper root]

What did you use before?

Lang is… concise

It’s only large because it covers a stupid amount of stuff

If you want to do AT stuff you could maybe just go and do it and you might already know enough to make some progress.

[narrow talon]

Herstein, but I never “got” field or representation theory (rep theory from Artin, really bad prof)

[dapper root]

Ah, yeah rep theory is a weak suit for me too lol, and field theory is shaky so I don’t have a great teccomendation hahaha

If I knew one I’d use it myself lol

[narrow talon]

And Herstein has little module theory

[dapper root]

You could try like D&F, Aluffi, Lang

I hear stuff about Jacobson as well

Realistically though in my (biased) opinion if you want to learn about modules you can do it via a commutative algebra book

The caveat being it’s only for… commutative rings

I’m not sure if you use noncommutative rings in AT tho so ¯_(ツ)_/¯

[dapper root]

Okay thinking more this is kinda a bad idea maybe idk

[narrow talon]

Haha yuck

[dapper root]

You will certainly get a very good handle on modules over commutative rings but you also do a ton of rings so it’s not like… efficient

[narrow talon]

I don't feel particularly comfortable with any area of algebra tbh, but I know enough that I also don't have a hard time when groups or rings are introduced. I tried using Lang to look up the parts that I don't know, but it's just too much to really get much from as a reference without significantly more algebra background on my partt

[dapper root]

That’s fair

I shill for Aluffi

But if you’re coming from another book maybe it’s not as easy to jump into

D&F is standard but it has detractors, although with the sheer number of ppl who use it that kinda makes sense

There’s a book by umm

Isaacs

Algebra, a graduate course

I haven’t read it, but I have read some of his finite group theory text and I think the exposition was very good

I can’t guarantee anything, but maybe give that a look if you can find a copy of it in your library or some other methods (upon looking more it seems the module theory is done in a very nonstandard way so )

[gray gazelle]

some other methods

also what books can i change from my list?

planning to go through:
-calc 3 probably with spivak idk
-munkres topology until algebraic topology
-artins algebra
-lang
-abbott analysis

idk where to put abbott

[quick hornet]

• lang
  dude lang has like 500 textbooks youre gonna have to be more specific

have you taken linear algebra before?

(also id recommend reading analysis either before or concurrently with topology, it motivates a lot of it)

[gray gazelle]

lmao yeaa mb mb

uhhh hold on

[gray gazelle]

nope just the bare minimum for vectorial calculus

[narrow talon]

@dapper root thanks, not sure I’ve got a better idea for a text but I do appreciate the help

[narrow talon]

Whyyyy

[gray gazelle]

uhhhh i guess its langs linear algebra or abstract algebra

i got told i could use lang after artin

[narrow talon]

This looks like a fast way to kill math fun

[gray gazelle]

why

[narrow talon]

You can but it doesn’t mean you should

[gray gazelle]

i had a great time with multivar calc

and linear algebra aswell

i can still change my books because im about to finish multivar calc

[narrow talon]

Topology is, in my opinion, pretty hard to really enjoy without specific motivation or experience in other fields of math. This also seems like a rather abstract path, especially without a lot of linear algebra.

[gray gazelle]

i see

how about i go thru artins algebra before munkres topology

[narrow talon]

So this would definitely be a doable path for sure, and if you're really interested in algebra, or algebraic geometry or something like that or just want to build some real algebra/topology chops go ahead, but it just doesn't seem particularly... fun? in my opinion

[narrow talon]

I'd say analysis or geometry before topology

[gray gazelle]

alr alr

btw should i go thru linear algebra before or after abbott analysis?

[narrow talon]

But if topology is interesting to you, ie. if you're really curious about knots or something then go for it

It's just that these books in particular, with the exception of Abbott and Artin, don't really provide a reason to care about the field. They're popular somewhat because they're rights of passage, and topology as a subject is only really useful after seeing at least some analysis (in my opinion I can only stand topology when I relate it to graph theory or another application, but that's personal preference)

[gray gazelle]

i watched a couple of vids about it and skimmed thru some pages of it and it looks really fun

[narrow talon]

Linear algebra is imo the most useful thing to learn period, but it's not mutually exclusive with Abbott and doing them both is definitely doable

[narrow talon]

Then feel free to give it a shot! There's just a rather large disconnect between fun topology problems and textbooks (in my experience, others may totally disagree and if you enjoy it then ignore me, it's all personal preference)

[cursive orbit]

I mean introductory topology is nothing like what the YouTube videos would have you believe

[quick hornet]

no topology is like what YouTube videos would have you believe

Even alg top only covers the "donut coffee cup" stuff briefly

With a far more general theorem mind

[cursive orbit]

I was thinking more like knot theory and that sorta stuff

[quick hornet]

Oh sure, but even then

The problems knot theorists think about are quite different from what's presented in a YouTube video

In fact, it often feels to me like YouTube videos focus more on stuff like "isn't this definition weird???" rather than anything of substance

An example being that many mention how common "knot like things" all reduce to the unknot, and phrase it as if it's a revolutionary or mind-blowing concept or whatever

When it's just a basic definition

(and theres no reason a priori that it's a correct perspective, it's just the angle knot theorists approach it from)

[humble flume]

which book would be better Linear Algebra and its Applications by Gilbert Strang or College Algebra by James Stewart or Algebra and Trigonometry: An Applied Approach by James Stewart

[analog pollen]

These are all different topics lmao

[humble flume]

College Algebra by James Stewart or Algebra and Trigonometry: An Applied Approach by James Stewart these two basically the same but the latter having trig

which one from those two

[humble flume]

nvm i figured it out

[analog pollen]

Btw I don’t recommend either of them cuz Stewart’s books are most of the time very expensive

Imo Khan academy is just fine for algebra and trig

[gray gazelle]

There also Paul online math note. But it does not cover the whole trig course

[solemn rover]

https://twitter.com/MathHistFacts/status/1432684471162220556

Math History Facts (@MathHistFacts)

Calculus was invented* by Canadian textbook author James Stewart in 1987.

• discovered

Likes

235

Twitter · Aug 31, 2021, 12:39 PM

[acoustic badger]

guys

i am looking for a good discrete math

textbook

[primal dawn]

any book recommendations for linear algebra and differential equations?

[pale sand]

any book about beginning algebra 2

[cursive orbit]

I'd just use khanacademy

[smoky surge]

Discrete math for ducks

[acoustic badger]

???

Discrete Mathematics with Ducks?

[smoky surge]

Yea

[gray gazelle]

I did Rosen and it was a fine text.

You may look into other discrete math texts like Liu's text, An invitation to Discrete Mathematics, Concrete Mathematics as well.

see what vibes with you

[acoustic badger]

ahh i see

ty

[gray gazelle]

👍

[ionic marten]

what are good textbooks for these on selfstudy?? to approach mastering them..?

[ionic marten]

and what is the roadmap u sir suggest for graph theory?

thanks in adv :D

[gray gazelle]

@ionic marten I liked Harris et al.'s "Combinatorics and Graph Theory"

easy going introduction

math roadmap where???

[ionic marten]

more pure deep maths :p

[ionic marten]

thanks, im gonna take a look at it :D

[misty wyvern]

Anyone here read Kempf's book on varieties

it good

?

[still jay]

Does anyone know the prereqs for Lattice Theory? I’m specifically looking at “General Lattice Theory” by Grätzer. It seems kind of advanced but I can sorta follow along okay.

[sharp latch]

Looking at the table of contents it looks like a general undergraduate skill set is desired, ie abstract algebra, number theory, linear algebra

But someone who has actually done lattice theory should probably answer lol

[narrow talon]

For graph theory? There’s really quite few prerequisites, just linear algebra. For algebraic look at algebra, spectral graph theory also has very few prerequisites. Diestel is a quite good, quite popular graph theory book so maybe see what the listed prerequisites there are

For analysis I’m not sure, people here seem to like Abbott so maybe that. Spivak’s “Calculus on Manifolds” would be my go-to, introducing some important topological ideas and exposing you to the basic ideas in (co)homology directly in the 4th chapter, though any book using differential forms will do this. The new book by Tristan Needham “Visual Differential Geometry” would likely be insightful and fun but less rigorous, and there’s also intro texts on manifolds though the only one I know of that doesn’t technically require topology as a prerequisite is the book by Tu and even that does assume some topology.

There is also the book on classical geometry by Do Carmo that keeps things at a just past calc-3 level and covers up to Gauss-Bonnet.

@ionic marten

[ionic marten]

wow thanks man

this is invaluable

lol you just repeated the same text 4 times

but thanks alot

[narrow talon]

Lmao wtf

[narrow talon]

No worries

[sage python]

@narrow talon I'm guessing someone deleted

[fresh tree]

does someone have pdf of algebra and trignometry?

by jay ambrson

[fresh tree]

mv got it

[crude sable]

book recommendation for PDE?

[gray gazelle]

Evans'

[crude sable]

full name?

[gray gazelle]

Lawrence Evans

[glad prairie]

Evans is the standard early graduate level textbook. There isn't a great undergrad level PDE textbook, but Strauss "Partial Differential Equations: An Introduction" is probably a good option.

(If you wanted something higher level than Evans, the Hormander "Linear Partial Differential Operators" series is the bible)

[gray gazelle]

you made me spend my time rereading that

[glad prairie]

[gray gazelle]

ok i spend my time reading that since covid is still invading this planet

[crude sable]

1963? that's old

[prisma snow]

Yeah, that's why it's called the bible

[crude sable]

which one exactly?

[split heath]

Do people actually read books for university modules

[crude sable]

there's another one divided into parts

cool then

I'll take all

[gray gazelle]

btw thank you for the hormander's book

[split heath]

Aren't the lecture notes typically meant to be "enough" 😂

[gray gazelle]

i'll check it after rereading strauss'

[glad prairie]

i mean it's a series of 4 books

keep in mind that these are fucking dense

and very very hard to read if you don't have a lot of background

[crude sable]

unless u want to do self study and skip classes like me

[split heath]

I do the same just with lecture notes or lecture videos

[glad prairie]

if you don't have experience with PDEs at the level of Evans then this will be completely impossible to understand

[gray gazelle]

ouch

[crude sable]

I'll try both and see which one suites me

[glad prairie]

if you're looking for a hard PDEs course, just read Evans PDE and Strichartz Distribution Theory and Fourier Analysis, it will give you a lot more than Hormander will if you're not prepared to read Hormander.

Also I love Strichartz's book

it's extremely relevant to anything people do in modern PDE

and is basically a more friendly, enjoyable version of Hormander's first book

[gray gazelle]

Strichartz is also good

[ionic wren]

...

[crude sable]

btw irrelevant question, what pdf reader do you guys use, mine doesn't support .djvu

[cursive orbit]

Okular

[gray gazelle]

Adobe Acrobat Reader

on windows

okular on linux

[crude sable]

I used to use this on my linux machine,

[solemn rover]

djview specifically designed for djvus

[crude sable]

Don't have it anymore, also Adobe acrobat sucks

[gray gazelle]

i prefer okular more than adobe 😌

[solemn rover]

and it's really good software, super minimalistic

i don't really understand why people like okular, i just use the default "Document Viewer" program, not sure what it's called.

but discord can't find DocumentViewer when i'm trying to stream so i switch to okular then

[viral hill]

Evince can also read djvu I think

[cursive orbit]

Pretty sure "document viewer" is just evince

[gray gazelle]

i will uninstall windows 10 because i think it's not worth it anymore for me

[solemn rover]

yeah, evince, that's it

i would recommend keeping windows, it's good for a lot of things, especially if you need to use other commercial private software, of which there is a lot

[viral hill]

sumatrapdf was quite nice when I used windows, I'm pretty sure that it was able to read djvu too

[crude sable]

yup windows 10 sucks, I'm keeping it just to play games,

btw Strichartz book is good

[glad prairie]

it's probably my favorite pde-relevant book

[gray gazelle]

yes

[remote ginkgo]

samsung notes

[crude sable]

[sage python]

Oh huh I should check out Strichartz

@frigid comet smh why you never told me about this book

[frigid comet]

just man up and read hormander.

nah idk have never looked at strichartz, but as a more accessible distribution theory book theres like friedlander-joshi which is awesome

[sage python]

Also I bought Dixon from a friend yesterday for $5 on harmonic analysis

[frigid comet]

as well as books like taylors which are broader obvs

[sage python]

Like classical harmonic analysis

I like it quite a lot

Covers less than Grafakos but it's quicker

I think

[frigid comet]

idk between grafakos and stein's books I have never felt I needed other general classical HA texts

[sage python]

Dixon yo mouth

[frigid comet]

👎

[sage python]

But yeah actually I did get Loomis Abstract harmonic analysis for $5 from a friend, this much is true

[frigid comet]

I might have seen that one, is it follandlike in content?

[sage python]

Along with an automorphic forms book. He was selling everything he had

[frigid comet]

nice. yeah I love when opportunities like that come past

retiring profs are often a good source of books also.

[marble solar]

Is grafakos that good?

I just gave Stein's mammoth

Have*

[queen copper]

Sumatra PDF or Evince if I'm on linux

[fluid bay]

Opinions on “math made difficult”?

[ancient hull]

Any good books on matrix algebra? More advanced preferably & free @quick hornet

[quick hornet]

what kind of opinions do you want

its very funny

[fluid bay]

thats all i need

[golden stag]

Any good recomendation for study max likelihood estimation?

[smoky surge]

statquest

has a nice little video on it

[gray gazelle]

anyone have good resources that give an overview for math symbols like therefore, iff, union etc?

ive forgotten most of them and need to brush up on it

[quick hornet]

first few pages of any introductory proofsy math textbook

munkres for example

[frigid comet]

idk about "THAT" good, but I learned a lot more from them than I did from steins books, because I read them first (and enjoyed them).

mind you there are parts of all of their books I haven't read so there may be shortcomings I am unaware of.

[gray gazelle]

Can anyone provide psets for elementary analysis and understanding analysis? Thanks

[sage kelp]

Just grab any analysis book (?)

[hallow lark]

Anyone have a good book for discrete mathematics?

I know up to precalc so I’d appreciate it if isn’t too advanced of a book

[mighty pelican]

just watch videos on utube

[analog lava]

rosen discrete math @hallow lark is the standard

[dense wren]

Is fulton’s algebraic curves a good into to algebraic geometry?

[gray gazelle]

@hollow current hows zorich going?

[hollow current]

finished

[gray gazelle]

no way

which volume

1st or 2nd

[hollow current]

both

[gray gazelle]

god damn

im just starting the first

is it difficult?

[hollow current]

second is harder than first

but first is not that hard

i mean exposure is nice and comprehensible

[shrewd eagle]

Any good books on geometry?

[gray gazelle]

what would you recommend for prerequisite knowledge

i kinda know all of the things in the preliminary section

and i have some maturity

[hollow current]

pre-calculus and maybe logic

[gray gazelle]

I know both 💯

[hollow current]

and also zorich uses physics in examples but you do not really need it

[gray gazelle]

okay

would you recommend doing every question?

how long did it take you?

[hollow current]

@gray gazelle i did most of the q of zorich from 1st volume but not second

it took for me about ~5 month but with breaks to go through both volumes

[gray gazelle]

did you publish your solutions?

[hollow current]

no

[gray gazelle]

damn

ill see if i can

[gray gazelle]

@steep egretlorobenzene

sorry

ididnt mean to

hey

guys

can you recommend some books for mathematics

[wind vapor]

what can i learn after doing apostols calculus (both of them)?

[crude sable]

anyone have any recommendations on abstract algebra ( intermediate-advanced) other than Dummit Footie or Gallian

[gray gazelle]

Artin

[uncut zealot]

intermediate-advanced it's more worth asking about a specific topic within abstract algebra depending on what you're interested in

[crude sable]

actually all of them

group, ring, field

[green estuary]

Hey guys, I wonder if you can suggest some books on NT covering elementary - algebraic.... And it would be cool if you recommend it in some order.

I already know the basics of elementary NT so I want only a light book or something like that. Thanks.

[sudden kindle]

Marcus number fields for intro to alg nt

[green estuary]

And for analytic?

For the one you mentioned above, should I have some prerequisites?

[orchid pollen]

Jacobson Algebra is a pretty good introduction. Artin is probably the best though, but it's definitely a heavier commitment. If you've got some experience already, then Lang is a good option. Also, on another note, Bourbaki's algebra 1 is wack.

Also, for analytic number theory, Apostol's book is good.

Although my previous comments were about abstract algebra.

[green estuary]

Yeah I need them too, thanks for the suggestions!

[obsidian valley]

anyone know Priestly’s CA book? is it any good or should I just reference a better book

i think S&S is too scary tho

[sage kelp]

Any suggestions of introductory set theory besides Goldrei and Enderton?

[solemn rover]

it depends what you need it for.

[sage kelp]

I just want to have the minimum knowledge of it (and understand how the ZF axioms work), and maybe in the hopes of complementing analysis

[dense wren]

What’s a nice text for an algebraic geometry beginner

And what are the hard prereqs

[sturdy sail]

Mainly commutative algebra

[sturdy sail]

What's your background? Maybe Harthshorne could do the job, but may be kind of a hard read.

[dense wren]

My algebra background is Dummit and Foote level, group theory and ring theory sections + field/galois theory, I suppose I should also go through modules as well

I heard fulton’s algebraic curves is a good starter

[sturdy sail]

Oh, I think with this background you should be able to start studying algebraic geometry. Just make sure that every once in a while you pick up the necessary background in commutative algebra.

Say localizations, Noetherian rings, ring extensions...

[sturdy sail]

Never read that one

I mainly use Harthshorne and some other Brazilian textbooks, but that may not be so helpful due to language barrier.

[dense wren]

@sturdy sail ok, thank you for the advice

[gray gazelle]

recommendations for high fantasy books

[gray gazelle]

Pre calculus

[gray gazelle]

I like topology

[gray gazelle]

Have you heard of khanacademy? I think you should check it out

Well it's very hard for us to say what you are expected to know, it's up to you. Having a textbook that your school uses probably wouldn't hurt

[stray veldt]

khanacademy is probably sufficient

if you want to supplement with a book i suggest "basic mathematics" by serge lang

(also computer science doesn't even really need any calculus, so even khanacademy might be overkill)

[blazing garden]

Pick up a book on discrete mathematics

I would just skip high school

If the book assumes you know something that you don’t, just go to khan academy, or Google, for that particular thing

If you’re interested in cs/cryptography, you’ll find discrete mathematics more interesting than high school math

And it’s good for building mathematical maturity

If you do that, you’ll have an easier time learning things later on

[blazing garden]

I think K Rosen’s is a good one

I know this may sound like putting the cart before the horse, but it’s not.

If you learn discrete mathematics well, you won’t have a problem 😆

Np

[valid condor]

Hi all

does Measures, Integrals and Martingales (René L. Schilling) mentioned in #books-old have problelms with solutions, for those who want to self study mesure thoery

[bitter raptor]

what's your issue with it?

[crystal lion]

he thinks it’s too scary

[obsidian valley]

too scary

[gray gazelle]

Is geometric measure theory by Federer good?

[solemn rover]

i've heard it's a very difficult book to read and understand. But I don't know much about the topic.

[misty wyvern]

It's notoriously challenging, I recommend a different GMT text.

[proven junco]

Some text of exercises to analyze type examinations of the field of R. Real analysis.?

[thin hollow]

What’s a good book I should read not a textbook or anything

But something that’s just awesome or really cool about physics math and cs

[sage python]

Brian Greene has this one good "layman's" string theory book

[inner ledge]

Best books on number theory?

[quick hornet]

||Please dont take this as an actual recommendation||

serious response: for a first course in elementary number theory? do you know basic ring theory?

[proven junco]

Not only, I have an essence of the terms group, ring, body and field but I have not deepened them.

[inner ledge]

I don't know any ring theory

[proven junco]

I am novice 🙂

[slate quarry]

why is that book such a meme?

[quick hornet]

because its a graduate level textbook on sophisticated algebraic number theory called "basic number theory"

in fairness, it is basic relative to research level, but still

the first 2 pages, for context

its just basic field stuff but its clearly written for very mathematically mature readers

[slate quarry]

lol

so, what would be a good recommendation on basic number theory?

I mean, basic for real.

[misty wyvern]

What's an R-rated math book

[flint bay]

Algebraic or analytic

[slate quarry]

Elementary

[slate quarry]

Thanks a lot. I shall take a look 🙂

[gray gazelle]

What's a good book for probability and/or permuation and combinations.

Is Ross's book sufficient to solve all probability questions?

[stray veldt]

"all probability questions" seems a bit of a tall order

[gray gazelle]

Of HS/College level 😄

[main skiff]

any good books on algebra and calc

[sudden kindle]

From Topics in Complex Function Theory. Automorphic and Abelian Integrals.

Looks like a good book

[analog pollen]

khan acedemy for algebra, stewart for calculus

or spivak

[gray gazelle]

ryc said that 3blue1brown: calculus is a good playlist in #math-discussion

[glad prairie]

More for understanding calculus than for learning it fully though

[sudden kindle]

Very good book

[sage python]

oo Siegel

[gray gazelle]

I need to know concepts and vocabulary of product notation and unique prime factorisation from the beginning, what books can be helpful

[quick hornet]

what is meant by "product notation"

[broken meadow]

\prod

?

[quick hornet]

do you mean like, $\prod_{i=1}^{k} f(i)$?

[hasty eagle]

Namington

[broken meadow]

guess so cus prime factorization

[quick hornet]

im not sure theres much to say then

nothing to warrant a full book at least

[broken meadow]

$\prod_k p^{k_p}$

[quick hornet]

ask in a questions channel

[hasty eagle]

Beaming Scale Mail of Champions

[primal summit]

Shouldn't you be indexing over p?

[broken meadow]

shiet

im dumb

ur right

im struggling these days

$\prod_p p^{k_p}$

[hasty eagle]

Beaming Scale Mail of Champions

[sage python]

Lmofa

[broken meadow]

Loofa

[lapis sundial]

Lmaof

[static crest]

Lamof

[earnest gazelle]

i highlighted all the key words

[fossil badge]

An Introduction to the Theory of Numbers by Hardy and Wright. I have the 6th edition.
The preface says "In the first 18 chapters we assume nothing that is not commonly taught in schools, and any intelligent university student should find them comparatively easy reading." This is mostly true, I think if you have a good understanding of high school mathematics and some knowledge of what constitutes a proof you can understand it.

[quick hornet]

eh those words are fair in the context of the books target audience

theyre all saying "This shit really shouldnt take you any effort to justify to yourself"

"and if they are, use a simpler textbook"

[fossil badge]

maybe the title should make it more apparent

[quick hornet]

i wont disagree that its poorly named

but if you buy a $300 book just from reading its title and not taking a look at the inside, even briefly

that's on you

[broken meadow]

i think titles like these are mildly humorous and should stay

[quick hornet]

also weil says basic number theory, never easy number theory; mathematicians are very picky with what words they use to talk down to people

"elementary" is harder than "obvious" which is harder than "easy"

"basic" doesnt even describe difficulty

[gray gazelle]

Paul's online notes and Khan Academy cover these two topics. In terms of a book, I can get behind Serge Lang's Basic Mathematics (skip the initial chapters) and Sheldon Axler's Precalculus.
For Calculus I did a book called Calculus with Analytic Geometry by Simmons which does a good job in my opinion.

[manic cape]

is Bredon a good intro for AT?

[craggy dome]

Hi guys, I just finished my undergrad. Do you have any book recommendations for any interesting lesser known branch of mathematics?

[slate quarry]

Thanks. I shall check it out :)

[marble solar]

Terry Tao Random Matrix Theory

Matrices whose entries are random variables

Another interesting topic is low dimensional topology

You can enter with knot theory by justin roberts, the wild world of 4 manifolds, etc.

[craggy dome]

Thank you so much, these all sound interesting, will look into these 😄

[abstract walrus]

books on olympiad number theory?

[night birch]

Modern Olympiad Number Theory by Aditya Khurmi

Personal favorite

@abstract walrus

or if u need basics

you can read Basic Number Theory By Masum Billal, which I didn't read but have heard positive feedback

[abstract walrus]

btw what's the difference between undergrad number theory and olympiad number theory

[abstract walrus]

mm no looking at the book by Aditya it seems fairly familiar topics

[night birch]

wym

[abstract walrus]

thanks

[abstract walrus]

yeah that was badly phrased

[tranquil ocean]

I guess the difference would be that undergrad number theory is more focused on the theory and the proof of things whereas olympiad number theory is more focused on how you can apply different theorems to solve problems

[night birch]

also more about wiring proofs ability

writing *

[glad prairie]

[analog pollen]

"dynamics and relativity by mccomb" does anyone here have a pdf of this book?

i know this isnt really a math book

but idk anyone who could have a pdf of this

[gray gazelle]

did you check l*bg*n

[analog pollen]

thanks

[broken meadow]

🦻 who?

[gray gazelle]

libgen.

that horrible website.

[broken meadow]

yeah what a horrible place

[gray gazelle]

i forgot how to compute

[broken meadow]

i would never go there three or four times a year

and download things

so bad

[gray gazelle]

[crystal lion]

not going there is a bad thing… so going there is a good thing?

#cancelmetal

[solemn rover]

yeah it's pretty good

[manic cape]

Thanks

[gray gazelle]

any recommendations for books on symbolic logic?

[velvet briar]

Levin's discrete mathematics was good

Free pdf on Google too

[night birch]

'An introduction to Symbolic Logic' by Susanne Katherina Langer.

[misty wyvern]

I think tricking young mathematicians into doing logic is a war crime

[atomic hound]

Good morning,afternoon and evening math fellas, so i would like a good about model theory and proof theory,any sugestions?

[prisma snow]

@karmic thorn

Take note

[karmic thorn]

This is a self-afflicted war crime

[prisma snow]

[valid condor]

Hi we have the same name

🧐

[gray gazelle]

[crystal lion]

extra T though

[valid condor]

R

does Measures, Integrals and Martingales (René L. Schilling) mentioned in #books-old have problelms with solutions, for those who want to self study mesure thoery

[solemn rover]

shitting on logic is a common coping strategy for people who don't understand logic

in the early days of point set topology, some of the greatest topologists in the world shied away from it because they didn't understand the set-theoretic constructions, the idea of a topological space was just too weird and foreign

Engel, one of the students of Lie, said "I am still of the opinion that everyone who is not an inveterate set-theoretician will find, as I did, that the general assumptions of section 1 (referring to a paper of Brouwer on point set topology) are not worded clearly enough... I cannot conceal the fact that, in general, the vast generality of the investigation and the great number and multiplicity of the necessary lines of reasoning strikes me with a slight dread. It is actually inconceivable to me that on the first try, everything should have been settled."

Elie Cartan also warned against trying to use point-set topology in the study of Lie groups because of the great "delicacy" of those arguments

Basically, I would encourage anyone to avoid sounding like Cartan, dismissing something as unimportant because you don't understand it

[sharp latch]

[blissful tiger]

Any good books for learning Differential Equations?

not a fan of our current textbook 🥲

[slate quarry]

What textbook is that?

[bronze raven]

i dont understand topology outside of point set

was it just neighborhoods or smnth

[atomic hound]

Based on real facts

[dapper root]

Wtf did topologists do before point-set??

[quick hornet]

you know euler characteristic

that

[misty wyvern]

shitting on logic is a common coping strategy for people who don't understand logic
in the early days of point set topology, some of the greatest topologists in the world shied away from it because they didn't understand the set-theoretic constructions, the idea of a topological space was just too weird and foreign
Engel, one of the students of Lie, said "I am still of the opinion that everyone who is not an inveterate set-theoretician will find, as I did, that the general assumptions of section 1 (referring to a paper of Brouwer on point set topology) are not worded clearly enough... I cannot conceal the fact that, in general, the vast generality of the investigation and the great number and multiplicity of the necessary lines of reasoning strikes me with a slight dread. It is actually inconceivable to me that on the first try, everything should have been settled."
Elie Cartan also warned against trying to use point-set topology in the study of Lie groups because of the great "delicacy" of those arguments
Basically, I would encourage anyone to avoid sounding like Cartan, dismissing something as unimportant because you don't understand it

too long didnt read. also give me your lunch money

[blissful tiger]

Fundamentals of Differential Equations by Nagel et al.

[gray gazelle]

U guys know a book for gender dysphoria?

Prob not a good place to ask lol

[misty wyvern]

Rudin

[crystal lion]

Rudin contains the answers to everything

[solemn rover]

This is one many things separating you from a mathematician of the caliber of Hilbert. Hilbert conducted a seminar on logic at Gottingen, contributed massively to the study of formal systems by inventing Hilbert systems, put deep questions about logic on his list of the great problems of mathematics at the turn of the century (1, 2, 10), posed the Entscheidungsproblem to logicians, developed the philosophy of finitism, and contributed to the development of the modern axiomatic method by writing an entire book on the foundations of Euclidean geometry. Beyond this he forced mathematicians to reckon with the question of legitimacy of nonconstructive proof by his pioneering work in commutative algebra.

But you're no Hilbert.

[quick hornet]

is this a pasta

is now i guess

[broken meadow]

this server has too many pastas

[marble solar]

I think this is a great over simplification of their concerns

[solemn rover]

yeah probably

it is weird that you focused on that tho and ignored the context of what i was responding to

[misty wyvern]

hilbert is a nerd, if he were alive id try to bully him

[gusty smelt]

You are a moron. You think you are being funny but you sound like a dumb teenager. If you keep this attitude up then you deserve to fail in math.

[misty wyvern]

😂

[broken meadow]

keep it civil

[agile cliff]

Hello, does anyone have a college algebra book recomendation?

[quick hornet]

college algebra meaning?

the term has different meanings in different contexts

(maybe a course description would help)

[agile cliff]

Sorry, Mostly just algebra 1,2 some trig and geometry would be nice

[split pond]

isn't that just HS algebra

[agile cliff]

The book I currently have just makes me question my existence

[gray gazelle]

linear algebra by gilbert strang

[agile cliff]

The book I have is called college algebra and has those so I just asummed that's what it was called

[gray gazelle]

or check khan academy

[agile cliff]

Thanks, but where can I find the pdf?

[gray gazelle]

amazon.com

[agile cliff]

Oof

Do you have any free book recommendations? I am a peasant you see

[gray gazelle]

i am also peasant

[split pond]

i don't think they are asking for linear algebra

[gray gazelle]

if you do not want to buy, then check khan academy or 3b1b

mb

[agile cliff]

I see

Oh

I thought it was alg 1 to linear alg

[split pond]

afaik alg 1 and 2 is not linear alg

[gray gazelle]

hs alg?

[agile cliff]

I mean't alg 1 all the way up to linear alg

[agile cliff]

Yeah

[gray gazelle]

khan academy is your best friend, then

https://tenor.com/view/mr-potato-cat-nataon-dimden-gif-22528109

[agile cliff]

Alrighty

[gray gazelle]

[agile cliff]

Sal khan here I come

[cunning kestrel]

beginner's book on NT?

[gray gazelle]

it is college algebra for non-stem ppl

[split pond]

wait alg 1 is topics like solving linear equations in two variables and some rules of exponents or something at that level right?

[gray gazelle]

precalculus stuff ig

[split pond]

so do they do those in college?

[gray gazelle]

those who didn't take it in hs

[split pond]

i see

[quick hornet]

sometimes they're also targeted at nontrad students

like, entering uni at 30 for a career change and havent done math in forever

want a refresher

[gray gazelle]

is Introduction to the Calculus of Variations Hans Sagan a good book for calculus of variations

[gray gazelle]

Can anyone recommend me a good introduction to model theory?

It should cover basic notions of models and satisfaction, submodels and embeddings, as well as Skolem functions, direct limit and ultraproducts

atleast thats what the book expects

I'm reading Thomas Jech's set theory book , chapter 12

[analog pollen]

Khan academy

[solemn rover]

first few chapters of the chang and keisler book should be fine for this stuff i would think. if you have more background in algebra, i know the algebra book by jacobson ("Basic Algebra" vol II) presents ultraproducts briefly, for more check out https://people.math.wisc.edu/~keisler/ultraproducts-web-final.pdf or the paper "Ultraproducts for Algebraists" which i think is in the handbook of mathematical logic https://www.sciencedirect.com/science/article/abs/pii/S0049237X08710991

idk what your background is

[gray gazelle]

I'll check it out

[misty wyvern]

95% of recommendations in this channel: Khan Academy
4.9% of recommendations in this channel: Rudin
0.1% of recommendations this channel: everything else

[gray gazelle]

some fraction of that 0.1% is me recommending spivak's CoM to literally anyone doing mvc

even if they're poor engineers forced to take the class who will never need to know what the hell a differential form is

[misty wyvern]

there is some fraction who will learn differential forms in a fixed-coordinate manner so they can mess with tensors but for real

com good, never apologize

[glad prairie]

not using stewart early transcendentals...

[solemn rover]

stewart is fine for like, the vast majority of engineering undergrads imo

but differential forms are cool and good

[misty wyvern]

I basically hate every calculus book, nothing so far has changed my mind

[solemn rover]

the only objectively bad path would be to not study either stewart or calculus on manifolds or anything that gives you computational practice with stokes' theorem etc, until grad school when you start studying de rham cohomology and have no idea what it is about

[misty wyvern]

Spivak almost did but nowadays all I need is a book on how to solve absurd integrals

And Spivak just feels like Rudin but worse. While I appreciate pedagogical intros, I grade books down for not being a good reference for the rest of its lifespan

[solemn rover]

haha

yeah it's hard for me to objectively assess a book as its value to the reader usually is highly dependent on their background

[lapis sundial]

i've heard some negative things about CoM (mistakes, or stuff missed out), is that criticism valid / anything to worry about in your opinion?

[misty wyvern]

I mean even though Rudin Principles is too babby for anything I care about now, I still refer to it for some slick proofs.

It aged well even into my career.

I almost never look at Spivak now.

[gray gazelle]

there are very detailed errata for the book online so there isn't much to worry about