book-recommendations

[worldly brook]

I love reflecting on it because It's great once I get it, however you guys are right

[sage python]

Just saying

[worldly brook]

I don't really do much exercise from the books

[heady ember]

Greub in the background:

[wet sentinel]

i was actually using it

[molten gulch]

here's dami's review of hoffman

[worldly brook]

cuz then, I can't feel good knowing that I'm barely making progress

[molten gulch]

I like greub as a reference

[wet sentinel]

i stopped linear algebra for a while, i should return soon

[molten gulch]

That's a problem

[sage python]

Hoffman-Kunze was what my analysis class had us teach ourselves from

[wet sentinel]

meanwhile roman:

[heady ember]

Same. I've stopped lin alg for three months to work on LaTeX lol

[molten gulch]

self teaching LA? doable but sounds terrifying for a first year student

[worldly brook]

how many exercises do you guys usually do?

[sage python]

I remember we were really confused about dual spaces and the double dual and we asked our prof in office hours and he started talking about how the dual of l^p is l^q

Like bro we were just trying to understand chapter 3 of HK what is this

[molten gulch]

Well it depends, we just did a class at uni on linalg and then did some proofs out of FIS occasionally because our class book was so boring, there's some theory we lack in that we only know from the shut up and compute side so-

[worldly brook]

I know right

doing exercises on the same topic is boring 😭

I like the shut up, someone probably proved that already approach

[molten gulch]

I mean many times the fix was just to go read the theorem and its proof in FIS or LADW or HK and then write down my interpretation, do some problems, use it and such, etc...

[molten gulch]

Oh I hate this, I hate ANYTHING that isn't proven without good reason, such as the proof being too hard. I utterly hate my current probability course because it's all just throwing formulas

[wet sentinel]

that doesnt sound horrible, i mean i was self studying LA

in fact i am self studying everything

[heady ember]

Some ways to get more fun out of math than you already are is to

1. Make beautiful figures
2. Do computations by programming, instead of by hand.

[molten gulch]

Well fair, we did 2 chapters of FIS before we got to class

[worldly brook]

oh yh that too, if my intuition can't figure it out then I do exercises

[molten gulch]

you should always do exercises

[worldly brook]

all of them?

[sage python]

It wasn't entirely my first exposure to LA, I had a summer thing taught by a combinatorist, but it definitely did things differently at times

[heady ember]

Once I was skeptical of a particular step in my proof, so I wrote a programme in Julia to do some tests.

[wet sentinel]

i usually do until i feel like i understand all (or maybe almost all) content of the chapter and am able to more or less solve exercises in a reasonable amount of time

[sage python]

And not everyone in the class did that summer thing

[wet sentinel]

or at least have the rough idea in my mind

[sage python]

Different parts have different intuition

[worldly brook]

yh, sounds like what I do I guess

[sage python]

Normal operators imo get their intuition once you learn the spectral theorem

[worldly brook]

I kinda skipped the logical exercises on the intro to proofs book I picked 😭

[sage python]

Like you learn spectral theorem for self-adjoint operators, and there's nice intuition there

[heady ember]

I see

[worldly brook]

I know that might come back to me some point in the future

[worldly brook]

where do you learn spectral theorem

[sage python]

Then normality becomes the optimal condition for the spectral theorem

[worldly brook]

linalg too?

[sage python]

Yup

[worldly brook]

sounds good

just to summarize things up, should I replace Kunze for something else?, also what do I do after baby rudins chapter 8

[sage python]

In fact, an operator is unitarily diagonalizable iff it's normal

[worldly brook]

oh and how can I get rid of the annoyance cauchy is for once 😭

[sage python]

For now read "Linear Algebra Done Wrong" by Treil, instead of the Kunze book

Rudin you can decide if you wanna do later

[worldly brook]

I'll give it a try, thanks

[worldly brook]

wut

do you just force yourself into one single book at a time?

[sage python]

More that you may not even need functional analysis

But the spectral theory side of finite-dim linear algebra is gonna be quite important

[worldly brook]

hm, my main goal are hilbert spaces though, the other ones sound cool but I don't know what do they do

[sage python]

So I'd hard prioritize it for now. If you later still see a need for functional analysis you can do it and you can decide how deep you wanna go.

Rudin will definitely be a high investment. If by then you're like yeah you know what let's do it I wanna learn analysis, then yeah go for it. If not there might be quicker ways to get to where you wanna go.

Though actually you might prefer Kolmogorov-Fomin to Rudin?

[worldly brook]

is the other one more complete then Rudin?

also which rudin, turns out there's a whole heritage for this dude 😭

[sage python]

Idk about complete or not but it does less of the calculus stuff and gets straight into the functional analysis after it does the needed topology

[worldly brook]

great

thank you so much man

last question but, where do I learn about cauchy

I swear

hes everywhere

hate that man

[sage python]

Cauchy the person, idk

The math that Cauchy did, analysis especially

[worldly brook]

ok thanks 🔥

[molten gulch]

why do you hate him? he's been dead for like almost 200 years

[worldly brook]

hes the math equivalent to "I pulled this from my ass"

[molten gulch]

He didn't! Also you'll find many instances of things that feel like that

for example, to me most of number theory feels like that

[worldly brook]

and how do you cope with it

[molten gulch]

I don't do number theory

[worldly brook]

do you go on a journey to find the man,

oh

[molten gulch]

I'm much more of a geometry enjoyer myself

[worldly brook]

fair enough

[molten gulch]

though there's some relationships between number theory and geometry, I'm not at the point where it's a huge deal yet

[worldly brook]

what even is number theory

[molten gulch]

google is your friend

[worldly brook]

this is just walmart analysis

[molten gulch]

no, number theory isn't all analysis though analysis does play a big part (cheboratev density is one of my favourite examples, same with prime number theorem, etc...) as many times we want to find the distributions of primes or distance and stuff

[mighty reef]

any recommendation on a book of differential geometry?

[marble solar]

Andrew Pressley has a good book with Solutions; Schaum's Outline to Differential Geometry is a good one too, as it has lots of solved problems

[radiant marlin]

have a look at Manfredo P Do Carmo's DG textbook

[nocturne badge]

check out umbeto bottazini, rise of complex function theory. it has like a 100 page chapter on cauchys work in the context of analysis and also includes context of his life

[slow roost]

sounds like fantasy, got any recs in that you like better? I'm reading The Steerswoman at the moment. Not very far in but I like it.. sort of blends fantasy with sci-fi. Magic vs science/rationality

[glossy cove]

Reposting because i got ignored to oblivion last time, but is titu's complex numbers book a good first introduction to them? (beyond the basics, that is)

[hollow swan]

is there a gud book to get started with advance number theory?

[crisp kestrel]

i was looking through princeton's calculus intro course and there's no book recommended.

Introduction to limits and derivatives as preparation for further courses in calculus. Fundamental functions (polynomials, rational functions, exponential, logarithmic, trigonometric) and their graphs will be also reviewed. Other topics include tangent and normal lines, linearization, computing area and rates of change. The emphasis will be on learning to think independently and creatively in the mathematical setting.

this is the summary of the course. i've been recommended to try spivak for this but it seems overkill. should i go for it or do you have any other suggestions?

[wet sentinel]

i dont recommend spivak, i recommend something like stewart's "calculus early transcendentals" or thomas' calculus

spivak is somewhere between calculus and analysis and imo not one of the best in either lol

[crisp kestrel]

what about apostol?

[crisp kestrel]

also do these fit the course requirements?

[wet sentinel]

idk about that book

[crisp kestrel]

alright.

i'll check out stewart. i've heard about his book quite a lot.

[wet sentinel]

any calculus book should probably cover the topics you mentioned

[wet sentinel]

but note that calc books will contain more than just this too

[crisp kestrel]

it's okay if it contains more. it just shouldn't contain less. should i go for stewart's calculus or stick with the early transcendentals one?

[wet sentinel]

idk what the difference between the 2 books is but i used the earl transcendental ones

i wasnt even sure if there exists another book just called stewart's calculus or something like that

[crisp kestrel]

right. i assumed they were different because usually everyone says calc. i'll do it. thank you for your help!

[wet sentinel]

yea in that case i dont think there is another book

its weird if there is tbh

[crisp kestrel]

yeah lmao.

[wet sentinel]

bc calc isnt a topic that requires multiple books to cover lol

especially if one of the books is 1300+ pages (and covers all calc topics)

[crisp kestrel]

yeah i looked it up

it's lengthy.

i'll go for it. let's see how content dense it actually is.

[normal crystal]

why does it matter what Princeton does
also, they have more than one intro course depending on placement and they do mention the textbook, currently Thomas for the regular options

[crisp kestrel]

princeton is good. i'm looking to do it through self study so i'm referring to uni courses for the general curriculum and the books they use. princeton has a really good reputation in mathematics and also a well described curriculum. i was just referring to it.

[wet sentinel]

if you want to self study then no need to follow a unis curriculum

[remote vortex]

On the one hand no, on the other I've often seen self-studiers have issues with editing and pacing

So a curriculum which says "within <this> timeframe you're expected to learn <that>" can be a helpful reference

[wet sentinel]

ohhh i see, yea in this case its reasonable

[sour cargo]

differential geometry is a broad topic, I am definitely not an expert but have read the following books/lectures, which is good (at least for me):

• Wedhorn - Manifold, Sheaves and Cohomology
• Loeh - Lecture notes on Differential Geometry

and of course these materials contain many references which you can/should consult, too.

[crisp kestrel]

yup.

[crisp kestrel]

thank you for explaining for me. really appreciate it!

[surreal cosmos]

hello what book do you recommend for a 10th grade to learn a lot of mathematics for national and International mathematics olympiad ?

[ivory talon]

Any good book recs for quantitative finance?? Pls

[hollow swan]

.

anyone

[wet sentinel]

wdym by advanced? like analytic nt for example?

[hollow swan]

algebraic

i think its called algebraic

those invovling class field theory and other stuff

[wet sentinel]

ah i see, in that case i cant help you sorry (of course because idk resources)

[hollow swan]

what would you say if I said analytic

[wet sentinel]

i would say apostol's introduction to analytic number theory, thats the book i am using rn

[hollow swan]

alright

[wet sentinel]

there is davenport too

[hollow swan]

i have gone through apostol

davenport

alright let me see

[wet sentinel]

ohhh i see, actually i am going through apostol these days

i havent started too long ago

[molten gulch]

I think marcus number fields is a common rec, there's also.milne's notes

[wet sentinel]

from what i know davenport is kinda more advanced than apostol, so you may get a few new things out of it but i am not sure

[wet sentinel]

also @wicked fractal can probably give you a good overview for books on analytic and algebraic nt

[wicked fractal]

For beginner intro you can try "Number fields" by Marcus but if you feel like it's too easy then you can try Neukirch or Milne's notes

Neukirch covers class field theory too but I'd also look at Milne's notes + Cassels and Flohlich

Marcus doesn't cover CFT

[hollow swan]

alright i appreciate it

[molten gulch]

@wicked fractal is there a mote geometric interpretation of class field theory and concepts in alg nt?

[mystic orbit]

Does anyone have a good book on inferential statistics?

Preferably something light on prereqs at the undergrad->masters level

[hushed vector]

2050 is the year Milne intends to publish it 💀

[mellow wren]

ah yes arithmetic duality theorems

the famous introduction to algebraic number theory

[remote sparrow]

how rigorous

does light on prereqs mean no measure theory?

you can look at casella and berger in that case

otherwise look at shao or keener

[mystic orbit]

Well, measure theory is fine ig, I dunno

[remote sparrow]

shao has a solutions manual associated with it if you care

[odd kiln]

Hi i'm a middle school student and im looking for an interesting math books, dont know what topic, just want to explore

[thorny copper]

You might like The Number Devil its a fun math story Or if you enjoy puzzles The Moscow Puzzles is really good too

[odd kiln]

Will check them out, hope theyre available in my country thanks ^^❤️

[thorny copper]

Np

btw we’re r u from

[odd kiln]

Poland

[wet sentinel]

maybe try "basic mathematics" by serge lang, i havent read it but i have heard some people recommend it before

there is also khan academy on youtube/google

[odd kiln]

Will add that to the list

[odd kiln]

But id prefer getting books in english so i can communicate better

[wet sentinel]

what did you take in math recently?

[odd kiln]

I dont quite understand the question

What did i learn?

[wet sentinel]

like what have you taken recently in class for example

[wet sentinel]

yes

[odd kiln]

Equations and inequalities of rational value with absolute value was the last topic, but i'm happy to learn more besudes school

[wet sentinel]

ohhh i see nice

good luck on your mathematical journey and whenever you have questions you can always ask in the help channels (read #❓how-to-get-help for more info about this) and there people will help you!

i hope you enjoy math

[thorny copper]

You should be able to find it in Poland, it’s available there too

[odd kiln]

Yeah shool now is kinda boring cause our teacher is sick and we cant start a new topic

That would be so cool

[ebon whale]

i need to get familiar with tensor products and some multilinear alg for rep theory. any recs?

[orchid vortex]

Any good supplement recs to Zorich's Mathematical Analysis II.

[lime blade]

anyone familiar with agarwaal mathematics book?

[foggy egret]

Do you guys think paul lockhart's belief on how mathematics should be taught is correct?
My teacher whom I study from online, highly believes in his methodologies and teaches in that manner.
So I'm confused, should I commit to that, hoping I will learn mathematics correctly

[deep moat]

I have read P. Lockhart's book back then and all that I could say is that yes

Math is all about "play-and-experiment"

experimenting lets you discover things pretty much without knowing

by

without knowing
I mean like you discover it yourself and when you read more about it you will soon realize that you have discovered that thing yourself

plus schools (for my own perspective) no longer teach you the beauty of math as it's all just "plug-and-chug" calculations

facts

[mellow wren]

He raises good points in many aspects but I think his view is a bit too idealistic

[deep moat]

mostly summer camps and those who're in a program for compet math

[mellow wren]

Beyond based

[remote sparrow]

hubbard and shifrin are lighter choices so either could make a good supplement

[foggy egret]

Okay I'll just do that

[wild blaze]

To get admitted to mathematical physics programs do I need physics classes??

[fresh wren]

Hey so im currently a college student studying electrical engineering, ive been doing calculus and realized that ive been mainly memorizing stuff rather than just understanding it. does anyone have any good book/textbook recommendations that could help me brush up on the fundamentals?

[hollow peak]

If it's a physics program: yes
If it's a math program: no

Most places don't offer explicit "mathematical physics" programs. It's just working under one or the other in the hybrid field

[near jewel]

When you already have things memorized, I feel it’s fine that you go through your book again and focus on the graphs. And also, does your book contain proofs and explanations for most of the definitions and theorems?

[wet sentinel]

i am interpretting this as wanting to understand why these formulas you use in calculus hold/are correct, in that case i recommend that you pick a real analysis book and study it

[ornate kiln]

There are numerous books

I'll suggest starting off from YouTube

You will find professors and real educators who are passionate about maths

[tulip swift]

hey can anyone recommend a good math book for high school kid

[mortal ore]

Calculus courses intentionally dont teach you why it works because its a waste of time for people who just want to apply it

Aa yassine said thats what real analysis is for

[hallow river]

any1 got any recommendations for a good practice book on like high school level math problems?

that are kinda hard

[young thorn]

arthur engels book Problem-Solving Strategies has p good problems

really teaches u how to write proofs along the way

[warped steeple]

wanted to get into number theory but my max knowledge is of primes and integers

what book is best for introductory number theory

[cunning elk]

try Burton

[limber rock]

Does anyone have a good book recommendation for Lie algebras?

[old elk]

As someone who works in the field of Lie algebra, I recommend this book in Portuguese.

[prime tree]

🇧🇷 mentioned

[foggy quest]

try https://mtaylor.web.unc.edu/notes/lie-groups-and-representation-theory/

[limber rock]

Thank you 🙏

[dry rune]

Does anybody have a book recommendation for the entirety of mathematics that completely changed their life and perspective? No, I'm not taking about those "Introduction to Calculus" or those shit ass rigid, formulaic, linear books made only for you to pass SAT exams. I'm talking about those books that are surreal beyond the abject viscera; those books that will hurl you into supreme bliss and horror due to its sheer gut-wrenching jarring grandiosity; books that will suck the very soul out of your lungs and leave you abhorrently breathless in a heavenly delirium of pure sublimity and ecstasy; books entailing platitudes of divine paradigm shifting, eureka moments, cosmic revelations, celestial salvations; books that will make you feel that you've just discovered an eternal goldmine... I don't fucking know anymore, my vocabulary bank is going bankrupt, I'm running out of adjectives. If you still don't get the memo, I just need... something orgasmic, eye-rolling, or gut-wrenching. Something enlightening or eye-opening, perhaps. Thank you very much 🙏🙏🙏, I'm not apologizing for the length of my paragraph

I'm looking for something transcendental

[remote sparrow]

new copypasta just dropped

[daring wolf]

that must be hartshorne AG, or Lang Algebra

[hallow river]

ohh thanks :DDD

[wet sentinel]

Maybe lang's complex analysis too especially problems of chapter XV

[restive pecan]

Bruh😭

[peak storm]

What are some good resources for a good foundation in discrete mathematics? One that doesn’t assume much, if any at all, prerequisite.

[dry rune]

Would you like your copypasta to be fettuccine or linguine with parmesan sauce

All puns aside, I'm actually being serious

I need the mathematics version of The Tao of Physics

Something similar in motif

Though Tao of Physics wasn't exactly life-changing, but you get what I mean

I hate you guys ☹️

I should have asked GPT instead

Next time someone asks for a book recommendation here, I'm going to say Mein Kampf as a petty retaliation against this server

[wet sentinel]

Idk what that book is but from a quick search it doesn't seem to contain any actual physics content, ie content to be studied as a physics course for example

So you want a book on math history or something like? Or do you want to study a topic new to you?

If the former then I don't have any recommendations since I havent read/looked for a book with that content, if the latter then we (anyone who may recommend and me) have to know what math you've learned to be able to recommend something suitable

[remote sparrow]

Marx:

There is no royal road to science, and only those who do not dread the fatiguing climb of its steep paths have a chance of gaining its luminous summits.

Feynman:

I have a friend who’s an artist and has sometimes taken a view which I don’t agree with very well. He’ll hold up a flower and say, “Look how beautiful it is,” and I’ll agree. Then he says “I as an artist can see how beautiful this is, but you as a scientist take this all apart and it becomes a dull thing,” and I think that he’s kind of nutty. First of all, the beauty that he sees is available to other people and to me too, I believe. Although I may not be quite as refined aesthetically as he is ... I can appreciate the beauty of a flower. At the same time, I see much more about the flower than he sees. I could imagine the cells in there, the complicated actions inside, which also have a beauty. I mean it’s not just beauty at this dimension, at one centimeter; there’s also beauty at smaller dimensions, the inner structure, also the processes. The fact that the colors in the flower evolved in order to attract insects to pollinate it is interesting; it means that insects can see the color. It adds a question: does this aesthetic sense also exist in the lower forms? Why is it aesthetic? All kinds of interesting questions which the science knowledge only adds to the excitement, the mystery and the awe of a flower. It only adds. I don’t understand how it subtracts.
your time is better spent learning math and science from textbooks rather than seeking out pop math/science books that try to push some weird mysticism. there are many textbooks that plenty of people find engaging and stimulating and that aren't simply dry and formulaic.

[wet sentinel]

Yea because D&F is boring

[remote sparrow]

it's fine

[wet sentinel]

Also maybe bprp for calculus addiction

[daring wolf]

lang algebra #1 book

[remote sparrow]

he has an undergraduate text on abstract algebra

[wet sentinel]

What's your opinion on it? And how do you think it compares to other textbooks on abstract algebra (like D&F for example)?

I am using it rn, I find it nice but I want to know what others think about it too

[dry rune]

Who would be interested to read something named "Dammit and Foot" anyway

I'm checking it out though, seems like a pretty good book

Not exactly what I'm looking for, but all recommendations are appreciated ‼️

[dry rune]

A Math History book would be nice!

I'm going to search up the names of authorities in mathematics and see if they published a book like Heisenburg in Q.M for example

Perhaps that would suffice

[old elk]

The book fulfills its objective: it is a book for graduates and that's it, Gallian and Judson fulfill the task better.

The book is a well-told dictionary, now it wants challenging exercises to give it

[manic cairn]

lang’s algebra changed my life, and it fits the grandiose part.

it is also too hard, i’d say

try lang’s undergraduate algebra: thats where i started

[heady ember]

[fiery drift]

Is there a gentle introduction to algebraic geometry, even if I only have basic knowledge of category theory? I have some knowledge of rings, group fields, and Galois theory.

[dry rune]

I didn't see this before until now, this is beautifully articulated! This is one part of what I'm looking for. Quite life-changing in its own way. Thank you for showing me this!

[dry rune]

Alright, thank you to those who contributed. I'll take everyone's word for it‼️

[molten gulch]

<@&268886789983436800>

[remote knoll]

@dry rune not cool

I'm sure you were joking, but it was in poor taste

[quick hornet]

fwiw wrt your original question i think youre putting way too much stock into randos on the internet who pretend to be into physics

they mythologize random books that they havent actually read because they were written by a name they recognize or whatever

mathematics doesnt have as prominent of an internet larp culture, but it does exist

those folks shill stuff like Lurie's books or the nLab

or Rising Sea or Principia Mathematica (either one)

i mean theres definitely a pop math culture, its just less focused on textbooks and lectures specifically

theres no equivalent to the feynman lectures

pop math culture is more focused on random open questions that are only relevant for having a simple statement

(almost invariably number theory questions)

and then like, OEIS

and shit like that

oh also a bizarrely large amount of focus on genus as a topological invariant

presumably because "donut = coffis cup" makes nice clickbait

but it leads to weird statements like "topologists think donuts and coffee cups are the same shape" which is just very obviously not true

sorry i shouldnt be rambling about this in #book-recommendations

[oblique hatch]

It’s probably the most intuitive invariant to explain

[quick hornet]

cardinality :)

[remote vortex]

Considering the preponderance of Cantor deniers, I'm not sure that's true.

I haven't seen nearly as many genus deniers.

[quick hornet]

if they knew the technical definition of genus they'd be denying it too

"how does this relate to the number of holes"

"how can a glued-together dodecagon have 3 holes"

anyway im not saying genus is a bad topological invariant but its only like, B tier

[wet sentinel]

I am talking about his book "undergraduate algebra" not "algebra"

[quick hornet]

compactness is an S tier topological invariant

genus 0 specifically can be A tier i guess

[wet sentinel]

A serge lang fan I see

I like his writing style a lot too

That's why I am using his undergraduate algebra and will use his CA book too

[quick hornet]

now i wanna make a topological invariant tier list

where would you put orientability

its an important property but i feel like its rarely used for topological means like this

maybe that makes it B tier too

[wet sentinel]

I also tried his algebra book but it's too hard and time consuming for a first exposure to algebra

[quick hornet]

path connectedness is F tier though

worst property

[sage python]

I like this idea of a tier list

[remote vortex]

It's a top tier tier list, to be sure

[fresh coral]

Has anyone read Mathematics for Machine learning by Marc peter diesenroth ?

[manic cairn]

how is it genus 3, isnt it just homeomorphic to a disc?

[quick hornet]

glue together opposite edges

confirm for yourself by finding the cuts

[manic cairn]

oh, you mean start with the dodecahedron then glue, not glue something into a dodecahedron

[hot moon]

Polyhedrons

Idk I just wanted to use that word.

[molten gulch]

It's polyhedra

[cunning elk]

my HS friend made this whole model of all the johnson solids

folded them all and made a little shelf for them

[gray gazelle]

any good collections of practice problems w/ step-by-step solutions for college algebra? been going through a few different books, but there's usually not a ton of step-by-step solutions. don't need them all the time but it'd be nice to have more than I do

[viral mauve]

any quick articles i could read to boost my ucan personal statement?

[fickle whale]

Wtf

[compact elbow]

What do you all think of any of Tom Apostol's books? I've been thinking of filling in a lot of my gaps in knowledge and I was hoping to start with "Introduction to Analytic Number Theory."

[wet sentinel]

i am using this book rn and i like it

i am still at the beginning though so my experience may not be too useful

[compact elbow]

Cool, I'm glad. I mean, at worst I pick up just a little and the book wastes some time, but I doubt that will be the case! Thanks!!

[bright epoch]

I'm about to have a long transit ride with no Internet connection, and I want recommendations for really good grad-level math texts. Any subject, just the best of the best in whatever you can think of.

[wet sentinel]

do you know multivariable calc?

[bright epoch]

I recently finished "prime numbers of the form x²+ny²" by Cox which was very good, for instance.

A bit lower level than I'm aiming at but about there

[compact elbow]

Enough to do basic stuff in it. If I'm missing something, I can refer back to a textbook I have, haha.

[wet sentinel]

hahahahahaha

yea you can start with apostol's book directly

also you wont really need it until later in the book

[manic cairn]

lang’s algebra.

i had it in the mental hospital with no internet connection

[molten gulch]

Hartshorne?

[compact elbow]

cool, thanks! 🙂

[graceful cloak]

Guys I love flatland sm but I wonder if it’s considered a math book

[compact elbow]

I don't know anything about it, but based on what I just read from it's summary, it is sort of like a math book in the sense a Veritasium video on math is a math video. They are more about entertainment and showing a cool concept (or collection of concepts) in a digestible way. I think it's a good primer for understanding how we actually go about representing higher dimensional spaces in 3 dimensions, and what the limits of that is, but based on my limited knowledge, it's more a math-fic book (kind of like science fiction) that draws on math. Still, seems like an interesting read, if anything.

[manic cairn]

i feel he cites a lot of out-of-book commutative algebra

lang builds things from scratch

[graceful cloak]

You should read it

[remote sparrow]

There are several books on classical algebraic geometry that don't depend on category theory at all. Here are the ones I've seen get mentioned:

• Beginning in Algebraic Geometry by Emily Clader and Dustin Ross (open access)
• Ideals, Varieties, and Algorithms by David A. Cox, Donal O'Shea, and John Little
• Algebraic Geometry: A Problem Solving Approach by Thomas Garrity et al.
• Algebraic Geometry: An Introduction by Daniel Perrin
• Basic Algebraic Geometry I: Varieties in Projective Space by Igor R. Shafarevich (the second volume does schemes and complex manifolds)

By the way, as the above books are all published by Springer except Garrity et al., you may be able to grab them at a lower price from Springer's website using discount codes they distribute periodically.

Relatedly, here are some references on algebraic curves from a classical viewpoint:

• Algebraic Curves by William Fulton (this book is out-of-print, but is freely available online. You could have the book printed with a print-on-demand service like Lulu if you really wanted a hard copy.)
• Plane Algebraic Curves by Andreas Gathmann (strictly speaking, these are notes rather than a full-blown book, but they are fairly complete and include exercises. Gathmann also has notes on modern algebraic geometry.)
• Complex Algebraic Curves by Frances Kirwan
• Algebraic Curves and Riemann Surfaces by Rick Miranda
• Algebraic Curves and Riemann Surfaces for Undergraduates: The Theory of the Donut by Anil Nerode and Noam Greenberg

The latter three books by Kirwan, Miranda, and Nerode-Greenberg cover algebraic curves from a complex-analytic perspective. Tangentially, Otto Forster has a book on Riemann surfaces that is a bit more sophisticated.

[remote sparrow]

The Foundations of Mathematics by Kenneth Kunen. From this [list](#book-recommendations message), you may also find Mileti and Westerstahl useful. Books on computability/recursion theory which require no background in logic are Bridges and Cutland.

[velvet flax]

unironically that was the only book i could stick with on algebra

[velvet flax]

intro to smooth manifolds by john lee

also maybe foundations of mechanics by abraham, marsden, and ratiu

not strictly a math book

but theres enough math in it to make it close enough

[languid bloom]

has anyone gone through the book Unsolved Problems in Number Theory by Richard K. Guy?

just ordered a bunch of used books for cheap to check out and that was one of them since it seems interesting

[vital chasm]

Ralf Schiffler's Quiver Representations reads ok for me so far

Instead of doing rep theory of groups why not do rep theory on graphs

[remote sparrow]

https://press.princeton.edu/books/hardcover/9780691207582/a-course-in-complex-analysis

70% off with code SHOP70 for orders shipping within the UK, Europe, Middle East, Africa, India, and Pakistan.

70% off with code SAVE70 for orders in US, Canada, Latin America, Asia, and Australia.

sale from october 1st to october 31st

[remote sparrow]

@sudden kindle @vital bane @heady ember

[languid bloom]

graduate as in undergraduate (if you study ahead enough)

[velvet flax]

does graduate level actually mean anything?

like kelleys gen top seems perfectly readable for most undergrads

[cunning elk]

what if your undergrad sucks

[orchid vortex]

Anyone able to order this? I tried but the site bugged out on me.

[fiery drift]

Thank you for your recommendations!

[heady ember]

Does the discount include shipping fees?

It appears not 😔

$87 shipping

[remote sparrow]

SEA isn't a part of asia then?

[heady ember]

I think the discount just doesn't apply to shipping

The book itself costs only 25 once I applied the discount

Hm perhaps I could email them and try to see if they could offer an alternative shipping method. Right now it uses "Priority Mail International" but I sure am not in any urgency to receive the book.

[remote sparrow]

just let neam be an intermediary

[heady ember]

Is the shipping fee to India much different though lol

[remote sparrow]

i would imagine so given india is listed in the promotional blurb

try some random address in india for a quote

[heady ember]

On another note, how's Princeton University Press' bind quality?

If its not good, then I might as well get it printed somewhere (e.g. some China vendor), and then bind it myself tbh

[remote sparrow]

from my sample size of 2, the binding for princeton's translation of Capital by marx is excellent; it's sewn and stitched. zakeri is a perfect bound hardcover.

[heady ember]

Perfect bound...

😔

[distant spear]

Checkout 'printster'

[floral vessel]

Hey! Does anyone know of a good secondary school book that cover, if possible, everything between primary school and high school?
Im trying to teach myself math and the books I've used dont explain much/as I'd like them to

[sudden kindle]

Oooh thanks

[dry rune]

Sorry, lol. My pol-sci humor got ahead of me. I'll tie a leash 'round my crude sense of humor next time

Nevertheless, does anybody know a thing or two about different figure authorities on abstractions and metamathematics besides Godel and Cantor? A particular book will also suffice

Philosophy of mathematics books would also be absolutely fantastic

[vital bane]

Is it only for that book?

[topaz delta]

What do you think guys of this book

[wild blaze]

How do we check for faculty strength in grad schools? I know the rankings are shit and subjective, so how can we check for it? I know you start by looking for fields you would like to study in, and then what? How do I know professor prominence unless it’s someone absolutely famous

[hollow peak]

You need to talk to people, whether at your school or otherwise

You can also just straight up email the people your considering working with and ask what the subject group culture looks like at their home institution ("how is the topology group here?")

Check their arxiv posts to see if they're productive and do work that you would find interesting

Look into seminars in the department (usually listed somewhere online, if not ask a current student). If the grown-up seminars (i.e. not run by students) are organized by them, it's usually a good sign

[steep kettle]

I want to study Stochastic processes, I have background of non-measure thory probability course(similar to but more rigorous than STAT110 by harvard), is there any textbook that you guys can recommend me

[golden blade]

is anyone has any reference material on (big M-method)

[visual delta]

What does this mean? I am ready to check out.

[mellow wren]

Are you in the cart?

[visual delta]

I got it. I think it was issues with a VPN where my address didn't match or something.

[exotic comet]

Any book recommendations/study materials for the gre subject test?

I haven’t taken abstract alg( groups rings fields)

[visual delta]

Thank you for helping me save 60$.

[timber mesa]

huh cool

sakeri's book looks good

[narrow gull]

Why couldn't the mathematician do their complex analysis?

They were on Ahlfors

[young thorn]

lmfao

[pine tundra]

Could someone explain it? I didn't get it

[molten gulch]

"on ahlfors" sounds a bit like "on all fours" so how can one do maths if they can't hold a pen

[pine tundra]

(I know that Ahlfors is a complex analysis textbook, though)

[pine tundra]

Ohhh I see, I didn't know the collocation "on all fours"

Thanks 👍

[gray gazelle]

any good books

for introductory to medium level number theory

[molten gulch]

ireland and rosen, apostol (for analytic), marcus (for number fields)

[young thorn]

apostol my love

[remote sparrow]

it's 70% off on selected books.

[lone epoch]

Does anyone have book recommendations for getting good at speed arithmetics (being able to multiply/divide numbers really quickly, using patterns to add and subtract numbers and whatnot)?

[meager kestrel]

I'm looking for good linear books other than gilbert strang , Jefferson and Sheldon axler

[molten gulch]

friedberg!

[cunning elk]

the cut the knot website has some speed arithmetic tricks you could look at

some of the most common ones I use are like

when I want to multiply by 5 I first multiply by 10 then divide by 2

or when I want to add 9 I add 10 and subtract 1

[daring wolf]

friedberg

[last tree]

Hello, I'm looking for a comprehensive reference book for mathematics (primarily covering up to undergrad college level) that i can use to just look up quick formulas, theorems, and identities relatively quickly. No proofs, don't need a textbook, I have plenty. Just purely reference. I know I can google/use AI but i really want the quickness and material object.

Even better if you know of a free resource that I can just print out for myself. I've found a few but nothing well laid out and far from anything comprehensive covering undergrad calc, trig, discrete math, linear algebra, and real analysis. Guess I'm looking for a math encyclopedia of sorts. Thoughts?

[wet sentinel]

there is no single reference book that covers all what you are looking for

i also highly doubt that there is something like a book that lists all theorems taken in a first course on real analysis without proofs for example

but who knows there may be something like that, best to wait for other responses

[last tree]

yeah I may be dreaming... but def get sick of wading through texts and opening new tabs just to recall a small factoid that i don't use often

thanks for yourr esponse

[wet sentinel]

but if you want something like a book on real analysis that contains the theorems (of course with proofs) but without much talk outide of that, ie a book that gets straight to the point, then maybe check rudin's PMA

for a reference on linear algebra maybe werner greub's linear algebra is suitable

[last tree]

Ah I see my mistake, i threw real analysis in there because I have it coming up soon in my math program but didn't yet realize it depends heavily on proofs to learn and operate.

[wet sentinel]

yea, real analysis and linear algebra are proof based

[last tree]

cool thanks for the tips

[wet sentinel]

so the nearest thing to what you want would be a reference book, which wouldnt omit proofs etc.. but would probably get to the point directly and contain most (maybe all) things that you encounter in a course on the topic at hand

[marble solar]

Here's a somewhat reference: Roger Penrose the Road to Reality. Another interesting type of book might be a history of Math book. Mathematics and its History by John Stillwell

[woeful venture]

Hi, do you guy have any math books for fundamental for BEng Computer Engineering and Digital Technology?

[last tree]

i'll take a look

[marble solar]

Yeah, both of them don't really meet what you're looking for. I don't think anyone outside of specialized experts can understand all of Penrose's road to reality

[lone epoch]

Oh nice

Thank you

I saw this one, was wondering if there was anymore?

I actually asked ChatGPT to basically web-scrape for me LOL

[normal crystal]

no piracy

[slow roost]

wasn't aware thats piracy; just a result that came up near the top of a Google search

deleted link

[mortal minnow]

howdy, I want to ask a recommendation for learnning calculus, any books that are easy to pickup?

[vital bane]

Most books are easy to pick up if you use both hands

[odd kiln]

Hello, im in middle/high school (16 yo) just read Basic maths by Serge Lang and am looking for more advanced books but still dont know what topic, maybe calculus

@wet sentinel i recently told you that im in middle school cause i misunderstood what that meant, i read that book quick and skipped some but still very good one!

[wet sentinel]

ohhh, alright then try stewart's calculus in that case

[wet sentinel]

@odd kiln if you want study one thing at a time then do this, if you want to study multiple things then maybe try linear algebra too

[odd kiln]

Okay i see

[wet sentinel]

that being said, there is no need to rush things but if you feel like studying multiple things then you can go for this

[odd kiln]

I suppose that's basic calculus and just curious, how far can you explore that topic until there are no books explaining this

[odd kiln]

And i see there are many editions of the book, is there a difference between them?

[pulsar veldt]

Yea, the year of publication

[wet sentinel]

yes there are probably some differences between some editions. Personally i used "Calculus early transcendentals" 7th edition

i think there is no good reason why i chose this edition, but more like its the edition i stumbled upon while searching (probably)

[wet sentinel]

stewart's calculus for example covers everything in calculus (most books on calc probably do that)

after calc you can jump into intro real analysis for example where you see proofs that validate what you were doing in calc

[daring wolf]

i mean there are no reason to get newer editions for this

obviously new versions have some more exercises but that's still waste of money

better to get cheaper edition and move over later

[wet sentinel]

yea, probably

i didnt think about that for obvious reasons

[daring wolf]

it's hilarious that the author has passed away but newer versions are still coming

the publisher is just too greedy

[wet sentinel]

he is probably writing and sending them from the other world

[cunning elk]

he’s saving up money for his self masturbatory vanity project “double integral house”

because a single integral wasn’t enough

[dusky pasture]

Can someone recommend me good algebra 2 books? It would be helpful if it wouldn't be rote memorization coz I suck at that

[timber mesa]

that's one of the combinations of words of all time

[visual delta]

Is there a way to gift someone a pdf book from Springer?

[slow roost]

anybody who’s gone into advanced diff geo, got any recommendations for texts on more specialized subjects after going through a core course in manifolds and curvature at the level of Lee or Tu? maybe something to get into Ricci flow more, or anything you find interesting

[remote sparrow]

@burnt sorrel

[cursive rivet]

i went into the study of special geometric structures, Joyce's book Riemannian Holonomy Groups and Calibrated Geometry is a pretty good introduction but somewhat light on technical specifics, for the other side of the coin there's Salamon's Riemannian Geometry and Holonomy Groups

Spin Geometry by Lawson and Michelsohn is a good book on a topic (spin geometry) that's everywhere in geometry and topology and used in special geometric structures all the time

you could also go learn complex differential geometry, which has lots of great uses and is really fun

[grim ore]

Do they go to the same uni?

chances are you could pull up a springer pdf if your uni has a license for it

[cursive rivet]

I actually really like Lee's new book for this, the books by Huybrechts or Moroianu are also standard references, and Joyce's book contains an introduction from the perspective of special geometric structures (but supplement it with others)

if you like the Riemannian geometry end, I'd also go learn Hodge theory and the basics of geometric analysis no matter which of these you go into, the complex differential geometry books should cover it (but usually applied to their specific case)

for Ricci flow, the geometric analysis first is at least morally a prereq, if not a hard prereq. I think Chow-Knopf's book is the best intro to it personally

[slow roost]

cool, thanks for your thoughts. Have you read Jost’s Geometric Analysis? I have it but find it very tough going. Maybe that’s just the nature of the subject for me though

[cursive rivet]

I haven't read it to any depth, but people I know don't love it overall as an introduction/exposition

[slow roost]

Riemannian Geometry and Geometric Analysis, I mean

[cursive rivet]

I sort of learned the stuff from a hodge podge of various complex geometry books, Aubin's Some Nonlinear Problems in Riemannian Geometry, and Besse's Einstein Manifolds (highly recommend both of those books btw, though they are a bit old and quite hard)

for Ricci flow, probably the thing you need most is the kind of comparison geometry you'd see at the end of Lee's Riemannian book

Chow-Knopf's appendix probably has enough if you're familiar with the material in Lee

though I am by no means a Ricci flow person

all this stuff is very much on or bordering Riemannian geometry, if you try it and want something else (e.g. towards gauge theory) feel free to ask

[slow roost]

awesome, many thanks. This should keep me plenty busy for a while

[velvet flax]

is this lee’s riemannian manifolds book?

[cursive rivet]

complex manifolds

[slow roost]

Lee is truly goated

I'll definitely pick up Complex Manifolds sometime soonish

[remote sparrow]

gift? all springer pdfs are drm-free, which means you could just send your file to them once you download your copy

oop

@visual delta

[molten gulch]

\ <@&268886789983436800> is this discussion of piracy considering that all springer books have TOS stating that they cannot be shared under the terms of download?

[fallow cypress]

sorry you can't ask people to help you pirate in this server

[normal crystal]

I'm not continuing that line of chat
but I was curious about the DRM claim
seems like they do watermarking instead

[visual delta]

I mean buy it for someone else. You can't have access to it yourself.

I didn't know if that was possible.

I'm pretty sure you can do that with Kindle, but I like sending a pdf to my Kindle rather than having the Kindle version because all of the typesetting and images are how it was meant to be.

[fickle whale]

Heheheh

Instead of pirating books, just write your own book on the subject and share with friends

[timber mesa]

to write your own book you need to read books though

where do you think the >100 references list comes from

[full cairn]

He's not asking someone to help him pirate, he's saying that if you want to gift someone an ebook from Springer, you can just buy it yourself and send them the pdf. Doesn't seem so problematic to me

[visual delta]

Is there a gift card maybe? The person sending me the gift definitely doesn't want to read a math textbook lol

[timber mesa]

seems like there's no gift card-like option in the Springer website, one option is looking in retailers that offer books from the publisher e.g. Amazon, Barnes & Noble etc

that said I have no experience gifting people Springer e-books lol

[molten gulch]

Yeah the issue is that you can't legally do that, the PDF's have a policy that they cannot be shared from the person who purchased them

[visual delta]

I never said that you bought it yourself. I said you gifted without ever owning it yourself.

[remote sparrow]

in any case, why not gift a physical copy instead?

[visual delta]

I guess it might be easier to carry around.

I guess I would be okay with a physical book.

[remote sparrow]

might wanna wait for holiday season too; usually springer hands out discount codes

last year's holiday sale wasn't that great; only 30% off compared to 50% in previous years, but it might be different this time around

[visual delta]

Yeah. It would be for the holidays.

[wet sentinel]

but wasnt that the point of the question, ie to know if its possible to share or no (more like to give than to share)?

(at least thats how i interpretted the question)

[languid bloom]

should I finish spivak calculus before starting his calculus on manifolds book or would it not matter very much?

[molten gulch]

yes

you should

[languid bloom]

ty

[molten gulch]

@mossy flume look what the cat dragged in (aka our uni's springer subscription being updated so we got the 5th ed now)

sadly we prefer pdf as we read off our computer

[true sail]

Are epubs good for reading math books?

[remote sparrow]

quality is kinda variable, but also i only looked at epubs on desktop with sumatrapdf, so maybe it's only ugly there

[umbral field]

pretty much a function of the quality of ebook conversion, and math tends to have more stringent layout requirements (easy to botch if done lazily) than literature

pdfs tend to be better since they don't require any changes in layout compared to print versions

[rose bloom]

hi guys, im somewhat close to finishing up abbott's understanding analysis, and i was wondering what i should do next

I have some ideas

1. pick up another book on real analysis with the same content like rudin's pma or apostol's calculus to get an in-depth understanding
2. pick up a book on real analysis with further content like charles pugh's real mathematical analysis
3. go to measure theory

(main reason im not sure is bc abbott doesnt have too much material and is has maybe slightly less depth than most real anal textbooks so im wondering what i ought to do next)

also idm doing things that arent on this list btw

[vital chasm]

If you wanna go to measure theory then Folland's book is quite good

Its basically enough measure theory, then a whirlwind tour of basic modern analysis

[remote sparrow]

#book-recommendations message

you can also consider reading axler's measure theory book: https://measure.axler.net

[rose bloom]

im more concerend about if the content in abbott has enough breadth/depth for me to tackle these topics

[rose bloom]

thanks for the rec

[rose bloom]

ooh nice

[rose bloom]

But yea this is the key issue—dk if im ready yet

[vital chasm]

You should try and then if you think you are having trouble then go back

Personally I dont think you'll have a problem, basic measure theory does not have many prerequisites

[rose bloom]

mmmm

ok

[rose bloom]

what about measure theory with a probability perspective

[vital chasm]

Folland has a section with probability, but its really touch and go

Maybe Durrett's book might be more suited for probability

[rose bloom]

mmm thanks

so basically just

try it out first, see if its reasonable, then decide?

[vital chasm]

Yeah

The content page

[rose bloom]

this is for folland?

[vital chasm]

Yeah

[rose bloom]

mmm ok

[remote sparrow]

try williams or rosenthal

https://www.amazon.com/Probability-Martingales-Cambridge-Mathematical-Textbooks/dp/0521406056

https://www.amazon.com/First-Look-Rigorous-Probability-Theory/dp/9812703713

you can keep billingsley around as reference

billingsley is still good and you can learn a lot from it, but given your modest background, i recommended williams and rosenthal instead

https://link.springer.com/book/10.1007/978-1-4471-0645-6

oh i heard of this too

@rose bloom

[rose bloom]

Great thanks guys

[mint mortar]

A tad late but https://www.amazon.com/Mathematics-Content-Methods-Meaning-Volumes/dp/0486409163

is the closest you will ever get to it

[sacred turtle]

Can anybody recommend a book explicitly on tensors?

[molten gulch]

Doesn't exist, please read an algebra text that covers multilinear algebra, a multilinear algebra textbook (like greub), or a differential geometry book

[sacred turtle]

Thanks.

[arctic hamlet]

I am a masters student in pure math
How much logic should I know
And any book for me to study it

Please help
Everyone tells different answers to this
My college logic prof said to do Richard Kayes
My logician friend said to do Kenneth Kunen

[full cairn]

Please stick to one channel, I see you posted in #category-theory and #foundations as well

[sour cargo]

Why not just follow your prof's suggestion?

And do you really need logic? I think many mathematicians know little formal logic but still have done perfect work.

[obtuse walrus]

but for like proof building logic kinda helps

[fickle whale]

Vector and Tensor Analysis by Tarapov (it's awful)

[fickle whale]

I know of one and it's not a fun read

I also haven't read most of it but it for example never mentions the Levi civita symbol by name

Though it does still talk about like solenoidal vector fields and helmholtz decomposition and the fundamental theorem of vector analysis

[arctic hamlet]

I just want to have it as a tool in my tool box

[vital chasm]

if you want to learn logic theres a ton of books out there, you can probably trust your prof and try Kaye, and if you dont like it switch to another text

ultimately its up to you

[sour cargo]

hmm I have no experience in research but, if you do not know what specific topics in formal logic you want to learn, I think you actually need no more logic other than some basic theorems in model theory (such as compactness thm and lefshetz property of algebraic closed fields)
and it's not necessary to read books for knowing how to use those theorems, just google them and you will find many lecture notes

[vital chasm]

recently in math there are more and more results that require some logic results, aside from the completeness thoerem and lefschetz property, one can construct counterexamples with ultraproducts, and recursion theoretic results have been seen in geometric measure theory and differential geometry aoming others

[arctic hamlet]

OK bro thanks

[arctic hamlet]

I want to do algebraic geometry how much logic should I know

[vital chasm]

you likely dont need any for that, but my model theory prof says model theory and alg geom have very strong parallels (idekwhat parallels), so maybe you can get inspiration idk

[pallid steeple]

Hi, I'm new here :0 Have there ever been any sort of reading groups on this Discord where participants go through a particular textbook and meet every week or so?

[loud cradle]

there have been quite a few, you can check #events to see the past ones and if there are any current ones

[pallid steeple]

Thank you!

[dusk hare]

are there any books to study the PDEs !

[lean juniper]

can someone recommend books for self-taught math

[molten gulch]

evans and taylor are both good

[marble solar]

Evans and Taylor are great for graduate students. But for undergraduates, Walter Strauss has a good book

[brisk silo]

There's a python book my intro class used on orielly lemme hunt

Are you looking for a specific data structure? An overview? Or handholding?

Hmm
Yee okay
Idk if the book i have is the best in mind, since it was more babies first python

I think there's a website/ book for design patterns that might fit the bill

Design Patterns in Python https://share.google/tIucpdQ3sUrehRxwK

[foggy quest]

go to codeforces for problems

you don't need advanced structures like segment tree and fenwick tree for leetcode problems

[brisk silo]

It might be worth doing a big ish project then?
At least for me, I do better with an actual application

Drilling coding problems can be good for getting familiar with the language, but in industry/ academia, there's application and context
though industry is typically just maintaining 30 year old code made before any of that existed

[remote sparrow]

mathematics research broadly does not depend on having any knowledge of mathematical logic, but if you want to learn, you can try one of these books: #book-recommendations message

[brisk silo]

Whatever you want truly
For me, I have a data analysis project where im utilizing sentiment analysis on song lyrics
If you want to do anything ai/ data heavy, there's a lot of ideas (i can drop a list here or in dms im new and idk the preferences cuz it isnt a book)! It also gets you familiar with gitlab, an industry standard. Plus employers like application of skills more than just the skill

[normal crystal]

for python specific DSA this is supposed to be good and is free
https://runestone.academy/ns/books/published/pythonds3/index.html
also Goodrich textbook

oops, forgot the link

[hushed vector]

i got interested in ordinal analysis, but I don't know any proof theory (yet) – what books / lecture notes are there to learn it from 0?

or should I just learn proof theory first. if yes, then what topics in particular

found this, but idk if it's good

[remote sparrow]

i never heard of this; i only heard of pohlers from the logic matters study guide

https://www.logicmatters.net/resources/pdfs/LogicStudyGuide.pdf

[hushed vector]

thank ya!

[remote sparrow]

pohlers does more of that ordinal analysis stuff. takeuti and troelstra/schwichtenberg do more structural proof theory

[timid elm]

Textbook preference is like music taste, everyone is gonna say theirs is the best. Go with what the professor says, and if you want more clarification, ask the prof what about the text they like. Heck, ask your friend also. You might learn that they value different parts of the text, or the 2 texts cover different kinds of math that are more or less important to different people

[silver stirrup]

Can someone please refer some resources on Lagrange multipliers with derivation?

My multivariate analysis class covered it in class but I got lost

And our textbook, “analysis on manifolds” by Munkres

[brisk silo]

Does anyone have any good books for number theory?

[wet sentinel]

what kind of number theory

elementary, analytic or algebraic?

[brisk silo]

Frankly any (Ive touched on all of them in an entry way for bachelors)
But analytic would be fun

[wet sentinel]

for analytic i would recommend apostol's introduction to analytic number theory

[young thorn]

Iwaniec & Kowalski Analytic Number Theory

[molten gulch]

Ireland and rosen

[wet sentinel]

if you've done that then i hear that davenport is more advanced but idk about it, but someone could give a feedback on it

[molten gulch]

Also apostol is good

[young thorn]

also if u wanna get into multiplicative number theory (Montgomery & Vaughan II) is rad

[wet sentinel]

there is also a book by montgomery - sniped

[molten gulch]

I'm familiar with montgomery 1, when was vol2 released?

[wet sentinel]

idk about it too but ive heard the name

[young thorn]

i have no idea when it was released but thats the title

[molten gulch]

Oh damn

[tardy bough]

does anyone know any books that cover pre calc-calc 3

[wet sentinel]

idk about precalc but for calc i recommend stewart or thomas

[young thorn]

anyone looked at those soviet books mir publication ?

they r p good and cheap

i studied calc mostly from those

[molten gulch]

Stewart precalc + stewart calc esrly transcendentals

[wet sentinel]

i would also say that you can first take a look at one of these bc you may find it unnecessary to go through a book for precalc

[tardy bough]

i dont actually need the pre calc section

[young thorn]

y can look at it too if u want it has good problemz

[cunning elk]

literally any standard calculus text

stewart is one of the most used

[gaunt night]

Any springer good books?

To learn linear algebra

[wet sentinel]

I recommend linear algebra by Werner greub

Although I need to say that it's a hard hitter

[gaunt night]

thanks bro

[wet sentinel]

I also recommend waiting for other responses too, because that would leave you with more options to choose from

[remote sparrow]

the best books are not springer

#book-recommendations message

[molten gulch]

not a springer book but we quite like friedberg insel and spence

[velvet flax]

baby rudin + itm + ism /j

unironically tho, spivak calculus then dgc if ur an engineet

if not, spivak then spiivak calculus on manifolds

[tardy bough]

i no understand

[tardy bough]

other than spivak calculus and stewart

[velvet flax]

apostol

[wet sentinel]

There is Thomas's book too

[tardy bough]

i might use this one if you dont have any recomendations

[wet sentinel]

Although I would say that there is only one (maybe two) books up to isomorphism

So like any textbook on calculus would be the same

[tardy bough]

nooo

[wet sentinel]

Maybe it's either spivak's or stewart's style (hence the maybe 2 books in the previous message)

Other than that they all are essentially the same

[tardy bough]

what would u say is after thomas's book

[tardy bough]

sigh

[wet sentinel]

There are multiple things you can do

You can do linear algebra, real analysis, abstract algebra or maybe elementary and then analytic number theory etc..

[tardy bough]

i was thinking of doing real analysis but where would i fit this

[wet sentinel]

What does this question mean

[tardy bough]

as in

wait nvm

so after this whole book I'm gonna do real analysis

but then what😟

[wet sentinel]

So after real analysis you can either do complex analysis or go to functional analysis for example

although a small note that you should learn linear algebra too to study functional analysis or even multivariable real analysis

the thing is that you will have to study linear algebra, abstract algebra and real analysis to proceed further

abstract algebra may not be necessary for things like FA

[cursive orbit]

you def should know at least undergrad algebra for functional analysis

[wet sentinel]

but say you want to study algebraic geoemtry later on or algebraic number theory or galois theory etc,,,

then you should have a background in AA

[wet sentinel]

even AA?

idk bc i havent studied FA yet

[tardy bough]

whats the full order of how i should study the books

[wet sentinel]

but ik that you need LA since FA is all about infinite dim vec spaces

[wet sentinel]

there is no strict order for the first few topics, ie RA LA and AA

you can do these in any order you wish

although some may argue that its better to do LA before AA but its not necessary

after that it will depend on what you want to do

[tardy bough]

so after calc 1 I should study RA,LA, and AA in whichever order I like b4 functional analysis and others

[wet sentinel]

After calc 1 You continue with calc until multivariable

[wet sentinel]

After you are done with multivariable calc You do this

Also you can study multiple things simultaneously if you feel like doing that

[tardy bough]

ohh

[wet sentinel]

In that case I would recommend studying linear algebra alongside calc

[tardy bough]

but thomac calculus covers this though

[tardy bough]

i could but i think i should study seperately for now

[wet sentinel]

It does, I was just pointing out that you shouldn't really toss that part and move on. Well technically you can but going through multivariable calc is probably good

[wet sentinel]

I see yeah go at your pace np, the important thing is to enjoy what you are doing

Well for RA,LA and AA you will have to study them all even if you don't enjoy them but yea

[tardy bough]

linear algebra was cool when i did some of it

[wet sentinel]

You will at least enjoy one of them, otherwise maybe choose something else other than math (jk)

[wet sentinel]

Nice, then maybe you will like AA too

[tardy bough]

abstract algebra was also calm

i did a lil of it too

i only recently touched real analysis

[wet sentinel]

So you are somewhat acquainted with proofs

[tardy bough]

yeah

[wet sentinel]

Great

[wet sentinel]

I see, so you are cooking

[gaunt night]

yeah, thank you guys for your advice

[tardy bough]

yeah but i was doing calc 1 and real analysis at the same time

im doing calc 1 on flvs

[gaunt night]

linear algebra is not the most difficult part, but it is quite vital

[wet sentinel]

what's flvs

[tardy bough]

also could you give books for LA,AA,FA,CA

[tardy bough]

florida virtual school

[gaunt night]

Some classical ones I’ve read

[tardy bough]

🤔

[wet sentinel]

LA: #book-recommendations message
AA: #book-recommendations message
CA: #book-recommendations message
For CA, i also add lang's complex analysis.
FA: #book-recommendations message
and finally ik that you didnt ask for RA but here is a list of recommendations: #book-recommendations message

These lists have many books along with detailed descriptions of each book so it's definitely better than anything I would've written

I would also note something too, there are other subjects like point set topology that open the doors to more advanced subjects too

But well there is too much math to study so it's a long journey hahahahaha

[tardy bough]

is there a photo of the list of math areas that opens other areas

if that makes sense

[wet sentinel]

I am not sure if there is such a thing

[tardy bough]

oh then nvm

yknow what i mean tho

it would be useful

[tardy bough]

whats ra

[wet sentinel]

But essentially RA, AA, LA, point set topology and maybe some discrete math (like combinatorics, elementary number theory ...) should be more than enough to give you a flavor of many things

[wet sentinel]

Real analysis

[tardy bough]

ohhhh

[wet sentinel]

Maybe here you wanted to say real analysis but wrote CA? (I interpretted CA as complex analysis)

[tardy bough]

i want to learn number theoru

where can i fit number theory in

[wet sentinel]

Yea number theory is nice

[tardy bough]

nah i wrote it right

[wet sentinel]

Ohh I see

[wet sentinel]

number theory itself is a whole branch of math

So like there is elementary nt, analytic nt, algebraic nt etc ...

And number theory is known to use ideas from everywhere

For example analytic nt uses complex analysis while algebraic nt uses AA, Galois theory etc..

You would want to start with elementary nt ig (before analytic, algebraic etc ...)

[tardy bough]

yeah

where would i fit this into the book order

[wet sentinel]

Well, as I said before it largely depends on you. Elementary nt doesn't really require any background in whatever was mentioned above. You just pick a book and start

Doesn't even need calc

But the same goes for LA, AA for example

So you start it whenever you want

[tardy bough]

okay phew

what about analytic

also can i get books for both of them

[wet sentinel]

Analytic usually requires complex analysis, but there is apostol's introduction to analytic number theory where you can get away with multivariable calculus without complex analysis ig

It also covers elementary number theory

[tardy bough]

then imma just use that one

[wet sentinel]

Actually I am using it rn and I didn't study elementary number theory before it

[wet sentinel]

Yeah you can do that, and you can always just stop if you find that you need to study something else before it lol

Also note that you don't even need multivariable calc until later in the book, for the first portion of the book you only need to know how to integrate single variable functions and you are good to go

For now I would say finish calc (since you said you want to do one thing at a time for now) and then choose what to do next

[tardy bough]

fr?

is multivariable calc really that hard

[tardy bough]

alrrr

also what are you studying right now

[gaunt night]

You did a wonderful job

[wet sentinel]

No it's not hard

[wet sentinel]

I am studying multiple things rn, reviewing and continuing with intro RA, studying AA, and analytic nt

I will jump to CA after RA (it will happen soon since i am near the end of intro RA) and probably resume LA soon

[wet sentinel]

If you are talking about me then tysm but I didn't do much

[tardy bough]

what year are u

[wet sentinel]

Technically first year but ah I am self studying these

Since my current uni is sadly too bad/useless lmao

(it's online and that should tell you everything lol)

Are you in uni or still in school?

[foggy wolf]

any good calculus books involving lebesgue integrals and a good explanation of them?

and/or any good book for stochastic calculus if you might know.

[wet sentinel]

Lebesgue integrals won't be covered in calculus books

You would see them in analysis books

[foggy wolf]

i mean, I just need a book that explains them well

[wet sentinel]

As for stochastic calculus idk about that sorry

[foggy wolf]

It alright, but can you recommend any good books for lebesgue integrals?

[tardy bough]

wrap it up

are your classes good

[tardy bough]

school

younger than u think

[wet sentinel]

I can't say that I have good recommendations since I haven't studied Lebesgue integrals/measures yet but you can see those in intro analysis books like Pugh's real mathematical analysis or browder's mathematical analysis: an introduction

But wait until someone else responds

[wet sentinel]

No

[wet sentinel]

Ohhhh nice

[daring wolf]

just get a book on measure theory lmao

[tardy bough]

???

whats that

[daring wolf]

see pinned message, there’s book recommendation on it

[wet sentinel]

I forgot that there is something like that

[daring wolf]

[daring wolf]

basically books like rca are measure theory stuffs

[wet sentinel]

Yea but I thought that it may not be reasonable to cover Lebesgue integrals again after covering them in intro ra books

[daring wolf]

all measure theory books should have lebesgue integrals

as it’s very important example of measures

[wet sentinel]

Ohhh I see

Yeah that's reasonable

[wet sentinel]

The quick shift is insane

Also I would leave measure theory to someone else for now, there are more important things to do

Things that are algebra and nt pilled

[daring wolf]

yassine reading a book on automorphic forms when

[wet sentinel]

Yassine's cohomology arc when

[daring wolf]

just start that in algebraic geometry

[wet sentinel]

Yassine is currently trying lang's algebra again

[daring wolf]

Grad one?

[wet sentinel]

The real one

Yes I used it today

I am thinking about using it along lang's ug alg since I feel like the ug one is missing a few things

Anyways I gtg sleep now, the grind shall continue when I wake up

gn, cya everyone

[cursive orbit]

I mean strictly speaking most things are self-contained, but it would be good to know at the very least like what a maximal ideal of a ring is

[echo junco]

closest idea to a ring I have is the one with quaternions constrained to i,j,k,h

[tawny crater]

You already "know" a lot of rings, you just don't call them that way.
Q, R, Z, C, polynomials,...

[echo junco]

wait. Those are rings??? Ohhhh thats actually badass af

[slow roost]

indeed

[daring wolf]

A ring is a monoid object in Ab

[slow roost]

they're lots of kinds of structure at once

not all the same; Q, R, C are fields (and rings, and groups, and vector spaces)

Z and polynomials are groups and rings, but not fields

[foggy wolf]

thanks

[ruby dragon]

Hello guys, im currently at high school doing calc 1 and analysis. I have finished the majority of it and trying to find a book to start linear algebra. Could you recommend me one?

I have found online books but i prefer physical books

Thanks!

[remote sparrow]

#book-recommendations message

[ruby dragon]

Hello thanks i will have a look

[manic perch]

guys any good book for practicing elementary NT? to substitute the practice for micheal penn playlist for elementary NT. which am doing

[molten gulch]

burton's elementary number theory is fine, ireland and rosen if you want something harder

[manic perch]

kayy thanks for the recs

[tardy bough]

uh guys what is thomas calculus seprated into calc 1,2 and 3

[molten gulch]

There's a one volume version with all 3

[pulsar veldt]

It is just called "Thomas' Calculus n" for nth calc.

[pulsar veldt]

He said "seprated"

[molten gulch]

He asked why it's separated, and I'm saying there's a version with all 3

[pulsar veldt]

I guess I don't know english, bcz that's not what I'm reading

[runic heron]

which book is best for olympiad math or deep understadning in mathematics,fuck any exams!?challanges and thrills of precollege mathematics 4th editon book and mathematical Circles Russian editon?

[molten gulch]

If you want a deep understanding of mathematics you should study (real and complex) analysis, algebra, and topology/geometry, maybe some (analytic and algebraic) number theory, etc..

[tardy bough]

fr?

[runic heron]

so the book mathematical circles Russian editon book and Challanges and thrills of precollege mathematics 4th editon book r great choices?

[tardy bough]

Its Thomas Calculus 13th edition

this version has all 3?

[molten gulch]

open it and check the contents

[tardy bough]

whats taught in calc 3

can u send images here

oh

[molten gulch]

the full version of the book should have about 1250 pages

[molten gulch]

yeah this has calc 3 in it

[tardy bough]

okay

where does it "break" off into each of them tho

like where would you say calc 2 starts and calc 3

they're less distinct then say alg 1 and 2?

[molten gulch]

Calc 1 is up to part of chapter 5, calc 2 is up to chapter 11, excluding chapter 9 (except for separable ODE), calc 3 is up to chapter 16 (sometimes chapter 15)

[tardy bough]

do they usually stop at a good spot

or they choose a bad spot

[tardy bough]

why not 9 and sometimes 15

[molten gulch]

9 is (first order) ordinary differential equations, most of that material is left out for its own course, depending on how your uni does things, calc 3 might be material up to chapter ~13-15 and then calc 4 is a separate course that does the vector calculus theory

It's all basically arbitrary

[tardy bough]

is there even a good spot to stop at

[tardy bough]

i see

[molten gulch]

my calc 1 class ended after introducing antiderivatives, riemann sums, and the fundamental theorem of calculus (and one lecture on definite integration)

[tardy bough]

i do my calc online

letme see where it ends

[pulsar veldt]

Early transcendentals' one has 3 books in one

[past dust]

what book/(s) yall recommend for diff eq and multivar calc

[molten gulch]

How much analysis do you know

[past dust]

not much i am planning to do these before proper analysis to be more mature in math

[normal crystal]

@green aurora look, your brothers in arms!
https://standardebooks.org

[molten gulch]

How much linear and multilinear algebra do you know

(at the level of friedberg, axler, or hoffman)

[past dust]

havent done a linalg course yet, i was planning doing it after these but i'm flexible to change it to do before hand

[molten gulch]

You should know some linear algebra prior to studying ODE or multivariable

For multivariable you ideally should know some multilinear algebra too

[past dust]

axler would suffice ?

i saw some people recommending artin book too idk

[molten gulch]

Artin is a book for abstract algebra which introduces matrix algebra and some linear algebra at the beginning

But I don't think Artin goes into say, gram schmidt process, a proper look at eigenvalues of operators, spectral theory in general, multilinear algebra, etc...

[past dust]

aight, there are couple good linalg books i have seen (axler, insel, huffman) not sure which one to pick up

[molten gulch]

Here's dami's reviews #book-recommendations message

My personal favourites are Friedberg Insel and Spence and Linear Algebra done Wrong (Treil)

[past dust]

thanks, appreciate it

[modern ruin]

i didn’t know you liked LADW

good book

[molten gulch]

ye I came across it a few months ago

I didn't really like what I saw of axler, I really can't tell why tbh

[modern ruin]

i’ve been a LADR hater for years

[molten gulch]

TBH I kinda wish FIS introduced tensors and wedges but at that point I may as well just read hoffman or one of the grad alg books in my library

[frozen perch]

There is a spot for you in linear algebra heaven

[radiant marlin]

wait why tho

what about LADR? i thought it was a good read

[remote sparrow]

they probably dislike the way he does determinants in the third edition

[molten gulch]

For me it was actually just the way the book was written, I don't think anything specific really stood out to me as "bad", but I just didn't enjoy it

[radiant marlin]

waiting until the last chapter?

[modern ruin]

sheldon axler writes like an annoying toddler

[radiant marlin]

fair

[remote sparrow]

no

[modern ruin]

oh this too

[molten gulch]

~~also @modern ruin got me into FIS like a year and a half ago so maybe she infected me with the axler hate too ~~

[modern ruin]

did i

[frozen perch]

FIS is the way

[modern ruin]

what is fis

[radiant marlin]

FIS?

[frozen perch]

Friedberg Insel Spence

[molten gulch]

Yeah like a year and a bit ago you recommended we try FIS and then we started doing problems in obsidian VC every other day all summer and you joined a few times

[modern ruin]

i remember doing the problems but i don’t think i remember ever reading or recommending fis

[molten gulch]

huh....

[remote sparrow]

delaying determinants until you can define it as the unique alternating multilinear function that maps the identity matrix to 1 is good actually

[molten gulch]

Maybe it was someone else

I could be misattributing here

[molten gulch]

multilinear algebra our beloved

[modern ruin]

source?

i wish i didn’t have access to this channel. sorry for starting a fuss.

[remote sparrow]

also determinants don't make sense in the context of infinite dimensional vector spaces that frequently occur in functional analysis, so ladr kinda helps prepare you for that

[modern ruin]

personally i recommend sun tsu’s the art of war

[radiant marlin]

imo axler made stuff fall in place, for most of the book you could kind of see the proof or the next step immediately

[remote sparrow]

Settlers: The Mythology of the White Proletariat by j. sakai is goated

https://readsettlers.org

[frozen perch]

How does it handle the determinant?

[molten gulch]

Via multilinear forms at the end of the book

unless you didn't mean axler

[modern ruin]

if you are determined to beat your enemy, you must employ good strategy

[frozen perch]

I was joking about this, which seemed random

[remote sparrow]

https://www.cambridge.org/highereducation/books/linear-algebra/2914578A070EC0AD761C80E9B70F3897

this book is pretty underrated

[tardy bough]

is it better than Hoffman and Kunze?

[remote sparrow]

on what basis is the comparison being made?

[wet sentinel]

so I am responding to this although i am very late to this conversation but isn't this overkill

[remote sparrow]

it's more elementary than hoffman and kunze for sure

[wet sentinel]

If it was multivariable analysis then I would've readily agreed with you

[tardy bough]

im planning on using that book so i was wondering if your rec is better

[past dust]

huffman is about 500-600 pages right ?

[remote sparrow]

well it covers less content, but i think the book is pretty digestible. you can read hoffman and kunze in parallel or as a second text if you like

[remote sparrow]

no, it's 400+ pages

[past dust]

it's really concise then

[hushed vector]

any lecture notes / books for those topics? <3

• cryptography
• knot theory

this isn't to pass a class, but to just read in spare time for fun ;3
background: real analysis, LA (of the relevant and important courses)

[molten gulch]

Katz and Lindell or Boneh and Shoup for cryptography

I think Adams has a book on Knot Theory

If I recall right, one should know some topology for knot theory

[fickle whale]

Lmfao

[hushed vector]

what's the target audience for each of those?

[fickle whale]

I will never stand behind this definition of determinant

[hushed vector]

the second one is titled "a Graduate course". would it be alright for a first pass?
[i'm all for it being challenging. just worried it might skip over some bits]

[tardy bough]

do yknoq the page difference between both of the books

[remote sparrow]

page count is comparable; meckes is like 40+ pages longer, but the writing is less dense since it covers less than hoffman

[tardy bough]

oh

[remote sparrow]

and there's like, 30 pages with hints and answers to selected exercises

there's a full solutions manual out there if you know where to look

[normal crystal]

Meckes is cheap
that's a real plus too

[remote sparrow]

do you know any algebraic topology?

[karmic pendant]

Hello, does anyone have recommendations for a book for highschool level geometry?

[hushed vector]

no but i'd love to!!

if u have any books in mind for it i'd appreciate them as well:3

[molten gulch]

rotman and hatcher are common choices, Dami has a pin with a bunch of AT books too

[remote sparrow]

https://link.springer.com/book/10.1007/978-0-8176-4719-3

here's a book that doesn't assume any algebraic topology

[mellow wren]

https://arxiv.org/abs/1103.5628
I really enjoyed these notes for knot theory

[hushed vector]

thank u three a lot!

[mellow wren]

note just they assume knowhow about algebraic topology lol

I just noticed you said you didn't learn that yet

[hushed vector]

it's okay
i'm interested in things that I don't yet understand ;3

[remote sparrow]

rolfsen seems like the classical choice for knot theory once you've had alg top; there are a lot of pretty hand-drawn pictures. on the other hand, it looks like it was written on a typewriter, so the text is very ugly

here's a sample page

[tardy bough]

how many math books did u read

[remote sparrow]

at least one

[tardy bough]

at least 50

🥲😟

thank u for this calc book from thomas

its great

[remote sparrow]

https://link.springer.com/book/10.1007/978-1-4612-0691-0

another source requiring algebraic topology

this one has material on jones polynomials, which rolfsen predates

[remote sparrow]

https://bookstore.ams.org/mawrld-24

here's a great way to improve your shoelace tying technique!

[toxic heart]

So apparently I found out my community college doesn’t offer linear algebra as a course for high school and dual enrollment credit, so I want to learn linear algebra over the summer by myself and just have a calculus 3 class after the summer during my sophomore year . I need help finding a good textbook to not only learn it but do a lot of practice problems. I tried researching many but I wasn’t sure there’s a lot of options

https://tenor.com/view/monkey-thinking-monkey-thinking-think-money-gif-9734025314392564509

[remote sparrow]

#book-recommendations message

[lone bloom]

Hello everyone. Would you recommend hoffman's linear algebra book for first semester physics?

[velvet flax]

lang's algebra (3e) /j

[molten gulch]

I wonder if this is truly such a bad option for some students

[velvet flax]

thats unironically how i learned it

[wet sentinel]

lmao

[toxic heart]

I ordered it

https://tenor.com/view/jgmm-monkey-think-monkey-meme-ponder-monkey-idea-gif-6401133862108294696

I searched up lang's algebra (3e) /j on google

Found it on eBay

[velvet flax]

you may also want to buy some adderall to go with that

[toxic heart]

I got it for $67.67 which is really cheap in this economy