book-recommendations

[hasty turret]

My belief is it's the former

Matrix multiplication was invented to "store" what manipulations you need to do to get the solution

[remote sparrow]

gaussian elimination and back substitution sounds a lot easier (when the theory of linear algebra was less developed) than doing matrix multiplication though

[finite heath]

What is that well-known place? I don't know it 😂

[remote sparrow]

library first book of the bible

[finite heath]

Ah yes😂I getchu

[gray gazelle]

does anybody have a good statics book

with lots of questions

[little bison]

Hello, I just had a general question about books: What is a good book for studying beginner probability,

Keeping in mind, I am still at an high school level but want to study some fields in mathematics as a side. I don't know much of calculus, which I understand is required to some extent in probability. If you would recommend any books before even starting probability please let me know about those as well.

[remote sparrow]

presumably engineering statics? i think old editions of hibbeler can go for cheap

[remote sparrow]

some discrete probability should be accessible to this person, but i'm not sure what should be recommended

i'd also suggest this person learn calculus while they're learning some simple discrete probability

i only recall AP stats is algebra-based, but idk any algebra-based probability books

[narrow relic]

Chapter 3 of the book Discrete and Combinatorial Mathematics 5th Edition by Ralph P. Grimaldi contains an explanation of discrete probability that is for beginners. You don't need to know calculus to read it.

You do need to read Chapter 1 first. Also, you have to understand the material of Chapter 2 though you could learn that elsewhere or you might already know it.

I also agree with Sour Drop that you should learn Calculus while you do this.

[tawny crater]

Heartily recommend "the best of mathematical writing", bees knees collections

[tawny copper]

You could do discrete maths in general. The basic principles of elementary probability and other fields like combinatorics are pretty much the same. And you will have to count in probability anyway. I'd suggest Bóna: A walk through combinatorics. Soberon is also really nice, but more difficult

I didnt read the answer of joesmith1042, maybe his/her suggestion is better than mine

[remote sparrow]

bona assumes you know calculus, but most of the content doesn't need it

[tawny copper]

Where does he say that?

Of course in the chapter on generating functions you would need some basic notions of calculus. But I don't think not knowing calculus should stop someone from getting into that kind of stuff, since the ideas involved are very basic

[weary cape]

If u still need one send a dm

Precalculus (Margaret L. Lial, John Hornsby etc.)

[deep lynx]

What's a good diff eq book for self learning?

[sullen raptor]

What would be a good quantitative finance book for self learning? I want something serious and none of that pop-maths stuff.

[oak pecan]

Shreve?

[sullen raptor]

Looks good. Intimidating though since it said that it's used for graduate programs but I think I can give it a shot. Thanks!

[oak pecan]

so im talking about Shreve vols 1/2, not Karatzas & Shreve to be clear. vol 1 I imagine you'll find quite easy and perhaps boring, vol 2 is where the meat is and vol 1 is not really required reading if you feel like skipping ahead

[sullen raptor]

Is this the v1 you're talking about?

[oak pecan]

that all said, the most common recommendation is probably Hull, and my favorite for an intro book is Baxter & Rennie, but these are less mathematical than probably "appropriate" for a mathematics server

[oak pecan]

it is indeed

[sullen raptor]

I don't know anything about finance in general, would that be a problem?

[oak pecan]

no, these books are all meant for people who don't know about finance/financial maths.

Hull's book is the most comprehensive in terms of teaching about finance - after all it's not all just line goes up/down, but there are many different types of products for many different purposes, traded in many different ways and venues

[sullen raptor]

Alright, I'll check all those books out. Thanks!

[remote sparrow]

are you looking for ODE or PDE

[marble karma]

Looking for concise online notes/book for Group theory or abstract algebra in general

With few but nice problems

[gray jungle]

old book but "shaums outline of theory and problems of group theory" could be what you are looking for

[deep lynx]

ODE

[remote sparrow]

#book-recommendations message

judson, author of the free abstract algebra textbook, has a draft of his ODE book available as well

[remote sparrow]

https://www.amazon.com/Visual-Introduction-Differential-Calculus-Manifolds/dp/3319969919

just found out about this calculus on manifolds book from this lecture playlist, which it primarily follows (occasionally relying on munkres for more difficult proofs): https://www.youtube.com/playlist?list=PLoWHl5YajIf6EnH5CCI9slsTtR-Ul69l3

[wary star]

I wanna get a book that about the application of drazin inverse matrix.

[tulip schooner]

Diary of a wimpy kid is a classic

[rapid lily]

Are there books which give a huge number of examples of Banach spaces? Would these typically be functional analysis books?

In particular, I'm not looking for elementary well-known examples.

[gray gazelle]

Good linear algebra book

If i want to get into abstract algebra

[fierce hedge]

Check pins on linear algebra. For proof based LA, I personally like Friedberg

[gray gazelle]

Thanks

[fast crow]

Hi, I've got a CS-engineering masters, so I've got some math education, mainly functional analysis, really basic linear algebra, graphs, basic mathematical logic.
I'd like to dive into group theory, category theory and type theory in a somewhat structured manner. I can learn alone, but I do need some proper structure. What would be your recommendation(s) and in what order?
I did dabble with each topic, meaning that when I wanted to familiarize myself with an algebraic structure for ex. I could just look up the wikipedia article and a few examples, but this way of learning tends to leave severe holes/concepts/important theorems that are left undiscovered

[remote sparrow]

Check pins for algebra recommendations

Aluffi is a grad algebra book that introduces category theory early and uses it frequently throughout

Awodey, leinster, riehl, and maclane are common references for category theory

[mystic orbit]

mainly functional analysis
really basic linear algebra

nani

[fast crow]

I learned engineering math

Was mainly functional analysis that got us to stuff like Laplace
And on another line, we had linalg where we learned about basis, linear transformations with matrices, and then that subject went into graph theory in the second semester instead of continuing on that line

During masters we had a subject called abstract algebra but to be honest it was a very half-assed one trying to pick up where we left off with matrices with stuff like Jordan decomposition, orthogonalization and a bunch of rando stuff

[mystic orbit]

but like, functional analysis is, to some extent, linear algebra in infinite dimensions

anyhow, I think you're gonna need several references

I don't recommend aluffi for learning category theory

[fast crow]

Sure, whatever, that's not how most courses teach it tho ime

[mystic orbit]

especially early on, the only category ""theory"" you're gonna learn is category theory jargon

and the universal properties of some algebraic objects

and I don't imagine that'd be super helpful to type theory, tho I don't know much about the subject

but if you couple that with another category theory reference it'd be quite a good reference for algebra imo

[remote sparrow]

Does kreyzsig functional analysis have fewer prereqs? They could have used that book

[chrome yacht]

kreyszig only has very elementary linear algebra and real analysis on real line as prerequisites i'm pretty sure

[spare ridge]

lol

[narrow relic]

It has fewer prereqs, I've looked it but never read it. It doesn't include L^p spaces.

[patent gorge]

Hello! Does anybody knows at least one good book from mathematical modelling which implies pedestrian flow models and self organization behaviours? I need a book rich in maths, means that it provides math background, theorems, lemas, etc that sustain the models and then numerical experiments. I've searched, but all I found is pretty leaky in theoretical content and more in experimental work.

[tawny crater]

looking for an introductory textbook that goes into this https://en.wikipedia.org/wiki/Fractal_dimension

[trim tangle]

"Pedestrian Dynamics: Mathematical Theory and Evacuation Control" by Andreas Schadschneider, Debashish Chowdhury, and Katsuhiro Nishinari.

covers overview of the mathematical modeling of pedestrian dynamics, ie self-organization behaviors that arise in crowds of pedestrians. It covers various models of pedestrian flow, including cellular automata models, social force models, and microscopic simulation models.

[patent gorge]

Thanks! But, by any chance, do you have a link or pdf with the book? All I can find is the same title but written by Pushkin Kachroo

[trim tangle]

had a hard copy, cant find it now sorry

[hearty steppe]

I liked kreyszig but when it gets to spectral analysis it kinda loses its charm. I mean halfway through chapter 4 it just jumps into becoming way more terse and less intuitive

[hearty steppe]

I find that a lot of books have a drop off point where they lose the charm they start with for better or worse. I would imagine most people going through kreyszig’s functional analysis overall are going to have an easier time even in the later chapters as opposed to a number of alternative books

[steep badger]

https://www.math.uh.edu/~climenha/fractals.html

Dunno if it's introductory or not tho.

[weak lake]

looking for a good book on vector/multivar calc

[remote sparrow]

rigorous or nonrigorous

[weak lake]

ig rigorous

[remote sparrow]

look at hubbard and hubbard or shifrin

[weak lake]

ty !!

[gray gazelle]

i want to improve my proficiency in mathematics what book should i start off with (iam upto par with an 8th grade student)

[trim tangle]

AOPS

[real veldt]

I (not recently) realized that my fundamentals in geometry are “terrible” so does anyone have recommendations for a fast paced book? I’ve just been using articles as references but I kind of want something that builds up to results, but with a decent amount of difficult problems as well. I’m an undergraduate if that matters for context.

[remote sparrow]

Are you talking about euclidean geometry?

[real veldt]

Yup

[gray gazelle]

Ig Evan chen- Euclidean Geometry might prove to be useful

[remote sparrow]

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

https://4chan-science.fandom.com/wiki//sci/_Wiki

[gray gazelle]

How is cengage for jee advanced

[grizzled tulip]

Is good.

[real veldt]

Thanks! I’ll check those out

[next wolf]

Any recommendations for self-learning Measure Theory?

I've been a bit pissed learning statistics and not being able to rigourously prove anything

[gray gazelle]

You could try Schilling

[next wolf]

Alright, I'll keep it in mind

[gray gazelle]

read Bogachev

[next wolf]

Is that a bad book?

[gray gazelle]

It's a good book but not for learning

Tbh

[karmic thorn]

Bogachev/Smolyanov?

[spare ridge]

swoleyanov

[gray gazelle]

https://link.springer.com/book/10.1007/978-3-540-34514-5

[twin hornet]

Any book recs for someone who wants to self study calc 1-2 by august?

[steel viper]

define calc 1-2

if your goal is to literally just learn the content of an intro calculus course for use in other things (or to do well in an intro calc class) then you can probably just read pauls notes online

if you want to understand the actual math then spivaks calculus

[sleek python]

Le Gall 's book is a pretty good introduction to measure theory

[next wolf]

thank you for the suggestion

[tepid kettle]

A little niche, but anyone know of a good fourier series book and applications to NT?

and if that's too nice, then idm a fourier series book (barring stein and shakarchi/ folland)

[remote sparrow]

axler looks good

it's legally free online too, which is a plus

https://bass.math.uconn.edu/real.html

this book also exists

Suppose one has completed taylor mechanics, griffiths electrodynamics, shankar qm, schroeder for stat mech, and landau for analytical mech, just to grasp the physicist's way of seeing things. And suppose this person is more of a math person. Is jackson's electrodynamics a must read, or can they just read an e&m for mathematicians book?

[sleek python]

Np, it's a standard text that french students use to learn measure theory, it only recently got a translation in english so I can finally rec it to english folks

[remote sparrow]

you could say you've got some gall to recommend it

[sleek python]

I'm not a fan of the way he presents probability though, but you're only interested in the measure theory part of the book

[remote sparrow]

https://www.amazon.com/Mastering-Quantum-Mechanics-Essentials-Applications/dp/026204613X/

has anyone looked at this book? is it any good? i know this guy has lectures on mit ocw.

[grave thorn]

the only bad Bogachev book

[solemn haven]

Are there different good set theory (undergrad) books with plenty of exercises apart from Karel Hrbacek, Enderton and Cunningham?

[sleek python]

idk about this book but my friend always recs the Cohen-Tannoudji on quantum mechanics

[remote sparrow]

lems likes goldrei

https://www.logicmatters.net/resources/pdfs/BeginMathLogic3_F.pdf

more recs here

[gray gazelle]

Wdym bad, I heard it's a great reference to measure theory

[narrow relic]

Thanks for this link!

[grave thorn]

idk I just don't like long books

[gray gazelle]

Oh

[sleek python]

Bogachev tackles lots of topics that most other measure theory books don't

But yeah it's long and is technically 2 volumes, though springer put both into one ebook

[grave thorn]

like what

[sleek python]

Like measure on topological spaces, it goes further than other books I find, with volume 1 covering standard material seen in MT and volume 2 going deeper. You can sometimes find some parts of the topics that treated in volume 2 but it's often just "on the go" e.g some theorems and definitions are given when needed

Or maybe I just don't know enough measure theory books and I'm biased because I meet mt mostly in the context of probability

[grave thorn]

measures on in topological spaces are covered in basically every graduate course (although tbf Bogachev goes more in depth and also looks at measures on topological vector spaces)

[grave thorn]

Finite measure theory is probability theory

[sage python]

Honestly what I wanna see is

A measure theory book that goes into detail about the perspective of differential forms being "smooth measures" on manifolds

[desert oriole]

george polya - how to solve it
is it worth reading it?

[orchid mortar]

yes

[gray gazelle]

Polya has lots of quotes from that book alone

[alpine rover]

anyone know a good resource to quickly brush up on real analysis (limsup liminf, riemann integral, sequences, convergence, open, closed, compact sets)?

[alpine rover]

thanks

is there a more modern resource?

[sturdy shore]

you might be interested in knapp - basic real analysis

its first chapter is a review of one variable real analysis (along with some fourier series stuff you can skip), second chapter does metric topology in depth up to you how far you need to go there

[crimson leaf]

I never looked at this book before is this supposed to be a first course?

[alpine rover]

thank you

[sturdy shore]

well, since it goes through all of single variable real analysis in 50 pages, not really

could be used as one if you already know studied a bit of analysis but forgot, and have some math maturity

[remote sparrow]

no coverage of the riemann integral, but carothers may interest you

[near wagon]

Would you consider How to Solve it a way to work through proofs? Or more of a general way to problem solve mathematically

[orchid mortar]

I think it's quite informal tbh, but that doesn't make it bad

[near wagon]

So more like a way to have a good mental model about problem solving rather than “math proofing”

[woeful ravine]

Personally I find it too simple as anything more than a casual read. It's still a good book worth reading. But, IMO, the best way to get intuition behind problem solving is by doing exercises and working through proofs in whatever book you're studying.

Of course everyone learns differently

[near wagon]

Yeah reading is for background, problem solving is for building intuition.

[near wagon]

You’d have to be very smart to learn only or mostly just from reading. And I am not very smart.

[woeful ravine]

Well, nobody can just read anything for the first time and automatically get it. But actually working through the material is, in my experience, the only way to understand it at a conceptual level.

[remote sparrow]

i skimmed a litte bit through lara alcock's How to Study as a Mathematics Major and it seems like it might help you

two of her other books, How to Think About Analysis and How to Think About Abstract Algebra seem good too

[woven glacier]

anyone know where i can find SASMO grade 12 past papers/sample papers?

[woeful ravine]

How to Prove It is nice as well

Similar titles

[near wagon]

So, How to Solve It
How to Prove It
How to Study as a Mathematics Major

[woeful ravine]

https://sasmo.ica.net.pk/sample-questions/

[woven glacier]

thank you so much

[woeful ravine]

There's only a solutions paper for grade 11/12, though

[empty orchid]

does anyone know a great book for geo

[heady ember]

What geo, be more specific

Alg geo, diff geo, etc

[empty orchid]

Alg geo

[empty orchid]

sorry

[heady ember]

No need to apologize, alls good

[woeful ravine]

For a more Introductory/undergrad Book: Silverman's "Arithmetic of Elliptic curves" and "Rational Points on Elliptic curves" as well as some good textbooks on the prerequisites. For a graduate level course: Hartshorne, Lefshetz, Silverman's "Algebraic Geometry", Liu

As well as the "Foundations of Algebraic Geometry" online notes by Vakil

Plus EGA if you can read French

However, Alg Geo is a very broad subject nowadays, these are just some good general texts

[thorn cloak]

Anyone know good probability theory book for undergrads (maybe with a tiny bit of advanced topics like basic measure theory?)

[distant spear]

klenke's probability book, is a good one but starts with basic measure theory

[torn storm]

What is the baby rudin of mathematical statistics?

Also, what is the most terse statistics book? I want to learn student t-test and chi squared as someone who already knows measure theory and other relevant real analysis

[grand thistle]

i dont think this counts as "a tiny bit of advanced topics"

i mean they develop like a lot of measure theory at the start and is imo quite terse

[remote sparrow]

grimmett and stirzaker

[sturdy shore]

I can confirm that klenke is not what they are looking for, just the first page of that book should be proof

if you know 0 measure theory this is probably the worst introduction you could possibly get

[torn storm]

ha yeah. I'm really looking for the stats that a social scientist would learn in their stats class, but explained in 20 minutes because I know math already

[sturdy shore]

I was not replying to your question

[remote sparrow]

idk if these are terse, but you may be interested in Theory of Statistics by mark schervish and Mathematical Statistics by jun shao

[fluid sleet]

i want to use calculus for astrophysics or physics genrally so can someone tell me a good books for calculus?

[hearty steppe]

I’m not sure if a terse statistics book is that insightful in the long run. If you are focusing more on physics, then a lot of jargon you get from statistics books, even math stat is always limited to context of the samples your measuring from an arbitrary population. So you always have to focus on details. Maybe jumping into measure theory is the more serious approach statisticians should be taking.

[fluid sleet]

thank you!

[near wagon]

When would you take measure theory? After real analysis?

[remote sparrow]

robert_ wants stats for social science

[remote sparrow]

if you're not interested in learning how to read and write proofs, spivak or apostol are the wrong choice. stewart's calculus is fine. look here too: #book-recommendations message. a middle ground book between stewart and spivak would be velleman's Calculus: A Rigorous First Course by daniel j. velleman

[near wagon]

Will the course be called Measure Theory? Or more advanced real analysis courses cover measure theory?

[hearty steppe]

I am considering eventually working through Schilling at some point. After I go through all my dynamical systems books I might learn Ergodic theory with measure theory

[rocky geode]

What would be a good book for calculus?

[hearty steppe]

Oh I guess in a way, going through an analysis book is basically learning measure theory more on the surface? But don’t you deal more with the generalization of metrics directly in an actual measure theory course ? Rather than consider differential forms?

[rocky geode]

I am undergraduate student pursuing bachelor’s in computer science, I have already completed my Mathematics 1 course which included foundations of multivariate calculus, I would like to study a bit more
I used thomas calculus for coursework

[remote sparrow]

have you taken discrete math or equivalent class where you've written a proof before?

[rocky geode]

Nope , I have linear algebra and complex analysis as part of my coursework this semester

[remote sparrow]

and you haven't written any proofs in these classes?

[rocky geode]

My semester starts tomorrow

[remote sparrow]

oh

[hearty steppe]

Also @remote sparrow are there other books you may recommend along with Schilling for measure theory?

[remote sparrow]

maybe a complex variables book like brown and churchill

there are still proofs in that book

but brown and churchill is often used by scientists and engineers that aren't necessarily looking to rigorously justify every result

[remote sparrow]

axler looks good

https://measure.axler.net/

[rocky geode]

This is given by my professor

[remote sparrow]

https://bass.math.uconn.edu/real.html

also this

more advanced books can be found in pins

slight modification, bass is still about the level of folland; it just uses "vanilla" proofs, i.e. proofs that are easily mimicked or adapted, especially for use on graduate qualifying exams

no cleverness involved

[rocky geode]

Thanks

Also I have probability and statistics

What book to use

[remote sparrow]

#book-recommendations message

these linear algebra books may interest you

[remote sparrow]

are you learning mainly probability or are you somehow doing both

[rocky geode]

Course name is probability and statistics

[remote sparrow]

can you give the course description

usually questions of inference, properties of sample means, theory of estimators, etc. are covered in a mathematical statistics class

[thorn cloak]

I just bought how to prove it and plan to lightly read it over the rest of the sem and more rigorously over the summer. Do you think it’s enough proof background for abstract algebra or real analysis?

[remote sparrow]

i'm not really familiar with probability and stats books for scientists and engineers

[tawny crater]

oh man do not disrespect proof writing
it's a common flunker

I just finished my cs program's proof flunker and the class got something like a 40 average before the factor

[remote sparrow]

but blitzstein and hwang's probability book is very nice. it doesn't go into statistics at all though.

bonus is that it's free online

[tawny crater]

can you find a friend to help you go over your proofs?

i think most of our class failures was because of low feedback

[remote sparrow]

i'm assuming your probability and stats class has calculus as a prerequisite

[remote sparrow]

https://www.probabilitycourse.com/

[thorn cloak]

Haha that was actually the plan for me but I’m already struggling with proofs in my calc 3 class and knew I wouldn’t survive

[remote sparrow]

actually i saw this book at my university bookstore a few weeks ago

it's free and also available as a cheap paperback

there is also a student solutions manual for purchase

might interest you

https://www.amazon.com/Mathematical-Statistics-Applications-Dennis-Wackerly/dp/0495110817

this book was used for my probability and mathematical statistics classes

[rocky geode]

Ya it has

[remote sparrow]

i think it's alright

used copies seem reasonably priced

[rocky geode]

Which book ?

[remote sparrow]

it may be a bit more "mathematical" and have less coverage of relevant topics for scientists and engineers however

the book i linked to from amazon

[rocky geode]

I can always check my library catalogue

[torn storm]

Thank you for the recommendations!

[remote sparrow]

So the probability and statistics books I've listed so far are as follows:
Introduction to Probability by Blitzstein and Hwang
Probability, Statistics & Random Processes by Pishro-Nik
Mathematical Statistics with Applications by Wackerly, Mendenhall, and Scheaffer

blitzstein and hwang have a website associated with their book

same with pishro-nik, as i just linked earlier

[rocky geode]

Thanks

[remote sparrow]

and i've already linked you some linear algebra recommendations

[rocky geode]

Thanks 😊

[remote sparrow]

paul halmos book on naive set theory

first order logic, you can look at enderton as long as you use antonio montalban's lectures

there's also goldrei and mileti

although if you're doing some mathematical logic, i don't see why you wouldn't want to do some axiomatic set theory as well

you don't need to if you're already know how to read and write proofs

just look at enderton or goldrei (who both also have set theory books)

hrbacek and jech (one book, two authors; jech has a graduate reference) is another choice

i don't think most people are learning from jech

even grad students

it's more of a reference rather than something you study from

you can look at kunen for graduate treatments of set theory and mathematical logic

also check out diligentClerk's pin in this channel

https://www.logicmatters.net/

a good source of recommendations and reviews for set theory and logic books

[trim tangle]

[hearty steppe]

Any good books for learning game theory?

[remote sparrow]

https://mathoverflow.net/questions/71848/looking-for-a-mathematically-rigorous-introduction-to-game-theory

[hearty steppe]

Well I don’t really study math rigorously so I hope these will be useful

[vale ember]

Hey everyone, I just started this small book about Algebra, please take a look at it and give me some feedback if you want!

[solemn rover]

Hi, Emiel.
I think this is a confusing example. "Both are approximately equal to 3.14, but one is rational and the other is not."
Your informal notation " pi \approx 3.14 \notin \mathbb{Q}" is confusing, because 3.14 is in fact a rational number. In the first line it's not clear whether you mean 22/7 is in Q or 3.14 is in Q.

Additionally pi might not be a good example here. If they have background in geometry they will understand what pi means, but are you expecting your readers to be familiar with geometry?

It is also extremely difficult to explain to your readers why pi is irrational, and they will not understand why this is true. So the example is unhelpful, I think, because they can't see why it is an example.

I am guessing you cannot explain to me why pi is or should be irrational.
I certainly cannot explain it to you. 😉

Your description of complex numbers probably overestimates the reader's background. If they have not seen complex numbers before, they certainly will not understand what they are after reading this. What is an imaginary number? You have only given an example of an imaginary number.

"i is an imaginary number because it does not correspond to the measurements of the real world." This description does not help the reader to understand what an imaginary number is.
For example, 3/0 is an undefined quantity and in general we cannot assign a value to it in a sensible way without totally destroying interesting mathematics. Why do you expect your reader to believe you can assign a meaning to \sqrt{-1} without totally destroying mathematics?

I think you may not have consulted a reference when writing this paragraph. As far as I know, quadratic polynomials are not used to model population growth or the behavior of a stock price over time. Were you thinking of exponential functions?

Here you say that there is no solution. But you just said that there is a square root of -1 called i, and we can use that number to solve this equation. You should be clear with your readers about what number system you are working in: the real numbers or the complex numbers.

In mathematics, expressions have meaning, and rules are valid because of the meaning of those expressions. If a student learns only the rules but does not learn what the expressions mean or why, they will be harmed later on when they need a deep understanding of why this statement is true.

You should explain to the reader why this rule is justified.

[sterile harness]

That should be called a discriminant btw (sorry for the ping)

[finite gale]

a better example to do this with is probably sqrt(2) or something, where you can actually prove it in a couple steps (and possibly showcase contradiction as well)

also does this discussion really belong here?

[desert oriole]

HOW TO PROVE IT: A Structured Approach, Second Edition
i want to become better at proof writing and was wondering if this book was worth it reading(chapter on proofs) ? or if anyone can recommened a book which teaches proof writing

[remote sparrow]

#book-recommendations message

any of those are good

you may even read more than one book side-by-side if you like

[desert oriole]

oh ok thank you

and to practice, proofing stuff i solve is a good exercise right? (dumb question, practicing can never hurt)

[remote sparrow]

what do you mean by proving things you solve?

[desert oriole]

like for example:
i had a problem where i had to get the amount of trailing zeros of n!

i know that the amount of trailing zeros is just

n/5 + n/26 + n/125 + n/625 ...

and every n/x is floored

but i havent proven it yet

thats what i meant

[remote sparrow]

well, we call unproven claims conjectures

you "solve" a conjecture by proving or disproving it

you might intuit or guess that the amount of trailing zeroes in n! is given by the formula you wrote down, but that doesn't count as "solving" it until you prove it

[remote sparrow]

any thoughts on Elements of Integration and Lebesgue Measure by robert bartle?

[sage kelp]

I loved this book. Totally recommend it

[trim crypt]

hello! im just strarting to lear the integral calculus, do u have any reomendations??

[forest sleet]

AMS bookstore has a sale for pi day

don't know if it combines with the member discount or not

[foggy relic]

thanks

[orchid mortar]

Sorry I don't think Klenke is a good textbook, unless one is very mathematically inclined.

[gray gazelle]

You're having something for pi day?

[gray gazelle]

Suggest good group theory book for concepts with intuition and quality problems

group action oriented approach preferred

[fierce hedge]

Stein and Shakarchi vs Ahlfors vs gamelin for complex analysis? Also, what would be the prerequisites for the textbooks

[daring lake]

Opinions on Roman's Linear Algebra? I have already taken a course on elementary LA and want to hit some advanced topics sooner or later. Currently speeding through problems in Hoffman and Kunze to make sure I remember things. Would Roman be a good place to start after this or would I need more pre-req knowledge?

[hazy elk]

Check pins. In my opinion you just need to know basic analysis (differentiation, integration, sequences and series). I find Ahlfors' writing to be cryptic (not terse like Rudin but what he is saying isnt exactly clear/highlighted well enough that you check it properly) at times (but if you have a good teacher this is a non issue ig) both Ahlfors and Stein has nice problems but Stein feels "more like analysis" and has a lot more problems that Ahlfors.

Also I think Stein gets to the nicer stuff faster than Ahlfors

I have a love hate relationship with Ahlfors' book lol, somedays when I work out every sentence of Ahlfors, I feel like it's a great book, other days when I can't understand what he's trying to say I'm like

[hazy elk]

Oh and also knowing the total derivative (as a linear transformation) and how partial derivatives work, along with a few basic differentiability results (existence and continuity of partials etc) is helpful.

So multivariable differentiation basically

[fierce hedge]

ah, I see thanks for the recommendation. I'll stick to gamelin+vca probably with ahlfors for questions

Would also try a bit of Ahlfors maybe

[forest sleet]

No, the ams bookstore

I just got an email from them about the sale

[gray gazelle]

I was asking if you're buying yourself something for the sale

Alright

[forest sleet]

Oh no I am not buying anything

I like their grad studies in math series

But since I have to move pretty regularly I'm trying not to accumulate books right now

Sry I just woke up and my reading comprehension is low

[narrow relic]

What kind of stuff are you interested in? 🙂

Are you interested in "continuous mathematics" (like calculus: stuff like curves and their slopes), or "discrete mathematics" (e.g. things you can count up)?

Okay, there's a really cool book called Calculus by Michael Spivak (3rd edition is fine). It'll probably be "too hard" for you to do everything in it but I really recommend just reading some of it. It gives you a great sort of view of what a lot of this continuous mathematics stuff is all about.

[thorn cloak]

I think the math sorcerer has a good series for math self study

[narrow relic]

You might need to review or learn "how to prove stuff" to understand the arguments in anything you read. There are a lot of recommendations here for that. I have some personal recommendations for that as well if you're interested

Sure will do. Have a good day 🙂

[narrow relic]

By the way, I'm not recommending that you even try most of the problems in that Spivak book, I'm actually just recommending that you read his prose and try to understand the arguments he's making there at first. If eventually you feel like, "this is really interesting but I feel like I can't read the prose of the first few chapters and follow the arguments without being really confused" I recommend you work through a lot of this book: https://archive.org/details/modernintroducto00dolc . I think this is the kind of book people used to use at the high school level in the U.S. at one point. You can read it by making an account on that site, The Internet Archive (it's a library).

Don't be worried by the term "analysis" in the title there, it's a term they used to (maybe still do) use in U.S. high schools for "the course before calculus."

[fossil arch]

What real analysis books do you guys like that focus heavily on motivation?

Particularly in the context of real-world motivation, not just math-in-a-vacuum-motivation

Like I like how this introduces Riemann integration

https://www.math.ucdavis.edu/~emsilvia/math127/chapter7.pdf

[torn storm]

https://www.amazon.com/Analysis-Introduction-Proof-5th-Steven/dp/032174747X/ref=sr_1_2?keywords=lay+analysis&sr=8-2 this is the book I used to get analysis enough when I couldn't understand Rudin

[fossil arch]

HAHAHA That was the first book I used for it too!!

That’s cute

Ig I mean more like practical real-world motivation?

Like if there was a “real analysis for physicists”

LOL

[gray jungle]

so i literally searched "real analysis with applications" and this book seems promising https://link.springer.com/book/10.1007/978-0-387-98098-0#toc

[torn storm]

Kot's Elements of Mathematical Ecology
Mohri's Fundamentals of Machine Learning
Shreve's Stochastic Calculus for Finance I & II

[fossil arch]

Can I be more picky? 💀

[fossil arch]

I’ll take a look at this ty!!

[pure iris]

beautiful book, I used it as well as my first analysis text

[remote sparrow]

spivak has a solutions manual available for purchase as well

you can find both books on amazon

[remote sparrow]

https://www.stumblingrobot.com/

has some book recommendations

[fierce hedge]

pretty good recommendations

[sage python]

Doesn't bash Axler enough 2/10

Also Lee Top Manifolds is absolutely a substitute for Munkres lol

Also the "differential geometry" list is a mess

Anyway I'm bored

[rapid lily]

What is the main problem with Axler?

[sage python]

Treatment of determinants and characteristic polynomials is smooth brained

[remote sparrow]

@sage python you mentioned you were a grader for a course covering spivak's calculus book. do you have a syllabus? also, were all the students people who had never taken calculus before?

[sage python]

The class I graded was mostly students who had calc

I took a class in undergrad and with only eh calc background

(Maybe more than AP Calc AB, less than BC)

[remote sparrow]

so it was an "honors calculus" class as pete clark would say?

http://alpha.math.uga.edu/~pete/2400full.pdf

btw this guy pete clark has full notes for this sort of class

[sage python]

So, the class Pete Clark graded in his second year

Was the class I took first year

[remote sparrow]

clark visited paul sally the summer after his junior year of high school at an interview at u of chicago

just some trivia

[sage python]

Did he?

Doesn't suggest as much here

[remote sparrow]

page 7

i edited the message

[sage python]

Okay lol

Very different

Yeah seems he visited Sally, said hey I did AP Calc and some multi at JHU, Sally's like aight read Spivak. He did that, placed into honors analysis. Not sure who taught that

[rapid lily]

What specifically is the issue with his approach? I admit that I am not that familiar with his book though.

[sage python]

But then he graded for honors calculus, which is what I took first year

384920: he dodges determinants and presents char poly for C as generalized eigenspaces. So the equivalent of "triangularize the matrix and take product of (t-diagonal)"

And then for the real case he says "complexify and take the char poly, zomg11111 the coefficients are real"

And if I asked someone on a linear algebra oral final to define char poly and they did that, and couldn't produce a native definition of char poly to R

That would hurt their grade

Also idt he does much (if any) mulitlinear algebra

[rapid lily]

Ok I see

I think it is quite hard to define the determinant in a useful way without multilinear maps

I mean you can do it with that sum of permutations of elements, but the other way is also quite useful to know

[fierce hedge]

Has anyone experienced this sort of issue with pdfs where the latex part goes way below the line? This is happening for me with all native linux pdf readers.
For reference this is knapp's basic algebra. Also, idk if this is the correct channel for this so remove if necessary.

[chrome yacht]

have you tried okular?

[fierce hedge]

This is okular

I also tried evince and other common pdf readers

[remote sparrow]

oh sweet, a new all-in-one open source ebook reader i haven't seen yet

what have you tried and which did you like most

[fierce hedge]

okular is the default reader for kde, it's a native kde app if I remember correctly

[chrome yacht]

doesn't happen on mine, why is your pdf yellow though?

[fierce hedge]

I have the bgcolour changed for comfortable reading

[chrome yacht]

well i changed my bgcolor to match yours and it didn't happen so...

[fierce hedge]

this is okular? why's yours so yellow

[chrome yacht]

might be a case of

[fierce hedge]

of?

[chrome yacht]

https://tenor.com/view/skill-issue-gif-22181257

[fierce hedge]

what's your okular version?

[chrome yacht]

okular 22.08.2

[fierce hedge]

mine's 22.12.2-1, maybe downgrading will help

[fierce hedge]

can you send the pdf you're using maybe the pdf doesn't have this issue

[fierce hedge]

yeah this one works normally

so, it seems that it was a pdf issue

[fierce hedge]

I like okular the most, it's the most comprehensive; supports almost all books formats although for ebook formats there are better ebook readers.
Another most common is evince, probably the most well known. It even has few useful facilities that okular lacks such as automatically expanding the bookmarks as you read although it's more of a poppler (backend) issue than a kde one.
Other than these foxit reader works fine on linux but it doesn't have night mode on the free linux versions.
No idea about adobe reader, haven't tried it

[unkempt gorge]

Book recommendations for people self studying? From middle school-high school level please :)

I’m currently at pre-algebra level, slowly moving onto geometry and algebra 1.

And some good workbooks too if possible

[fierce hedge]

well, turns out this is the 1st edition not the 2nd edition. nvm I'll just use judson

[rapid lily]

Are there books which classify certain properties of various Banach spaces, such as what the compact subsets are for example?

[gray gazelle]

I've saw such a characterization for l^p spaces in a book by Bogachev

[rapid lily]

Ok thanks. I saw something about that one having a condition on the summation of the tails approaching zero uniformly. What was the name of the book?

[gray gazelle]

Real and functional analysis

[rapid lily]

Ok thanks. I'll take a look in that book.

[rancid orbit]

Any books containing every areas?

Or typical books for each areas?

[grave thorn]

if you are interested in compact sets in Banach spaces, you are probably also interested in compact operators (maps bounded sets to compact sets)

[rapid lily]

Ok thanks. I will look up more about this topic.

[rapid lily]

Well, most books will specialise in some area. At the moment, your request is quite vague so it's hard to suggest anything. Perhaps you can mention the topics you are interested in looking at or how much knowledge you have at the moment.

[rancid orbit]

Sorry, To tell you the topics, Logic, Algebra, Geometry, Topology, Analysis, Number theory, discrete math

[tulip blade]

Princeton companion to mathematics

[rancid orbit]

wtf it's writen by 130

[heady ember]

Are you sure you wanna get into logic, beyond the basics like what is a conditional statement?

[rancid orbit]

Of course, there must be some books outlining the basics ahead.

[rapid lily]

Getting a book on logic won't really help any of those other areas unless you need reasonably advanced results. I don't know your background, so if you are not familiar with discrete maths, you can start there.

Otherwise another option is something like Analysis I by Amann and Escher which covers some analysis and a bit of the discrete maths in the first chapter. Otherwise you can take a book like Real Analysis with Applications by Davidson and Donsig if you would like something less abstract.

For algebra, again I'm not too sure what your background is. I only really read algebra books when I was very comfortable with proofs, so I don't have many good suggestions. Perhaps try Undergraduate Algebra by Lang. I think many of Lang's books are quite clear and you learn a lot about how to think about the subject, but they can be a bit abstract at times.

I don't have great recommendations for the rest. But those two subjects are quite important.

[rancid orbit]

My goal is to become a math pervert. Just know that your help has been great help to me. Thank you.

[rapid lily]

You're welcome and all the best with learning more maths!

[remote sparrow]

https://edwardfrenkel.com/rites/

is dr. frenkel your inspiration?

[rancid orbit]

I don't know who he is

[river glacier]

Hii guys! I've a question

Any book suggestion for the preparation of this test

general mathematics!! I don't get it, what does it mean?

[rich sun]

general abstract nonsense, it's in the category theory III class, right?

[tender birch]

Multi-part question:
When should I incorporate proof/logic into my mathematics learning (self-study) and what would be a beginner friendly book?
(Currently trying to learn Calculus 1)

[river glacier]

Hmm but this is for undergraduate students

[river glacier]

😶

[tender birch]

Yeah I've read that. Just wondering everyone's opinions on when is a good starting point

[river glacier]

hmm but I've only 2 months for preparation

any kind of outlines or topics that's would be enough for this test

[grand thistle]

incorporate it now

just use a book like apostol or spivak

u get to do both

(learn calc and proofs)

[tender birch]

Cool, thanks 👍

[grand thistle]

dunno about logic tho

[narrow relic]

I haven't actually read this yet but it was on my list of books to look at and from what I can see it looks excellent: https://forallx.openlogicproject.org/forallxyyc.pdf . It's called forallx: Calgary. An Introduction to Formal Logic. It teaches you something called Fitch natural deduction which is used for proving things.

[tender birch]

Appreciate it, I'll check it out

[gray gazelle]

"Soil heats up much faster than water when the two are exposed to sunlight. Use that fact and your understanding of heat transfer to predict which way the wind will blow near the surface of the earth as the sun rises near the seashore." Hello hass anyone seen this type of question in any book?? If yes can you please name the book? Although the chances are very slim still the power of internet can not be underestimated!! Thanksss!!!

[grizzled tulip]

Actually I did find something

But not the book

https://www.physics.utoronto.ca/~jharlow/teaching/everyday05/test a.pdf

Question 13

[gray gazelle]

Aye thanks for the inputt!!

[gray gazelle]

😃😃 i think we got it!!!

This could potentially be the name of the book

But still if anyone else finds a clue let me know here thanks!!

[grizzled tulip]

This book does have some related questions.

[tame plaza]

This sentence appears to be a question from a quizlet flashcard set titled "How Things Work Chapter 3"¹. It also appears on other websites that provide solutions to homework questions²³.

Source: Conversation with Bing, 16/03/2023(1) How Things Work Chapter 3 Flashcards | Quizlet. https://quizlet.com/443180573/how-things-work-chapter-3-flash-cards/ Accessed 16/03/2023.
(2) SOLVED: Soil heats up much faster than water when the two are exposed .... https://www.numerade.com/ask/question/soil-heats-up-much-faster-than-water-when-the-two-are-exposed-to-sunlight-use-that-fact-and-your-understanding-of-heat-transfer-to-predict-which-way-the-wind-will-blow-near-the-surface-of-th-85204/ Accessed 16/03/2023.
(3) Solved Soil heats up much faster than water when the two are - Chegg. https://www.chegg.com/homework-help/questions-and-answers/soil-heats-much-faster-water-two-exposed-sunlight-use-fact-understanding-heat-transfer-pre-q72247334 Accessed 16/03/2023.

[gray gazelle]

I don't think he meant it that way guys, lol

[remote sparrow]

that's what a math pervert would say

[short hill]

What would you all recommend as a game theory textbook for an advanced high schooler

[gray gazelle]

My university course would recommend this one https://www.cambridge.org/core/books/game-theory/B0C072F66E027614E46A5CAB26394C7D

[molten mirage]

Is there any difference between thoams’ calculus and thomas’ calculus early trasidentials?

[crimson leaf]

Does anyone know which Stanley book covers finite difference methods?

[remote sparrow]

log, exponential, and trig functions are treated earlier in early transcendentals

the "late" transcendentals version postpones using them until sufficient calculus machinery has been developed to rigorously define log, trig, and exponential functions

it doesn't matter what you go with tbh

though early transcendentals seems more popular since science and engineering students need to see those functions early

[molten mirage]

Ahh alright, thanks

[crimson leaf]

What are some good discrete geometry books? I only know Adam Sheffer's book

[foggy relic]

Winning ways

[gray gazelle]

Wow

[woeful ravine]

The only discrete geometry book i'm aware of is GTM 212 "Lectures in Discrete Geometry".

[uneven finch]

Hey any advice on how to approach the book "Problem solving strategies" by Arthur Engel ?

[crimson leaf]

This seems pretty good, thank you!

[torn storm]

What's the baby rudin of game theory?

[gray gazelle]

People usually don't take game theory as a mandatory course

[torn storm]

hm, what I need is a terse reference

[gray gazelle]

Rudin is an introduction

[torn storm]

ok, but a terse one

[gray gazelle]

I can hardly call it a reference but alright

Do you just need a textbook to study from

[remote sparrow]

according to this post, "game theory is a big field with several essentially disconnected areas, and one can't really hope for a comprehensive introduction from a single text." can you explain what you want to get out of a game theory book?

https://mathoverflow.net/questions/71848/looking-for-a-mathematically-rigorous-introduction-to-game-theory

i've also found some other links

https://mathoverflow.net/questions/18794/how-to-start-game-theory

https://mathoverflow.net/questions/233221/what-does-game-theory-cover-and-how-should-it-be-called

https://math.stackexchange.com/questions/2316833/game-theory-book-recommendations

https://math.stackexchange.com/questions/3779545/books-for-game-theory

https://math.stackexchange.com/questions/4245930/book-recommendation-for-game-theory

https://www.reddit.com/r/math/comments/lt046/a_good_and_rigorous_game_theory_text/

https://www.reddit.com/r/math/comments/1ju1m3/what_are_some_good_introductory_books_on_game/

https://www.reddit.com/r/math/comments/b1esq/can_you_recommend_a_good_game_theory_textbook/

https://bookstore.ams.org/view?ProductCode=GSM/115

[torn storm]

according to this post, "game theory is a big field with several essentially disconnected areas, and one can't really hope for a comprehensive introduction from a single text." can you explain what you want to get out of a game theory book?
Thanks, that's already helpful! I was starting to feel crazy that I couldn't find "the reference" to get started.

[gray jungle]

doesn't game theory has 2 types , the combinatorical game theory and economics game theory.

[strong oyster]

maybe a bit advanced but on numbers and games is very cool

just might be slow going

[hearty steppe]

Hey thanks for listing more links @remote sparrow 🙂

The combinatorial game theory is the meta

[crimson leaf]

For combinatorial game theory you could probably do winning ways or lessons in play then do combinatorial game theory by Siegel

[short hill]

ty for the references damn

did not expect this comprehensive of a response LOL

[solemn haven]

Hi people, i'm someone who's actually learning undergrad axiomatic set theory, is there other topic of pure math that i could learn at the same time? If there is, could you recommend some books? Thanks.

[remote sparrow]

mathematical logic

could read goldrei, enderton with montalban's youtube lectures, or mileti

[narrow relic]

Could you share the name of your textbook?

[solemn haven]

I'm learning with these three: (1) Set Theory A First Course by D. Cunningham, (2) Elements of Set Theory by Enderton and (3) Introduction to Set Theory by Karel Hrbacek.

[narrow relic]

Cool thanks.

[cinder zenith]

AoPS has too many books to choose from 😄 Any recommendations for an 11th grade student (germany)? Im good at maths but not extraordinarily if that makes any sense.

[sterile harness]

do you have any experience with competition math?

[cinder zenith]

A tiny bit, I participated in some first rounds (school round) of the german math olympiad, but mostly in 3rd to 5th grade. So no experience to really speak of I guess

11th grade first round problems would be really hard for me to solve

[sterile harness]

Maybe try Algebra

Which math are you in right now?

Like in school

[cinder zenith]

We just got started on derivative basics a few weeks ago @sterile harness

[sterile harness]

Ok if you were in the US I’d prob say Intro Algebra but idk about German school system

How in depth do you think you learned Algebra

you can take the tests that they have

that test if you’re prepared or if you’re good enough for the book

[cinder zenith]

are you talking about the intermediate algebra one?

[sterile harness]

No intro

https://data.artofproblemsolving.com//products/diagnostics/intro-algebra-posttest.pdf

I know it sounds kinda easy but they give much deeper understanding and challenging problems

Ok honestly that test is way easier than the book

[cinder zenith]

oh in that case thee book is probably good

cause the test isnt "hard" but also not trivial I would say

[sterile harness]

alright then

hf w/ it

After that just do geo -> counting and probability -> number theory (if you decide to go on with it))

[cinder zenith]

tyty :))

[flint bay]

Working on some Toric Variety stuff, and it seems like i should def know some Classical Invariant Theory

anyone got a reference for that

at abt the level of shafarevich/hartshorne chapter 1

i feel like i gotta be able to find this in any CA book

[turbid blaze]

http://www.math.toronto.edu/~ila/ClassicalInvariantTheory.pdf

There's this undergraduate book on it

[gray gazelle]

any good (undergrad) books on PDEs that only cover linear PDEs?

2nd order linear PDEs

[vagrant mason]

question, what are really good calculus books out there that show at least calculus 1 and 2

[slim peak]

beginnign of Evans, mostly

[gray gazelle]

thanks

[cinder zenith]

I would like to read a math book for learning/fun. Any recommendations? Im in 11th grade in Germany (just began learning derivatives)

[finite crane]

if you want a real math book read Tao's Analysis 1.
But if you are focused on winning olympiads for now then you may have to cram the AoPS books

Unfortunately there' s a choice to be made here, and I wish there wasn't, but yeah. In the long run learning actual maths is better but olympiads could let you get into prestigious unis if you win some good prizes

[cinder zenith]

I actually didnt plan to do olympiads at all, but that might also be interesting 🤔

[hazy elk]

Why not? There's no rule that says you can't learn analysis before calculus

[cinder zenith]

I dont even know what the difference is 😄

[hazy elk]

Calculus is just a gimmick to do analysis without understanding why what you're doing works

[cinder zenith]

ohh interesting

could you give an example?

[hazy elk]

It wasn't meant to you, sorry

[cinder zenith]

all good

[hazy elk]

Calculus is the study of functions, continuity, limits, derivatives, integrals... A shorthand way to understand derivatives would be as rates of change of functions

[cinder zenith]

Does this mean that there is a better explanation for derivatives? They feel like cheating to me 😄

[hazy elk]

Limits help us study what happens to the value of a function when you get close to a particular value

[hazy elk]

Actually it's better to think of them as a linear approximation of a function

Which in one dimension, manifests itself at a rate of change

[cinder zenith]

thats interesting 🤔

[gray gazelle]

idk if it's best to think of them like that. seems more like an application

[cinder zenith]

I was thinking about their limit definition and it seemed like you try to get closer and closer to a value but WHY do you "reach" it if you are just getting closer and closer if that makes sense

[hazy elk]

No in the multivariable case, this is the way to think about them

[gray gazelle]

idk in my class we still did linear approximation as an application more than a viewing of them

[hazy elk]

That's fine, just saying that the 1D case can be seen as due to a more general thing

[gray gazelle]

atleast over R, seeing it as a rate of change works well imo

[hazy elk]

Sure

It gives a good intuition

[hazy elk]

Not sure what you mean, can you make it more precise ?

1/2, 1/4, 1/8.... has limit 0, and the set {1/(2^n)} does not contain 0, so can you say 1/2, 1/4,... reaches 0?

[cinder zenith]

so basically, the two points x|f(x) and x0 f(x0) are moving closer and closer together to approximate a tangent at x. But why do we eventually get exactly the tangent if we are just approaching it more and more closely?

[gray gazelle]

it never gets to it exactly

but the limit is the notion of like kinda what would happen if we did go to infinity

or infinitely close or whatever

[hazy elk]

Let's move to #calculus

[finite crane]

tao analysis actually starts with natural numbers and logic/proof, so it does indeed start from the beginning

the real worry is that a student in highschool might become too bored with it, but we'll see. there are many self-motivated students out there

[crimson leaf]

I wish the book did metric spaces earlier

[karmic thorn]

I wish the book did analysis earlier 😭

[crimson leaf]

That too lol

[remote sparrow]

the construction of the number systems should be covered at some point in every year-long real analysis course. minimally, one should impress on the reader why completeness of the reals is so important.

[remote sparrow]

https://www.youtube.com/watch?v=-yksoVsb47s

strauss, zachmanoglou, and weinberg may be some other helpful choices

[gray gazelle]

thanks

[cinder zenith]

I don't even know exactly what type of book I actually want to read and for what purpose 😄

[analog lava]

hello

where can i learn about older AG

like problems and motivation

before the abstract language

adn what do i need to know

[stray veldt]

hartshorne chapter 1

[analog lava]

yea i really wanted to try out harthshorne to see whats the fuss about

but i didnt complete atiyah mcdonald so..

didnt know if i had enough background

[lapis sundial]

i would recommend doing more comm alg, like you should be comfortable with the Nullstellensatz and stuff at the least

[analog lava]

atiyah mcdonald uptill what chapter

so i can read harthshorne?

i just wanna explore for the fun of it and do problems

[lapis sundial]

kinda depends on what you wanna do, like i'm p sure hartshorne uses every chapter of Atiyah Macdonald (and more)

[cinder zenith]

@finite crane You recommended the AoPS books to me. Do you think the first contest one is fine for a grade 11 student (not sure if I mentioned my grade yesterday) or should I take a look at some intro ones before that? Asking because they are actually quite expensive

[finite crane]

unfortunately I don't know your level

[cinder zenith]

the book doesn't seem to have a "are you ready" thing sadly

[finite crane]

for instance at grade 11 I was already well set into olympiads

[cinder zenith]

I would say I don't know that much more than the normal curriculum

well but that doesn't help because you don't know it obviously

hmm

[finite crane]

you also have to take into account whether you want to pursue olympiads now. high school is short

all depends on your preferences

[cinder zenith]

Well I'd say I would like to try, probably some good experience to be gained there 🤔

[finite crane]

sounds like you know what to do then

[sage python]

@analog lava if you don't want as much commutative algebra there are some other AG books that are classical and rely less heavily on commalg

[cinder zenith]

You are probably right 😄 I'll try

[inner vault]

what do you guys think about principles of mathematics by bertrand russell? i read the first couple pages and nothing so interesting so far

[quick hornet]

only relevant as a historical work rather than as anything to seriously study

russell himself said as much later in his life

[analog lava]

damn

i think AM then is the best text for com algebra ig

[analog lava]

i jhust want to have motivation

like there was AG before like comm alg and i just wnat to knwo what these people are trying to do

what problems are they trying rto solve

and what problems did they actually did and what they couldnt without the new tools

do u get me

[tulip blade]

You can read more classical algebraic geometry

You can see it used in more concrete settings if you want motivation

Algebraic curves by fulton is whats used for the ug alg geo class at harvard. I think Ideals, varieties, and algorithms; codes over algebraic curves are cool books.

[analog lava]

algebraic curves sound cool

[tulip blade]

https://people.math.harvard.edu/~bullery/math137/ you could try to follow the course

[analog lava]

this looks like new AG but dumbed down

[dawn mirage]

I wanna try to get into topology, what's a good book rec for beginners? (background: only high school math)

[broken meadow]

Munkres

[dawn mirage]

[karmic thorn]

I remember Armstrong's book takes a slightly nonstandard approach

And there are few books that have a different take on the subject

[dawn mirage]

oooo, thank you 🙏 .

[broken meadow]

but uh if you only know highschool math you would probably spend some time working through the first chapter talking about like

[karmic thorn]

I have not read them so I cannot say anything more

[broken meadow]

sets and logic stuff

everything is proof based as you might already know

So you will need to be comfortable in some capacity with proving things

[dawn mirage]

yeah , it's okay, I'm trying to self teach myself about it before college.

[dawn mirage]

👍

[dawn mirage]

Ooo

[gray gazelle]

I recommend learning about metric spaces first instead @dawn mirage
They're more intuitive and a lot of topology lingo and definitions comes from them imo

A book here is Topology of metric spaces by Kumaresan
Though it does assume some knowldge in examples from what I saw

(e.g. integrals give raise to interesting metric spaces)

[gray gazelle]

well which book can be better than my maths textbook?

of highschool

[gray jungle]

Imma be honest with you chief
"my math textbook of highschool" isnt a lot of information , how am i supposed to know what book you are talking about?

And generally speaking the book choice isnt that much of a big deal at highschool @gray gazelle.

[gray gazelle]

There's Lang

[fluid hull]

Hello there.
I've recently had to take certain applied courses which require certain knowledge of Calculus.
I've passed both Calculus 1 and 2 during the beginning of my undergrad years and had great difficulty through its lack of proof. I've also passed two analysis courses (the first taught on Kenneth Ross and the other from baby Rudin) and strangely, even though the fundamentals of Calculus is discussed in the analysis courses, the subject is too fundamental to help with Calculus itself.
So, I imagine a proof-based calculus book is still not analysis as it is usually discussed in math forums.

All that said, I was wondering if anyone had a proof-based calculus book that is able to bring me up to speed with the necessary material? Something better but with a generally similar set of subjects as James Stewart's Calculus books.

Thanks in advance!

[gray gazelle]

its stp mathematics 3a

[gray gazelle]

any book with good explanation and doesnt assume the reader knows something

[finite gale]

What topics are you looking for a textbook on

Because I have no idea what math 3a is

And generally speaking, the specific textbook used for high school doesn't matter

You can very easily supplement your current textbook with just looking stuff up

[foggy relic]

Why do you want topology

[gray gazelle]

To explore a topic I assume; out of interest

What's the point of that question, Alrighty is still in high school

[finite gale]

I feel like learning about metric spaces first makes more sense than going straight into topology, no?

Though I guess it's not really necessary

[gray gazelle]

Yeah. That's where all motivation and geometric intuition is

[gusty smelt]

well invictus' question is to gauge why they want to learn topology so they can taylor recommendations supposedlty

[gray gazelle]

My point is that a person in high school might not know why other than simply "out of interest"

It'd be surprising otherwise

[gusty smelt]

"out of interest" is an answer to the question, and its not what your point is, you specifically asked the point of the question

[gray gazelle]

It was a rhetorical question

[gusty smelt]

if it was rhetorical, that would mean that you wanted to imply its a pointless question, which as i stated is not

so you are wrong in either case.

[foggy relic]

Some people might want to learn it for itself, some people to learn algebraic topology after which I would recommend different books for

[gray gazelle]

Maybe not as much pointless (those are your words), as you can safely disregard that as the person you are asking is still in high school

[gusty smelt]

idk what ur saying anymore. some coherence please.

anyhow I myself did AT in highschool and know many other who did other stuff with topology, so idk why highschool disqualifies people from knowing what they want with their topology

and before you put some specific info about the person requesting, how would invictus know lol

infact the point of asking is so he could learn that info

[gray gazelle]

I never said it disqualifies them. Just that it's a safe assumption to disregard that. Besides, don't you think that if someone knew what kind of topology they want to learn wouldn't be specific about it

[gusty smelt]

this is called communication, you ask questions to figure this stuff out instead of assuming

[gray gazelle]

They specifically said they want to learn it for college anyway. Thus just your standard topology

[finite gale]

Except for the part where they didn't

[gusty smelt]

i dont really know what ur saying anymore

[glacial crypt]

tfw arguing in book recommendations

[gray gazelle]

Sure I interpreted it this way though @finite gale

[finite gale]

I didn't see that one, my bad

[gusty smelt]

I dont really know how you can go from that to "they dont know why they want topology for" but you do you lol

[gray gazelle]

that will take me from beginning to end'

[gray gazelle]

3rd yr of secondary or grade 9

[finite gale]

Can you list some specific topics?

I'm not sure what grade 9 math consists of

[gray gazelle]

like a begineer math book i need to fix my foundation of maths

[gray gazelle]

commercial maths algebra(quadratics) trignometry surface area and nets and volume of shapes circle properties etc'

But i am looking for a book that could fix my foundation of maths as of now

[gray gazelle]

hmm

[gray jungle]

Instead of a book , you could use this website " https://www.khanacademy.org/math/in-class-9-math-foundation" but as i said your book should be enough.

youtube must have plenty of friendly videos too

[finite gale]

If you do as many exercises as you can or feel as needed, you should be okay tbh

[gray jungle]

because i dont think many people in this server have the experience to tell you about "good grade 9 books" better to ask your teacher

[gray gazelle]

thanks

[finite gale]

But also khan academy is good resource for pre-university material

[gray gazelle]

but it assumes i know some stuff which i dont

[finite gale]

I think they also have generated problems with solutions so that might be good to do as well

[gray gazelle]

well he referred to a pearson ebook which would prepare someone for a levels!

[gray gazelle]

they do but their formulas sometimes my tr doesnot like them

[gray gazelle]

@gray gazelle Lang Basic Mathematics

[gray gazelle]

ok lemme check that out

[gray gazelle]

by lang serge?

just confirming

Lang's Algebra is not a continuation

[gray gazelle]

Yes

[gray gazelle]

i think i see this guy in youtube sometimes with a black screen writing stuff and teaching

[gray gazelle]

the emoji scared the hell out of me

[dry rose]

Any good math pdf? for calculus 1

[dawn mirage]

I see I see, I'll probably study both at the same time cause it's just for fun atm.

[dawn mirage]

It just looked like fun and challenging .

[gray gazelle]

Topology is really fun, good luck

[dawn mirage]

thanku 🙏 .

[cursive sable]

guys

how do i read books

wihtout getting bored asf

i need a book thats liek enticing to read and keeps me hooked

idk what happened but i suddnely jsut got bored of books

or my book decisions arent good

oh wait i forgot this is math server iw as talking about normal books 💀

[hollow shore]

getting into the zone of reading is a time taking process

start with something simple and short

like a novella or a short story

and then slowly try to move ahead

[remote sparrow]

kingkiller chronicles

[karmic thorn]

Any references for integral equations? I'd like something that tries to go over both the specific solution aspects (at least for simple Volterra and Fredholm equations) while also covering the general theory (which I believe is functional analysis heavy).

[gray gazelle]

I have a book (actual physical copy) about this, but idk how good it is. It covers Volterra and Fredholm equations. Let me see the title one second

[karmic thorn]

[gray gazelle]

Oh wait I don't it has an English version

[karmic thorn]

I see

[remote sparrow]

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

try looking here

[gray gazelle]

They don't even recommend any good point-set topology books

Those two are not really that good, Lee is viable, idk the third one

what do you think of the book: a synopsis of element of mathematics?

[fierce hedge]

is willard bad? I heard some praise about it few months ago

[gray gazelle]

My experience with Willard is one proof. Not only it's wrong, but also written in a way like everything is obvious, preventing reader even more from clarifying the mistake

If the whole book is like that then idk

The material he presents is really cool though...

[gray gazelle]

Like I had the same proof in van Mill but it was elaborated on more so I could fix the mistake but good luck to anyone who stumbles upon it in Willard

💀

[gray gazelle]

@sturdy shore

[sage python]

Willard to me feels like it has the same problem as Munkres where it just seems like it has way too much shit

For most people spending that much time on raw point-set topology is not useful

[gray gazelle]

Well sure it feels like there is 3 types of books from topology
Topology everyone should know, topology an AT person should know and topology for topology sake

[sudden kindle]

do what i did: work through Viro's problem textbook Elementary Topology

[sage python]

Blitz I wouldn't quite say that

I would say there's a "core" amount of topology

Then it kinda veers off into different directions

[sudden kindle]

3 types of topology: general topology, algebraic topology, (smooth) manifolds

[sage python]

Blitz is saying within point-set

Basically everyone should know about, okay basic defs and results about a topological space, quotients/products/subspaces, connectedness, compactness, continuity, sequences, Hausdorffness, and in particular metric spaces

Maybe nets/filters are also good to know (though depending on what you do... might not be necessary)

But then it's like, each area kinda has its own set of fucky spaces that you care about

For categorical reasons in algebraic topology you may want compactly generated weak Hausdorff

Analysis likes nonsequential spaces a bit, so you actually need nets/filters to properly probe things. Closely related are countability axioms. Apparently in some settings you like things called "uniform spaces", where (as you'd expect) you can make sense of uniform convergence/continuity

Probably also analysis, esp functional analysis (maybe topological dynamics?), is where you care about those weird theorems like Tietze and Urysohn and all

Zariski in AG is prob the main example that comes to mind off the top of my head where people care about non-Hausdorff things. Number theorists like profinite shit

etc

So it's kinda pick your poison with how much topology you need beyond the gcd

[sturdy shore]

which proof?

willard is my favorite math book

[gray gazelle]

Mazurkiewicz theorem

[sturdy shore]

haven't read it in full yet but I've yet to find a contender

hmm I haven't reached there yet, I've read it until like halfway through the compactness part

I have found a couple mistakes but none in the proofs, though ofc I might just not have the expertise to spot the mistakes

[gray gazelle]

It's a result about existence of arcs in metrizable spaces with enough assumptions

Connected, locally connected, complete metrizable I think

[sturdy shore]

I'll keep it in mind, but I doubt there are loads of egregious mistakes like that

nlab actually cites willard as reference for the proof of that theorem lol, so if you are right about it that is actually pretty bad

[tacit abyss]

i think I have no excuse not to know what a net (in topology) is at this point, does anyone know good books that give a reasonably comprehensive theory of them?

[sturdy shore]

willard - general topology

[gray gazelle]

Unrelated but I actually found errors on nlab before lol

It was a result in AT but not relevant to general theory where spaces are assumed to be nice enough so no one cared

[tacit abyss]

will check it out

mainly want to understand the result continuous <-> sequentially continuous with nets, that result has been at the back of my mind for ages

[gray gazelle]

Just shows you people don't actually always check if those things are correct, and write down the same errors

[tacit abyss]

i do sometimes see errors copied across sources

like i remember there was this weird omission of a step in yosida (?) that was copied almost word-for-word from the original paper and i never figured out how the argument worked the way it was supposed to

[tacit abyss]

this is actually a peak Mathematician Moment negl

[gray gazelle]

Yeah I think Willard and van Mill are the only books with this version of the theorem, others prove a slightly different (iirc less general) version using different methods

Ping me if you get to that part, or dm, I'll send you it but you need to correct it yourself

The proof in van Mill is much better

[sturdy shore]

[fierce hedge]

Oh, I don't think that discredits the whole book but I'll probably stick to other books then anyway I don't need to much point set

[fierce hedge]

Have you worked it out cover to cover? Also did you use any other book as supplement?

[sudden kindle]

i worked out the first half

the part about general topology

[fierce hedge]

I see and any other book used in conjunction?

[sudden kindle]

i used different books

not munkres tho

but the book i really solidly learned general topology from was through working thrrou that book

[tacit abyss]

well that was somewhat underwhelming - TIL I guess

[narrow relic]

Can you elaborate? I'm interested in that topic as well.

[leaden cliff]

Can anyone recommend books on D-operators with differential equations?

[tacit abyss]

idk it's all quite simple in the end

if i taught a general topology course it wouldn't be much to just stick at the end

[narrow relic]

Okay, thanks.

[remote sparrow]

https://www.reddit.com/r/math/comments/pj0xae/regarding_munkres_analysis_on_manifolds/hbulku1/

any thoughts about this review?

[sage python]

Before reading this, my friend TAd last semester for an analysis class that kinda ran out of Munkres

And uh

Nope

It was not great

It's basically evidence that multivariable Riemann integration is stupid

[narrow relic]

What approach do you recommend for multivariate integration?

[sage python]

I mean Munkres or more likely Spivak might be fine if you wanna learn multivariable Riemann integration

But tbh? Just do measure theory is my take

[narrow relic]

Like using Tonelli's Theorem?

[sage python]

That, change of variables as well seems much better with measure theory, etc

[narrow relic]

I've studied these theorems but I don't think the books I used had any examples of practical integrals, but I might be mis-remembering

I need to re-study measure theory from scratch after finishing the appropriate chapters of this Carothers book

[narrow relic]

At the time I didn't think much about practical examples, I was just going through the proofs of the theorems

[sage python]

Try "Functions of Several Variables" by Fleming

Iirc it actually does multivariable using measure theory

[narrow relic]

Hey, I've seen that book, I'm surprised to hear you mention it

[sage python]

But it's a multivariable calc book rather than a measure theory book if you get what I mean

[narrow relic]

Yeah, I have a syllabus for it (two actually) but I had taken it off my reading list

[narrow relic]

Since I sort of gathered that you can do multivariate integration with measure theory the same as the Riemannian way, so I didn't see the point of working through all those justifications/proofs... is that kind of the correct "take"?

[sage python]

So, the theorems in multivariable calculus like Fubini and change of variables can be done both with measure theory and with Riemann integration

The latter proofs, as far as I can tell, tend to be gross

Measure theory takes slightly longer to get through at the beginning, but you'll have to learn it eventually anyway

[narrow relic]

I mean, for example, the integral of x^2 I assume works out to x^3 / 3 + c.

(with the standard Lebesgue measure or whatever)

[sage python]

So, once you have Riemann integral on R, and especially fundamental theorem of calculus

That's really how you'll compute a lot of stuff

And anything that's true in Riemann integration is true in Lebesgue

[narrow relic]

Oh, right, isn't there a theorem that says the Riemann integral is the same as the Lebesgue integral in a lot of cases or something?

(I know I sound like an idiot, I have not learned this stuff systematically.)

I'm just trying to get a sense of the map of the terrain ahead.

[sage python]

Yeah

[narrow relic]

Cool thanks 🙂

[sage python]

If a function, let's say on a compact rectangle, is Riemann integrable, then it's Lebesgue integrable and the integrals agree

So Lebesgue basically subsumes Riemann

(Improper is mildly messy)

[narrow relic]

Got it. Thank you. What do you think of this book for studying measure theory: https://link.springer.com/book/10.1007/978-3-030-38219-3

I came across it sometime recently.

[sage python]

Hmm, looks fine? Not super standard, idk if it does the multivariable calc stuff you'd want in Munkres (e.g. differential forms)

[narrow relic]

Oh, I am not concerned with that part, thanks, I just meant in general

[sage python]

Ah, so as a measure theory book it's probably fine. I am more familiar with "Real Analysis for Graduate Students" by Bass

[narrow relic]

I liked how this is one book for both functional analysis and real analysis, and that it covers the nets/topology stuff

[sage python]

And then there's also "Real Analysis" by Folland which is probably the most common book

[gray gazelle]

I don't think it's a book for measure theory. I've only browsed first pages but it was functional analysis

[sage python]

Both of those two do some topology and some functional analysis

[narrow relic]

Yes I'm sort of trying to avoid that book, the last time I tried it it was like super dense, maybe I could try it again

[sage python]

Maybe try Bass then?

Like this looks fine but I don't know it as well as I know Bass

[narrow relic]

Really? The first 150 pages were topology and measure theory.

[sage python]

So I can't quite recommend it with my full chest

[narrow relic]

That's okay I just really appreciate your advice so wanted to run it by you! Appreciate you taking a look at it.

[gray gazelle]

interesting

I wasn't asking because I knew, but because it didn't seem like a book which would introduce measure theory

[narrow relic]

Oh that's fine. I'm not sure if it's a good introduction or not since I don't know that material well.

[coral prawn]

Where can I like read up on-

how to do p series, calculate/simplify expressions with capital Pi (its usually easy for those expressions with only Sigma, but Pi?) I'm not exactly sure what field of mathematics this would be considered.

[karmic thorn]

Analysis, although books rarely focus on the techniques of computation themselves

[coral prawn]

ic

[karmic thorn]

But rather concern themselves with results about convergence, etc.

You will still end up getting a hang of some of the common ideas

By proving results about them and doing exercises

[coral prawn]

gotcha, ty

[remote sparrow]

gradshteyn's book or similar handbooks on integrals, series, products, and mathematical formulae may interest you

[coral prawn]

[orchid mortar]

1k+ pages book, isn't that difficult to find interesting things in particular

[coral prawn]

hmmge

some are okay (in terms of length), but 1k pages is a bit... overkill? Idk, I should probably check out the content before judging too quickly

[orchid mortar]

Gadshteyn is definitely interesting though, I will say. Maybe you can take a look at the sections that you want to focus on first.

[turbid mural]

functional analysis book recommendations ?

[grave thorn]

undergrad or grad?

[gusty smelt]

why do you want functional analysis? if its for operator algebra kinda stuff (or softer analysis as one might say), id recommend pedersons "analysis now"

[grave thorn]

for undergrad I think "linear functional analysis" is good

[turbid mural]

undergrad

[gusty smelt]

whats your background

[turbid mural]

i have finished real analysis and point set topology

[gusty smelt]

real analysis as in? first year level or stuff with measure theory

[turbid mural]

measure theory

[gusty smelt]

I see, and you didnt answer but is there anything in particular you want to explore with func analysis

[turbid mural]

i just want to learn the subject

[gusty smelt]

right i see

hmm I like pederson "analysis now" but it does lean towards operators rather than things like PDEs

I still recommend it because it is a really good read

[turbid mural]

alr

[thin remnant]

Any module theory recommendations?

[turbid mural]

what's the author's name ?

[grave thorn]

rynne + youngson

it doesn't go very deep, but it covers a good selection of contents for undergrad

@turbid mural

[turbid mural]

alr

[gusty smelt]

imo if u know measure theory you can probably just go for a grad level book, but its upto you

[turbid mural]

i will start from the undergrad stuff first

[grave thorn]

ngl I'm always surprised how little some undergrad books cover lol

[gusty smelt]

right vmm kek

it makes it easy to tutor UGs though, i just learn whatever topic in a week lol

(its how i learnt model theory at first, some UG wanted me to tutor them)

[turbid mural]

if i cant find the youngson book i might just go for the grad one

[versed magnet]

Do you have something to differential equations?

[grave thorn]

you can find it on certain websites (if you know what I mean)

[turbid mural]

ye

[sick wasp]

Hello
wanted to start learning calculus. any recommendations?

[heady ember]

Pauls' Online Math Notes, Khan Academy

Spivak's Calculus if you want smt a lil more rigorous

[trim tangle]

i find Peter D Lax's calculus book to be useful and more in depth than others

[fleet bramble]

Functional analysis by Conway can give some fundamental knowledge abotu functional analysis and Classical Functional Analysis (maybe this name) by Lindenstrass can give some relatively new things about topics of spaces

[sick wasp]

thankss 🌹

[sick wasp]

thank u 🌹

[fleet bramble]

some books recommended for basic pde? (true basic, i've already learnt ode before

[rich sun]

Evans' PDE is a standard reference

[fleet bramble]

thx

[remote sparrow]

evans is not basic undergrad pde. it's basic grad pde. you probably want strauss, zachmanoglou, or weinberg instead.

[fleet bramble]

does grad pde need undergrad pde?

[remote sparrow]

no

[fleet bramble]

then what's the difference

i know few about how to learn pde

[remote sparrow]

but arguably its prerequisites are more sophisticated

undergrad pde just requires some basic ode and real analysis

grad pde needs functional analysis and measure theory

[fleet bramble]

oh fouturnately i've learnt fa and measure theory before, maybe i'll try one of those recommendations

thx very much

[versed magnet]

anybody?

basically nothing, but basics of mathematical analysis. Tbh, all I know, is differential equation is in form y'(t) = f(t,y(t))

I want it, because I can't keep up on my teacher on uni, on 2nd year of bacherol

yeah

[marsh yew]

Guys I have Bartle and sherbert book, I wanted to ask, for a thorough study of real analysis, should I read each and every chapter of Bartle and sherbert ?

Including the chapter 1 of preliminaries

Where they discuss Infinite sets, machines and transformations, sets and Mathematical Induction

[sturdy shore]

preliminaries are preliminaries, you should read it if you don't know these concepts already

[marsh yew]

Hmm ok

[fallow cypress]

Yeah, what lems said ^ skim stuff that you already know to make sure you know it

Maybe do an exercise or two just to be sure

Then do the stuff you don't know

[marsh yew]

Ohk gotcha

[remote sparrow]

you can use evans then

[fleet bramble]

Okay i ll take a try! Thank u so much!!!

[narrow relic]

I would skip the "gauge" parts (some of that was in Chapter 5). I would also learn integration from another book.

[marsh yew]

My teacher actually said to study everything from it

Is the integration part not good ?

If so what book would you suggest for it

[narrow relic]

I don't know because when I was reading the book I noticed that those parts were kind of different from some other things I was looking at, so I just skipped those parts.

[marsh yew]

Hmm

[narrow relic]

I just learned the standard Riemann integral treatment, not the gauge-based stuff they have there.

[marsh yew]

I'm gonna practice problems from Kaczor and Nowak

[narrow relic]

Gauges are used to define something they call the "generalized Riemann integral" (Henstock-Kurzweil integral). But that didn't seem very relevant to me at the time, I just wanted the regular Riemann integral that most people talk about.

[marsh yew]

Hmm

[narrow relic]

The benefit of the Henstock-Kurzweil integral is according to Wikipedia that it's more general than the Lebesgue integral. But I think the Lebesgue integral is good enough for my purposes anyway.

[marsh yew]

I'm studying real analysis for an exam

Which I'll give in my final year of uni

For masters and all

[narrow relic]

Oh, well then just do whatever that syllabus says.

[marsh yew]

Ye

Kaczor and Nowak has really good problems

I love that book

Even tho I suck at solving most of its questions atm

Hehe

[gray gazelle]

For most purposes other integrals don't matter

[narrow relic]

Good to know 😀

[marsh yew]

Hmm

Idk why people think I'm a spoiled brat cause I take notes on an ipad

I have ADHD and OCD (some symptoms) and messing up notes makes me cringe hard

[gray gazelle]

How is that relevant to this channel

[marsh yew]

Ok sorry

Shit I thought I was in #chill

My bad I'm sleepy

[gray gazelle]

[marsh yew]

https://tenor.com/view/sorry-dogeza-wave-apology-bow-gif-8906394

[exotic robin]

Hello, what books and resources you guys suggest to learn linear algebra ?

[magic zenith]

any recommendations on differential geometry for newbies?

newbies as in with experience in multivariable calculus and linear algebra

[gray gazelle]

Warning this is not first hand information, the author is not knowledgeable about these matters so questions should be directed elsewhere
Source: http://www.geometry.org/tex/conc/differential_geometry_books.html
Do Darmo’s Differential Geometry of Curves and Surfaces if no Topology.

[magic zenith]

@gray gazelle thank you, i'm going to check it out.