book-recommendations

[neon tiger]

any one of you ever participated in ioqm or prmo

.

.

[terse heron]

Olympiads

Nope

I gave Kvpy, that's it

[blazing wharf]

Kvpy now ded

[neon tiger]

Have you participated in anything

?

[vagrant path]

Maximum Ride Graphic Novel 👌

[willow pecan]

Omniscient Reader's Viewpoint

[glacial leaf]

Could I ask for a good introduction to calc 3 book? I've been thinking of getting apostols p2, but I don't know if it's beginner friendly. Thank you.

[willow pecan]

Do you want a proof based multivariable calc book

Or not proof based

[foggy relic]

Spivak COM

[glacial leaf]

I prefer a non proof based, but a proof based one is fine

[willow pecan]

I think Stewart is the standard non proof based multivariable calc book

[glacial leaf]

thank you, I'll look into that

[remote sparrow]

hubbard and hubbard is also designed to work for honors multivariable calculus classes if, in the author's words, you design your course around omitting some of the more difficult and sophisticated proofs (which are generally relegated to the appendix)

shifrin's multivariable mathematics also works for this purpose, though its hard copy is more expensive than H&H

[glacial leaf]

thank you for the recommendation, hubbard and hubbard definitely seems like a suitable choice

[narrow relic]

Has anyone here had experience with the book Measures Integrals and Martingales by Schilling?

[heady ember]

Look in pinned

[narrow relic]

I read that already 🙂 I had a question about it though

[heady ember]

[narrow relic]

I'm wondering about how long it would take a normal person to do the first 13 chapters or so, and what kinds of feelings or experiences people have had with it.

For context, I couldn't really make sense of some of the other books I looked at, and this one seemed to make sense and be written well, but it was taking me quite a long time to get through aspects of it

[surreal heart]

Hey! Just looking for a book recommendation for a young person. I'm a senior in hs taking a Calc 1 course, and I just want something fun to work through in my free time, I'm happy to hear any and all recs even if they may be slightly too easy/difficult as long as they're interesting and new in content

[agile void]

Is this for math books, or just reading in general?

[surreal heart]

Math books! Something to work through and hopefully improve my skills

Although I guess I would take math-related reading recommendations too but probably wouldn't read them at the moment

[hallow oriole]

book of proof

by richard hammack

free on his website

https://www.people.vcu.edu/~rhammack/BookOfProof/Main.pdf

solution to odd exercises are in the back, i think

could be wrong

[surreal heart]

Ok cool, thanks for the recommendation, it seems like something I'll be very interested in

[heady ember]

Spivak

[hallow oriole]

spivak is good too

read book of proof first

[heady ember]

Enderton is interesting for axiomatic set theory. But tread carefully... this book isn't easy to read at all, at least in my personal experience lol

[heady ember]

Last time I originally tried Rosen discrete math, found it too boring. Then tried Enderton, which is quite spicy lol . But pretty interesting.

[sturdy shore]

axiomatic set theory will feel unmotivated until you have seen some other proof based stuff

something like book of proof or other books of that sort will cover more than enough naive set theory for a beginner

and honestly most people will never have to learn axiomatic set theory anywhere in their undergrad

[frigid flax]

Any book for matrices and vectors?

[heady ember]

I just did Enderton for fun lol. I was curious about cardinals, ordinals n stuff

Haven't reached there yet but yeah

[sturdy shore]

If you are interested for the sake of it, that's great (same for any topic)

but cardinals and ordinals (beyond a basic overview of cardinals given in any proof book) won't be of use to anyone studying math until they at least take introductory courses in fields like analysis algebra etc

[heady ember]

Yeah i know

[grand thistle]

literally any linear algebra book

check pins if you want a detailed review on linalg books

[sage python]

For what it's worth my books were more theoretical, something like Strang might make more sense in case "matrices and vectors" does in fact suggest, as it seems to, that the aim isn't necessarily that

[tawny copper]

Honestly, I don't get the point of reading books about proofs when you have never proven anything

[sturdy shore]

so that you learn how to prove things?

[remote sparrow]

Was there a misunderstanding here? Seems like no one is talking about proof theory.

[tawny copper]

^

[tawny copper]

this is why kids read books about swimming instead of actually swimming when learning to swim

This was just a general comment, this section is about #book-recommendations I don't think this was out of place at all.

[sturdy shore]

you know book of proof, or any other book that is about transitioning to advanced mathematics, also has plenty of things to prove?

question, have you even glanced at any of these books? lol

[tawny copper]

Also the comment was not about proof theory itself, but rather about methods for basic proofs

instead of like proving stuff

[sturdy shore]

yeah these books have plenty of stuff to prove in them

thanks for the concern

[tawny copper]

sure lol I'm not an idiot

I just think its completelly unnecesary, you can learn basic proof methods while you are learning from a book that has in the title "calculus" or something like that

[gray gazelle]

Thoughts on Euclids writings?

[sturdy shore]

1. this is the reason why I dislike the nomenclature of these books. They are called "proof books" while the vast majority of the book isn't even about proof methods but about naive set theory, functions, relations, equivalence relations and generally the stuff that is ubiquitous in mathematics

2. it is true that you could technically learn most of these stuff by going through introductions and appendices of other textbooks, but you definitely can't guarantee that your journey will be smooth, and you probably shouldn't have to suffer in your courses because you never learned wtf a preimage is, what equivalence relations are and why rational numbers are countable while the reals are not

going through book of proof (or any equivalent) before any other mathematics is by far the most obvious thing you can do imo

[tawny copper]

actually readable, but I'd recommend to not only rely on Euclid ofc. The elements look like a problem sheet with solutions, so you can take it as a set of exercises

[tawny copper]

I never learnt what a preimage is from a proof book. The thing is, it might create the wrong impression that proofs require a novel way of thinking, when it's just something very intuitive to do. I'm not saying you shouldn't learn what a function is, or any other basic set theoretic concept... I'm just saying that if you want to learn math, pick a math book on a topic you like and start solving problems. Like, set theory book != introduction to proofs book lol. These type of books seem to make the transition between high school regular mathematics to actual mathematics much harder than it actually is. I just don't think this type of transition should exist in the first place, but whatever. Maybe its all in my imagination.

[sturdy shore]

I never learnt what a preimage is from a proof book.
I have book of proof and how to prove it open for reference and they both have it, so maybe whatever book you used was just bad

Like, set theory book != introduction to proofs book
Again, these books are called proof books while the majority of the content isn't about proofs, and they will all contain naive set theory in them which is mandatory for any beginner

These type of books seem to make the transition between high school regular mathematics to actual mathematics much harder than it actually is.
But the transition is hard if you go into a proof based math book while having no knowledge of the things these books cover. As I said, introductions and appendices can cover you but they can also feel terse or lacking

also, nobody is saying you shouldn't read another book concurrently, especially if you feel the transition book is unmotivated

you probably should do exactly that

[tawny copper]

^

[sturdy shore]

okay, disclaimer the discord user valley doesn't completely represent my own beliefs and if you feel book of proof feels unmotivated you are allowed to read it alongside another math book

[tawny copper]

I meant that I never read an introduction to proofs book, yet I know what a preimage is. I just learn what that was in context.

[tawny copper]

Sure. But I was mainly responding to user valley, and you all thought I was a lunatic or something xD

[sturdy shore]

I literally said like 5 times you can "pick up" most of the concepts in these books from other books exactly because they are ubiquitous in math but you can't guarantee your learning process will be smooth

[tawny copper]

You thought I read an intro to proofs book that was bad, then I clarified that that was not what I meant. It was just a clarification.

It's not like I'm trying to convince you of anything.

Have a nice day.

[zealous light]

What's a book that covers filters nicely? They're being taught in my topology course and I'd like a supplemental resource

[remote sparrow]

willard's general topology according to its table of contents

[dense hamlet]

For those of you who've worked through folland before, I'm doing the problems listed in problem sets, but I'm also trying to dedicate my limited time for doing extra problems, are the problems in the book with bolded text considered mandatory to do?

this is for his book on measure & integration

[zealous light]

Those exercises provide new definitions usually. I wouldn't say they're necessarily required, but at least look through the exercises that provide those new definitions

[dense hamlet]

thanks

[heady ember]

~~Just do Enderton ~~
(Joking, of course)

[exotic crow]

what's a good book for interesting proofs in mathematics accessible to an undergrad (any subject)

[remote sparrow]

Proofs from THE BOOK by Aigner and Ziegler?

[fierce jungle]

Any Indians here who have prepared for ISI?

[hybrid sequoia]

Am in 10th, thinking to but parents all want IIT and nothing
I don't even know what I'll do next year

[fierce hedge]

I gave the exam without much prep, I think the TOMATO book should be enough

[west rampart]

Guys, what's a good book for practicing data analysis?

like I am well versed with the theory but couldn't find any source to practice...

[grand thistle]

as a person who wants to get into probability theory mainly, what would be the best order in which to read these books with a background in baby rudin chapters 1-7?

• rudin RCA (big rudin)/ folland real analysis
• jacod protter probability essentials
• spivak calculus on manifolds

[loud cradle]

if your goal is probability then imo read the probability book. it covers the needed measure theory albeit in condensed form (but not any more condensed than rudin or folland)

calculus on manifolds seems unnecessary for this

[grand thistle]

yeah that’s a more general knowledge thing i’m tryna cover bc i never learnt multi variable calc

[grand thistle]

right, what do you think of covering the measure theory needed concurrently with the probability book from folland or rudin

[loud cradle]

folland and rudin are both good books, no reason you can't use them as supplementary reading

but you don't have to treat them as prerequisites

[grand thistle]

hmm right sounds good

spivak com could probably be done at any time right?

since it’s mostly disjoint from the other two

[loud cradle]

yeah, if you've done baby rudin you have the background for it

can read it whenever

[grand thistle]

alright great thank you

i think i’ll finish chapter 6-7 by the end of the month

so i should be able to start probability soon yay

[fierce jungle]

I am preparing for JEE, how hard was it relatively?

[carmine lintel]

[carmine lintel]

i’m preparing, but i don’t think i have a chance

[fierce hedge]

These are very different exams. ISI exam is subjective exam and they ask questions close to the level of RMO I guess

[remote ginkgo]

id throw away spivak and get shifrin multivariable mathematics instead

covers all same stuff except tensors

which you can just pick up in bishop&goldberg

[grand thistle]

hmm this actually seems like a pretty good idea

i've been wanting to od a down to earth book like shifrin for a while

[remote ginkgo]

yea shifrins super down to mars.

[grand thistle]

😂

[remote ginkgo]

for probability i havent read the book u asked about

but billingsley is nice

[grand thistle]

but really, the last time i did a computational exercise was back when i was learning linear algebra haha

[remote ginkgo]

more linear algebra is always good

stats surprisingly turns out to be linear algebra under the hood for all interesting results anyway

but in particular. chapter 8 of shifrin is what i mean to suggest

it covers diff forms

stokes theorem on manifolds

[grand thistle]

mmm all the good stuff

it's in definition theorem proof format right?

i still want it to be rigorous with proofs for everything

[remote ginkgo]

yes

[grand thistle]

what's the difficulty of the book?

how fast you expect one to finish it if they work on it say, about an hour a day

[remote ginkgo]

who cares

it's easy

just read

[grand thistle]

fair enough

[north hornet]

Hello everyone! This is a survey for our research project regarding Investors analysis . Please take 5 minutes out of your time and fill it up. It will be of great help. Thank you for your patience and time https://forms.gle/1XHmT79Bu1ski5DT9

[willow pecan]

Is this a book recommendation

[fierce jungle]

I felt that

I am able to solve TOMATO subjective questions, but it takes way too frickin long to solve them

[delicate trail]

hey guys, any books for a nweebye in math analisys?

i m first year in phys

and i really need to catch back with math

so i need to really set the base

[grave thorn]

I recommended it (I think?)

In any case Jacod and Protter is a very good book

[grand thistle]

yeah you did

[carmine lintel]

the UGB paper is the one i’m most worried

[fierce jungle]

yeah its definitely harder

[fierce jungle]

any books you would recommend

[carmine lintel]

what grade u in rn?

[fierce jungle]

12

you?

[carmine lintel]

i’m the last person to get recommendations from

12th

ayy

i just solve tomato

[fierce jungle]

I have Maron and SL Loney

and solve Tomato

apart from that I only do jee stuff

[carmine lintel]

hmm trigo isn’t very hard off isi no?

[fierce jungle]

coordinate geometry

[carmine lintel]

jee

hav you been doing number theory?

[fierce jungle]

yeah

that is one thing not in JEE

[carmine lintel]

yes

[fierce jungle]

I love number theory

[carmine lintel]

[fierce jungle]

even mathematical induction is not in JEE

[carmine lintel]

wait what

it isn’t?

[fierce jungle]

idts

[carmine lintel]

well it doesn’t matter, its very trivial ig

[gray gazelle]

what's jee?

[fierce hedge]

Induction is pretty non-trivial. You can prove a lot of things using induction, much more than you might initially assume

[hazy elk]

Anyone here read Janich's vector analysis?

Is it a pretty dense book? The topic coverage feels like it would be pretty hard for someone who just knows pointset and analysis

[sturdy shore]

an amazon review

Do not get this book. It is incomprehensible. For each page he introduces a term that is previously undefined. For example, page 1 undefined term: homeomorphism. Page 2: diffeomorphism. Page 3: Hausdorff space, Second countable etc. I have read Walter Rudin's Real and Complex Analysis (measure theory - not even necessarily taken at even the phd level) and that is the only way in which I am familiar with Hausdorff spaces. The other things, I was unaware of. While they are not impossible to comprehend with a quick search, the book is pedagogically unsound as it assumes the reader knows FAR too much.

If you are reading this book as a second year math undergrad: may God have mercy on you because you are in for the struggle of your life.

seems like one of those fake undergrad texts

i.e. german undergrad

[hazy elk]

seems like a dumb review tbh

Cus measure theory is not that uncommon for ug

[sturdy shore]

well here's the description for the book:
The material is accessible to readers and students with only calculus and linear algebra as prerequisites. A large number of illustrations, exercises, and tests with answers make this book an invaluable self-study source.

if u don't think that's misleading idk lol

[hazy elk]

Idk

I just wanted a reasonable person's opinion of the book

[sage python]

Wait Janich actually looks kinda sexy ngl

[fierce hedge]

Just get it on libgen and try it for yourself smh

[hazy elk]

I've tried parsing a couple sections, at least the manifolds ch isn't that hard

[hazy elk]

Might be too sexy for the average ug 😅

[fierce hedge]

This book is about manifolds, differential forms, the Cartan derivative, de Rham cohomology, and the general version of Stoke's theorem. This theory contains classical vector analysis, with its gradient, curl, and divergence operators and the integral theorems of Gauss and Stokes, as a special case.
This definitely not for ug

[sage python]

I mean it looks like it's fine as long as you know multi, in particular if you know measure theory/Lebesgue integration

Will all undergrads know this? No

But many will

[hazy elk]

Multi meaning implicit, inverse or like proper multi (stokes + other stuff in spivaks calc on manifolds?)

[sage python]

Calculus on R^n by the looks of it, this handles the Stokes c

[fierce hedge]

I mean if you're willing to go for it then sure, this looks more or less like spivak's calculus on manifolds

[sturdy shore]

bro the book says you'd need "a few notes on basic topological concepts" I'd say you need a full course for this

book definitely looks sexy tho

[hazy elk]

Ill attempt to read it, if I survive, Ill let you guys know how it went😁

[willow pecan]

Is this a book recommendation

[gray gazelle]

Can someone get me a good book on Algebraic Number Theory? As a quick introduction to Elliptic Curves. Also, can I get an Arithmetic Geomdtdy book as an introduction to Sheaves & Perfectoid Spaces?

[abstract rapids]

how good is topology and geometry and bredon? Should i use it or should i just stick to the classic algebraic topology by hatcher?

[stray veldt]

standard book on algebraic nt is neukirch and on elliptic curves is "the arithmetic of elliptic curves" by silverman

i like them both @gray gazelle

[sage python]

@abstract rapids I like Bredon

[devout sphinx]

I did this last semester and then forgot all of it. Our textbook in that class was Munkres

[solemn rover]

It's ok. I think it's probably friendly enough that even if you don't understand it all you'll get exposed to a lot of cool shit

some books are meant to be full comprehensive rigorous treatments of the subject matter and some are more expository

[hearty steppe]

Any books on representation theory for dynamical systems?

I need to omega brain

@solemn rover great to see you. I am still working through your glorious complex dynamics recommendations

Might want recommendations for applied math motivated p-adic stuff as well. Finding some interesting papers on QFT stuff

Sorry quantum mechanics*

https://arxiv.org/abs/2210.01566v1

Unrelated I guess but this one also tickles my fancy https://arxiv.org/abs/2210.01145v1

If you like what you see, you should follow me on Twitter 😂

[solemn rover]

no problem boss

[limpid gazelle]

What’s a good book on quantum mechanics that assumes that you know linear algebra?

[hearty steppe]

I really really really like Griffiths

And I only was able to read the first chapter cuz of all the stuff I am trying to do at the same time but also the exercises are so much fun

[remote sparrow]

maybe shankar's Principles of Quantum Mechanics for an undergraduate treatment?

[forest sleet]

I like Shankar

Introduces Hilbert space/bra ket sooner than Griffiths

[hearty steppe]

Oh here is another taste of what I find on Twitter https://arxiv.org/abs/1704.07764v1

Motivation with learning more about topological dynamics 🧐

[hearty steppe]

I’m not sure I have looked at Shankar but I need motivation to learn more about Hilbert spaces

[forest sleet]

Particle wavefunction lives in a Hilbert space

Bra ket inner product uses riesz rep theorem for Hilbert spaces

[sudden kindle]

Anyone know where I can find a proof of Riemann existence theorem?

Esp one that involves pdes

[lavish apex]

any book to learn calculus? pls

[remote sparrow]

do you want proofs or just something intuitive

[lavish apex]

something intuitive

[remote sparrow]

generally stewart's calculus is recommended here

physical copies of old editions can usually be found much more cheaply than the latest editoin

[narrow relic]

There's a neat book by Gilbert Strang called Calculus that I believe is available for free, it has a lot of intuition.

[narrow relic]

Here I found it for you: https://ocw.mit.edu/courses/res-18-001-calculus-online-textbook-spring-2005/pages/textbook/

[remote sparrow]

also tons of free or free open-source calculus textbooks out there

#book-recommendations message

[remote ginkgo]

these are all ug topics

[remote sparrow]

anyone watch the math sorcerer's book reviews?

[hearty steppe]

Pretty fundamental stuff. I’m thinking more like Field trajectory projections on spaces tbh when I think of the application of Hilbert Spaces?

Well I haven’t really taken the time to look more into the abstraction of Hilbert spaces but I’ll get there.

[safe relic]

Hey guys! I want to learn "mathematical induction" and "recurrence relations" at least to a basic level for a programming book I am reading, however, I can't commit to a full "discrete mathematics" course/book at the moment(still working on my precalculus). However, is there a resource that I can read/watch to at least get the idea of these 2 ideas for someone who sucks at math?

[remote sparrow]

trefor bazett's discrete math videos

he has a video on induction

somewhat related is this: https://www.fm2gp.com/

[safe relic]

Thank you, sir/ma'am. I will check these out.

[safe relic]

This book looks mad interesting. I guess this is a "learn math for programmers" book?

I will definitely give it a try.

[hearty steppe]

So hilbert spaces are the glue for representation theory

This stuff is crazy deep man. Good lord. It just goes places

Infinite maths hole

[sage python]

Pretty important in rep theory yeah. In finite dimensions you can always manufacture some inner product with respect to which your representation plays nicely

(I'm assuming here reps are over C)

[slim peak]

Every sane person do Rep Theory over C

[sage python]

Tate module does not want to know your location

But yeah in infinite dimensions you often want to assume your representation is unitary

[idle oracle]

any recommandation for higher galois theory ? (category theory, galois cohomology, galois reps, alg number theory on global fields too perhaps, things like that)

i’m mostly interested in the study of absolute galois groups if anything comes to mind to anyone

[wooden frost]

what are some good trigonometry books that doesnt really dive deep into the geometry aspect of it and just focus on algebric part of it ?

[hearty steppe]

Dude linear transformations are super meta. I been telling people to pay close attention to them these days while learning linear algebra. Literally one of the most important if not the most important thing linear algebra teaches you.

Linear Transformations still hurt my brain sometimes

[sturdy shore]

that's like telling people to pay close attention to integration while learning calculus

I guess technically it is good advice

[hearty steppe]

Dude integration even more meta

Two areas where I feel it’s literally impossible to learn anything remotely close to everything

It’s hard to say how though that’s the problem. That’s how meta they both feel. How do you learn this stuff more intuitively the deeper down the hole you go? 😂

[sturdy shore]

ok

[broken meadow]

Huh

[delicate trail]

hey guys, any books for a nweebye in math analisys? i m first year in phys and i really need to catch back with math

[hearty steppe]

A linear transformation really is just a kind of meta in integration itself really. If you break your brain hard enough about it.

That’s my opinion though. I don’t really study math like you guys do.

I can say I barely study it in that sense 😂

If I’m computing a distance function which is most likely a lebesgue integration on a Hilbert space, I am effectively mapping out all potential tensor bundles that give me field-like trajectory projections on an infinite yet also infinitesimal kind of continuum where continuity or discontinuity exists based on converging or diverging factors. Like we have holes, we aren’t differentiable somewhere, we are intractable, etc?

We have non locality that gives us noise that doesn’t make sense maybe, or maybe it does if we can find a pocket to converge on for a computationally reducible outcome? The pockets themselves can exist on a continuum? Uh oh now we talk about rulial spaces again because we have enumerable outcomes to potentially deal with?

[primal summit]

are you just stringing words together

anyways

#book-recommendations

[sturdy shore]

I'm gonna read all this but I gotta smoke a joint first

maybe I will understand meaning of the universe and linear Transformations

[still nebula]

What is a good actuarial maths textbook for beginners?

[granite canopy]

theorem by markov chain

[delicate trail]

Man, it s my first week at university, take me easy

I m an average brained girl, not some geek or nothing special anyway

[delicate trail]

Something for math analysis? 🥺 please please please

[sturdy shore]

#books-old

[delicate trail]

Thank you so much

[peak anchor]

is this channel for math books only?

or can it be like science communication books also?

[sturdy shore]

read channel description

[peak anchor]

thank u

[hearty steppe]

No, this is my interpretation of it? At least to the extent I can make sense of it due to my lack of refinement

I don’t know as much math as any of the regulars here and I’m humble about that but I can understand math in my own way I guess. Take what you will from that. I’m just a master of none.

Like seriously you guys have helped me so much

And I might barely understand what I’m reading but who really understands this stuff with absolute perfect refinement?

I’m only human, I guess

[hearty steppe]

I also forgot I posted this stuff in book recommendations 😂 well I’ll entertain it somewhere else in a separate thread if people want

[gray gazelle]

I've liked this one https://books.google.pl/books/about/Actuarial_Mathematics.html?id=Wx2mQgAACAAJ&redir_esc=y

But it's also the only one I tried. But hey, I liked it

[jaunty acorn]

how good is topic in algebra by I.herstein?

[rapid lily]

I read a few pages of it in a university library and it motivated the concepts very well and even the importance of algebraic structures. I have heard it has good problems and plan to get it in the future, so it sounds like quite a good book if you want to look at it for group theory.

[sterile harness]

how good is grant sanderons course on khan academy?

[remote sparrow]

thoughts on krantz's and apostol's real analysis books?

[fierce hedge]

Manifolds and differential forms in ug . It might be the case in usa but I was taught these in my masters

[dapper root]

Not the case, many (who go into pure math) do see it, but it’s not standard

[remote sparrow]

multivariable analysis is offered as a 400 (undergrad) and 500 (grad) course at my uni

it's not often taken by ugs though

i'm at a pretty average state school too

[fierce hedge]

Hmm... well my college definitely had a weird curriculum. Our first calculus course was multivariavte calculus and then the next year we could choose intro to manifolds as extra

[still nebula]

Thx I was told it was a recommended book by my lecturer but I can’t seem to find a section on nominal interest rates

[gray gazelle]

looking for some good elementary linear algebra and discrete math books if you guys have any tips

was searching for something introductory but i am not sure

[heady ember]

Look in pinned

Friedberg and LADR are common recs

[gray gazelle]

Oh interesting!

our required book in the syllabus is "David C. Lay, Linear Algebra and Its Applications, 6th Edition,"

which is probably for the pearson connectivity

[crimson leaf]

That book sucks

[gray gazelle]

why is that

[crimson leaf]

Because it barely teaches any of what linear algebra is really about, just useful algorithms. It serves it's purpose of teaching computation but I don't think it offers much in the way of understanding the concepts of linear algebra despite its attempts.

[gray gazelle]

then what are the other options?

LADR?

[crimson leaf]

Check the pins

I'm using Friedberg right now which I like

[heady ember]

Yeah so far I like Friedberg too

[gray gazelle]

How I used the book, is I read it until I heard something that I didn't know. Then, after that, I googled it, and tried to understand from the sources I've found.
The book isn't "complete" in this sense, but it's still a very good book to learn from

Of course, you could complement it with another book or maybe a book about finance

It does assume some finance knowledge, but it's all googleable tbh

[remote ginkgo]

i just learned em

during calc 2

[remote ginkgo]

shilov

ladr is stupid as hell

[sturdy shore]

isnt shilov the book that starts with determinants in the first chapter

I really do not think that is a good idea

[remote ginkgo]

why

they are like

the fundamental tool you use to say things in matrix analysis

[sturdy shore]

sure but in the first chapter?

[remote ginkgo]

yes

you would presumably have seen vectors in calculus/physics/trig classes

they don't need an explicit introduction beyond "ok what is a basis"

which he covers when it is necessary

[viral roost]

determinants are just sums of products, taken in a very simple way from coefficients of a matrix - the first chapter presents it in a self contained way, tells you how to take these products and stick a + or - in front of them, and immediately shows you how it solves linear equations

[sturdy shore]

I guess I just prefer a much different pedagogical approach then

[viral roost]

there isn't a pedagogical approach, you're solving linear equations

there is a meandering and repetitive approach, and an approach that just tells you once

[sturdy shore]

there is most definitely a pedagogical approach, mentioning systems of linear equations to begin with
compared to halmos it is entirely different at least

I just don't think it feels as self-contained and "worked from ground up" but w/e

from the couple russian/soviet books I've read it seems to be a theme for the book to be information,information,information just getting thrown at you
while halmos book for example is 50% like reading a novel
you start with the humble definition of a vector space and over time build more machinery

[viral roost]

linear equations are why the subject exists

[remote ginkgo]

^

[viral roost]

I don't see what else there is to say

[remote ginkgo]

halmos is better than LADR so if one is to make recommendations

[viral roost]

you might prefer pretty pictures, but the application matters

how we come up with math matters

[remote ginkgo]

id say start with shilov but if you dont then at least dont present ladr

[sharp latch]

Friedberg does it best imo as a first or second pass through linalg- you get a very deep understanding of vectors and matrices and how they transform, and then determinants are almost an afterthought of the built up intuition

[golden locust]

Determinants are very confusing to students, it seems like you'd lose people quickly if you intro them in the first chapter

[viral roost]

not in shilov

[remote ginkgo]

^

[golden locust]

lol

[viral roost]

most people just suck at explaining

he literally does it in one page

[remote ginkgo]

yea from what ive seen of people reading shilov it doesnt confuse anyone

[viral roost]

and then solves linear equations

[remote ginkgo]

presentation is bad elsewhere it seems like

[sturdy shore]

I'm not sure how we got to pretty pictures but ok
I've also said what I said, I guess the overarching point would be that different people prefer different approaches and you should look at more than 1 book

[viral roost]

determinants in last chapter of LADR lol

just lol

[karmic thorn]

Axler's book feels nice until you realise you effectively can't find eigenvalues of matrices by reading the 5th chapter

The self-imposed handicap is ridiculous

[remote ginkgo]

yep

[viral roost]

read a nice blog explaining how Axler isn't a good lin alg book, but it is a good dynamics book

because of his approach to things

[remote ginkgo]

dynamics?

tf

[viral roost]

like iteratively applying maps and such

[remote ginkgo]

oh lmao

[viral roost]

the way he proves things

[remote ginkgo]

goofy

[viral roost]

well it's something I suppose

anyway I don't see why you wouldn't just learn what is fundamental and useful first

tourism is for weekends

[karmic thorn]

Yeah it's an "abstract" approach that avoids matrices as far as it can

[viral roost]

which is weird because change of basis for matrices is one of the most fundamental things you can do for the abstract approach

which requires knowledge of determinants to fully justify

[karmic thorn]

Right, I don't think he talks much about that aspect at all

[fickle whale]

are you the ker? do you know lukyon and cat

[fierce hedge]

How does shilov compare to Hoffman and Kunze?

[viral roost]

you can compare page counts, since the contents are similar to a point

twice as efficient

[fierce hedge]

I am not sure I would say less pages means more efficient plus that could also means shilov is more terse. Shilov does some slightly questionable things.
Like for short book it dedicates a whole chapter to Coordinate Transforms on the other hand a whole chapter on bilinear and quadratic forms seems interesting

Seems like it is designed with physics in mind rather than pure mathematics

[manic cairn]

lost you at tensor bundles

also, i think you mean the hilbert space is of lebesgue integrals

[remote ginkgo]

imagine not knowing how to do coordinate transforms as a mathematician

[hearty steppe]

Yes thank you I thought my grammar was screwy

Tensor is some n dimensional arbitrary object

It can be more than n dimensional as it can be a composition of dimensions and other objects (we can have bundles of objects too yes)

[remote ginkgo]

infinite dim tensors are fine

[fierce hedge]

Doesn't answer my question but sure if that helps

[hearty steppe]

I can explain a bundle. Do you know what a partial differential equation is? I think I can explain that too. Well I don’t want to get ahead of myself

[remote ginkgo]

ker answered it

[hearty steppe]

So like I have a object differentiable on some infinite/infinitesimal continuum where I have points of convergence or divergence on a surface, or manifold. That is what a PDE represents. You can have compositions of PDEs

A bundle is like imagine a tangent line. Ok now imagine you have PDE derivable tangent lines on a manifold. Kinda a way to think of a bundle I guess. I may be not explaining it well enough

[remote ginkgo]

no

a bundle is a collection (E, M, p)

where E and M are topological spaces

[hearty steppe]

Oh yea it’s a collection of sets

[remote ginkgo]

and p : E ->> M is a projection

no

it's a total space, base space, and projection

[hearty steppe]

Oh so it was more fundamental than I thought 😂

[remote ginkgo]

yeah

you don't need anything about manifolds

it's kind of a generalization of product spaces

[hearty steppe]

I think with PDE same thing, we can generalize it to a topological space

[remote ginkgo]

?

no

[hearty steppe]

We can’t?

[remote ginkgo]

you need differentiable structure to talk about differentiability

topo spaces don't have any differentiable structure

[hearty steppe]

There is differential topology?

Ahh wait that’s still requires geometric characteristics

[remote ginkgo]

u need to review basics

[hearty steppe]

I need to watch those videos more haha

Only watched like the first four.

[remote ginkgo]

its in every geometry book

[hearty steppe]

I mean you can have continuity of point sets right?

[remote ginkgo]

topological spaces come with continuous structure, yes

[hearty steppe]

Yea I gotta review some of this

[remote ginkgo]

the category Top has as its objects topological spaces and as its morphisms continuous maps

[hearty steppe]

Yea I like that book

What did you think of Mendelson?

[remote ginkgo]

it's fucking crap

[hearty steppe]

Munkres has very nice motivational verbosity

It just clicks when you read it

[remote ginkgo]

it's one of only two books that thoroughly just lays out the jargon of topology

[hearty steppe]

Do you think it’s worth learning about Collatz stuff?

[remote ginkgo]

what

[hearty steppe]

Anything pertaining to Collatz Conjecture in particular that can motivate applied use outside of mathematics into domains such as cognitive neuroscience, molecular dynamics maybe?

Seems like people are not very friendly about that stuff 😂

[remote ginkgo]

what the fuck lol

[hearty steppe]

Yea some guy was hitting me up about Collatz conjecture and I’m like… alright well, why should I care?

[remote ginkgo]

just read actual math stop wasting time

[hearty steppe]

Yes I need to get to my Ergodic theory texts. I might just start looking at them a little just to see if I can understand what’s going on even tho I didn’t really finish my complex dynamics or dynamical systems texts 😂

So much stuff to read

I been handling it decently tho

[remote ginkgo]

ergodic theory is kind of dead

subject fizzled out

just read

no point in obsessing over little knick knacks

[hearty steppe]

Why are you not interested in Ergodic theory? Seems quite fundamental

[remote ginkgo]

it isn't

you just like it because it has a funny name

it's not useful

there was suspicion it might be

but people invested effort into it

and it turned out not to be

many such cases

[zealous light]

Learn things in a balanced way so then you aren’t accidentally making weird claims about things you know nothing about (aka me in early undergrad)

[hazy elk]

WHAT

[remote ginkgo]

yea sorry

[hazy elk]

Disagree

There are many people doing cool shit in ergodic theory

It's just as active as most fields

[remote ginkgo]

citation needed

[hazy elk]

I know a couple of profs who do research on ergodic properties of group actions on homogeneous spaces

Who are pretty active

I don't want to link any academics cus that would sorta dox me

[remote ginkgo]

ok

doesnt really disprove my point

[gray gazelle]

Alright. I'll just throw out there that we should recommend books here

[zealous light]

On the topic of books, I’ll just plug Cedric Villani’s topics in optimal transportation again

[hearty steppe]

Ergodic theory is all about deterministic behavior that results from iterative state space behavior, which can supposedly arise from arbitrary behavior that is allowed to persist overtime

[remote ginkgo]

actually this came up yesterday when i was reading about tropical study of wasserstein manifolds

[remote ginkgo]

this

lemme grab links again

https://link.springer.com/article/10.1007/s41884-021-00046-6

[hearty steppe]

So I think Ergodic theory is pretty important especially when we examine stuff like strange attractor behaviors

[remote ginkgo]

https://zbmath.org/1156.53003 <- cedric

[hearty steppe]

Nice find I am gona check that out

I am not convinced that we cannot be differentiable in a purely topological space that does not assume geometric properties

[remote ginkgo]

then you are like

completely obviously wrong

lol

[crimson leaf]

It has use in additive combinatorics and some Ramsey theory stuff can be proven using that's about all I know

[hearty steppe]

Like ok we have relativistic frames of reference when we are in topological space no? We are relative to the regions and localities of points

We don’t care about the geometries yet until we need more constraints

[remote ginkgo]

what the fuck

are you talking about

[hearty steppe]

Before we even get to a coordinate space mapping in Euclidean space for instance

[remote ginkgo]

euclidean space is metrizable even if you throw away the metric

[hearty steppe]

Wdym

Just cuz we get a distance calculation?

[zealous light]

Why are we back on this, I recommended a book to move topics back on book recommendations

[remote ginkgo]

read this im not gonna try teaching you topology in a chatroom

thats my book recommendation

[hearty steppe]

So fundamentally we still have a difference equation because we have distances between points in the point set collections?

Anyway I think I didn’t realize this assumes a geometric projection

[dapper root]

There’s axioms a space can satisfy which means it’s metrizable

https://en.m.wikipedia.org/wiki/Metrizable_space

[hearty steppe]

Also again I am not a mathematician and I’m not trying to claim I’m one

But I still go through math books when I can

[remote sparrow]

Try Meckes' Linear Algebra. Meckes has answers for odd-numbered problems in the back of the book and a full instructors solutions manual available if you know where to look. For two free ebook alternatives (with low cost physical copies), try Hefferon's Linear Algebra or Beezer's A First Course in Linear Algebra. A promising low cost ebook and paperback would be Linear Algebra: Theory, Intuition, and Code by Mike X Cohen. Coding the Matrix by Philip N. Klein seems particularly slanted to computer science and is available as an affordable ebook and paperback.

https://hefferon.net/linearalgebra/index.html

Hefferon has a ton more resources than the other books (like a complete solutions manual, lecture videos, slides, and lab manual), but feel free to take a look at the other books as well.

[remote ginkgo]

you need, in a derivative to divide by the difference in a parametrization

the bottom of the difference quotient, that is

you have to have a metric to know what that denominator ought to be

[tacit abyss]

has anyone used Deitmar's intro to harmonic analysis to learn harmonic analysis? considering starting it

[still nebula]

I’ll try doing that thx!

[remote sparrow]

https://www.amazon.com/Joy-Abstraction-Exploration-Category-Theory/dp/1108477224

this book just dropped if anyone is interested in reviewing this

[restive falcon]

yo it's the funny category theory person

[warm glen]

would y'all ever recommend the linear algebra parts of artin over a linear algebra book

just curious how good they are i feel bad having a physical copy but only using the parts on groups

[fierce hedge]

I am going through Artin and I would recommend doing a standard LA book. Artin is a bit too terse for LA

[hearty steppe]

Dude I found so many math journal accounts on Twitter it’s crazy

Twitter is meta

I love this

[hasty turret]

broke: using arxiv for reading papers
Woke: using Twitter

[fierce hedge]

what does being meta even mean?

[hearty steppe]

I’m following over 800 accounts rn and I just made an account on Tuesday but I want to follow another 400 accounts rn but Twitter be like “you too new”

I retweeted like over 50 papers 😂

I still gotta look at over 15 but they not pure math papers

[remote sparrow]

it's a gamer word whose acronym (or backronym) is "most effective tactic available"

[hearty steppe]

I mean I skimmed the ones I didn’t quite look at yet is what I’m saying

[fierce hedge]

So, like Munkres is meta?

[hearty steppe]

Definitely

[fierce hedge]

Got it

[hearty steppe]

Principles of mathematical analysis and Munkres go together like pb and j

[fierce hedge]

What's meta for abstract algebra? D and F

[hearty steppe]

Oh I didn’t really get that deep into abstract algebra tbh. I just kinda spent a little time learning about groups in some detail but not really

Just enough to work with intuitively

Was able to sort of understand a geometric group theory book I skimmed through as a result so I’m happy

But I think it’s nice to spend a little time there and mess around in linear algebra land a bit cuz it helps you better understand being introduced to linear transformations

[fierce hedge]

Makes sense, what are you using for linear algebra?

[hearty steppe]

I am not learning math like that anymore. I don’t work through books like that these days. I kinda figured out a way to sorta jump around but also just get knowledge checked in the process in a way that works cuz I’m always talking to people on the internet

Uh, you probably would really enjoy Klaus Janich’s Linear Algebra book. It’s not easy but it’s also really well motivated

On the other hand I was working through Lay’s text as well as Johnston’s first text on linear algebra.

I think Janich is harder but much more motivating in direction. Lay and Johnston have nice illustrations though and some examples might be easier to follow

[upper flicker]

aluffi

D and F is not meta my friend

Can we get a several people are typing 🙏

[hearty steppe]

Also Lay seems pretty watered down sometimes in terms of really laying out the abstractions

[fierce hedge]

I mean if you really wanna be quick go for Lang's algebra but aluffi nahh

[hearty steppe]

Johnston is harder than Lay but more watered down than Janich still

[upper flicker]

aluffi is the opposite of quick because it's bloated with exposition, but the exposition is good

using lang as a textbook 🤔

[fallow cypress]

oh there's a backronym for "meta"? lol

I just think of meta-X as meaning "X about X"

according to wiktionary, meta as slang comes from metagame, i.e. gaming the game

[fierce hedge]

I am currently going through Artin for both abstract and linear algebra but artin is a bit too terse for me. Might switch
Although the questions are extremely good albeit a bit frustrating

[upper flicker]

Operating with knowledge outside the game

[hearty steppe]

Artin wasn’t a book I didn’t give much of a chance. Also too late for me to care too much now. I don’t have much motivation to want to look at Artin again. I remember Artin being a bit weird in approach

[grand thistle]

lang

[fallow cypress]

I like Dummit-Foote

[grand thistle]

i dont like algebra

[crimson leaf]

I'm interested in Lang's undergrad algebra just because it's so thin

And also because my library has a copy

[sturdy shore]

aluffi gang

[heady ember]

Thin often means more difficult. So, timewise you might not save any and you might experience more pain

[hearty steppe]

I mean like I don’t know how many people have the time to go through so many rigidity based refinement based books. I mean if you got people giving you that time, that’s super amazing. Part of why I keep coming back here is because at some point when you are adulting, you gotta “work” and you might not have the privilege to sit down and spend hundreds of hours going through pure math books and the exercise problems in them.

I know that sounds like a cop out to some people but like… I know I don’t have that time anymore. I’m lucky I can pick things up somewhat the way I do with the help I get from time to time, seriously.

I got a lot of respect for people that been on this server for years and still putting in the hours of work in pure math texts

I mean I might get to spend a good amount of hours here and there with certain books but I have to afford to be much more selective now. That’s why I like to toss around the term “study scoping”

[crimson leaf]

Idk I feel like unless you have a very solid foundation that could lead to some pretty gaping holes in your knowledge

[orchid cobalt]

does anyone here know the book "The Joy of x"?

[cursive orbit]

what is x?

[remote sparrow]

i've heard of The Joy of Cats (an introduction to category theory) and this recently published book: https://www.amazon.com/Joy-Abstraction-Exploration-Category-Theory/dp/1108477224

[orchid cobalt]

I don't know what math books to buy

most of them are probably out of my budget

[mystic orbit]

Rise up

[safe aspen]

Anyone has a good book on proofs, that explain techniques and things to watch out for?

[vital bane]

Lmao

[topaz rune]

Scihub and zlib saved me like $4000 I guess

[tawny copper]

Thoughts on Bergman's invitation to general algebra and universal constructions?

[tawny copper]

You don't need to buy books

[orchid cobalt]

alright

[tawny crater]

i'm browsing for a linear algebra book just to cover over Axler's treatment of characteristic polynomials. Thoughts? Dami doesn't seem to have a specific recommendation

[tawny copper]

Roman

[tawny crater]

Dami gave that a 'lol', do you know why?

[tawny copper]

I don't know who Dami is

[tawny crater]

o it's this message most people refer to when you ask about linear algebra

[tawny copper]

I have only read the first chapters of Roman, but the exposition is just so great. The first part is basic linear algebra really, and it covers everything any linear algebra text will cover, but in a much more clearer manner, and not bullying finite fields

ah

Yeah, I have read that. I think the "lol" is because it is very good though I may misinterpret that xD. Or maybe because the later chapters are really advanced linear algebra

[tawny crater]

oh ok

will i be ok without knowledge of finite fields? axler ignores them

[tawny copper]

It's not that he goes deep into them, not in the first chapters at least, but mentions them and so on.

You will be ok

[tawny crater]

thanks!

[willow pecan]

Omniscient Reader’s Viewpoint

[cursive wren]

Im suddenly struggling with basic algebra like negative and fraction -exponents and fractions over fractions. Any good algebra books i can buy/download to consult whenever needed

[hearty steppe]

I think I have a good enough foundation to work with. I’m not trying to be a mathematician by career here at this point. I already am leaving that in the past. It is not possible for me to learn that much math. It doesn’t stop me from understanding high level math concepts just enough to work with what I’m doing.

That’s why I spent about a little over 2 years just studying math and a bit of a physics/chemistry foundation when I originally joined this server.

I don’t know how many hours that amounts to. I’m going to generously say I probably put about over 150 hours into learning mathematics rigorously without really focusing on much else

I can’t just sit at my desk and look at a book for hours cuz I work in bursts so I’m generously throwing a number I know isn’t too high but maybe low enough

[topaz rune]

Tfw your courses are 180hrs each a semester

[hearty steppe]

Nobody will be able to refine their mathematics knowledge perfectly I don’t think that’s possible.

“Oh well you should have went through these entire books” bro I am not a mathematician 😂

[topaz rune]

Non mathematicians can read books too

[hearty steppe]

Yes but the way we digest content like pure math is different and way less refined. My knowledge refinement is limited, which gives me a lot of reasons to come back to this server, obviously

I think humans have an epistemological limitation with knowledge refinement

Let alone the epistemological limitation of knowledge discovery itself which is limited based on perception.

[ember quiver]

Hey, anyone know some books/resources in mathematics relating to computer science and trigonometry ?

[hearty steppe]

I also think that the limitations of epistemology are purely phenomenological fundamentally speaking as verified through what we deem as the scientific method.

[junior isle]

good calculus books for someone that is just starting?

[hollow shore]

https://ocw.mit.edu/courses/18-01sc-single-variable-calculus-fall-2010/

[sage python]

@tawny copper and @tawny crater that book is much harder, probably the only book on that list (maybe along with Greub but not even sure tbh) that I consider as being necessarily a "Linear Algebra 2" book. So likely a veeeery different audience than the others

[tawny crater]

Understood

What would you say is your recommendation for reading with axler for the parts axler are bad at?

I'm just coming in to the eigenvalues section so

[remote sparrow]

some dover books are good if you really want or need physical copies

if you are willing to buy used books, they're also a good way to get your hands on books that are normally more expensive

if you live in a jurisdiction like the u.s. where the supreme court specifically ruled it is in fact legal to buy international editions, buy those (but of course check the reviews with respect to printing quality, whether any content is omitted, etc.)

sometimes, books change very little between editions, but older editions are much cheaper (usually early undergraduate books like calculus textbooks), so you should buy the older editions

a few free open source books like jim hefferon's Linear Algebra have low cost print copies, so you should be on the lookout for those

some books may only have ebook versions, but see if the author would allow you to have their work printed at a print-on-demand service and bookbinder like lulu

[sage python]

So I updated my book list a good bit if you're interested @tawny crater, though if you've already read a decent subset of Axler then... hmm

[neon abyss]

Hi, I finished UG a year and a quarter ago,

favorite course was dynamical systems, I went into the chat and found a book by Robinson but the reviews lead me to believe it's focused entirely on discrete,

Is there any text past UG that goes into depth on things like ergodicity?

[willow pecan]

Have you read Brin and Stuck

Or Coudene's Ergodic Theory and Dynamical Systems

[neon abyss]

Nope, just strogatz

[willow pecan]

Ok you can try those two

[neon abyss]

cool ty

[gray gazelle]

Ok, I need a couple of books to kickstart my math education:

-I need a Probability Book that only requires Multivariable Calculus, and is a gentle, but comprehensive introduction to the subject
-I need a rigorous mathematical analysis book that introduces proofs slightly well (to complement Rudin, I think I heard Tao or Abott was good for this?)
-I need a good Linear Algebra book
-Calculus to PDE book? (I know Single-Variable Calculus very well, but I might need supplements because it was AP, and that was in highschool)

[willow pecan]

Abbott is good

For linear algebra, try Friedberg

What do you mean by calculus to pde

Like covering everything in between?

[gray gazelle]

A course that covers Calculus I-III, ODE, and PDEs

[willow pecan]

Or like an intro pde book

No book does that

[gray gazelle]

Any book that splits it in two then? Calculus & ODE/PDE

[willow pecan]

ODEs and PDEs are usually not taught together

[dapper root]

ODEs is closer to Calculus than PDEs IMO

[willow pecan]

For calculus do you want a more computational approach or a proof based approach

Also there are no good ODE books

[gray gazelle]

Jack Hale

[gray gazelle]

I also see that you have the Applied Mathematics tag, what would you say the prerequisites for a course on Numerical Analysis would be?

[gray gazelle]

Functional Analysis is a prerequisite for ODE? I guess this isn’t the average course in ODE and rather closer to research?

[willow pecan]

Ok yeah this is definitely not what chocobon is looking for

[gray gazelle]

He said there are no good ODE books

I found one

[willow pecan]

If you want to do a course on numerical analysis, ODEs and linear algebra is sufficient background I think

For a first course that is

[gray gazelle]

Alrighty, thanks for the help. Lastly, any good calculus-based probability books?

[gray gazelle]

Probability and Stochastics by Erhan Cinlar

[willow pecan]

You can try Grimmett and Stirzacker

The Cinlar book is not suitable for chocobon

[sturdy shore]

is this ToC for hale? seems neat

[gray gazelle]

Yes thats just the beginning. I definitely recommend Ordinary Differential Equations by Jack Hale

[gray gazelle]

Speaking of functional analysis. I discovered this book called Lectures and Exercises on Functional Analysis by Helemskii which uses category theory throughout the book

[remote sparrow]

Introduction to Probability by Blitzstein and Hwang is available for free on their website and has tons of resources, including lecture videos. Mathematical Statistics with Applications by Wackerly, Mendenhall, and Scheaffer is okay to learn probability out of if you can only afford one book (don't buy new, it's a pretty old book so used editions are significantly cheaper). It was used for both my probability and mathematical statistics classes. There is Advanced Engineering Mathematics by Erwin Kreyzsig that really does cover calculus, ODEs, PDEs, complex variables, linear algebra, and more. But it might not be helpful to someone learning this stuff for the first time. I don't think you need supplements for AP Calculus depending partly on whether you were taught the epsilon-delta definition of the limit (which I was not taught when I took AP Calculus), but analysis books should fill the gap. An ODE book that I would recommend would be Ordinary Differential Equations by Tenenbaum and Pollard. You could also look for older editions of Boyce/DiPrima, which includes an introduction to boundary-value problems and partial differential equations if you buy the book labeled "with Boundary Value Problems." I own the 10th edition per the recommendation of my professor. For linear algebra, you could try Meckes' Linear Algebra. A cheap and promising book would be Linear Algebra: Theory, Intuition, Code by Mike X Cohen. Two free alternatives (with cheap hard copies available) would be Linear Algebra by Jim Hefferon or Linear Algebra by Robert Beezer. Jim Hefferon has created a bunch of supplemental resources, including lecture videos and a complete solutions manual, to accompany his books if that is at all relevant to you.

Oh, two more books. Quite a lot of ODE books focus on analytic techniques, but one that deemphasizes this and focuses more on qualitative and graphical analysis would be Differential Equations by Blanchard, Devaney, and Hall. As for PDE, a commonly used book would be Strauss' text.

[tribal coyote]

What precalculus book / resource would you guys recommend?

[mystic orbit]

Khan academy

[tribal coyote]

hm... is it better than reading a book?

[mystic orbit]

I don't know any books about precalc tbh lol

But everyone recommends Khan for precalc so that's what's I'm recommending

[acoustic crypt]

have yall read they both die at the end

[mystic orbit]

I think it's only important to get used to using books to study at the University level

Coz a LOT of resources are available below that

[tribal coyote]

The good part about books is that they often get in more detail about concepts, and they also give a lot of exercises

Khan Academy seems like it only teaches you how to solve the problems, instead of teaching the concepts of that specific topic

[mystic orbit]

But I think that's what all pre calc is about lol

[tribal coyote]

hmm

and what about calculus itself, would you still recommend khan academy?

[mystic orbit]

Not sure

Depends on your familiarity with proofs, whether you wanna do pure maths or just applicable stuff, your grasp on HS algebra etc etc

Precalc isn't even absolutely necessary for calc

[tribal coyote]

Well, would you mind if I describe my background?

[narrow relic]

For Calculus, I recommend the Gilbert Strang book I recommended to someone here the other day: https://ocw.mit.edu/courses/res-18-001-calculus-online-textbook-spring-2005/pages/textbook/

[tribal coyote]

Thanks for sharing, Joe

[narrow relic]

For Precalculus, I recommend the Dolciani book I recommended the other day: https://openlibrary.org/works/OL19058195W/Introductory_analysis

[tribal coyote]

Thank you

[tribal coyote]

Interesting, so Introductory Analysis counts as precalculus?

[narrow relic]

In the United States at the high school level they sometimes call precalculus "analysis"

[gray gazelle]

Definitely not.

[tribal coyote]

Well, I wouldn't say that algebra is my strong suit. I'd say I'm pretty standard when it comes to mathematics, I don't have much knowledge - I've learned a significant amount of discrete mathematics, so that means I know quite a bit when it comes to proofs, etc.

[narrow relic]

By the way Bortolotti, it looks like there is a much earlier version of that book available from the Internet Archive: https://archive.org/details/modernintroducto00dolc

I think the content is similar to that 1991 version I recommended. So maybe you could try this one since it is available for free.

[gray gazelle]

This book is pre-calculus, but don’t count the title as a reference for other pre-Calculus texts because Modern Analysis normally refers to something else. However, I still think AoPS’s “Precalculus” is a good course.

[tribal coyote]

Thanks for sharing

[tribal coyote]

I see, ty

[narrow relic]

You're welcome. That is the book from which I first started to understand math, back in high school

[tribal coyote]

Sounds like a good place for me to get started then

My goal is to learn calculus, so, after going through one of these books about precalculus, would it be okay for me to start reading a calculus book?
Or should I study something else?

[narrow relic]

After Modern Introductory Analysis you can read a book like the Gilbert Strang Calculus book just fine

[tribal coyote]

Alrighty, ty for your time 🙂

[narrow relic]

You're welcome!

[warm glen]

alright thanks, maybe i'll just use artin for LA exercises

[tribal coyote]

I'll look him up, thx

[remote sparrow]

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

https://github.com/nculwell/MathStudy

i see a lot of people recommend stewart's precalculus book, though

lang's basic mathematics is another common rec for those that want to learn how to do some basic proofs along with basic mechanical precalculus skills

[tribal coyote]

@remote sparrow, thank you, lovely person

[remote sparrow]

[hearty steppe]

Nice books on introducing tropical geometry? Also motivated for data science, working with Feed forward neural networks, econometrics stuff too would be cool. I need a reason to care more about finance

Ahh yes dynamical systems theory focused as well

[remote sparrow]

tropical geometry? just pack a copy of euclid's elements to the carribean

[hollow peak]

applications of tropical geometry

[grave thorn]

Applications of tropical geometry: {}

[zealous light]

[fickle whale]

are there any applications for subjective geometry

[grave thorn]

applications of geometry: {}

[fallow cypress]

applications of existence:

[pale scarab]

Any good recommendations for visually appealing textbooks? I have really been enjoying visual complex analysis and I am looking for other books that are similar. It really doesn't matter the content.

[grave thorn]

[upper flicker]

applications of topology ({}, {{}})

[upper flicker]

office hours with a geometric group theorist

lots of diagrams there

[zealous coyote]

Indra's Pearls

[grand thistle]

hatcher's alg top has some pretty pictures i think

[quasi cave]

Can somebody lend me their Math notes? I will do child labour. By supplying you memes.

[stray veldt]

[loud cradle]

i already have a battalion of children in poor countries sending me memes for a very good price

[narrow linden]

a nice book is "Pegasus novus vocabularium"

[remote ginkgo]

don't fall for it!

[karmic thorn]

Have you looked at Carter's visual group theory?

[hearty steppe]

I thought Ahlfors (what little I skimmed through) seemed really fun to play around with.

Needham is way way more watered down but very visual

[fallow cypress]

visual number theory

I forget the exact book name

[hearty steppe]

Carter’s book seems fun too, I recommend that to a lot of people. I didn’t really play around with it much but it’s a nicely illustrative book

[gray gazelle]

Hey, besides just looking into Universal Algebra or Category Theory...
Any good texts that get into magmas that are like anti-involutionary, anti-commutative, or maybe anti-associative? Or maybe there's some good stuff on how to handle zero divsors systematically?

[gray gazelle]

What about survey of binary systems by Richard Bruck?

[gray gazelle]

https://en.wikipedia.org/wiki/Quasigroup?wprov=sfla1
https://en.wikipedia.org/wiki/Isotopy_of_loops?wprov=sfla1
https://en.wikipedia.org/wiki/Moufang_loop?wprov=sfla1

These topics are part of what's covered in the above book

Since you have nothing helpful or intellectual to contribute, please refrain from engaging with me. Thank you.

[gray gazelle]

Thank you.

[gray gazelle]

Right. I'm interested by the Moufang stuff especially as well as where extensions to the reals will get you. Thank you.

[gray gazelle]

does anyone have any university book recommendations for calculus, algebra, or “logic” type stuff? i’m struggling without having a set textbook or youtube channel to follow

[tame tree]

@remote sparrow Yo, sorry for the ping, but I'm getting through Meckes Linear Algebra pretty well, was a good rec. Do you have any suggestions on a second book on linear algebra after im done with this? The subject has surprisingly captured my attention and I'd like to go more in depth, but I don't know which book would be a logical progression after I'm done with Meckes.

[remote sparrow]

Axler, Friedberg, Hoffman/Kunze, Shilov, Garcia/Horn, Meyer, Shapiro. Depends on what you want. G&H and Meyer are slanted towards results and theory useful for applications. Shapiro is very combinatorial in some parts.

The rest are reviewed by Dami in the pins here.

Axler is controversial here apparently but others really like it.

[orchid mortar]

Standard proofy-calculus books are Apostol and Spivak. More computational might be Stewart. You might also want to read how to prove it by Velleman, which isn't a textbook but it sounds it could help

[remote sparrow]

At the very least I got it when it was on the cheap side.

[gray gazelle]

thank you so much!!

[tame tree]

i assume that i wouldn't have to read each part as if im learning it from scratch either no?

kinda a dumb question lol

[remote sparrow]

They are logically complete but much less time is spent on material that should be covered more thoroughly in a first course. It's still a good idea to "review" what you already know just so you can get a handle on their notation and get a taste for how they perceive the subject.

There is nothing wrong and it is actually quite beneficial to revisit and massage old material over in your brain. Though if you get stuck, refer back to the old book.

[tame tree]

yeah ill review and do old material. im kinda a stickler for that

i might vie away from axler as i hear that its treatment of determinants is not so bueno

and also, what would come even after that?

[remote sparrow]

You might be interested in Axler's essay titled "Down with Determinants" which pretty much lays out why he wrote LADR.

[remote sparrow]

Graduate books like Roman's Advanced Linear Algebra for example

Maybe numerical linear algebra or heavy matrix theory as with Horn.

[tame tree]

actually axler may be the right choice for me here

he even says it's intended as a second course

and the reviews say its more theoretical and abstract

which i like

[willow pecan]

Axler is not really second course material in my opinion

[remote sparrow]

Axler has videos to go with his book, though i think he kinda just reads off of it

It's his book tbf, it accurately represents how he thinks about lin alg

Just read a little from the recommendations and see how you feel

You can even mix and match treatments

[tame tree]

what would be in your opinion?

[remote sparrow]

These books are all theoretical btw. Some emphasize linear transformations, some emphasize matrix results and decompositions.

[willow pecan]

I mean

How in depth did your first course go

[tame tree]

friedberg i've seen criticized for being too spread out and bloated

im currently reading meckes linear algebra

[willow pecan]

Friedberg is fine

Did you cover all of it

[tame tree]

not yet

still going through it

[willow pecan]

You're not going to see anything in Axler that isn't in Friedberg

[tame tree]

i see

[remote sparrow]

I want FIS on my shelf but it's too damn expensive

[tame tree]

ya 😬

its something like 200 dollars last i checked

[remote sparrow]

H&K can be super cheap if you buy an int'l edition. Pretty tough book, it's no joke. Very abstract. Shilov is quite cheap too. Very unique approach by literally beginning with determinants.

[dapper root]

How tf do you know so many LA books lmao

Did you decide to do every LA book on earth haha

[remote sparrow]

No, I just read tons of reviews and skim the contents.

I guess I'm an amateur librarian/information services person

[inner token]

I love books

[acoustic ridge]

Can anyone recommend me a book for learning the core of calculus and graph's?

[quasi cave]

Can anyone recommend me a book for learning the core of Algebra and Trianometry

[fallow cypress]

anyone have any book recs for computable analysis?

[hallow oriole]

https://eccc.weizmann.ac.il/resources/pdf/ica.pdf
this pdf has some book recs in it

[fallow cypress]

yooo ty

[tame tree]

I found a 23 dollar FIS intl ver. On ebay

[remote sparrow]

i'll look around

[tame tree]

Intl versions are the same right?

Just way way cheaper

[gray gazelle]

I have had that book on my self for a year now

I already took a course that used ladw but I wanted an actually LA book

[gray gazelle]

I think its missing a chapter for that one

I heard someone complaining about it in this server before

[warm glen]

when ppl here recommend matsumura for commutative algebra r yall talking ab "commutative algebra" or "commutative ring theory"

[tough zealot]

its kinda the same thing afaik
the commalg is basically commutative ring and module theory

[solemn rover]

commutative ring theory, I think

https://mathoverflow.net/questions/25411/matsumura-commutative-algebra-versus-commutative-ring-theory

[dapper root]

Commutative ring theory

[heady ember]

Print and bind it yourself

[heady ember]

Pauls' Online Math Notes
Khan Academy
Spivak's Calculus

[gray gazelle]

Any calculus PDF ??

[inland raven]

Try

[weak nymph]

hello, currently i am learning Discrete Mathematics, if anyone can help me with any materials you got(which can help me improve), please send me ❤️ thanks in advance

[gray gazelle]

I'd delete this comment if I were you

[stiff sentinel]

any recommendations for cellular automata?

[inland raven]

Why? There should be no obstacles to knowledge

@gray gazelle

[gray gazelle]

[willow pecan]

Discord ToS

[inland raven]

MIT OCW has a nice course on it and things related to that

[stiff sentinel]

thanks but im primarily looking for a book

[compact imp]

Any recommendations on where to start for learning Bayesian probability?

[orchid mortar]

http://www.stat.columbia.edu/~gelman/book/
Not really 100% 'to start learning' but it's free and the starting chapters are doable

https://bayesball.github.io/BAYES_NOTES/
and the book https://bayesball.github.io/bcwr/index.html
could be gentler. But the notes are free but the book isn't

[haughty vine]

does anyone know any good books on mental math? I wanna get good at that before I get to advanced math, someone told me it makes it a million times easier, and just the extra math practice (prefer a dm)

[inland raven]

What do you mean by mental math?

[frosty wyvern]

Hi! Anyone here who works on incompressible fluids? What book should I read first to understand the incompressible navier-stokes equation?

[inland raven]

My advice is that if you wish to get into advanced math, you should do precisely that. What makes studying math easier is not how fast you can add up numbers in your head, but how much you wish to understand the new concepts. As such, develop your interest, and the ability develops throughout the process.

[willow pecan]

Acheson maybe

[haughty vine]

Just being able to solve large but basic calculations in your head, like big addition subtraction multiplication and division problems

[inland raven]

I don't think that would be a good use of your time, honestly

[haughty vine]

Hm

[zealous coyote]

Gotta say I don't think that's terribly helpful for 'advanced math,' whatever you mean by that

I think most mathematicians can't add two 3-digit numbers in their head.

But if you're interested, that's your perogative

[glacial crypt]

I can barely add a two digit number nowadays

[haughty vine]

Because wouldn't that just help me be able to comprehend more easier, calculate faster and stuff

[zealous coyote]

I'm also curious if there are any books

[zealous coyote]

There are rarely calculations like that.

[inland raven]

Well, advanced math is much less about calculating

[haughty vine]

Wouldn't that also help with spatial reasoning which can help in math with comprehension

Idk

[glacial crypt]

If you want to git gud at mental math practice

[inland raven]

And a lot more about structure, form, concepts

[zealous coyote]

Not really, no.

Which it to say, just no actually

[glacial crypt]

If you want to git gud at math math also practice

[haughty vine]

I dont know much about math I do want to get really good at it though

[glacial crypt]

Consider why do you want to do it?

[inland raven]

To get better at that you need to grapple with the very concepts you wish to understand better

[glacial crypt]

What really is motivating you to do it

[haughty vine]

Ig being able to do most math in my head

[glacial crypt]

But why

[haughty vine]

Save a lot of time

[glacial crypt]

A calculator is faster

[inland raven]

I don't know if that's terribly realistic

[glacial crypt]

And makes almost no mistakes

[haughty vine]

I want to learn how to think not how to use a damned calculator

[glacial crypt]

If you want to learn to think pick up a proofs book or something

[haughty vine]

One thing I do know is that calculators are bad for learning math unless you need one like a graphing calculator

[inland raven]

One issue is that your motivation for this pursuit will extinguish pretty fast, as it isn't particularly fun to add numbers in your head.

[glacial crypt]

Mental sums are "trivial"

[haughty vine]

Probably true lmao

[inland raven]

Agree with this.

[glacial crypt]

How to Prove it by velleman is what Im using

[haughty vine]

The way I see it is that there are a lot of side benefits by being able to comprehend and manipulate large numbers in your head

[haughty vine]

Hm

[glacial crypt]

Not really

[inland raven]

That would be a very one sided math development

[glacial crypt]

If I need to add 2 2-digit numbers im pulling out a calculator

That's just arithmetic

Math is not arithmetic

[inland raven]

You would probably be better at it at the expense of knowing a lot of other things and of being a lot more creative

[glacial crypt]

It's a superset rather

[haughty vine]

I gtg for now, got work, but yeah not sure, I'm just looking to get a big foundation in basic mathematics which will help me a lot in advanced mathematics

Yeah

Ty for your thoughts

Have a good day guys

[inland raven]

Try how to prove it by polya

[glacial crypt]

If you want to get a foundation in advanced math you want a proofs book

[inland raven]

Or he above book

[glacial crypt]

Like I said

If you want to do arithmetic then just

[haughty vine]

Can u dm me these books

[glacial crypt]

Generate random numbers and practice

You can write them down yourself

[flat lantern]

dunno lol

[willow pecan]

Lol

[quick hornet]

did you set up a calendar notification for this shit

[flat lantern]

I had a notepad file on my desktop titled "OCTOBER" and it kept reminding me

[smoky zephyr]

legend

my god

[flat lantern]

please don't reply to old posts, thank you :)

[smoky zephyr]

[shy compass]

why is this frowned on

[frosty wyvern]

Hi. Are you referring to this one: https://www.amazon.com/Elementary-Dynamics-Applied-Mathematics-Computing/dp/0198596790

[willow pecan]

Yes

[frosty wyvern]

Thank you

[dapper root]

Did you set an event on your calendar or something wtf

[flat lantern]

I tried to warn u...

I was a day late

[dapper root]

Wtf

I missed that

[plush arrow]

A book with a lot of recursive functions

[quick hornet]

generatingfunctionology

[plush arrow]

thanks sir

[hearty steppe]

brought to you by my twitter feed https://www.biorxiv.org/content/10.1101/2022.10.04.510897v1.full

I reached out to Pang cuz I want to talk to him about this paper.

[grave thorn]

intro analysis >category theory

those two do not mix

[remote sparrow]

The most abstract introductory analysis text I'm able to think of would be Amann and Escher's three analysis volumes.

I don't think much category theory is explicitly used, though. Many connections are made with topology and modern algebra, however.

[fallow cypress]

you can do something with.. subspace topology having a universal property or something..

[hearty steppe]

They said ergodicity is dead, I say... Have a taste of my twitter feed... 🤣

https://arxiv.org/abs/2108.03460

oh for eigenstates, I thought this was a pretty satisfying definition https://en.wikipedia.org/wiki/Introduction_to_eigenstates

[hollow peak]

[tribal coyote]

Beginner friendly Calculus I book with lots of exercises

[tribal coyote]

Recommendations?

[hollow peak]

Stewart?

[tribal coyote]

Is that a question?

[hollow peak]

There are basically an unlimited number of beginner calc textbooks

Stewart is the one everyone uses

Or at least, its a typical calc 1 textbook

[tribal coyote]

Ah, I see!

I didn't know him yet, that's because I'm teaching myself

[hollow peak]

I also like strang's calculus book on MIT OCW

[tribal coyote]

Does his book has exercises at the end of the chapters?

[crimson leaf]

Is that the same as the openstax one

[hollow peak]

Openstax is a different thing

[hollow peak]

Tons

[tribal coyote]

That is perfect!

Thank you

[hollow peak]

[crimson leaf]

Strang wrote two sets of calculus books geez

[hollow peak]

And if you're looking for a rigorous, challenging intro calc book, people often recommend apostol or spivak

[tribal coyote]

Thank you, I'm gonna look them up 🙂

[remote sparrow]

https://www.reddit.com/r/math/comments/y1nu9q/linear_algebra_done_right_4th_edition_will_be/

[timid pier]

bro

how does one self study stewart calculus early transcendentals 8th edition

[quaint pine]

First check if you have the algebraic knowledge needed. If so-just start reading and walk through the problems. @timid pier

[cedar ridge]

used em yourself?

[lime sapphire]

ik lochverstarker has used them you can ask them

[gray gazelle]

Any one knows a good book on Riemannian Manifold for self study?

[hearty steppe]

It’s not a self study book. It’s a book that is meant to complement a standard Calc 1-3 course

[forest sleet]

Lee and Petersen are pretty standard books

assuming you already know basic manifolds

[timid pier]

Wtf

I've heard it is self study

[hollow peak]

I mean, it technically has all of the content of a calc sequence

You definitely could self study

It is in fact a textbook

[gray gazelle]

Yeah that's thing we did have some differential geometry and topological manifold before but I barely passed those uni kinda forced me on reimanian manifolds

[forest sleet]

Lee has a Smooth Manifolds book if you want to review that before riemannian

[gray gazelle]

Ok and is Kobayashi good for self study I have heard a lot about it

[forest sleet]

I'm not familiar with that book sorry

[gray gazelle]

Oh ok thanks anyway

[remote sparrow]

It's a great book to have on your shelf regardless as a reference and as a source for problems to work through. I like it, but it's not uncommon for people to call it not ideal for self-study, given the book tries to be a jack of all trades in being both a comprehensive reference and as a learning tool.

[remote sparrow]

Just read some reviews and skimmed the book.

[timid pier]

I've been self studying from stewart

The proofs allowed me to understand the concepts

And the practice questions are great

[hearty steppe]

I think Stewart is very rigid in formality still.

Not sure what your background is but that is impressive

[stiff sentinel]

🙏

[sick river]

Anyone have any recommendations for more category theory? My class is using Aluffi so any books with an eye towards the ring and group categories would be awesome

[timber mesa]

have you read Riehl

[gray gazelle]

Mac Lane

[timber mesa]

yeah these two are the usual intro references

[sick river]

I’ve tried Riehl but I’ll try Mac Lane, thanks

[dull otter]

the way of the superior man is a good book

[remote sparrow]

Eugenia Cheng just released her new book The Joy of Abstraction which is supposed to be an introduction to category theory. It's possible that it's pitched too low for you, though. In any case I would appreciate if you or someone else reviewed the book to see if it's worth putting on my shelf.

[inner token]

Group Theory book

I'm specifically interested in group theory but if it contains other structures that's fine but I need the group theory part to shine

[willow pecan]

D&F

[inner token]

ok

thanks you

[brisk ice]

@gusty smelt Maybe overlooked but I think you should update your early books your group finished so they don't have "coming soon' in the "More books this series" and now have the available links.

Might just be something you have to add on the "todo list" after you all finish a book.

[orchid mortar]

Has anyone taken a look at this?
https://openstax.org/details/books/calculus-volume-1

Wonder how much this can be used instead of the more standard calculus books

[remote sparrow]

looks alright. reviews say the problems are a bit too easy, so you can just borrow some problems from stewart to get some practice in. but there are TONS of open source, free calculus ebooks (some with low-cost hard copies too). i don't think there's much of a clear consensus yet.

[livid ermine]

is kashiwara schapira sheaves on manifolds good?

[remote sparrow]

i do hope some day these low cost options replace mainstream textbooks

[orchid mortar]

oh, any recs? I don't think I know of a list of FOSS calculus ebooks

[livid ermine]

this book doesn't really cover what big rudin does

[gray gazelle]

That was 2 years ago

But yeah it's a book about measure theory/probability

Rudin takes more functional/complex analysis approach

Rudin's not hard though, imo there's just better books

[woven cypress]

What is it really?

[granite ferry]

Thoughts on these books:

In regards to proof writing/logic

[willow pecan]

You don't need 4 of them

[sleek python]

Browse them in a library (or libgen) before choosing which your prefer to buy

[crimson leaf]

Then people would have to actually grade calculus homework

[granite ferry]

Well.. Proofs from THE BOOK is pretty advanced it sounds like. Book of Proof is entry level and I'm unsure about Foundation of Higher Mathematics.

"How to Solve it:..." is mostly unrelated to actually writing proofs and more about approaching solving unique problems in general.

[fluid bay]

what are some good resources for learning about the fourier transform (with emphasis on operator algebraic consequences/interpretations)?

to elaborate on the "()", I've heard for example that the fourier transform is the gelfand transform on the convolution algebra L^1(G) for a L.C. group G. It'd be cool to have an introduction to fourier transform which discusses this approach

[lean pagoda]

You already said it yourself, but Polya and Aigner don't really fall into that "Intro to Proofs" category of books. The other two books do fit into that category from what I can tell. Also worth pointing out that Hammack is freely available online

[granite ferry]

Thanks. I was hopeful others may have read them.