book-recommendations

[hasty turret]

So what are some good intro books for algebraic complexity theory?

[glossy schooner]

Does someone knows a good reference for the relation between cyclic homology and non-commutative geometry ? I heard that cyclic cohomology is the non-commutative De Rham cohomology analogue and I would like to understand this.

[atomic hemlock]

Anyone have suggestions for (any level) applied mathematics textbooks? I don't care about proofs, I want to learn math in order to use math, not looking to do math.

[orchid mortar]

Applied math is still math

Even if you go for a very applied context like engineering

You'll still have to do math

[quick hornet]

this is like the vaguest possible thing you could ask for

applied math is a biiiig field and most people who study it dont read "applied math" in the abstract

at best, one reads a specific topic like "optimization" or "numerical analysis" or whatever

also applied math will involve proofs FYI

not as many as in pure math but still a lot

if you dont want to prove things, you shouldnt be studying something called "mathematics"

look into e.g. engineering, or econometrics, or whatever

[quick hornet]

e.g. here's the first(?) exercise set of isaacson-keller, a famous numerical analysis textbook studied by most applied math students

[ocean mulch]

Even most applied area of math, like cryptography, uses as much advanced stuff as pure math.

[orchid mortar]

There definitely is low-math Econometrica, low-math Management Science, but that doesn't mean it's easy

[quick hornet]

im not saying low-math

im saying low-proofs

my point is that if a field is labelled "mathematics", even applied, that indicates the presence of proofs

[orchid mortar]

There's high-math/high-proof for both, I'd assume

[quick hornet]

otherwise another label is given

[quick hornet]

yes, and that is covered under the label of applied mathematics and usually published in crossdisciplinary journals

like "mathematical methods in ___"

[orchid mortar]

I mean I'm responding wrt to the phobia of math

[quick hornet]

my point is the explicit presence of the word "mathematical" indicating "proofs"

from the perspective of academic jargon these two things are essentially synonymous

(at least as far as like, publishing papers and non-intro textbooks go)

(i know a lot of intro courses are called "mathematical methods in finance" or whatever and dont involve proofs, thats just to indicate to inexperienced students "you actually need to compute shit")

[atomic hemlock]

By applied I meant no proofs, if some mathematicians proved it,I would consider it true and would only care about formulas.

[quick hornet]

again, then youre not looking for what academia calls "applied mathematics"

which is fine

but it means that your question is even more vague

since the answer becomes "look up a methods book in any field that uses math"

a group theory text used by chemists, or an econometrics text used by first years, or any finance or engineering text ever

people dont really study "computations without proofs" for their own sake

they do so in the context of an existing field

so youre at least going to have to specify the field

[atomic hemlock]

Thanks I'll dig into those 👍

[gray gazelle]

Physics Methods typically has the most mathematics of this kind (e.g. Arfken)

There's probably more recent books than Arfken but it is passed down from generations of students, someone can recommend a book that does more

[viscid sky]

guys i just saw mit integration bee, i was really wondering if there exists a book that covers all integration techniques like i want to be able to solve any problem

i already finished calc 1 and 2

perhaps the book i used was not that good and didnt include hard integrals

[heady ember]

You probably won't ever be able to solve every (computational integration) problem. But perhaps Valean, Cornel Ioan (Almost) Impossible Integrals, Sums, and Series comes close to what you want

[gray gazelle]

My answer was a subset of this answer so I deleted

[heady ember]

I see

[viscid sky]

@gray gazelle@heady ember thank u guys , really thank u sooo much i really appreciate it

[heady ember]

To read that book you should have your fundementals down though, might need some real anal knowledge iirc

[viscid sky]

oh wow, thanks for that information .

[heady ember]

Im not that sure about the exact prereqs but you can flip open a copy and see for yourself

There are... creative ways to obtain PDFs of a book

[viscid sky]

oh ok ❤️

[viscid sky]

i got u dw!

[gray gazelle]

Hey @viscid sky doing some Physics math methods books can help out your integrating too since a lot of those crazy integrals you see are from Physics itself. Sorry, just remembered this was the case

[viscid sky]

u mean those mathematical methods for physicists and scientists and engineering books?

[viscid sky]

i have got a couple of those not sure which one is the best btw do u have a personal favorite

[gray gazelle]

Yeah! I'm not sure what's the best either, but Arfken & Morse are highly recommended

[strange plume]

rd sharm is best

[pliant valley]

lol

[tacit abyss]

Hey does anyone know where to get exercises for spectral theory with integrals over resolutions of the identity

ie. some more stuff like this (I've solved these qns already)

[heavy pelican]

stein shakarchi functional analysis

[tacit abyss]

cheers

[heavy pelican]

i also like hall’s quantum mechanics for mathematicians but i forget if it has exercises

i think it does

i learnt this stuff from there

[tacit abyss]

uh to ask a stupid question where's spectral theory in this book

Hall has what I'm looking for though thanks, (with exercises) just diff notation and just self-adjoint

[heavy pelican]

i misremembered, sorry. its in stein shakarchi, real analysis. delegates to an appendix in chapter 6

[heavy pelican]

cool glad that works for you

[tacit abyss]

ah fair, will check that out thanks

[sick root]

hello, any suggestions for books with math related topics? I dont want math textbooks but either popular-science books related to math or even novels with a math related topic for a friend with zero math background.

[slender crown]

is there a list of classic undergrad math books?

like really good ones

[slender crown]

uh for competition math, i just read "the math olympian"
otherwise uhm math with bad drawings maybe?

[plush geyser]

I liked Infinite Powers by Steven Strogatz
Why Study Mathematics? by Vicky Neal is an overview of different university math subjects but not really a novel

[slender crown]

what does why study math talk about
(i second the comment on infinite powers)

unless idk where it is there really should be a general doc with recommendations pinned or smth

[plush geyser]

It goes over

• what different degrees involve
• what to do with a math degree
• where/how math is commonly applied

[slender crown]

hm sounds like my yt feed kinda

zach star or smth

[plush geyser]

Yeah I found it pretty helpful, I'm starting to decide where to go next myself

[hallow oriole]

if anyone has any interesting and fun probability/stats textbook recs hmu!!

math-related is prefereable

preferable

[hearty pollen]

looking for math textbooks focused on biology applications, in general

[orchid mortar]

https://applying-maths-book.com/
Does this count

[faint garden]

Many, many areas of maths have biology applications these days. I've applied information theory to genome assembly. Introductory Biostatistics by Chap Le is quite good, IIRC, if you're interested in that particular field; biostatisticians were the unsung heroes of the pandemic if you ask me.

Biostatisticians also do things like work out which cattle to selectively breed to increase the overall value of the milk produced. I also briefly worked on that once.

Or are you more interested in something like biomechanics?

[hearty pollen]

I'm seeking novelty and applications I haven't heard of in general. Biomechanics sounds intriguing and I'd like to explore that further. But, one of the things I'm looking for is an ideal textbook that would be suitable to help me work through this paper with more clarity: The Eigenvalue Value (in Neuroscience) Georgia Christodoulou & Tim P. Vogels https://scholar.google.com/scholar?hl=en&as_sdt=0%2C5&q=The+Eigenvalue+Value+(in+Neuroscience)+Georgia+Christodoulou+%26+Tim+P.+Vogels&btnG= (sorry I can't upload the pdf)

[hearty pollen]

I'll take it. I like motivating examples but I kinda want something that teaches all of the math through applications in a single domain (a subfield within bio, any) while explaining the abstractions (or at least not shying away) and providing intuition for their implications in the domain. Ideally in something uncommon, I had heard of population growth and recently learnt about the stochiometric matrices so I'm curious about what else is out there.

[orchid mortar]

I think the book you're looking for would be super massive if it were a book

So you'll have to contend with multiple books specialising in their topics

[hearty pollen]

yeah I had a feeling. Right now just amassing texts

[hearty pollen]

This looks interesting I havent much of an idea as to what information theory is though. Having recently learnt about Reed-Solomon codes I was curious if nucleotide sequences could act as a field and came across this paper: A New DNA Sequences Vector Space on a Genetic Code Galois Field. Does information theory require this approach at all? I'm just trying to find ways to learn more so I can engage with these ideas better...

[orchid mortar]

Whole paper seems to be linear algebra, but even touches introductory random matrix theory...

I'd say you want a matrix algebra book

The random matrix theory part you can get an introductory random matrix book....I think, it's not simple stuff in general when you get to random matrices

You don't need to read fully a full matrix algebra book, but that will help a lot

Actually a general linear algebra book, scrolling a bit more down

https://www.cambridge.org/core/books/matrix-analysis-and-applications/182A4A2FF1185E0D6C037A502E256EF4
A rather heavy book having everything mentioned inside the paper I believe, except

• random matrices (check a random matrix source)
• stability of systems (you need a DE/dynamical systems source/book I think)

@hearty pollen In short the paper covers a lot of ground

[hearty pollen]

haha. thank you, much appreciated

[faint garden]

I would have to take a look at it. I did design an error-correcting code for DNA sequences once, but it wasn't a linear code, so didn't depend on GF(4). And the code was used, so I technically designed some DNA sequences that got synthesised. First step towards my clone army, and you will all fear me some day.

[maiden halo]

Yeah that is stuff you probably wouldn't see until an advanced undergraduate or graduate class is neuroscience. But there's a book by Ischikevitch "Dynamical Systems in Neuroscience" that I think covers similar stuff to that paper.

[ornate haven]

Any books that can make me appreciate math and its beauty?

[ornate haven]

I'm currently trying out How not to be wrong. That's gonna be next!

[plush geyser]

Infinite Powers - Steven Strogatz
Intro to Mathematical Philosophy - Bertrand Russell is pretty dense and basically builds math up from its roots of logic if you're into that

[kind elm]

nah that would leave u confused

not a book that exactly gushes over the beauty of mathematics

[slender crown]

Why baby rudin?

[fossil arch]

Do any of you have comfort books?

This is gonna sound silly but I’m pretty down right now and math feels like the only thing I can turn to

Just want something easy to read, cheerful, pretty

Insightful and motivating

Not a textbook but not something too unserious either, just an entertaining, enlightening math book

[hollow shore]

fermat's last theorem by simon singh

[fossil arch]

This looks cool! Thanks for the suggestion :)

[ocean mulch]

Hilbert by Constance Reid

He also has Courant, tho I haven't read it yet

[fierce hedge]

Is it a biography of David Hilbert?

[ocean mulch]

Yes

[hazy elk]

There's Oscar Zariski's unreal life too

It's a phenomenal book

Zariski was quite based

[fierce hedge]

Anyone read the book written by Cedric, The birth of a theorem?

[hazy elk]

https://link.springer.com/book/10.1007/978-0-387-09430-4

[restive falcon]

@wanton tide friedberg insel spence is very good i hear

[wanton tide]

Thanks

[austere zephyr]

Y'all should read The Hungry Hungry Caterpillar

[kind elm]

I agree

Will help you out tremendously in life

[smoky zephyr]

this is #book-recommendations just so you know lol

[hearty steppe]

Oops I thought it was chill

[cerulean cypress]

would you recommend friedberg to engineering major?

on linear algebra

[smoky zephyr]

i don’t think engineering majors do proof based linear algebra so it’s really up to you

[thorn canyon]

relatable af right now.

[mossy flume]

I loved Friedberg so yes

but it is a proof based book

so yea it's just up to you

I think it's really nice tho

[reef cosmos]

I'm a mechanical engineering major and while I am also doing math, I think Friedberg is really good for truly understanding the why behind linear algebra topics (at the undergrad level). If you are just looking for ways to solve systems of equations, understand vector computations, and approximation stuff, then maybe Howard Anton's Elementary Linear Algebra is better.

[cerulean cypress]

okay thanks for recommendations

[remote sparrow]

#book-recommendations message

[gray gazelle]

does anyone knows a good textsbook that explains first and second mean value theorems of definite integrals ?

[gray jungle]

Is "Mathematical Methods of Classical Mechanics" by Vladimir Arnold a good book for lagrangian mechanics?

[sweet scaffold]

I think I found errors in anton and also the fullness of the literature is just not there. It's a hollow book. Friedberg insel spence is great for an intelligent presentation of Lin alg. For a less mathematically mature audience but verbose coverage, lin alg and its app by lay, lay and someone else.

[toxic cradle]

does anyone have a pdf version of the statistical book of ray sharma

[sweet scaffold]

Finite Mathematics by Goldstein, Schneider, Siegel; Linear Algebra and Its Application by David Lay; Calculus by Stewart; Probability and Statistics for Engineers and Scientist by Hayter; Differential Equations by Blanchard, Devaney, Hall;

[shrewd kraken]

someone @ me if they do

[reef cosmos]

Yeah, after doing proof based lin. alg. I'd have to agree with you. I went back through it and found it lacking in areas, but I still think it has value for someone interested in an introductory/computational approach. But if someone feels inclined to learn more, then absolutely 100% Friedberg, Insel, and Spence is the way to go. Two different audiences i suppose. I've seen the Lay book around but never picked it up, also heard good things about pairing Strangs book with his MIT OCW lectures.

Also I have a book called Differential Equations and Linear Algebra by Goode that is a good treatment of both, taking a break after first order ODEs to cover lin. alg. I recommend it for someone looking to learn both concurrently

[sweet scaffold]

woof

i did strangs book but it only worked before I became mathematically mature. now, I cannot recommend the fluid style of strang's writing; i require pedantry. I hate to say it but I think math students have just tried to dodge the presence of english by doing a butt load of math. Thus, I have suggested lay's book because people just need more literacy in their lives and the earlier they can encounter piles of words, the better.

[crimson leaf]

Lay is honestly one of those book where you can do almost no reading and be totally fine kind of like Stewart

More words does not also guarantee that the book is worth reading most of those giant computational books like Strang, Lay, or Stewart really don't teach much except how to follow a formula

[prime oak]

opinions on de barra?

(ping when anwering ty)

[mossy flume]

I like Awodey's text

[sweet scaffold]

1. it may appear that I am suggesting lay for pure quantity of words, I am not. I read it and also suggest it for clarity.

2. never have I ever suggested that more words implies worth reading. What you misread was: the earlier they can encounter more piles of words, the better; which, as the author of the statement, was intended to mean: experience as a reader is useful for students.

[sweet scaffold]

3. you can do no reading at anytime. In fact, it's not just lay's book, or strang's or stewart's, but every book can be left unread. That statement is perhaps the smartest thing I've ever not read. Let's be honest here, English (or anyone's native language) comprehension is not a joke. I don't even know why I am entertaining a response but I strongly feel the need to dissuade students from considering any advice that steers them from developing literacy. Whatever this totally fine phrase means, it's at least suggesting a lax, anti-alert behavior to early undergraduate texts and reading in general.

[crimson leaf]

Lay may be a perfectly fine English book but as a math book it is severely lacking. You do not have to actually read it to gain what it is teaching just look at the examples and do some computations. It requires no mathematical thinking and does not progress a student in anything meaningful or teach them the true concepts of linear algebra. Any student is much better served by reading pretty much anything suggested in the pins for linear algebra. You will learn how to better comprehend math books by reading math books especially proof based ones where you actually have to think about what the author is saying and the ideas used.

[sweet scaffold]

I believe you are mistaken about how little mathematical thinking there is. Each audience has a different idea of mathematical thinking. I would be sensitive here about how much math thinking you see vs someone who isn't you; perhaps someone who isn't as mathematically mature.

[sweet scaffold]

I don't even know who or what your talking to, but it isn't me, it's the strawman in the field. In an earlier comment, I can be found describing my own needs for pedantry, or as you know it, mathematics with proofs. I am keenly aware of pedantry. I don't know what you're saying either. Is it that people should skip mathematics without proof and only do mathematics with proof? You would be wildly wrong. See MacTutor archive of von Neumann's essay The Mathematician where he talks about Euler in an age before modern formalism. Is von Neumann wrong?

[crimson leaf]

If anything you're the one having an imaginary argument coming back half an hour from your last message to reply again

[sweet scaffold]

I think our service to students must be partitioned by degrees of mathematical maturity.

Why are you telling me and the public that there is no mathematical thinking in Lay?

[crimson leaf]

My first message was really just saying that books like Lay are fundamentally a disservice to student and the rest is me talking about why I dislike Lay and think it's a poor book. There should really be no distinction between computational and proof based linear algebra and Lay is a computational approach where you just rote learn to do linear algebra

[sweet scaffold]

Why are you telling me/everyone all of that comment??? How is this directed to me?

[crimson leaf]

Why are you so upset lol

I stated my opinion on a book

[lapis heart]

<@&268886789983436800> I think someone should stop this

[sweet scaffold]

Ok then we shall stop

[dense pumice]

I remember enjoying "Discrete Mathematics" by Richard Johnsonbaugh

[worthy venture]

i dont know about lay but i agree with stewart. that book is really good for calc 1-3 students. i feel like its an appropriate difficulty to get students comfortable with the types of questions being asked. that said it has no rigour and i find its use is only good for familiarizing myself with calculus rather then understanding calculus

[crimson leaf]

Yeah if you just wanna know how to do calculus Stewart is fine but I think there are better books/resources especially at multi variable

[dense pumice]

I'm not totally sure what you mean, like standard operations on boolean logic?

[crimson leaf]

I think it's too bloated also

[worthy venture]

i find Feldman. Rechnitzer. Yeager to be a good place to learn honestly. its more rigorous and its examples are sufficently difficult. my only down side is i do have an appreciations for laying out formulas as its helpful in a pinch

[dense pumice]

The book i recommended goes over that stuff

[worthy venture]

multivariable especially. stewart only serves its purpose for calc 1 and 2. ive looked through it for vector and multivariable calculus and its just sad. not enough examples, explanations and rigour for some of the most important types of integrals in engineering

[dense pumice]

Chapter 1 is literally "Sets and Logic"

[crimson leaf]

Yeah that's the other thing that's weird about these books to me is they're supposed to be for engineers but then engineers always tell me they never use what they learn. This is especially bad in diff eqs and calc 3

[worthy venture]

thats true.

irregardless math serves a greater purpose even though it wont be used in the type of career electrical engineering often offers.

[vague granite]

hi, are there any good books to self study lin alg and diff eq? I only need to know the results since I'm trying to study for some physics prereqs. Thanks in advance! :)

[remote sparrow]

goode and annin

[vague granite]

does this book cover both intro lin alg and d.eq? or is it intended for someone who knows both well and combines the info

[remote sparrow]

it covers both

there is no coverage of boundary value problems or very basic PDEs, though

boyce and diprima does though

[vague granite]

cool, what are your thoughts on strang's linear algebra and its applications?

[remote sparrow]

it's okay

[vague granite]

would this book be enough to cover intro courses in both subjects?

[remote sparrow]

yes

[vague granite]

thanks! :)

[sturdy flame]

@remote sparrow sorry for the ping but you seem to be somewhat like a librarian.

do you know any good and strictly computational diff eq books with solutuons and explanations. like Problems -> Hints maybe -> worked out solutions

[remote sparrow]

https://www.amazon.com/Differential-Equations-Essential-Practice-Workbook/dp/1941691390

maybe something like this

but boyce and diprima has all the answers in the back

i'm pretty sure there's a place that steals chegg answers for the 10th edition of boyce and diprima

paul's online math notes i think follows boyce and diprima for diffy q's

[sturdy flame]

oh sweet, i love thay website

tysm

[hearty pollen]

Whats a good book to learn how to prove simple things in linear algebra, with detailed solutions/hints

[remote sparrow]

define simple

[hearty pollen]

the fundamentals? ideally proving things from the concept of 4 fundamental subspaces, i have some geometric intuition with 0 mathematical maturity

[remote sparrow]

umm i don't recall the term 4 fundamental subspaces except from lay's book

hefferon's book is good though with respect to having solutions for every exercise provided by the author himself

and it's free online

[hearty pollen]

its central to strangs approach but i think dual spaces is analogous

[remote sparrow]

https://hefferon.net/

[inner token]

Yes. The row space is the column space of the dual map

[pale summit]

I loved Hefferon's book, I used that in my LinAlg class. It is very helpful, imo

Also this book, though it might be more dense than Hefferon.
https://a.co/d/6YybEU7

Separate statement - anyone have resource/book recommendations for coding? Beyond R and Octave I'm clueless and would like to spend the summer learning to code.

[weary cape]

Has anyone here read "Linear algebra for everyone" by Gilbert Strang?? I saw his MIT lecture on YouTube the other day any many peeps were saying he is the best lin alg instructor and I found he released a book. Currently looking for a good lin alg book other than the one by Axler.

Granted, I'm not taking lin alg yet but I would like to have my hands on a some texts before taking it next year.

[marble solar]

I don't think he's the best linear algebra instructor, but a lot of people find his textbooks easy to follow and understand

And to be associated with MIT certainly doesn't hurt

[pale summit]

As mentioned earlier, Hefferon's book was the one I used when I took the course. It was also recommended by another user.

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

It's a personal favorite of mine. His site includes an answer key for the exercises, too, if you are interested in working through the problems on your own.

[remote sparrow]

it's purposely designed so that no calculus is needed

someone remarked that the book might be a little easy

still, it's nice to have a book like that

[remote sparrow]

if you're just interested in learning how to code, probably any old coding bootcamp site will do

presumably you're less interested in the computer science stuff

[cerulean cypress]

https://www.amazon.com/C-Programming-Modern-Approach-2nd/dp/0393979504

is it only me or this book actually is a bit challenging?

like I was stuck at the first step since the book didn't have any instructions on how to set up IDE so I had to look up online

i don't have programming experience whatsoever that could be the reason since the book assumes the person to have at least basic compsci background for prereq

the book is k n king's c programming a modern approach

also can I get any recommendations for precalculus or any type of book that has summarized math from elementary to high school level that has prerequisites for caclulus? for review purpose

[maiden halo]

That might have been me. It is very light on the proofs (if there even are any, I don't quite remember). But it is a good book for someone's first look at linear algebra. Also it's cheap for how big it is

[maiden halo]

there are loads of introductory books and tutorials online. I've heard pretty good things about this one (PDF warning): https://web.itu.edu.tr/~tokerem/The_Book_of_R.pdf

[slender crown]

yo wait wtf

sup man

wait what grade r u in?

[bleak pebble]

Dear all,

any suggestion on a book for recent update on spectral graph theory?

[sage python]

I don't know of any comprehensive + advanced surveys, would be interested to know what's out there

[vague granite]

im a rising 10th grader in hs

[sage python]

Regarding my particular angle on this subject, one book I very much am meaning to read is "Discrete Groups, Expanding Graphs, and Invariant Measures" by Lubotzky

[heavy pelican]

lubotzky is a cool guy

hes visiting my school sometime next year

[sage python]

Nice

[heady ember]

Hi Dami

[sage python]

Sup grass

[fierce hedge]

Excuse me, that doesn't look like a cow to me

[vague granite]

lol

[gray gazelle]

Going on an exchange for a year and won't be able to take an algebraic structures course I was planning on taking at my home university, I would still like to work through the subject on my own so I can have a head start once I get back from my exchange. Is there a consensus on the best abstract algebra books for self study?

[gray gazelle]

There are three that are popular here:

Dummit & Foote - Artin - Aluffi

[fierce hedge]

Usual self study recommendations are Judson, gallian, artin (in order of increasing difficulty)

[night knot]

Dummit-Foote is comprehensive but a bit dry - gets the job done if you have it

Artin's book is pretty good if you can get that instead

[gray gazelle]

Well the common denominator here was artin so I guess I'll start there lol

[fierce hedge]

I won't recommend artin for first time self study of abstract algebra, just my 2 cents

[gray gazelle]

Ty

[gray gazelle]

No worries I've done self study before

[fierce hedge]

I meant first time self study of algebra

[gray gazelle]

I just don’t agree

Welp looks like the answer to my original question was "no" lmfao

[fierce hedge]

best you can try and see, start with artin if the pacing is fine go for it

[gray gazelle]

I don’t think anyone except a high schooler should do something on Fraleigh and Gallian and indeed even high schoolers can get through Artin, I would of course recommend skipping the misc. exercises on a first run

[fierce hedge]

I didn't like the pacing and so switched so Judson

[gray gazelle]

Well most of these are relatively expensive books from what I can tell

I find it very difficult to study using a pdf I downloaded online

Would much rather have a physical book

https://www.abebooks.com/servlet/BookDetailsPL?bi=30868860895&ref_=ps_ggl_11147913055&cm_mmc=ggl-_-US_Shopp_Textbook-_-product_id=COM9780132413770NEW-_-keyword=&gclid=CjwKCAjw67ajBhAVEiwA2g_jEDvG-IUnKxEKVTFazafYYRGXmnvZ5ZSUR-JkIuV91U0xtLZC1DaFZhoCHqUQAvD_BwE

$17

[fierce hedge]

Judson is free to download and print

[night knot]

You could use online notes as well - there's Dexter Chua's notes, for instance

[heavy pelican]

i vote Artin

[gray gazelle]

Nah that's wild 💀

First 5 results on google are all over $80

Scam world fr

[gray gazelle]

I'll def give these a look

[fierce hedge]

Buying books in this economy

[night knot]

Just one thing to note - the topics are spread out over several notes, so be sure to take into account what your class covers

[gray gazelle]

Alright I'll keep that in mind

I also have a pretty good idea of what topics I'm interested in

[night knot]

That's good

[gray gazelle]

I've also already been through a course on introductory ring and field theory anyways

[gray gazelle]

Yeah you’re going to have to get used to studying pdf books though because at a higher level you aren’t finding anything cheaper than $50 and these often end up ranging to $200

[fierce hedge]

Don't make me feel stupid for feeling it's dense

[gray gazelle]

buh

Can't wait

[gray gazelle]

If you had little introduction to pure math, Artin will be a fight for your life I agree, you’re not stupid at all

Misc. Exercises are trolly and very project-like

[heavy pelican]

i dont think youre stupid i just think artin is the best book for a first introduction

im teaching a high school kid group theory from there

[gray gazelle]

I have a pretty strong foundation in pure math so I'll prob start with artin and work my way around from there

[fierce hedge]

I despise Artin especially for these, the normal exercises are too easy while misc would take 1 a day for each question

[gray gazelle]

Well "strong" for an undergrad at least 💀

[fierce hedge]

in general yes, for self study without help no

[heavy pelican]

possibly, my opinion differs

i learnt everything from artin

[gray gazelle]

There’s another book I tried but I found it too terse but you have more p. Math background than me

Knapp- Basic Algebra

[heavy pelican]

basic agenda wtf lol

[fierce hedge]

went a bit political there xD

[gray gazelle]

We'll I can't say I'm immune to a book being dry/boring either

Munkres topology has not been treating me well 💀

[night knot]

IIRC Artin has an Algebraic Geometry book now - wonder how that goes

[gray gazelle]

Although tbh I mostly blame my instructor for this

[fierce hedge]

some say it's a better written Artin, I've also heard that the book is a scam

[gray gazelle]

I’m doing a reading group on this June 1st, you’ll probably be done before then though

Final is on the 1st lmfao

An end and a beginning

Tbh I'll def have to go back through it at some point

A lot of stuff has been going over my head

Especially near the end

[heavy pelican]

why do you want to read munkres

[gray gazelle]

Because it's the course literature in the basic topology course I'm taking

[fierce hedge]

I want to join but then munkres

[gray gazelle]

And most of the hw problems are ripped straight from the book

[heavy pelican]

ok so you just want to read it as part of the course

gotcha

[gray gazelle]

Pmuch yeah

[night knot]

What are the alternates to Munkres if you're doing point set?

[gray gazelle]

Lee is good I’ve heard

[night knot]

I can only find Munkres at my store, apparently

[gray gazelle]

Dugundji too, but that is more so if you’re interested in Topology

[fierce hedge]

what do you suggest? Hatcher notes or brendon chapter 1?

[heavy pelican]

If you want to learn topology? Ignore everything else and just read https://pi.math.cornell.edu/~hatcher/Top/Topdownloads.html. Yes, you too can become an expert in topology from reading just 50 pages! Bookworms hate this trick.

[gray gazelle]

Hmm

[night knot]

Lee is at my library but that's it

As far as purchasing a book, I've only gotten Munkres

[fierce hedge]

Unless you're doing some convoluted point set research I don't see why you'd need Dugunji

[night knot]

Smooth Manifolds, right?

Or is it called something else?

[gray gazelle]

I only recommend it because Blitz, the topologist, recommended it to me

[heavy pelican]

youll almost surely never need most of point set topology that you learn

[fierce hedge]

I should have seen that coming

[gray gazelle]

This is missing some of the topics my course covers but I might end up going back to this instead of munkres if I ever have to freshen up

[heavy pelican]

eg i agree with this

[fierce hedge]

btw a really good book on topology is - Elementary Topology _ Problem Textbook-AMS

I forgot who recommended it to me

ah yes, it was eigenyuwu

[sullen loom]

might be a little of a noob questions but are there any books that one would say is required reading for someone who wanted to get a little more into math? my experience goes up to multivar calc but im taking proofs this fall, and im currently going through How to Think Like a Mathematician by kevin houston

[gray gazelle]

Like a technical book or non-technical book?

[sullen loom]

i'd say a beginner-friendly technical book would be best, but i dont mind non-technical reads too

[gray gazelle]

Maybe How to Prove It and learning "Lean" at the same time

"Lean" is a new form of computer proving that is very formal, even by pure math standards and it might be our future, there is currently a project to reprove all of Mathematics in terms of Lean; thus, guaranteeing they are True with a capital T

https://www.youtube.com/@xenaproject

[pale summit]

I am fond of "Proof and the Art of Mathematics" by Joel David Hamkins for more on proof writing and general conversations about different math subjects. It's what I used when I took a proofs class.

[grizzled flume]

"All the mathematics you missed"

[sullen loom]

ooo thank you for the suggestions! i'll check them out

[grizzled flume]

I can't even solve a simple math book given by my college i suck

[pale summit]

no such thing! you just process things differently, doesn't mean you suck 🙂

[gray gazelle]

What does this mean?

[grizzled flume]

U see i am in a board that gives out standard math book for basic concepts

And i can't solve them 😔

[gray gazelle]

By the way switch roles from pre-university to undergraduate since you are in college

[grizzled flume]

Uh no i am not ug

[gray gazelle]

I'm confused

[grizzled flume]

I will be next year here they use "college" for grade 11,12

It's local slur

Sorry

[maiden halo]

I haven't finished it but I like "Reading, Writing, and Proving" by Daepp & Gorkin

[foggy relic]

The springer sale is massive, so many books are $16.99

wtf

[safe lintel]

Can anyone recommend me a good book on trigonometry? I have a basic understanding of it, but I'd like to go deeper and build a solid foundation

Is the one by I.M. Gelfand recommended?

[heavy pelican]

russian; always recommended

always read the russians

[gusty smelt]

gelfand is also a top tier mathmetician and the founder of my field basically lol, I know he wrote some elementary textbooks so I'd guess they are good

[slender crown]

Imo fs

[vague granite]

wym

[slender crown]

IMO

lol

[gray gazelle]

Is your field Operator Algebras or NCG?

[gusty smelt]

operator algebras

[gray gazelle]

Nice

[gusty smelt]

wbu, you interested in operators?

[gray gazelle]

I'm interested in its role w.r.t to QM and then with NCG and QFT but I'm still at Rudin I

[gusty smelt]

haha i see, yeah its very rich and connection to physics are very nice

feel free to ping me if you ever want resources or to talk about operators/ncg

[gray gazelle]

You're already learning NCG as a 3rd year student :0

Nice

[gusty smelt]

oh yeah my website is a bit outdated oof

I will be a grad student this upcoming fall

[gray gazelle]

Congrats for getting accepted

[gusty smelt]

Idk how much NCG I will be learning as my grad school does other stuff in operators mainly, but I do want to go through connes whole book at some pt

[vague granite]

not quite yet lol
going for MOP this yr tho

[slender crown]

sheeesh

i need to network u with someone lol

[vague granite]

who

[dark plinth]

I need to learn some stochastic calculus

[gray gazelle]

same

tf is a sigma algebra

[remote sparrow]

lower than an alpha algebra, higher than a beta algebra

generally a "lone wolf"

[gray gazelle]

yeah they're also socially competent but choose not to associate with people

[fierce hedge]

What Russian books have you read? By any chance have you read Zorich?

[hallow oriole]

is the typesetting in concrete mathematics when read on pc weird for anyone else?

or is that just the used notation

[gray gazelle]

hm haven't tried knuth's book

[remote sparrow]

are you reading from an epub file or some other non pdf format?

[hallow oriole]

it's a pdf

[alpine rover]

Can anyone recommend some introductory analytic number theory texts other than Apostol?

[wispy bison]

what is the consensus on judson’s book?

[fierce hedge]

I really liked the book but it's an easy read like too easy at times

and the exercises are similar, rarely you'll find them difficult

[fierce hedge]

@heavy pelican

[heavy pelican]

Oh whoops, thanks for reminding me, forgot to respond.

I have not read Zorich. I like to read Arnol’d a lot. My field was started off by Russian mathematicians so I read them almost all the time.

I also taught myself calculus from Piskunov in high school. In fact, now that I think of it, my interest in mathematics was sparked by a couple of popular math books by Ya. Perelman

Ah, and Fomin-Genkin-Itenberg is a classic for the high school level

[fierce hedge]

Wait, is it THAT Perelman? Destroyer of Poincaré conjecture?

[heavy pelican]

No, very different Perelman

That one’s Grigori

(or Grisha)

[fierce hedge]

Ah, okay

[nocturne hull]

Which maths book that is relatively cheap (not text book, more just book) goes over the very very basics up to basic integral and differntial calculus of one variable and introduces differential equations. i really want to learn a good amount before i start doing higher level mathematics. Thank you all ❤️. I had a look at #books-old and I didn't find anything that was within my price range or really what I was looking for or the type of thing I was looking for.

[gray gazelle]

Apostol - Calculus
Legally free online.

[civic python]

You can find most math books free online.

[fierce hedge]

The secret ingredient is crime

[atomic hemlock]

It's only a crime if you live where it's illegal 👍

[fierce hedge]

It's only a crime if you get caught

[fierce hedge]

any good books intended for college level (ug/grad) mathematics?

[worthy venture]

Mathematical methods for physics and engineering

Fav book imo

It’s just a collective handbook so it covers everything noteworthy and explains it well but doesn’t explain it thoroughly. Like no proofs

It’s free online

Legally free

[fierce hedge]

Who's the author?

[worthy venture]

Riley, Hobson and bence

[dense summit]

algebra 2 books to do over summer

can someone recommend algebra 2 books to do

[heavy pelican]

try arnol’d’s classical mechanics or intro to odes.

any specific field?

[fierce hedge]

I know Zorich for analysis, Viro for topology so maybe something for algebra?

[heavy pelican]

i remember you not liking Artin, so trying to think of something else

[fierce hedge]

Wait what, M Artin was Russian!??

Wasn't he German mathematician

[crimson leaf]

Artin was German

and his father Austrian

[heavy pelican]

oh you specification want Russian authors?

specifically*

[fierce hedge]

Not really but I thought that was the context imo

My bad

[heavy pelican]

Armenian I think

[ocean mulch]

Michael Artin?

Yes, he's German-American

Son of Emil Artin, iirc

[ocean mulch]

Gotta specify the field, otherwise I'd say National Library of Congress

[heavy pelican]

It’s funny, the Armenian names usually end in ian, eg Levon Aronian is an Armenian chess grandmaster. By that logic, his name should be Artinian

And Artinian rings should be called Artinianian rings

[crimson leaf]

He was born in Vienna

[heavy pelican]

Ah OK Armenian descent though

[crimson leaf]

Yes from his father

[maiden halo]

Artin grew up in the US

[fierce hedge]

Honestly I am open to any field, send me anything interesting in pure maths or cs related. No physics though.

[ocean mulch]

That'd still be tough

[crimson leaf]

What's your background though

[sage python]

Problem is you're ready to learn at most finitely many fields

[fierce hedge]

Thanks dami very cool

[ocean mulch]

I can give you enough books to read for the next six months, but that won't do any good.

[fierce hedge]

Completed 5 years of maths (masters in maths)

[gray gazelle]

What can I talk about math..um..

[sage python]

I'm phrasing it tongue in cheek but the intent is clear

Could send you a book on linear algebraic groups

[ocean mulch]

What would you consider to be interesting?

[sage python]

You're prob not ready

So that would be a waste

So what's your background? Do you have proof-based math? Calc/analysis? Linear algebra?

[ocean mulch]

Some ppl like non-commutative alg, but it disgusts me, so...

[ocean mulch]

with a MSc in Maths, I think he is ready

[fierce hedge]

Total 15+ maths courses

[heavy pelican]

read algebraic geometry from Shafarevich

cool book

[sage python]

That means nothing to me. Calc 1-15? 1-12th grade math + 3 classes?

[fierce hedge]

You asked for it Dami

I have done an Integrated masters (3+2 years) in mathematics. I have taken courses in
Algebra - Group Theory, Linear Algebra, Field Theory, Rings and Modules, Commutative Algebra
Analysis - Real Analysis, Metric Spaces, Complex Analysis, Numerical Analysis, Functional Analysis
Calculus - Calculus of Several Variables, Geometry of Curves and Surfaces
Prob and Stats - Probability Theory, Statistics, Lebesgue Integration, Introduction to Stochastic Processes
Discrete maths - Discrete mathematics, Graph Theory, Algebraic Graph Theory
Topology related - Topology, Algebraic Topology, Introduction to Manifolds
Others - Differential Equations, some Theoritical CS courses
And few Chemistry, Biology and Humanities courses + 1st year common courses

It's certainly a very different question of how much I remember from it xD

[ocean mulch]

The thing with CS is there's no good book that is in depth...

[fierce hedge]

Fair enough

[ocean mulch]

I can recommend cryptography, that's the most math-y it can get, but I didn't learn it from any books, so..

[fierce hedge]

I wanted to revisit differential equations and introduction to manifolds

[crimson leaf]

You should check out Analytic Combinatorics

[fierce hedge]

Umm.... Ramsey Theory?

[fierce hedge]

Or is it something different?

[heavy pelican]

necessarily russian author, or russian-minded will suffice?

arnolds ode book is great but personally i prefer smale-hirsch. super concrete and lucid

intro to manifolds, quick and dirty is milnor

[crimson leaf]

Different it's more about enumerations and combinatorial classes very generating function oriented

The second part dives in to getting asymptotics using complex analysis

[ocean mulch]

Don't forget Pollack, although i think it's too basic now.

[fierce hedge]

Any would work

[fierce hedge]

Is this a book or do you have any recommendations especially cause I might not have the necessary prerequisites on generating functions.

[crimson leaf]

It's a book if you wanted to learn about generating functions you could probably read like bona or something there's also generatingfunctionology which is good but a different approach to generating functions

Both generatingfunctionology and analytic combinatorics are free online

[fierce hedge]

Noted

[crimson leaf]

If you wanted to algebra instead (you seem pretty into that) I would recommend Lie Algebras by Erdmann if you're not comfortable or if you are comfortable Humphreys Lie algebras and rep theory

[fierce hedge]

I originally wanted to do algebraic topology and category theory after which I'd jump into Homotopy Theory but I'm not very sure about that route.

There's very few people in India who do Homotopy Theory in maths

[ocean mulch]

Oh, almost forgot. Galois' dream by Michio Kuga. It's a hidden gem, great for advanced undergrad and grad. I can say I learn the basics of differential Galois theory from there. He introduced everything necessary to study Fuchsian differential equations.

It's a great invitation to how modern theory for diff eq works.

[fierce hedge]

So many things to study, so little time

[ocean mulch]

I guess 1-2 months can give a pretty good hold of a topic.

You can always study something on demands in a short time. That's what a Math degree is for.

[fierce hedge]

I'm trying to get into grad school, self studying that too in home is difficult

[ocean mulch]

self-studying is always difficult. Doing it long enough, and you'll get better at it

[finite gale]

the nice part though is that you get to go at your own pace

[ocean mulch]

As I said earlier

[fierce hedge]

Earlier? You mean like more than a week back

[crimson leaf]

Yeah you can always jump around too which is nice do what you feeling like doing on any given day

[ocean mulch]

These are my quotable words

[loud gull]

soft question: would anyone be able to comment on the difference (if there is any) between the levels / maturity expected of Leinster's basic category theory and Riehl's category theory in context?

[stray veldt]

riehls book tells you in the introduction, so just read that?

not familiar with the other book

[loud gull]

I've read the first 3ish chapters and feel a bit overwhelmed so I am thinking about reading a bit of Leinster to try to familiarize myself with adjoints

[heady ember]

Wtf i thought you were just a random , when did you get a masters

[heady ember]

That's set theory

[mossy flume]

I would argue that Riehl's book, to be appreciated, requires more maturity than people give it credit for

It's in context but that context is useless unless you've seen a good portion of those examples

[orchid mortar]

Yes including PhDs

[brazen flax]

god imagine reading books

books are for dumbasses

[weary cape]

I got this recommendation too lol. Haven't checked it out yet but it looks more promising than the one I have right now (Matrices and linear transformations by Cullen)

[thorn cloak]

[weary cape]

Interesting and yeah I think you recommended that one iirc

[weary cape]

Ur sounding like Tate

[inner token]

Imagine having so little to do

[weary cape]

Me rn. But I am excited for the calc 1 I am about to take in a week

I was going to buy the Hefferson's lin alg book but then I was like "hmm.. Imma save my money" and here I am with 3 more books all on real analysis I have ordered with Abott's one just arrived.

What's the difference between Understanding Analysis 1st ed and 2nd ed?

[inner token]

I love that book

Abbott

[weary cape]

I like the newer cover honestly but the contents seem the same other than maybe more exercises and stuff

[inner token]

Nothing beats it as a first pass at analysis

Love all the motivation and historical background

[weary cape]

I hope it gets me ready for analysis. I'm not taking analysis for a while though.

[inner token]

It will for sure

You said calc 1?

[weary cape]

Yes then hopefully (if I feel ready enough) calc 2 in July

When does one take analysis?

Or real variables

[inner token]

Usually after 3 semesters of calc

[remote sparrow]

usually after calculus after an intro to proofs type class

some places let you take it straight after calc

[inner token]

And possibly a basics class

[thorn cloak]

trying to grind the book in two months b4 my rudin based intro to analysis 😅

[weary cape]

For proofs I bought "How to prove it" and skimming through it gave me a headache 😥

[inner token]

I think that's plenty of time on that book

[weary cape]

Gl I heard so many good things about baby rudin

[thorn cloak]

i hope i hope

[weary cape]

How does one know they are ready for real analysis?

[thorn cloak]

yeah im a bit excited cuz of the rigor and challenge. im just a bit scared since its also my first proof based class

[weary cape]

I'm hoping to get through calculus by this year and maybe even basic proofs

[inner token]

The exercises in rudin are fun

[thorn cloak]

i am a bit curious, how long should i expect each problem to take? 2ish hours each?

[inner token]

Hmmm I'm not sure. I signed up for the class and it was sink or swim I guess

[inner token]

Some you'll get right away, some might take a day or two

You'll find that analysis proofs have a certain flavor. You'll gain intuition on the steps you should take

[thorn cloak]

very interesting. it seems so cool to take a fully rigorous class where nothing is taken for granted

[weary cape]

Uhh 😭

[remote sparrow]

rudin is a very commonly assigned class text, so full solution manuals on the internet exist

nowadays if you aren't at a super high-tier uni or taking honors analysis, i don't think rudin is assigned so much

maybe abbott or bartle and sherbert are class texts

[inner token]

You'll be fine. You only sink when you give up

Sour drop knows every book

[thorn cloak]

i suppose so but i also feel like part of the class is struggling until you get it. I wanna avoid looking it up but at the same time deadlines... I just hate the modern education system lol

ye my class is honors

idk what the non-honors uses

[remote sparrow]

don't expect to know everything in your class even by the end of the semester

[weary cape]

I've actually stated on a different channel here but I was going through ENT and I had a lot of difficult + felt like I should focus on calc and analysis first so I ditched that book and started reviewing for calc.

[remote sparrow]

it's normal to not know everything

grades are usually inflated in high school, so you get the sense that you actually know stuff when you've gotten easy As much of your life

[thorn cloak]

yeah thats true. doesnt help exams are mad easy too

it just hurts my pride to get a poor exam grade and have it curved up

[weary cape]

I get that how usually I learn more about the previous topic while learning that specific topic

[thorn cloak]

doesn't feel like i earned it. I had to kinda come to terms to it last semester that the days of 100's are gone

[weary cape]

I never focused on grade during hs so I want to change that for college

[remote sparrow]

you can read How to Think About Analysis by lara alcock to help orient yourself for real analysis

[weary cape]

I think I saw that but for complex analysis

Or category theory..idk

[remote sparrow]

lara alcock only has books giving advice for math majors in general, analysis, and algebra

[weary cape]

Love the cover on that one

[remote sparrow]

maybe you're thinking about Visual Complex Analysis by tristan needham

[weary cape]

Probably but I did come across that book as well I just...didn't buy it for some reason?? lol

[crimson wolf]

just bought this. i hope it's good 🙂

[weary cape]

I see its 10 on ebay and free shipping too but also my wallet is at a 0 so Idk

[remote sparrow]

people generally regard this as a supplement rather than a textbook

just fyi

[crimson wolf]

hmm interesting.

[weary cape]

For supplement, I actually bought (idk if this helps)
"Introductory mathematics: Algebra and Analysis"

It said analysis and the chapters seem good so I gave it a go

[crimson wolf]

I don't think the supplement thing makes sense tbh. It has soooo many ratings on amazon. There's not that many people buying supplementary material lol.

[weary cape]

Oh no people buy supplementary material absolutely

[remote sparrow]

https://people.bath.ac.uk/masgcs/book1/

this book has a website to go with it

[weary cape]

Might not be intentional but it really helps especially for people like me who flipped through the pages of Understanding Analysis and feeling like they should start at square 1.

[weary cape]

Amazing thx

[remote sparrow]

yeah this looks like one of those intro to proof type books

[weary cape]

That's exactly what I was looking for so good

[remote sparrow]

in the vein of How to Prove It by velleman

i've recommended hamkins' intro to proof before as well

[weary cape]

Have this one

[coral prawn]

ah damn that book

[weary cape]

It's the one that "looks" hard for me and gave me headaches just flipping through

[coral prawn]

it's pretty swell

[weary cape]

You had a hard time with this book as well?

[remote sparrow]

gets the job done

[coral prawn]

that's why you shouldn't "flip through" and go through the book page by page?

[coral prawn]

a bit, took a while for me to digest, but still doable

nothing too difficult

[weary cape]

Flipping through the book to see whats ahead is not a bad idea, I do that with all books and in a sense gets me seeing what I am up with

I'm working through it rn

[coral prawn]

it is if it's gonna demotivate u and make u just give up starting in the first place

[weary cape]

Well it looks intimidating, but if I would have given up I would already and not have signed up for a major in math.

It works for me, do what works for u

How do you guys go through math texts?

[heady ember]

I didn't say that

[orchid mortar]

Should have said yes

[remote sparrow]

you're a random until you get a phd

you're a random until you earn tenure

[orchid mortar]

random until become named professor

random until featured article on Wikipedia

[smoky zephyr]

that last one though

[coral prawn]

you're random until you've won the field's medal

[cinder mist]

recommend me a small book to understand graduate level probability. it better to it contains example, not only formulas

[heavy pelican]

durrett

[orchid mortar]

I don't recommend small books

[halcyon garden]

Maybe you could benefit by learning some things that your curriculum missed, say : PDEs, Rep theory, Category theory, Algebraic geometry, Riemannian geometry, Algebraic/Analytic number theory, Dynamical systems (maybe ergodic theory in particular since the field is too vast), Geometric group theory, Fourier Analysis, Set theory and logic.

Although once you're done with the basic curriculum I think it's more profitable to focus on learning grad level material on specific topics you found interesting and then to get an advisor who can get you started with research

[fierce hedge]

I mean yeaah but like I don't wanna spend my entire life only studying. Also there's a whole list of courses. Maybe something focused would be better but again the thing is that I'm not pretty sure on what I wanna do 🤷‍♂️

[steep badger]

that's always the hard question. better will be you start working on something and then get deep into whatever comes.

[old elk]

What do you think of Stefan Waldmann's Topology book?

[languid pivot]

Whats a good beginner calculus textbook

[gray gazelle]

stewart

[marble solar]

I'm partial towards Thomas' University Calculus

[old elk]

I calculate stewart, the best real analysis you can find is from the author elon lages lima, he explains the demonstrations with plasticine

[gentle seal]

are stewarts calculus books overrated?

[gray gazelle]

yes but you should still use them

[gentle seal]

bro do you know how expensive they are

[rapid lily]

The Stewart calculus book looks way too long though

[heady ember]

“bro who says you have to buy them to use them”

[gentle seal]

casually searches up the book on a illegal website

Honestly I found the 7th ed on 45 bucks used, might buy it tbh

[inner token]

I copped an old edition used on thriftbooks.com

[gentle seal]

What are some great pre algebra books?

[cerulean cypress]

tbh use any books for that subject

[gentle seal]

why

[smoky zephyr]

<@&268886789983436800>

[finite gale]

They all cover the same material in roughly the same manner, so which text you use doesn't really matter; also, you can use khan academy if you want

[gentle seal]

Already completed it on khan academy; just want to go over everything again to make sure I know everything

But thanks for letting me know

[finite gale]

Honestly grade school math goes in circles so much it is probably fine to just go on with whatever is next and you'll almost surely encounter the materials you've already practiced on again as "new" material; or at least this was what i remember of my experience

[gentle seal]

yeah

[worthy venture]

any recommendations for vector calculus

ive taken the course but im intrested in taking a deeper dive.

[rich sun]

how deep

[worthy venture]

i havnt done proofs and i wouldnt say im intrested in that

but as deep really

practice would be good to

[sonic stag]

What book should I read for multidimensional geometry and polytopes and all that stuff

I really like the format of topology without tears, so it’d be great if it was written like that

[rich sun]

Hmm, my standard recommendation would be Spivak's Calculus on Manifolds or Jänich's Vector Analysis, but if you're not interested in proofs (and more in computations and applications), maybe you can take a look at Keenan Crane's lecture series on Discrete Differential Geometry.

[worthy venture]

alright thank you

mabye ill look into proofs if that what math develops into

[worthy venture]

is it really around 160 pages long?

[rich sun]

Calculus on Manifolds? around 140 pages

[worthy venture]

bet bet

[gray gazelle]

I mean if you want an intro to proofs "How to prove it" by daniel vellman is the one of the best

[past tiger]

i want to be a mathematician from self study, so can someone tell me best books to be mathematician

[coral prawn]

Frfr

[worthy venture]

ill check it out

[coral prawn]

Depends on your current status, as in what you know, what you're familiar with, what are your interests

[past tiger]

i just finished high school

[coral prawn]

That's not clear enough, it also depends on what you've covered in HS

[past tiger]

and i really love calculus and i want to be a theoretical physicist

[past tiger]

i just want to start from very beginner no problem

like form pre-algebra to finish

A-Z

[coral prawn]

Then start off with khan academy

It's an online learning platform with a buncha math courses

[past tiger]

ok but how i will get exercises to solve

i already watching someone called professor leonard at youtube

so how i will get exercises to solve

[coral prawn]

They have exercises on the learning platform

[past tiger]

ok but it is not hard i saw it is just very easy

[coral prawn]

Then just do the more advanced topics

It all the more means that it's too basic for u then

[past tiger]

ok but they have like 5-10 problems max and it is not enough

[coral prawn]

They have more, just look at the course test. And if it's still not enough u can repeat, or look at wolfram problem generator

[past tiger]

ok, but is it better to see workbooks for the topic i take?

[coral prawn]

For simple topics like that books aren't necessary, though if you really wanted just look for a highscholl textbook

[past tiger]

ok but topics for advanced algebra, calculus

[coral prawn]

Then you should reference books, which book exactly depends on 1. Your preference, 2. The depth u wanna cover, 3. Your current prerequisite knowledge and a few other factors, but if you wanna "start from scratch" there's a long way to go, so no need to worry abt it for now

[slim bramble]

you can start studying one of uni calculus books and if you stumble somewhere and find it hard to understand try studying it using online resources like khan academy and such and by the time you go through half of the book you'll probably get a sense of what's out there and how much you know

[wooden elbow]

Can someone recommend a good book series for me

[slim bramble]

I'm not sure though what book to recommend if you decide to do so you can ask for calc books suited for high school grads

[finite gale]

if you just finished high school and have done computational calculus to some extent, i would say start with linalg or some proof-based calc book (e.g. spivak)

[coral prawn]

What types of books are u looking for

[coral prawn]

Seeing how they wanna start from scratch? Eh idk if they've done calc in sch

[slim bramble]

isn't spivak too hard, shouldn't study proofs before it?

[finite gale]

i think it's a good introduction to proofs tbh

it shouldn't be too bad

and usually people use calc/analysis to introduce proofs anyway i think

[coral prawn]

Some intro to proofs would be nice to complement ig

[slim bramble]

idk about him or you but i only felt comfortable going through spivak after studying how to prove it by daniel

[coral prawn]

XD it is really tough for me, I'm doing both at the same time rn

[slim bramble]

yeah me too😅 the structure how to prove it gives you really helps

[coral prawn]

That book's pretty swell

[finite gale]

i wasn't really ever formally introduced to proofs honestly, i kinda just picked it up as i went in high school

[slim bramble]

💯

[coral prawn]

LOL SAME

[finite gale]

but there isn't really much to pick up to write proofs i think

[wooden elbow]

Fictional

[coral prawn]

I literally just went with my intuition of what's a proper proof

And then tried to see if I could destroy my proof

That is to say, attack it and point out some error

[slim bramble]

yeah i can see it if someone reads a lot of proofs

[crimson hearth]

I just watched a bunch of Michael Penn videos on competition math to pick up proof techniques xdddd

Not that I'm any good at competition maths anyway

[turbid mural]

book recommendations for grad PDEs

[slim peak]

Brezis

[turbid mural]

👍

[remote sparrow]

evans is a common choice

[sonic stag]

bump

[past tiger]

i am just starting calculus can someone recommend me an amazing book

[remote sparrow]

do you want the book to emphasize proofs or not

[past tiger]

yeah

[remote sparrow]

are you saying yes proofs or yes for less emphasis on proofs

[past tiger]

yes proofs

[remote sparrow]

spivak or apostol

[past tiger]

wtf idk i just wanna book

[vague granite]

theyre both books

lol

author name

[past tiger]

anyway

i saw the stewart calc book but it is explanation it doesn't make sense for me, so can someone tell me a calc book has good explanation for beginners?

[thorn cloak]

i mean Stewarts is like the easiest it gets. Perhaps try supplementing it with khan academy or yt but sometimes it takes effort and time to get it

[lime sapphire]

try pauls online notes for calculus

[dense summit]

anyone know highschool algebra 2 books i can do over the summer because im taking the class next year

i already refreshed everything ive leanred in algebra 1

ive also started looking at unit circle graphing sin cos tan and polynomial graphing and divison

i also looked at logs and exponential graphs

[finite gale]

imo high school algebra 2 shouldn't exist

there's literally 0 difference between high school algebra 2 and precalculus

[dense summit]

but i mean i still have to do it

[finite gale]

yes

so just find a precalc book and use that

[dense summit]

are u sure?

what precalc books should i get then

[finite gale]

any really, they all cover the same material

generally speaking, book for computational calculus or before are pretty much the same thing

ok i worded that terribly, but within each topic

you can also just use (or supplement) using khan academy as well

but if you find it too hard, you can go back to algebra 2 i guess

[dense summit]

so i should just do pre calc on khan academy?

[finite gale]

you can, or if you prefer a book to read through, any should be fine

i can try to find what book i used for precalc, which was fine as i remember, but it really shouldn't matter much

[dense summit]

alright

[clever pier]

Pre-calculus books tend to cover a lot in a short amount of time though. It's never as thorough as say a proper book on a subject.

[dense summit]

wdym

[finite gale]

iirc the lessons in precalc were almost identical to those in algebra 2, or at least they were when i had it in high school

but that said, i also didn't really pay attention in either class

[dense summit]

ok

[finite gale]

i just remember doing the entire week's worth of homework in precalc class lol

[dense summit]

dang

i dont think i can do that

[clever pier]

James Stewart - Algebra and Trigonometry. That's my book recommendation.

[dense summit]

ok ty

[dense summit]

wait is it supposed to be 300$

[clever pier]

I'm not saying you can find books for free using Google but you just might.

--> trigonometry filetype:pdf

[dense summit]

so i should look for a digital version

[clever pier]

Physical textbooks are expensive. Heck, even digital copies are expensive.

[dense summit]

yeah

so wherre should i look?

[clever pier]

Google

Google --> stewart trigonometry filetype:pdf

Hmm, no hits.

[dense summit]

yeah you still have to pay for those

someones selling a used one for 30$

maybe ill get that

ty for your help i bought it for 30$

[hallow oriole]

hi!

[austere zephyr]

Hello

[hallow oriole]

maybe not this

in chat

[austere zephyr]

Y'all should read The Silmarilion if you hate yourself

[hallow oriole]

it's very much not allowed

but you can put it in dms!

(dm me and i'll tell you where to get a link)

[remote sparrow]

this book is near identical to his precalculus book iirc

[gray gazelle]

you should NOT go to library genesis and you should NOT type the book you want there and YOU should not click the GET button. I repeat DO NOT DO THAT

[fierce hedge]

The super reaction is basically her head getting exploded into multiple copies, wild

[finite gale]

[coral prawn]

for once a super reaction that fits the emote

[wicked merlin]

Hi i just need help to find a book for analytic geometry from like no knowledge to collage lvl

[lime sapphire]

collage level is going to be hard to find

look at one of the early chapters of moise’s calculus

[naive ridge]

https://www.youtube.com/watch?v=H6XejQOsfBY&t=36s

[bitter path]

I'm interested in self-studying real analysis/advanced calculus, but haven't taken an introductory proof-writing class yet. Should I just read a real analysis textbook, or should I just find a book or some class notes on honors calculus (e.g., Pete Clark) so that I can be exposed to writing proofs and some form of analysis?

[weary cape]

I got 5e used for 25

[weary cape]

I'm in a similar position to yours but I decided to read through a proofs book first and mastering that first before going into analysis. I have Abott's Understanding Analysis and I just read the first few sections but I don't feel ready yet.

Also, someone recommended "How to think about analysis" for analysis-prep

Which is now in my buy next list

[sonic stag]

whats the best book for studying multidimensional geometry or polytopes

[gray gazelle]

what are some good boolean algebra books that cover as much of it as possible?

[ocean mulch]

You should know basic proof techniques, (strong) induction (over multiple indices), contradiction, contrapositive, etc.

But at the end of the day, it only goes so far. If you're good with it, I'll say go with real analysis textbooks, and rewrite the proofs, especially if it's your first time.

Real analysis' proofs are most accessible imo

[bitter path]

Hmm, I think Clark’s notes go over induction and strong induction, so I’ll just review his notes and supplement it with other analysis books then. And thank you for the tips 🙂

[cobalt arch]

Any books that have a comprehensive account of properties of functions?

[flat thistle]

best geometry book?

[ocean mulch]

Euclid's Elements, easy

[flat thistle]

i supposed so, but a friend of mine told me it was going to tell me more about Euclid than its science

[lavish radish]

I have this book “calculus with analytic geometry” by Murray Protter and Charles Morrey Jr. from 1965 and I’m wondering if it’s a good book. I have a 75 year old retired colonel who graduated with an organic chemistry degree and something else. He has tons of books from accounting to thermodynamics and advanced engineering mathematics

He wants me to choose some books to take home and study at a later date

[worthy venture]

Any suggestions for a deep dive into the math behind data science? Furthermore, a deeper dive into statistics/probability and it’s application? Ive only taken the first year course for stats so I’m not well versed with what to expect. Pls pin when u suggest a book

[crimson leaf]

An Introduction to Statistical Learning it's totally free online, right now it has applications in R but they're coming out with a version (I think this summer) that does python instead

Once you get more math you could probably for Elements of Statistical Learning.

[worthy venture]

Bless your heart

Thank u

King 👑

[gray gazelle]

[1] Ian Goodfellow, Yoshua Bengio, and Aaron Courville. Deep Learning. MIT
Press, 2016. http://www.deeplearningbook.org.
[2] Gareth James, Daniela Witten, Trevor Hastie, and Robert Tibshirani. An
introduction to statistical learning, volume 112. Springer, 2013.
[3] Sheldon Ross. A first course in probability. Pearson, 2010.
[4] Sheldon M Ross. Introduction to probability models. Academic press, 2014.

These resources were cited in the lecture notes of my intro to data science class

meant to reply to @worthy venture

[worthy venture]

Thank u my lord

[heady ember]

You mean loch's summary of intro to proofs? I don't think Clerk has one right

Oh opps nvm I guess you're not referring to , got confused for a sec

[lavish radish]

Hello?

[rapid lily]

I've never used this book before, but after skimming through the book it looks like a good introduction to calculus.

Yes it is. Most well-known analysis books will be good.

[tawdry steppe]

My calculus prof gave us a proj for finals about integrals. He told us to make example questions for the first 100 rules of integrals in the table of integrals. I was wondering of there are any resources that go in depth. Thank you

[hasty turret]

Why are there >=100 rules of integrals

[tawdry steppe]

I'm not sure. He just said that there are about 300 rules in the table of integrals

[fierce hedge]

There's no way that's true

[rapid lily]

What is the table of integrals?

[tawdry steppe]

I cant send a screenshot here

[rapid lily]

Ok you can send it in a message if you would like

[tawdry steppe]

Ok i'll send you a message

Can anyone recommend me a calculus book with a really good explanation about integrals?

[sinful locust]

Hi, is there any books that focus on solving nonlinear equations?

[untold eagle]

Like ? ax² + bx + c = 0 ?

[sinful locust]

No not like that

Crazier equations with square roots and terms that is a degree of 2 or even higher

[untold eagle]

oh hmm Problem solving books ?

[sinful locust]

Yeah that's good too

[untold eagle]

The volume 1 is really good learn you by doing problems

I just started out and I really like how fast and good the explication is

[sinful locust]

the name of the book is Problem solving?

[untold eagle]

The Art of problem solving: Vol 1

i don't know if it could help you into these equation but it will certainly help

[sinful locust]

I'll check it out thanks

[wooden elbow]

Is pre college maths a good book for a 15 yr old

[lime sapphire]

is there a book that transitions from like calc 2 to more and more integration techniques so you can prepare for integration bees and the sorts

[velvet gyro]

Does anyone have some good recommendations for an introduction to Clifford Algebra?

[heavy pelican]

Lawson-Michelson could be a good one

But it depends on what you want to do with them

[velvet gyro]

Thank you, I’ll check it out

[velvet gyro]

Hm, in which sense? I honestly only know very little about it, but I’m interested in this topic since it appears to generalise many concepts across different branches of math. I know it also has applications in physics, for example, it simplifies concepts in GR and QM, but I’m mostly interested from a pure math perspective

[heavy pelican]

Fair enough, I think you’ll gain from Lawson-Michelson then. Some people care a lot about them from the algebraic POV, say from the perspective of central simple algebras.

https://people.math.ethz.ch/~salamon/PREPRINTS/witsei.pdf chapter 4 of these notes might be a consolidated resource also

[velvet gyro]

It does seem helpful, thank you

[wheat urchin]

Bertrand Russell was a mathematical author.

[past flax]

Could someone suggest me a book for calculus?Like the best one I can get(pdf)

[jovial parrot]

idk abt pdf but i used the ap calc prem

is beach & blair's abstract algebra any good? it looks like it was published in 2006 so idk.. anyone got any beginner abstract alg recc?

[remote sparrow]

undergraduate material does not change much in the span of 17 years

my friend used beachy and blair and he likes it

bit on the expensive side but it's used as a course text by one of the professors at my college

[jovial parrot]

ah alr

do you know any cheaper?

[remote sparrow]

pinter or judson are good

[jovial parrot]

$102 aint in my budget lol 😭

oh ok

[remote sparrow]

judson is also available free online

[jovial parrot]

so is pinter

[remote sparrow]

well, i mean legally

[jovial parrot]

lol

[jovial parrot]

its from uni of mayland, i assume its legal

[remote sparrow]

did you just do a google search? sometimes people host random books online

doesn't mean it isn't pirated

[jovial parrot]

ye i did

[jovial parrot]

ig so

[mighty reef]

I think Calculus by Stewart is a good book to learn the basics https://www.fd.cvut.cz/department/k611/pedagog/K611GM_A_soubory/GMliteratura_soubory/Stewart_Calculus_6ed.pdf

[heady ember]

Piracy ftw

[tame sphinx]

I need an internet obtainable book, which is a very easy and beginner friendly introduction to fourier analysis... I'm only gonna be using R^n as my domian (or what it's called), I don't need hausdorf spaces and such.

[heady ember]

I mean, you can find pdfs of just about any book on the internet

[tame sphinx]

I found one recommendation, but I could not find it online, even difficult to find to buy

[heady ember]

If you know where to look then it becomes easier

There are... creative ways to get the PDFs

But piracy is against discord tos so you totally shouldn't do it

[tame sphinx]

yes ofc, I would never do such a thing

but suppose I do know where to find such things... then maybe, hypothetically, it's not there either

[fierce hedge]

Which particular book are we talking here?

[tame sphinx]

fourier analysis by baggett and fulks

[fierce hedge]

No luck for me either

This is the second time I didn't find a book on the sites

[west zenith]

Book recommdation in every topic of physics in which I can find only solved examples of various topics and then the practice questions

I am having schaum series but they are having less solved examples

[gray gazelle]

anybody knows books/sites with difficult exercises on trigonometry?

[hollow glade]

no

[wintry quartz]

Hi

could I get recommendations for linear algebra books that deal a lot with the dual space and the adjoint

[wintry quartz]

103 Trigonometry Problems by Titu Andreescu

[gray gazelle]

thanks

[wintry quartz]

the book is at an USAMO/IMO level

[fierce hedge]

Not sure but almost all proof based linear algebra books should deal with dual spaces and adjoints

check pins for proof-based LA book recommendations

[wintry quartz]

I was hoping for this type of treatment of the subject

#linear-algebra message

I know that LADR doesn't really do anything like this \

neither does hoffman and kunze or friedburg

is Artin good for this kind of treatment?

or roman?

[subtle mango]

hoffman-kunze does cover dual spaces

see chapter 3

adjoints are as well, see chapter 8

[wintry quartz]

yes but it doesn't treat it like in the question

[subtle mango]

ah gotcha

[fierce hedge]

that's seems needlessly super specific

[subtle mango]

could always just ask the person what textbook it's from

[wintry quartz]

its exercises from course notes

[wintry quartz]

I see

maybe a more abstract coordinate free exploration of LA?

[subtle mango]

maybe Aluffi's Algebra 0 would suffice?

haven't read to the lin alg part but it's super abstract

category theory focused, treats lin alg in the context of modules and whatnot

[wintry quartz]

thats a bit too advanced for me unfortunately

I suppose my response are a little contradictory

[gray gazelle]

what are reccomended things to know for the advanced problems(they seem really hard)? and should i read the book or just jump to exercises?

[wintry quartz]

tbh I have never done the problems

But I would imagine being fluent in geometry and trigonometry is the first step

[gray gazelle]

analytic geometry i suppose?

[wintry quartz]

that too, but to a less degree

[gray gazelle]

what about reading chapters before doing exercises is it reccomended there are many things there but idk

[wintry quartz]

it is

because they'll prolly introduce a thing you might have never used/seen before

[viral sundial]

Book recommendations for studying mathematical analysis for the first time. I just finished High school and am thinking of trying either mathematical analysis or abstract algebra (or perhaps both)

So, any good books.

[chrome yacht]

either tao vol 1 or amann escher vol 1

[wintry quartz]

you know any calc?

[viral sundial]

I've taken IB AA HL math, so there is basically all the calc I have taken

[wintry quartz]

(if so understanding analysis by abbott is pretty good introduction)

[chrome yacht]

if you're looking for a more advanced text for linear algebra than axler then there's greub, or kostrikin-manin

[wintry quartz]

https://link.springer.com/book/10.1007/978-1-4684-9446-4

this one?

[chrome yacht]

yep, i did the first couple of chapters and enjoyed it, covers all the abstract algebra prereq you will need at least until then, don't know how it is after that so there's that...

[wintry quartz]

so its good for after LADR?

cuz I see some scary looking chapters lol

like what is "Gradations and homology"

[gray gazelle]

why math books are so expensive damn

[wintry quartz]

I get this for free

[chrome yacht]

well you seemed to be looking for an advanced text, also i saw aluffi mentioned which is an abstract algebra text so...

[wintry quartz]

I guess so, lemme look into it a lemme get back to you

[fierce hedge]

Isn't amann escher a bit too advanced for hs students

[chrome yacht]

No.

[gray gazelle]

ye well i could too but i really like paper books

[wintry quartz]

apparently my uni library has this

so I am lucky

[ocean mulch]

As always, there's a will, there's a way

And there are always... interesting ways

[wanton yew]

Best calculus book?

Something around say….calc 2

[ocean mulch]

Calculus on Manifolds

[grand thistle]

nah

it’s kinda easy to read

as in it has good exposition

[marble haven]

Hello guys. I would like to know a book where i can find the theory about the Hessian Matrix for multi-variable calculus. Thank you so much!

[gentle arrow]

@ daminark

this is the job for you

[marble solar]

Not even Spivak's best book on Calculus

[sage python]

@viral sundial so, if you haven't had linear algebra before, I'd say go with either Knapp or Artin for algebra (I'm having eigenfelinegluten work through Artin atm)

As for analysis, depends a bit on what you have already. People here like Tao, I've been having eigenfelinegluten work through Schroder

Schroder starts off easier than, say, Spivak Calculus, but by the end covers more than Baby Rudin

So in principle if you only have high school calculus, or in principle not even that much, and the ability to think, if not some proof experience, Schroder is a good starting point

Tao seems similar, perhaps a bit more leisurely? Though 2 volumes as a result

If you already have experience, well depends on how much

Default is Rudin, I'd say Browder is similar to Rudin, slightly different organization for better or worse, and a less stupid treatment of the multivariable stuff

[heady ember]

Dami made me buy the physical copy of Schroder as well

[crimson leaf]

I also have a physical copy of Schroder

I like it

[heady ember]

Nice

[sage python]

I mean I don't make people buy stuff but yeah

[paper ferry]

Is going through Hatcher's point-set notes sufficient to read through his algebraic topology book or should I brush up on other concepts?

[crimson leaf]

Dami actually threatened to get me suspended if I didn't buy Schroder

[remote sparrow]

dami forced me to buy a copy of schroder

(i am not a book hoarder)

[fierce hedge]

Definitely not a librarian

[fierce hedge]

You can always pick up other concepts as per need

[heady ember]

Yeah well I was joking

[heady ember]

I totally don't have 100+ PDFs of books on my computer. Even if I, very hypothetically, had them, I would totally finish them in my lifetime.

[remote sparrow]

some are just notes/aren't books, but i have 3839 pdfs, epubs, and djvus in total

[heady ember]

Ok you're a hoarder

I only download what seems interesting and which I might potentially want to read

[remote sparrow]

you're not going to stay at 100+ at this rate

soon you will join the dark side

[heady ember]

I haven't downloaded books in a long time