book-recommendations

[daring lake]

I felt like rudin was quite high while writing PMA because his own work RCA is written better (in sense, followable)

[left falcon]

thanks for answering my question

becuase had he required his own 2 calculus books as prereqs then his analysis book would be out of question

[daring lake]

His calc book is in a weird spot

[left falcon]

I'm in chapter 4 of rudin so maybe I should just read them both?

i've passed through that hellish chapter 2

[daring lake]

For beginners I would recommend something like Stewart, if one already had brush with calc and wants to understand its workings, I would recommend some real analysis book. His calc books fall in the middle of two ends and end up stranded.

[daring lake]

If you got the time. Maybe you can just breeze over Apostol and fill in concepts which Rudin skipped.

[vital bane]

[daring lake]

feel that

[left falcon]

Yeah thats the thing actually. the problem with rudin is that he sometimes skips important detail

[vital bane]

yes Abbott is indeed very well written and extremely beginner friendly

imo Abbott + Rudin is like the best combo

[left falcon]

he assumes the reader knows or reader is capable of magically infering it but its not the case for me unfortunately

[vital bane]

use Abbott to learn, use Rudin for problems

[left falcon]

like queestion 22~30 of rudin ch2 should actually be explained as contents

not as questions

[daring lake]

just dont be like me and pick RCA first not knowing its grad level

[left falcon]

i was actually quite surprised at first when I've heard people talking well about rca

thought it would be the same case as pma but turns out i t wasn't

[daring lake]

I feel like he wants you to develop theory on your own. Many authors do that.

Its a book which works wonders if you got 2-3 people to discuss & work with

One thing I love about Rudin's books is that he doesn't omit half the proofs as an exercise to the reader.

[grand thistle]

chapter 2 in general was kinda goofy

that one page of just dumping every point set definition was crazy and definitely not beginner friendly 💀

[daring lake]

lol

[rain wren]

it was down right personal 💀

[narrow relic]

I don't think Carothers is very good by the way; the writing is too unclear for my personal taste. I felt like I wasted a lot of time on some parts of the cardinality section that could have been made a lot clearer. There is also at least one massive mistake in Chapter 1-2.

[fossil arch]

Just gonna throw a wild ask out there in case there's anyone besides Zanarcane and I who studies this kind of stuff

Does anyone know of an intermediate book between these two?

This is the book I'm currently using

https://www.amazon.com/Mechanics-Thermodynamics-Continua-Morton-Gurtin/dp/1107617065

It's decent but I don't like how little exposition there is and it seems to be more of a reference than a book to learn from. Both too easy and not enlightening enough

Whereas this one I really like the exposition but it's too demanding mathematically 😭 I can't parse through it well nor do I have the motivation to care yet

https://www.amazon.com/Mathematical-Foundations-Elasticity-Mechanical-Engineering/dp/0486678652

[tawny copper]

Does anyone know about the quality of the books from Forgotten books ?

[dusk wind]

varies

would not recommend unless you really need to read certain ones

here is an example, do you really want to read this? https://www.forgottenbooks.com/en/readbook/YourForcesandHowtoUseThem_10049803#0

[tawny copper]

I was considering Gauss' book on curved surfaces

there are nice pdfs available, it's just to have it in physical form

[dusk wind]

physical is probably fine

[tawny copper]

this editorial seems so weird

[brazen rivet]

Can someone recommend a book on geometric invariant theory that's written more for an applied math/engineer researcher audience? The Mumford book is great but its quite difficult to read.

[distant void]

I actually like these chapter titles

"Strength is born of Rest." "Strength is born of Rest." "Strength is born of Rest." "Strength is born of Rest."

"But it was the thought that led you first into the kingdom of horse-flesh."

[snow flower]

Anyone have a good book for graduate level functional analysis? I'd like something that I can get a physical copy of without too much trouble if possible

[north hare]

Adding my request to the list: are there books on umbral/operational calculus? I think many of you will notice where am I coming from (yes, those two youtube videos), and I already searched those topics, not without encountering a few issues. First of all, the videos don't cite references or link anything to go deeper into the topics, so I'm on my own. Next, it seems like "umbral calculus" isn't exactly what's shown in the video. At least to me, it isn't very obvious that the Steven Roman book on the topic has this thing of going back and forth between the discrete and continuous worlds. Then I tried with operational calculus, and found something that seems interesting, from Glaeske, Prudnikov and Skornik. It has a glimpse of the thing shown in the video, when plugging in the derivative operator inside a power series, but it goes into a lot of integral transforms like Fourier, Laplace, etc. It's not like I'm not interested, more like the absolute contrary, but it's kind of not what I was looking for. What topic are those videos actually about? Is it worth learning? Where can I learn that? Maybe I just have to give those books a second chance to start seeing what I wanted? Thanks in advance.

[dapper inlet]

whats a good calc 2 book?

[manic cairn]

Serge Lang, Real and Functional Analysis

[real marsh]

Is Lang's functional book actaully any good? I've steered clear from him because his books tend to be great as references not as learning materials

[misty wyvern]

Rudin is unironically good for this. Lax or Brezis or Stein & Shakarchi are also common choices.

Also worth mentioning Taylor's PDEs books. The appendix of Vol. 1 has a full course's worth of functional analysis content.

[snow flower]

Awesome thanks for the recommendations

[crimson leaf]

Conway also has a book you can check out ( I should clarify not the British Conway but the Conway known for his complex analysis book)

[gray gazelle]

what should i read first micheal spivaks calculus or from calculus to analysis by pedersen?

[vital bane]

depends on what you want to learn

[tame sphinx]

Hello everyone! I wish to dive into Linear Algebra in my free time. Are there any books you recommend?

[heady ember]

[tribal crow]

if you’re interested in a rigorous treatment of LA, i would probably recommend either Axler’s Linear Algebra Done Right, or Friedberg, et al.’s Linear Algebra

[tame sphinx]

Oh, thank you

[vital bane]

Axler good

especially the 4 edition

definitely a 8/10

[gray gazelle]

i mean i want to learn real analysis but im not really good at proofs(rn reading hammack) so i wonder which of this books should i use next

[vital bane]

Then

Abbott is literally THE perfect book for you

Before I started Abbott I knew literally nothing about proofs

after Abbott I'm doing proofs like a G 😎

This book is designed to teach you both real analysis and teach you how to write proofs in real analysis

By Abbott I mean

"Understanding Analysis" by Stephen Abbott

My opinion: Just pick up Abbott, Get started with real analysis

[gray gazelle]

thanks i will look into it

i will propably pick it up after hammack doe

[vital bane]

you can do it along side hammack

[gray gazelle]

yeah thats a good idea

[gray gazelle]

What is the estimated time to cover the book (7 chapters out of 8)?

[vital bane]

you mean 8 chapters out of 8 (trust me the last chapter is super cool)

[vital bane]

it depends tbh

depends on how much time you spend everyday

[gray gazelle]

Fr? Then yes include it.

[merry sphinx]

last chapter is the payoff for all your hard studying

[gray gazelle]

About 3 hours in a day.
But according to my schedule I will study analysis one day and linear algebra on other day and repeat this.

For example:
On Monday:
3 hours analysis and 2 − 3 hours remaining proof writing.
On Tuesday:
3 hours linear algebra and 2 − 3 hours proof writing.
(I am including making notes too).

[gray gazelle]

Damn for real!!?
Before your reviews, I was thinking of skipping it. But I shall definitely read it. (Currently I am at chapter 2 lol too away)

[vital bane]

literally this bro

[merry sphinx]

yeah c8 gives you an intro to some topics that you can look at after intro anal (like fourier), or just cool results like the pi^2/6 sum, its fun

[vital bane]

and henstock-kurzweil some metric space stuff

[gray gazelle]

Aw wow looks kinda interesting

[vital bane]

Also ari I see you lurkin in my thread

[merry sphinx]

he goes over construction of the reals at the very end which is funny

[gray gazelle]

Looks interesting hehe. I am feeling curious to study

[floral fern]

can somebody recommend/give me a useful book for calculus II, as "CÁLCULO II: TEORÍA Y PROBLEMAS DE FUNCIONES DE VARIAS VARIABLES" -for example-?

[north hare]

Nothing? 😦

[marsh ingot]

Spivak ig

Its in spanish

[molten mason]

Hay un libro llamado "Cálculo Infinitesimal" de Michael Spivak

[marsh ingot]

Mmmm wait

@floral fern Calculo diferencial en varias variables e Integral de Lebesgue en R^N de Mazon ambos

I used both and Mazon teached me during the 2nd year of the degree

And now is teaching me about Sobolev spaces

[rigid barn]

Do any books besides Spivak, Abbott, and Axler get recommended in this channel?

[tribal crow]

I was recommended Lee, so yes

[ocean mulch]

A book loved by French ppl is "Infinitesimal Calculus" by Dieudonné, though Ig it has more to do with complex analysis than multivariable, though with the same name.

Other than that, Munkres, of course

which I only found the first half to be useful for me

[remote sparrow]

yes

[unborn jackal]

stewart

or d

idk

[manic cairn]

modern algebra often ends where noether and hilbert start.
it's more like 150 years ago.

[hardy folio]

Espanõl but is a good book

[chilly sentinel]

I found this server by looking up the solutions to the exercises

[rugged maple]

I think the only time I can tolerate statistics is when it is applied to statistical mechanics

Can anyone give me a more mathey statistical mechanics textbook?

[uncut salmon]

Do you guys know a book that covers well jordan forms? I am studying from artin and I think the paragraph is too short, I'd like to know more

[floral fern]

thanks guys ❤️

[gray gazelle]

I'd recommend Cohn: Algebra Volume 1. Another brilliant exposition is Brešar: Undergraduate Algebra

[uncut salmon]

Thanks

[rigid barn]

If you know Germany by some chance, I can share with you my professor's linalg notes, I think she covers this topic pretty well.

[molten mason]

Are we in the post-modern phase

[molten mason]

I'll take them!

[finite crane]

We are in the post-Grothendieck phase

[graceful moon]

Looks up anything vaguely algebraic my lecturers mention theyre intrested in

Grothendieck

[dusk wind]

hypermodern probably

[wise umbra]

We are in the post-Lurie phase

[vital bane]

[left falcon]

has anyone heard about book called elementary classical analysis by marsden?

my school uses this book but i've never heard of it before

[remote sparrow]

@molten mason There's a calculus book I've heard of a while ago, written by Joseph W. Kitchen, that's supposed to be comparable in level to Spivak and Apostol. The main advantage is that it's a Dover reprint, so it's much cheaper than its competitors. I wanted to evaluate the book for myself, but I only see a PDF of the Spanish language translation. I see you previously said you could read Spanish; would you mind evaluating this book for me?

[remote sparrow]

the table of contents seems fairly standard

[left falcon]

I made the stupid mistake of not taking look at past syllabus

and have been studying the wrong book all this time lol

[remote sparrow]

it's just analysis in R^n as opposed to restricting itself to the real line or using the full power of the metric space formalism

[left falcon]

i guess then rudin is sort of like higher level version right?

[remote sparrow]

yeah

[left falcon]

I don't get why anybody would restrict analysis in R^n only though

[remote sparrow]

it's for pedagogical reasons

From the preface:

In presenting the material, we have been deliberately concrete--aiming at a solid understanding of the Euclidean case and introducing abstraction only through examples. For instance, if Euclidean spaces are properly understood, it is a small jump to other spaces such as the space of continuous functions and abstract metric spaces. In the context of the space of continuous functions, we can see the power of abstract metric space methods. When the general theory is presented too soon, the student is confused about its relevance; consequently, much teaching time can be wasted.

[left falcon]

oh okay then it makes more sense

i get the authors intention

[molten mason]

I can't find the Spanish version myself, but sure.

Also the reprint is 2020, but the book itself is 1968, crazy.

[remote sparrow]

it's on gibrary lenesis; the translated title is Cálculo

your search query should be "Cálculo joseph kitchen"

[molten mason]

kk

[molten mason]

Chapter 1 and 2 is giving me a Naive Set Theory combined with Basic Mathematics vibe and it's actually awesome haha

[dim sierra]

Why does gibrary lenesis seem particularly familiar? Hmmm…

[dusk wind]

bro taking directions from captain sour

[molten mason]

Seems to be the same level as Spivak, but with more application examples and problems similar to Stewart's. The illustrations are plenty and detail is great considering the year. The "Calc III" section of the book is brief... for example it goes over vectors, Jordan form, partial derivatives, quadric surfaces but not multiple integrals. The series section is very thorough, great explanations on everything.

[remote sparrow]

spivak was originally published in 1967, while apostol was originally published in 1961

i have the scan of the second edition of apostol's Calculus, which has a copyright date of 1967

[molten mason]

That's crazy

The good ole days

[remote sparrow]

spivak has gone through the most editions; the fourth edition was published in 2008

[remote sparrow]

@sage python @loud cradle seems like we have a cheaper competitor to spivak and apostol

[molten mason]

I wonder what happened to Kitchen or why it wasn't as popular. There's a million things about Spivak and Apostol but pretty much nothing about Kitchen

[remote sparrow]

me neither. i just happened to find it mentioned on math stackexchange

[molten mason]

All random lol

[remote sparrow]

https://archive.org/details/calculusofonevar0000kitc/mode/2up

i searched through worldcat and it turns out a scan of this book exists

@molten mason

right now someone else is borrowing it though

an 80ish page preview is also available with google books

[molten mason]

Oh weird I looked and I didn't see that pop up. The English version is 1960s and the Spanish version it seems is 1980s so I wonder if there are any differences. Plus I wonder if they changed anything in the 2008 Dover one

[remote sparrow]

it can take a long time before something gets translated

or whether anyone even wants a translation

[molten mason]

Yeah but sometimes it's a 1:1 translation, sometimes they add or change things.

[maiden glen]

may i ask, what good books are there about advanced algebra?

[molten mason]

What do you mean by advanced algebra?

[maiden glen]

homological algebra, representation theory

[remote sparrow]

set theory doesn't fall under advanced algebra

[maiden glen]

yes, im sorry.

i just want to learn.

set theory is mathematical logic

forgive me

[remote sparrow]

An Introduction to Homological Algebra by joseph rotman is well-regarded

[maiden glen]

thank you

[maiden glen]

how about number theory?

[remote sparrow]

https://link.springer.com/book/10.1007/978-1-4757-2103-4

good if you have some prior experience with elementary number theory and abstract algebra

[sudden kindle]

I didnt like that book

[remote sparrow]

if not, take a look at burton, dudley, or niven

[remote sparrow]

what do you prefer?

[sudden kindle]

I kinda don't like elementary number theory

[maiden glen]

what book would you suggest?

im willing to accept other opinions.

[sudden kindle]

Just try that one

See if u like it

[remote sparrow]

ireland/rosen?

[sudden kindle]

Yeah

I didnt like it

[marble solar]

Apostol's Introduction to Number Theory? The first few chapters aren't analytic

[molten mason]

Roughly in ascending order of difficulty:

• Popular
• Beiler, Recreations in the Theory of Numbers: The Queen of Mathematics Entertains
• Ogilvy & Anderson, Excursions in Number Theory
• High School
• Dudley, Elementary Number Theory
• Friedberg, An Adventurer's Guide to Number Theory
• LeVeque, Elementary Theory of Numbers
• College Non-Major
• Silverman, A Friendly Introduction to Number Theory
• Andrews, Number Theory
• Math Major
• Stein, Elementary Number Theory: Primes, Congruences, and Secrets
• Jones & Jones, Elementary Number Theory
• LeVeque, Fundamentals of Number Theory
• Niven, Zuckerman, & Montgomery, An Introduction to the Theory of Numbers
• Apostol, Introduction to Analytic Number Theory
• Graduate Student
• LeVeque, Topics in Number Theory, Volumes I and II
• Hardy & Wright, An Introduction to the Theory of Numbers
• Borevich & Shafarevich, Number Theory
• Ireland & Rosen, A Classical Introduction to Modern Number Theory
• Cohn, Advanced Number Theory

@maiden glen copied from somewhere else, but look through those.

[maiden glen]

@molten mason thank you dearly, baymax.

[dusk wind]

Silverman is a good introduction

Steins is also good and is free

[remote sparrow]

https://www.amazon.com/Logic-Computer-Science-Foundations-Automatic/dp/0486780821

check this out

i was browsing through dover's logic catalog and found this @lean pagoda

[remote sparrow]

have you asked the physics server?

[hot dagger]

Understanding Analysis - Abbott or Real Analysis - Keneth Ross

Which one and why?

Note that English is not my mother tongue so this will be my side literature

Im not bad with English but its kinda hard to familiarize with more complex terms both in my mother tongue and in English

[slender wasp]

I assume you mean: Elementary Analysis: The Theory of Calculus? by Kenneth Ross. I don't know about it, and curious about what ppl think but wanna make sure the title is correct.

[maiden glen]

is "CRC Standard Mathematical Tables and Formulae" a good book?

[vital bane]

Abbott is based

[fossil arch]

Nope, but good idea thank you

[trim kayak]

Question for everyone- This may be subjective but I'm curious what you think. I really like Algebra I and II as well as Geometry, Trig, and Stats. Should I continue reading about and practicing problems relating to those topics since I enjoy them or should I start reading more advanced topics that I'm not as familiar with? I feel that I should learn more about advanced topics and concepts rather than just the basic, easier topics.

[molten mason]

What is your goal though? How advanced and why?

[trim kayak]

@molten mason Honestly, I'm not sure. I really like math and enjoy practicing random problems sometimes. I'm not studying anything for a degree. So I'm not sure if reading through and learning advanced math concepts is really that important. May be interesting to learn just for fun but I don't know for sure.

[molten mason]

Others can chime in, but for more traditional problem solving like in algebra and trig, next steps would be linear algebra, calculus, and differential equations. For more great math knowledge that isn't necessarily that type of arithmetic, there's number theory and combinatorics.

There's books for every level. Not everything is heavy and proof based.

[trim kayak]

@molten mason That makes sense. Should I look into linear algebra maybe? I took a few calculus classes in college. I passed them but didn't really understand it. I still don't.

[molten mason]

There's no wrong answer, it's all personal preference.

[trim kayak]

@molten mason Thats what I figured. Since I'm not familiar with the more advanced topics, I'm not sure if I need to learn or read through linear algebra first before reading or studying another topic. Im not sure of the correct 'order'.

[gray jungle]

finishing pre-calculus then moving to calculus and reading a proof book (like "how to prove it") is my recommendation

linear algebra has no prerequisites but is a "college subject" that needs some more comfortability with math in general

even tho they are unrelated id wait till you are doing calculus, but you can try to read a book, you may have the talent to immediately vibe with it

[trim kayak]

@gray jungle That makes sense. Should I go with linear algebra next before pre-calc and calc? I don't know much about linear algebra at all. Should I find a decent book to read through and practice problems?

[gray jungle]

there is a course by gilbert strange on the website "mit open courseware" with videos, assignments and other course content. You can use it to check if its doable. However the course assumes multivariable calculus so once again, i recommend you focus on learning pre-calculus and calculus as well as picking up a book of proofs.

you can find pre-calculus on websites like "pauls online math notes", "khan academy" and many others (even coursera probably)

Calculus has many books, as well as a nice course on mit open couseware website

[hot dagger]

Alright thanks 🙏. I'm not going by American or likewise systems where there's 'calculus' so I'm not quite sure what that is? We did sequences, basic functions, derivatives and integrals in 4th grade of high school

[molten mason]

All five of the topics I sent you don't have much pre-reqs, technically I suppose Calc needs Pre-Calc, but I feel like you can fly through that.

[hot dagger]

Now in uni we are doing similar stuff but more into detail like recursively given sequences, proofs of limits, Taylor approx for limits etc

Some people don't consider that being real analysis but I don't know really

[molten mason]

If you go calc -> proofs route. It'll unlock a lot more. For example there's basically high school-level computational linear algebra, but there's also advanced proof-heavy linear algebra.

There's also common modern computational calculus books, and more rigorous proofy calculus textbooks

[trim kayak]

@molten mason Ahh, gotcha. Could you recommend a beginner or basic book on linear algebra? I can Google it too but want to see what you would recommend.

[maiden glen]

you can also check out Mathematics Libretexts

[tribal crow]

some people consider real analysis to be the stuff starting from lebesgue theory and such

[hot dagger]

💀 I don't know if I were supposed to know but I have no idea what's this

Although we did calculate surface of integral (if it's called like that?)

[outer terrace]

Any book recommendations for JEE?

[molten mason]

I don't sorry, maybe Lang's Introduction to Linear Algebra but I'm sure there's better alternatives

[molten mason]

Sounds all like regular Calculus stuff

[molten mason]

This too.

[molten mason]

Actually Howard Anton has a Linear Algebra book, and I loved his Calculus book

[remote sparrow]

learning calculus will reinforce your algebra and trigonometry skills.

many students say calculus is not difficult conceptually, but rather that they struggle because they are not fluent in algebra and trig

you have already had calculus and you are not under time pressure, however. you should expand your horizons

[trim kayak]

@remote sparrow I'm not sure why I struggled with calculus. The other basic math subjects were easy for me, then I took calculus and had a hard time. Good points, thanks. Should I start with linear algebra or should I go deeper into trig and stats? I know it's up to me, but I'm just not sure what to start with.

[trim kayak]

Is that Elementary Linear Algebra?

[molten mason]

All of my calc issues are algebra and trig issues lol

I hated spending waaaaaay too long on a problem just for someone to come up and be like oh this can be done obviously just by completing the square or whatever

[remote sparrow]

you can start working on linear algebra now if you want; however, knowledge of calculus will let you appreciate the more sophisticated calculus-based examples. and linear algebra books tend to assume the reader has had a course in at least single variable calculus, even if the content is mostly independent of calculus (sans inner product spaces)

[molten mason]

Like integral of a square root? You can just turn that into $(e^x - e^(-x))$ like oooookaaaay

[molten mason]

My first run through calc was rough. It all made sense the second time.

[molten mason]

Yes! His pdf was the first search on Google and I think I might go through it for fun to reinforce some things. Skimming through it, it looks great.

[trim kayak]

Oooohhh cool. I just found the pdf of it. I love free pdfs so I don't have to purchase anything, but also prefer a hard copy book. It's a long one but it looks good. I'm so nerdy for wanting to learn another math topic on my own. 🤓 📖

[molten mason]

Yeah personally it should be Calc 1 and 2 -> Linear Algebra -> Calc 3. If I were to go over and review/study everything.

[trim kayak]

Should I go through Calc 1 and 2 first, before reading through that elementary linear algebra book?

[tribal crow]

imo, you can do both calc 1/2 and linear algebra simultaneously, but others may disagree

[molten mason]

You've been through it before. I would at least review it anyway and utilize #calculus and the help channels.

Idk your comfort level, it might take you a week or two to review, maybe you need a couple months.

ING is right they can be done simultaneously

[trim kayak]

Makes sense. Thanks. I know you've mentioned that you read through various math books at times. Do you practice the problems and really learn the material on your own? I really want to do more of this....

[tribal crow]

I don’t really see how one can learn math without doing the problems…

[molten mason]

You can read all about the chain rule you want, but that doesn't replace looking at a problem and knowing when and how to use it. Most books have exercises at the end of each section and the answers to the odd problems in the back, I do all those.

[trim kayak]

True.

@tribal crow and @molten mason , I may have asked this before...Do you take notes as you read through the chapters and work through the problems as you go?

[maiden glen]

has anyone got any book recommendations for analysis and real analysis?

[molten mason]

Notes? No. Any notes I do take would be in middle of a lecture or video and it's simply just a reminder to look something up or to work out a problem. Otherwise I almost never take notes.

[marsh ingot]

Spivak or Apostol

[molten mason]

#book-recommendations message

#book-recommendations message

[maiden glen]

could you be more specfic please

[maiden glen]

that's the channel we're in, baymax.

oh wait i understand now

[marsh ingot]

If you click the link its gonna guide you to a old msg

[maiden glen]

sorry

i apologize.

[marsh ingot]

If you put on google those ones with analysis you are gonna find the books about it

Spivak-Mathematical analysis
Apostol-Mathematical analysis

Apostol have one about Advanced calculus

[maiden glen]

thank you

[gray gazelle]

anyone ever used a book with no exercises? if so how would you reccomend doing it

[narrow prairie]

I would recommend not doing it

If you must, find exercises elsewhere

[gray gazelle]

yeah i kinda have but i still wanna use the book somehow

[molten mason]

What book

[gray gazelle]

because there is a lot of stuff there

[gray gazelle]

i dont think you will recognize it

its not in english

[molten mason]

That's fine

[gray gazelle]

its by G M Fichtenholz

you should find it by just searching his name

[pulsar ledge]

Hello. May i ask a question, What is the most recommended method for math self study based on a text book?

[dusk wind]

read and write

[trim kayak]

Hey Renji and birdy

[opal lark]

This is going to hurt by Dr. Adam Kay

Very interesting it's about the medical world as well as some dry humour

[north hare]

Should I keep asking or is it better to ask somewhere else?

[vital bane]

"gilbert strange" it's strang lol

[gray jungle]

gilbert strange

[molten mason]

Well that's weird

[molten mason]

You can keep trying, a lot of us who have seen your post have no idea, but who knows. You can also ask in any of the discussion channels

[dusk wind]

you could ask again with a shorter question

[hallow oriole]

yeah i got u gimme a sec

nvm i dont got u

mm

there's a discord server for umbral calculus

if you ask there you'll probably get a better answer

i think i left around a year ago but it should still be active-ish, maybe?

[heady juniper]

Anyone know of any resources by Po-Shen Loh? I didn't see any books on his wikipedia page, but it also looks incomplete. I know of his Daily Challenge videos.

[remote sparrow]

https://www.poshenloh.com

he has a website

[vernal coyote]

Does anyone have a good recomendation for calculus with a lot of practice problems?

[remote sparrow]

any mainstream calculus book

[vernal coyote]

Like?

[dusk wind]

a book that has a title with calculus in it

[remote sparrow]

like stewart or larson

[vernal coyote]

ok bro

[remote sparrow]

you can't really go wrong with any calculus book

[dusk wind]

because it has calculus

[remote sparrow]

they've evolved to be pretty similar

[vernal coyote]

I have just found one

Calculaus 9th edition by Ron Larson

Calculus

[remote sparrow]

yeah that's fine

it doesn't really matter which edition you get either

older editions tend to cost much less for basically identical content

[vernal coyote]

Thanks a lot bro 🙂

[vital bane]

Yea lol people have been writing calculus books for like 300 years now

at this point you can pick just any calculus book

They're all isomorphic

[heady juniper]

Would you consider Spivak's Calculus pretty good for someone asking about best calculus books?

Or Janusz Calculus? Or Apostol if they don't have a particularly strong math background (for example, didn't have a strong high school experience, but has to take calc for their freshman year)?

[dusk wind]

any are fine, depends which they would like more

going with stewarts or larson is good though

[heady juniper]

The differences in the calculus books I mentioned and Stewarts is which one a student likes more?

Spivak's Calculus and Stewarts book might as well be two different subjects because they are. Spivak even said it was a mistake to call it a Calculus book.

My point is that "any calculus book" probably isn't helpful to someone who is asking about beginner calculus books.

[dusk wind]

ok well

they weren't especially specific about what they were looking for

likely though if its for a beginner text stewarts would show up first, along with others that are similar

[dusk wind]

these are two completely different questions and cannot be gauged from assumptions. Best? Beginner? The best book is the one you need for your specific use case. It could be one provided by a school or a reputed author. In general though its the same

[oblique hatch]

What do I need to understand wrt analysis/differential geometry to understand abelian varieties?
Or is there an abelian varieties book that doesn’t start by going over the analytic theory?

[trail hemlock]

abelian?

yoo

[sturdy sail]

Any recommendations of references on modular forms from a more geometric pov?

[tawny copper]

Haruzo Hida's book

[sudden kindle]

Like algebrogeometric?

[sturdy sail]

Ye so

I have heard that somehow modular forms are related to the picard group of some complex varieties

I'd like to know better about this relationship in particular

But in general, I just would like to see an intro to modular forms which focuses heavily on motivating the concepts from a complex geo pov

[sudden kindle]

let me know if you find something

[raw ibex]

I found this book in the bibliography of my discrete mathematics class (from my math undergrad) called "combinatorics, topics, techniques and algorithms" from Peter J. Cameron, does anyone know if it's a good book? I mainly need some reinforcenment in arguments that rely on creating bijections

If you have any other recommendations please tell me (and ping me)

Or is it better to use as a main undergrad book for discrete mathematics richard P. Stanley's books? Although it has 2 volumes

Oh volume 2 is postgrad

Yeah just volume 1

[remote sparrow]

you can look at A Walk Through Combinatorics by miklos bona

[vital bane]

oh wow I always thought modular forms were mostly like algebraic/number theoretic

[gray gazelle]

Does anyone know any good books on general and special relativity? Thanks.

I heard Einstein's official book was a bit difficult to understand, so, I'd like to get some recommendations.

[tribal crow]

i've seen people recommend Carroll's GR book before, but i have not read it myself yet

[gray gazelle]

I'll check it out, thanks.

[visual wagon]

anyone have any good book recommendations for learning linear algebra?

[molten mason]

#book-recommendations message

[visual wagon]

this channel is literally named "book recommendations". what are you smoking?

[molten mason]

Click it, trust me

[lusty ermine]

the 6th pinned message

[visual wagon]

uhh

a lot of options but i couldn't understand much lol

like, i just need a book that intuitively and comprehensively teaches linear algebra from scratch

[molten mason]

Ah I see

just google "Howard Anton Linear Algebra"

Good author, good book, probably more what you're looking for.

[visual wagon]

aight i'll check that out, thx

[dusk wind]

see 'tea time linear algebra'

[heady ember]

Look in pinned for some reviews

Fis is nice

[dusk wind]

that is the pin

theres other books though that are much easier for what you want

[molten mason]

I didn't realize Axler's Measure, Integration & Real Analysis is Open Access

[finite gale]

every textbook is open access if you can run fast enough :^)

[remote sparrow]

#book-recommendations message

[raw ibex]

I'd really like something that is quite a challenge and needs pencil and paper to read even tho I've just started the subject, is that the case?

[remote sparrow]

sure

[vital bane]

that is literally every math book

at least every pure math book

And that's how you should learn mathematics/physics, they are not spectator sports, there is something very active about learning math/phys

[raw ibex]

Yeah ig, but maybe I didn't get my point through

[ocean mulch]

every textbook is open access if you know where to find it

[ocean mulch]

one recent non-trivial application of modular form is Fourier-Viazovska-Radchenko interpolation

[vital bane]

what is that

[ocean mulch]

where a Schwartz function f is uniquely determined by its values and its Fourier transform's values at points of form sqrt(n) for n integers

[vital bane]

"The formula expresses the value of a function at any given point in terms of the values of the function and its Fourier transform on the set {0,±1–√,±2–√,±3–√,…}."

wow

[ocean mulch]

notably, it gives rise to an optimal function for a theorem by Cohn and Elkies, that proved the optimal sphere packing density in dimension 8 and 24

[vital bane]

Ooh nicee

[ocean mulch]

the construction of the basis is non-trival however, and uses a lot of modular forms

afaik, there's a generalisation to higher dimensional, where instead of the points +/- sqrt(n), now it's the spheres of radius sqrt(n)

which is even more cursed

[vital bane]

so it's like a multivariable schwartz function?

[ocean mulch]

yes

[vital bane]

wait then wouldn't it be like k-dimensional vectors with length +/- sqrt(n)

instead of +/- sqrt(n)

[ocean mulch]

actually no, it's the spheres of radius sqrt(n)

I won't go into the details, but essentially there are a lot of integrals, and the sphere naturally comes up

[vital bane]

Lol fair enough

[ocean mulch]

For a Fields-medal-winning work, it's surprisingly easy to read

tho this shit is still aesthetically cursed

[vital bane]

Wait wtf this won the fields medal?!

that's super cool

which year?

[ocean mulch]

Viazovska won a Fields medal in 2022

She initiated all of this back in 2015 or 2016 iirc

[vital bane]

wow amazing!

[ocean mulch]

I'd say it's a decent topic for a Master thesis tbh, if anyone wanna take a look

The math is not super heavy and elementary enough. It's just that it requires some superhuman power to do calculations and almost infinite imagination

[vital bane]

[sleek python]

Care to share the references [4] and [5] pls? Seems interesting to look it up

[heady ember]

Sure! Gimme a sec

[snow dune]

Any suggestions advance trigonometry book that is for physics or engineering rather than heavily based on pure math

Thanks

[deep nebula]

Hello, I was looking to learn math from scratch, any book recommendations? i have forgotten pretty much everything from school, besides basic arithmetic and algebra. ( like, single variable linear equation basic. )

[daring lake]

Serge Lang Basic Mathematics

[gray gazelle]

I know some basic stuff, Is it still worthy to read this book.

[daring lake]

Wouldn't hurt to go through it (holds for any book imo). There might be a point or two you might be unaware of, or you can try problems to see if you know the topics covered

[gray gazelle]

Yeah that will be a good idea. Thank you i shall try

[deep nebula]

Thanks! Any other recommendations? I wanna sample multiple books to see which one I am comfortable with, but i dont really know much about math books.

[maiden glen]

Is CRC standard mathematical tables and formulae a good book?

[prime dune]

Hey chat, what is a good intro or real analysis textbook that is highly exercise driven, much in the same vain as Dummit & Foote for algebra?

[vital bane]

Abbott

[prime dune]

springer

[molten mason]

I downloaded the PDFs of a large percentage of Springer's UTM and GTM series last night and now I have to do more than stare at the cover pages

[molten mason]

Like you want a Springer text specifically?

[vital bane]

[prime dune]

No I looked it up and it was springer lmao

[gray gazelle]

Approximately how many?

[molten mason]

70 or 80 maybe

[gray gazelle]

Wow. It would be an amazing collection

[molten mason]

I finally got my institional login to work, a lot of universities have a deal with Springer and when you login you can access anything any Springer PDF, I grabbed a couple new 2024 stuff too.

[potent coral]

wow

insane

[prime dune]

Is there a general preference for (baby) Rudin over Abbott

[molten mason]

This discord is pretty split between the two. A middle ground consensus is do something like Abbot first, then use Rudin as a second or reference

[prime dune]

I’ve done more Rudin exercises, I’m more wondering about the scope and how it’s laid out

[vital bane]

Pedagogically Abbott is much better than Rudin

[prime dune]

Rudin I can actually borrow from someone, I’d have to pay for Abbott most likely

[vital bane]

well any book is much better than Rudin's PMA

[prime dune]

I learn better from exercises and working shit out or going over proofs opposed to being just told something

[vital bane]

yes but there's a fine line

[molten mason]

What about Lang

[vital bane]

[potent coral]

you pay for your books????

[molten mason]

I'm learning through Lang's Understanding Analysis right now because I like pain. Thankfully, there's a solutions manual lmao

[prime dune]

I’m at a small satellite college right now that doesn’t have math textbooks beyond like Calc 3

[potent coral]

thats the right thing to do, rather than doing something morally abhorrent like using z-library through the link singlelogin.re, that would be obscene and wrong to do, just letting you know so you dont make such a mistake

[gray gazelle]

Do you mean, every university?

[slender cargo]

I've been using Bartle and Sherbert, but weirdly enough when I'm confused on something, I go to Rudin which tends to have a short explanation that cuts to the heart of the matter. Rudin often doesn't have the full details, but its brevity is nice when you know things

[vital bane]

[molten mason]

I would hope so, but I can't speak for every one.

[prime dune]

I can’t get myself to do it digital but I could probably pay a printing place to print it out for me lol

[gray gazelle]

Oh okay. I will try with my university

[potent coral]

thats fair, ive pretty much only used digital

[prime dune]

Accidentally clicked on your profile

Jumpscared by your about me

[molten mason]

I do that, I enjoy physical texts. I print out the PDFs and use a 3 hole punch and put them in a binder.

[potent coral]

ok ibuprofen flame text

[wind osprey]

i just bought a copy of baby rudin and it didnt empty my bank account !

[potent coral]

so based

[unborn jackal]

for lin alg, does it make sense to use two books parallel (one like strang and one like hoffman&kunze)?

cause ive noticed that there is a lot of stuff not covered in hoffman when going through strang and vice versa

[quartz minnow]

I mean definitely

As long as you’re following along

Filling the gaps between each book

Should be fine

Also I would really like to self study quantum physics, can anyone provide me with some resources? (Books mostly)

[mossy flume]

it may empty your soul

[snow dune]

Any suggestions on advance trigonometry book that is for physics or engineering rather than heavily based on pure math

[remote sparrow]

https://web.archive.org/web/20220530182041/http://www.mecmath.net/trig/Trigonometry.pdf

[snow dune]

Nice, thanks

[snow dune]

The content seems pretty simple, is there other advanced books?

[earnest wolf]

does one need any kind of differential geometry / measure theory to study complex analysis?

and more generally, any of those topics:

• Darboux integral
• Labegue's criterion, Labegue's measure
• Peano–Jordan measure
• Fubini's theorem, Cavalieri's principle
• Line integral, surface area, surface orientation
• Stokes's theorem, the divergence theorem (Gauss's theorem)

[remote sparrow]

no

[remote sparrow]

is there a reason you want more advanced topics?

[earnest wolf]

like, you mean, it's safe to skip all of those topics?

for a proof oriented course ofc

[remote sparrow]

yes?

[snow dune]

Yeah for signal analysis and processing

[remote sparrow]

why not read a signal analysis textbook then?

they shouldn't assume that much

they should fit into a standard electrical engineering curriculum

[snow dune]

Very good point and I havé it but i want to use this as a reference book

[snow dune]

I see

[remote sparrow]

authors don't try to make anything too esoteric

is there a reason why you think something particularly advanced is going to show up in your signals textbook?

as far as i'm concerned, the trig you learn plus some calculus and linear algebra is enough to understand fourier series, at least according to course catalogs for electrical engineering

[trim kayak]

Hey Sour, are you a student too? You seem to know a lot about various resources and materials. Was just curious 🙂

[remote sparrow]

yes

[snow dune]

They mentioned about Fourier series and Eulers formula in the book

But doesn’t go through more information

[remote sparrow]

which book?

the trig book i sent or your signals book

[molten mason]

I use 2-3 books per subject personally

[remote sparrow]

linear algebra is so ubiquitous that you can't really expect one book to cover everything

[snow dune]

The signal book

[remote sparrow]

yeah, i'm pretty confident you only need basic trig and some awareness of complex numbers

plus calculus and linear algebra obviously

[molten mason]

I mean, I have a ~900 page two-book volume just on Fourier Analysis, you can get super in depth, but what you need for your class/textbook should be included.

It's actually just over 1000 pages

[snow dune]

Ok

[snow dune]

Wow nice

[remote sparrow]

https://www.ece.uvic.ca/~frodo/sigsysbook/

http://www.dspguide.com/

more resources on signals and systems

[snow dune]

Thanks

[tribal crow]

...but why

surely you're not gonna read them all... right?

[molten mason]

I have another ~400 page text called Fast Fourier Transform: Algorithms and Applications by Rao, Kim, and Hwang too, that one's cool

[molten mason]

By 2100, possibly

[molten mason]

Half of them I think I do want to read eventually, the other half are more just to have as a reference.

They're pretty much every Lang text, every Stillwell text, every text on Number Theory, and then the rest is mostly all complex analysis, differential geometry, and lie group stuff

[tribal crow]

i see, best of luck with that lmao

[molten mason]

oh a few probability texts of course

[molten mason]

Oh like 10 of them are problem books.

Problems in Analytic Number Theory is 500 pages

Problems in Algebraic Number Theory is 300 pages

Plus a bunch others.

[trim kayak]

hey salagos

[potent coral]

does anyone have any recommendations on books on the philosophy of mathematics? never read anything about it but thought it would be interesting with a mild philosophy background

[maiden glen]

what's it called?

[maiden glen]

what's this called also

[maiden glen]

give me all of that too

please

[earnest wolf]

is algebra chapter 0 doable for a first course in algebra (fields rings groups)?

i heard that it is a really great book that gives amazing perspective on algebra, but I'm not sure if I will make it

[molten mason]

It's in the message

[molten mason]

Modern Fourier Analysis and Classical Fourier Analysis by Grafakos

[maiden glen]

thank you

i also apologize for my very oddly structured requests

[modern ruin]

how do people find the time to write such long books anyways

[unborn jackal]

do you buy physical copies for every book you use?

idk but i hate using pdfs but its still better than spending 200 on a book i wont use after 3months

[molten mason]

No

[cold elbow]

oh wait i read the message wrong

[lethal orbit]

true

also they have time bc they have nothing else to do

[modern ruin]

write them

[unborn jackal]

idk

[modern ruin]

oh lol

[unborn jackal]

money

[cold elbow]

sorry lol

[unborn jackal]

make all your students buy the book which is obviously overpriced

[molten mason]

A few of Serge Lang's books are basically just his notes when learning a subject lol Like his textbook on the subject was also his first time really learning the subject.

[uncut salmon]

I usually borrow books from library

[remote sparrow]

https://mitpress.mit.edu/9780262542234/lectures-on-the-philosophy-of-mathematics/

https://www.youtube.com/playlist?list=PLg5tKDNI_a86OO6J9HuIngyROBsUqcf_z

[potent coral]

you are awesome!!! thank you!!!

[unborn jackal]

oh thats a good idea

[molten mason]

I normally have 1 physical and 1 PDF

[remote sparrow]

it can be, though you should be stronger than average. i would recommend pinter, judson, or aluffi's other book, Algebra: Notes from the Underground for the more typical reader.

[remote sparrow]

authors may request sabbaticals and/or grant money to write textbooks

[modern ruin]

hm

neat

i had no clue

[gray gazelle]

How does chapter 0 compare to Artin or Herstein in terms of coverage and difficulty?

[remote sparrow]

linear algebra features much more prominently in artin than in its competitors. herstein writes functions from left-to-right (for example, if you have a composition of functions, we would normally write it as (f o g o h)(x) and do h, then g, then f. however, in herstein, you do f, then g, then h). in Chapter 0, category theoretic language permeates the text. i think it covers group actions and homological algebra, which are absent in herstein and artin.

[gray gazelle]

Cool, thanks!

[remote sparrow]

herstein has a reputation for some notoriously difficult problems. some people feel artin's regular problems are a little too routine or straightforward, while the miscellaneous problems are too long and complicated. i don't know about the quality of aluffi's exercises, but daminark didn't approve.

[lusty ermine]

which is the easiest book to get started with linear algebra, is there any easy read for this?

[tribal crow]

#book-recommendations message

though i suppose that list is more geared towards a second course

[lusty ermine]

those are only hard to read books tho

[tribal crow]

you're right, perhaps someone else will have better recommendations

[modern ruin]

I will say that aluffi has some typos in the exercises that can be frustrating if you don't already know algebra

even though I love the book

[remote sparrow]

#book-recommendations message

[molten mason]

Did you not like Howard Anton?

[lusty ermine]

I didnt knew about Anton's Elementary Linear Algebra

I will take it a look aswell

[molten mason]

Oh maybe it was someone else, but google "Howard Anton Linear Algebra" and it'll pop up

[dusk wind]

why link this archived version?

[molten mason]

The main website doesn't work for him for some reason

[dusk wind]

#book-recommendations message all easy to read

[dapper inlet]

can i get a req for linear algebra the one for my class keep breaking

[remote sparrow]

what do you mean by "breaking?"

[dapper inlet]

the formatting on examples is broken

[dusk wind]

check my post above

[dapper inlet]

tysm

[remote sparrow]

are you reading an ebook?

[dapper inlet]

yeah

[remote sparrow]

what's the book's name

[dapper inlet]

Linear Algebra with Applications by Jefferey HOlt 2e

[remote sparrow]

holy shit, yeah, i looked at the pdf and it looks like it was converted over from an epub or something. sorry about that. a book that has similar content is Linear Algebra and Its Applications by david lay. alternatively, you can download the first edition of your book.

[dusk wind]

david lay is fine or any of the other books

[dapper inlet]

[maiden glen]

May I have some suggestions for applied mathematics and mathematical modeling?

[void gazelle]

Idk why but recently I like Bartle's Elements of Integration and Lebesgue Measure

It's short

[daring lake]

its nice yes

Though, I read it after reading Rudin's RCA so it didn't add much new info

[remote sparrow]

Nonlinear Dynamics and Chaos by steven strogatz

Differential Equations, Dynamical Systems, and an Introduction to Chaos by hirsch, smale, and devaney

Numerical Analysis by burden and faires

[void gazelle]

My fave intro numerical analysis book is Scientific Computing an Introductory Survey by Heath

[maiden glen]

thank you both

[sturdy shore]

definitely check out introduction to applied math by holmes

[maiden glen]

my goodness I love this server

[maiden glen]

thank you dearly

[violet shuttle]

trefethen's numerical linear algebra, for numerical linear algebra.

iterative methods for sparse linear systems, for more on that.

[lusty ermine]

what would be a good introduction pdf for learning set notation

[remote sparrow]

Book of Proof by richard hammack

appendices to many math books briefly go over this as well

[daring lake]

Other authors might use different notation. Due to this, most books do have a section on sets.

[earnest wolf]

it seemed to be very motivated and gave lots of examples

and the proofs were also very clear

[violet shuttle]

Shankar's Quantum Mechanics was where I learnt linear algebra from (first chapter, hardest chapter)

Definitely my favorite textbook.

[earnest wolf]

i mean, determinants aren't sweet: it's no harm to leave them for the end 😆

[heady ember]

No iirc the treatment of dets in the first to third eds were considered by many to be just bad

[earnest wolf]

Guys, what are some great complex analysis textbooks?
Like, looking for something like 'understanding analysis' but in the world of complex

for (pure) math students ofc, not engineers

[heady ember]

Look in pinned if you haven't; Dami has some reviews there.

Yamin stans her professor's book, but idk if it's truly beginner friendly.
https://press.princeton.edu/books/hardcover/9780691207582/a-course-in-complex-analysis

[earnest wolf]

u mean here?

[heady ember]

Yes

[earnest wolf]

hm, couldn't find anything there

[loud cradle]

treatment of char poly still funky even in the 4th, but he did greatly improve the determinants chapter

[earnest wolf]

thanks 🙂

[heady ember]

np

[heady ember]

#book-recommendations message

[heady ember]

[violet shuttle]

I liked Conway's book in the GTM.

(no, not John Conway)

[crimson leaf]

I think they're both named John Conway

[heady ember]

AYYO!

Princeton university press is having a 75% sale for math books!

I think it might be all of their books

Unfortunately not the case

[heady ember]

But this is!

[daring lake]

Not available in my country

[heady ember]

rip

[gray gazelle]

Same here

[heady ember]

where do you guys live

[gray gazelle]

Pakistan

[heady ember]

I see

[gray gazelle]

Yes. Unfortunately foreign books (in hard cover or original books) are not available here. Furthermore buying from Amazon is very expensive. (Maybe because Amazon has no direct deal with Pakistan).
That's why the only option remains is to make print copy of the book. I only need pdf of the book, then it is easy to find shops who can provide hard cover print copy of the book

[earnest wolf]

#book-recommendations message

xD

[graceful moon]

It is available in Pakistan

[gray gazelle]

Oh wow. I didn't notice this. Thank you so much.
Let me check the prices and methods.

[graceful moon]

None of them really appeal to me but 75% of is a great deal

[heady ember]

Physical books are nice (to me), especially a hardcover.

Idt you can find a pirated copy of that book anyways.

[daring lake]

^ same

[earnest wolf]

yeah, unfortunately I didn't 😦

just googled some other ones (and the ones Daminark recommended)

[coarse osprey]

Hey what's up! I'm just about to start university, and I currently do very well with precalculus concepts (such as Algebra, functions...), but I seem to have a very bad base in geometry and trigonometry, and I want to learn it from scratch. To have a reference, I already knew basic concepts like Pythagoras, angle formulas, and so, but at the same time, I struggle with basic concepts such as triangle ratios, the appendix of a triangle, etc. It's not like I find it hard to study, but that I have to study again so the concepts stick out in my head.
So, any book recommendations for this?

[novel obsidian]

Khanacademy is your friend

[tall juniper]

i need book recommendations for trigonometry
i have good knowledge of the basics (sin, cos, tan, etc) and i use these pretty often too since i work with graphic/game programming
but i'm pretty bad when it comes to trigonometric identities such as sin(a) + sin(b) or sin(a + b) etc and i need a book that teaches identities like these and has good problems based on them

currently doing fourier series in uni and it's painful to do since i don't know these identities

(pls ping if reply)

[molten mason]

https://mecmath.net/trig/

Chapter 3

[fierce hedge]

It shows empty collection for me what the hell

[graceful moon]

You don’t deserve books

[fierce hedge]

This would be my 13th reason

[remote sparrow]

gamelin

bak and newman isn't quite like abbott, but it's also good

most exercises have answers or solutions in the back

[slender wasp]

I'm also looking for the same in complex analysis. Something like what Spivak calculus or Abbot are for real analysis. Looks like Gamelin might be it? Btw does Gamelin require any topology (more or less than Abbott)?

[remote sparrow]

no

[ocean mulch]

A French classics is Dieudonné's "Infinitesimal calculus"

which is translated to English, dw

the CA course I'm taking is based on it, and it goes pretty smoothly so far

[earnest wolf]

but doesn't the word calculus in the title imply it's non-rigorous / computation-based?

[ocean mulch]

Remember, Dieudonné was a Bourbaki founder

if his book is not rigorous, i'm not sure what is anymore

[tribal crow]

i mean spivak calls his book “calculus” too, but it’s definitely not computationally focused

[earnest wolf]

tbh didn't read it. abbott, tao and some others were more than enough

tao vol 1 i mean

• escher, rudin, and mit analysis notes

(only now realised that was the first course I've used more than 2-3 textbooks for 🤣)

[graceful moon]

Analysis is just called calculus in a lot of Europe

[earnest wolf]

i thought spivak was an american lol

[graceful moon]

He is I believe

[trail hemlock]

i hope spivak is arrested for war crimes

[tribal crow]

[trail hemlock]

i love spivak but man...

[tribal crow]

his book is not that bad imo

[trail hemlock]

theres like 2 problems that genuinley took me half an hour to solve in Spivak's calculus

maybe i was just being a lil slow tho..

[tribal crow]

half an hour for a chapter??

[trail hemlock]

no no

problem

[tribal crow]

oh

[trail hemlock]

half an hour per chapter is some terrence tao shit

[tribal crow]

yeah thats normal for me lol

i'm very slow

[trail hemlock]

it was my favorite section tho

series and sequences

its alr i solved them and now they are trivial

[tribal crow]

if only i found them trivial...

[molten mason]

Well he's dead, sooo....

[trail hemlock]

o shit mb

[molten mason]

I feel that's normal in math though

[trail hemlock]

nah after solving them i realized how many wrong turns i took 💀

soln was too obvious

chat my copy of baby rudin coming tmrw

i scammed some dude found a good deal thru a friend

only paid for shipping

[dusk wind]

a lot of so called prealgebra books are sus https://www.amazon.com/Math-Practice-Workbook-Grades-6-8/dp/1951048229

the 'everything you need to ace' book seemed fine but it has errors apparently

[trail hemlock]

maybe ap pre calculus will finally standardize precal

[dusk wind]

like maybe you could just sit them down with a non clickbait algebra text and give them a good middle school tutor/class

this seems kind of ok https://www.amazon.com/Pre-Algebra-Building-Workbook-Explanations-Examples/dp/1947508121

workbook with some explnations+solutions too

[earnest wolf]

whut

[earnest wolf]

u r saying 30 mins is too much for an exercise? 🙃

[trail hemlock]

it was an easy exercise

like it should not take 30 mins

[tribal crow]

how i feel when doing literally any spivak problem lmao

[trail hemlock]

lmao fr

[earnest wolf]

😐😑😐

imo 30 is not that much for a chapter either. I mean, there are easy and hard chapters. I remember to fully get some theorem I had to revisit it multiple times over an extended period of time. And even not counting that, 30 mins is nothing when it comes to rigorous math 😅

[trail hemlock]

idk i love the spivak problems they are so interesting

[earnest wolf]

/not talking abt spivak specifically, just math textbooks in general/

[trail hemlock]

well spivak was my introduction to calc, so 30 mins per chapter is basically unheard of. but yeah if im gonna review some chapter, 30 mins is def enough time.

maybe like a day for the chaper, few days for the exercises, rinse and repeat

yeah doing the rudin made me realize 30 mins is nothing 🤣

[heady ember]

30 mins per chapter sounds very tame to me tbh

[trail hemlock]

30 mins per chapter for your first time doing calc, in the spivak, including practice problems ? that’s terrence tao behavior

[heady ember]

A full chapter in any proof based math book taking 30 mins only feels very

[manic tendon]

Recommend a Differential Geometry book contains the standard speech about curves and curvature

[hardy folio]

"Fundamentos de Matematica Elementar " Is good ?

[dusk wind]

what were the major discoveries of logic prior to the greeks (any recs on this?)

[north hare]

Wow that is such a specific topic to create a server for. I'll look it up, thank you!

[north hare]

May I ask what server is that? I'm having trouble finding it

[hallow oriole]

sure nw give me a few

[void gazelle]

I'd like a recommendation for something niche and weird please, I wanna spice up my life

[void gazelle]

I always like physical hardcover books and try to collect them

Reading a pdf is three clicks away from youtube

[magic spade]

What's your math background?

[void gazelle]

I'd say grad but like the lowest level of grad im still taking measure theory and grad level linear algebra/numerical analysis

If that makes sense?? I can show you what im taking

If you dont have a general idea

[magic spade]

I think I know. Let me think about it. Do you like analysis, algebra, geometry, or combinatorics?

[void gazelle]

I love analysis

[north hare]

I'm reading "An introduction to p-adic numbers" by F. Gouvea. I really have no idea what you are looking for, but it's general enough for me to come to mention it. I didn't finish it, but I'm really enjoying the ride.

[magic spade]

This is a good recommendation

[void gazelle]

Thank you

[crimson leaf]

You could start looking at stuff professors at your university are doing and reading about those

[void gazelle]

Ok thank you

[hallow oriole]

oh idk if it's allowed by the mods

oh well

[north hare]

To share the invitation?

Maybe ask first? I'll wait so that you don't get into trouble.

[hallow oriole]

nah ur good to join

i'll js delete it

[north hare]

Done. Thank you

[hallow oriole]

nw!

good luck

[magic spade]

I think p-adic numbers is a great recommendation. Another option is fractional analysis

[void gazelle]

Thank you

[molten mason]

Quaternion Algebras by John Voight

[void gazelle]

Ty

[trail hemlock]

any interesting philosophy of math books yall read? or like essays? im bored

[modern ruin]

https://web.maths.unsw.edu.au/~norman/papers/SetTheory.pdf

I do unironically believe that people should give this paper a read, it actually makes for really interesting discussion if you're just talking to your undergrad math friends

even if it is njw

[trail hemlock]

njw?

also i dont have undergrad math friends but ill read it anyway fuck it

[dusk wind]

shitpost paper real

[trail hemlock]

chat please cease trolling me 🔪

[novel hound]

what is the tl;dr of this?

[modern ruin]

he basically says "infinite sets are BS and don't make any sense, also some of the techniques that mathematicians use are a bit strange once you think about them"

[novel hound]

yeah that's a lot of words to say so, not sure if he likes ZFC or not?

[modern ruin]

All completely clear? This sorry list of assertions is, according to the major-
ity of mathematicians, the proper foundation for set theory and modern math-
ematics! Incredible!

in case you were still wondering about the ZFC question (I know that it was deleted but I wanted to answer it)

[modern ruin]

the guy who wrote this is completely serious

[trail hemlock]

please im confused enough as it is

[past palm]

I asked this before, but what textbooks/courses could I take to learn about college algebra and especially group theory?I was recommended to read Lang, but I've heard mixed reviews about it.

[modern ruin]

either don't learn it from textbooks or pick up Lang basic mathematics

uh if you're looking for a video series there are a few good ones

[past palm]

I just doubt they would be in depth enough

[modern ruin]

I think there are some lecture series that are sufficient for college algebra

I will find one

[molten mason]

College algebra as in elementary algebra such as polynomials, or abstract/ modern algebra such as fields and groups

[past palm]

But no examples etc

[gray gazelle]

Does anyone know any good books for starting calculus?

[past palm]

I learned polynomials in highschool algebra 1 and 2. So abstract algebra.

[molten mason]

Actual calculus or pre-calculus

[gray gazelle]

Actual calculus.

[molten mason]

In that case don't use Lang lmao that's for advanced Algebra.

[gray gazelle]

I've already done precalculus.

[modern ruin]

oh okay don't use Lang basic mathematics

I thought you meant like hs/precalculus

[molten mason]

#book-recommendations message

[past palm]

I am in calculus BC right now so that would be useless.

[past palm]

But I heard lang goes into group theory and my algebra courses never included it.

[modern ruin]

lol okay great, I used some open-source textbook my first passthrough of abstract algebra lol, i didn't have a professor I could talk to at the time so I just sort of did the only thing I could do and look up "free abstract algebra textbook" online

[molten mason]

In my part of the world, college algebra = high school math/precalculus stuff taken in college.

Abstract algebra = fields and groups

[modern ruin]

and I turned out fine (that is to say, it doesn't really matter what textbook you use as long as you pick one up and try it, look at the pinned (?) reviews for more info)

[past palm]

That's my bad. I don't really know the names of the courses yet.

I just assumed most people take basic algebra in highschool. MB

[molten mason]

He has Undergraduate Algebra which would be fine, Groups is chapter 2. But his Algebra textbook is advanced.

[past palm]

I have the same problem as you. The only teacher in my school who actually cared about math outside of the curriculum left last year.

[past palm]

Because I want to learn specific about abstract algebra.

I'll probably just pirate his book and then decide if it's worth buying.

[past palm]

I'll try that too

[molten mason]

Any textbook is fine, Calculus is all the same. There's 3 main ones for something rigorous, Spivak, Apostol, aaaaaand there's one more that's cheap but I forgot name I would have to look up.

There there's mainstream calc books, the major 3 are Stewart, Thomas, and Anton.

But really any calc book, any edition in the last 80 years, it's all the same. Just whatever you can get your hands on.

[gray gazelle]

I like rigorous books. So, Spivak, Apostal and... the other book?

[molten mason]

Yeah Undergraduate Algebra is for undergrads. Algebra is for graduate school, those already graduated college with a math degree.

[gray gazelle]

I guess I can throw in Stewart, Thomas and Anton if you're saying they're the mainstream ones

But I'm looking for rigor

[molten mason]

This one

#book-recommendations message

[molten mason]

Stewart has all the answers to both odd and even problems on the paid version of Quizlet.

Thomas I don't know anything about but it seems to be what the other half of schools use if they don't use Stewart.

Anton is a personal favorite. Great writer, also has a great Linear Algebra book, but he's in the same arena as Stewart and Thomas.

[gray gazelle]

This is gonna be fuuuuuuuuun damn. Finally out of the trenches of Highschool Algebra, Geometry, etc.

[molten mason]

Spivak is probably the most popular rigorous book, it's what this discord crams down everyone's throat.

Apostol, which is 2 volumes, is IMO superior but it's very expensive to find a physical copy anywhere.

Kitchen is at the same level as both, probably right in between as far as content. And the physical book is only $50 I believe?

[trail hemlock]

spivak's calculus. beocme a masochist.

[tribal crow]

really? i dont usually see spivak mentioned all too often

why am i getting 'd

[trail hemlock]

to be fair to spivak, it was my introduction to calculus and i turned out just fine (I have severe ptsd from the phrase "show that")

[gray gazelle]

💀

[flat crown]

pete the cat

[gray gazelle]

Alr. Thanks for everyones help 🫡

[marble solar]

Apostol is more difficult than Spivak's book; doing integration theory first is something most students aren't ready for. What I like about Spivak is the depth it goes to. Certainly the best Calculus book in existence

[tribal crow]

spivak's book is kind of in a weird position; it's really rigorous for a calculus text, but doesn't introduce enough to be considered a "proper" introduction to real analysis

so i dont see many people recommend it usually

[molten mason]

I see it mentioned a dozen times a day in this server since I joined

[trail hemlock]

oh theres also
"Calculus: A physical and intuitive approach" my M.Kline that is hella thick and filled with problems, if u dont want to start with spivak (like a normal person would..)

plus its cheap af on amazon used

[tribal crow]

huh. i have not

[trail hemlock]

anything but stewart

[tribal crow]

whats wrong with stewart

(i've never looked at it)

[trail hemlock]

it turned me into a slave.
|| DO NOT TAKE THIS OUT OF CONTEXT MODS||

[slender wasp]

really, I did Apostol I and it is mostly computational problems, maybe a few proofs here and there. While Spivak had more proof problems I think?

[marble solar]

More difficult to read

Spivak's Problem Sets go into extreme depths

(For a calculus book)

[trail hemlock]

Spivak wants you to harm yourself in the process of doing math

[tribal crow]

spivak has a knack for writing interesting problems ig

[trail hemlock]

but ive never seen a more effectice style of self-learnng than pulling your hair out at ever problem, only to realize the answer is obvvious and you are fucking dumb

[tribal crow]

they're just really hard at times

[slender wasp]

Ah I see, yeah Spivak chapters are easier to read I guess but problems are harder. While apostol's writing might require more effort but problems not so much...

but Spivak throws in a LOT of hints. The hints are almost like spoilers lol.

[tribal crow]

this is why we should recommend rudin as a calculus text instead

hard to read and hard problems

[marble solar]

I think this is a bad motto to do mathematics by. Being able to get your hands into calculations is a big part of math

[trail hemlock]

yeah ofc. i learned computations with competitive math before i ever learned rigor, so my outlook is weird

[modern ruin]

I like the phrase "show that" more than I like the phrase "prove that" becuase I tried to read "putnam and beyond" way before I was ready to

and now I am traumatized by the phrase "prove that"

[slender wasp]

Since you have PDEs in your profile, I gotta ask is Strauss PDEs good if I want to then do Fourier Analysis - Tolstov and Stein Shakarchi?

[trail hemlock]

oh my god please not putnam

[modern ruin]

at least I think that's the source of my trauma

[trail hemlock]

please

i did some putnam problems to practice for calculus competitions

omg the headache it induced

[molten mason]

I like how much Linear Algebra Apostol has, and how approachable his Volume II is.

[marble solar]

Volume 2 of Apostol is really something

It's a shame Spivak never wrote a proper Multivariable Calculus book

[trail hemlock]

i have vol1, i loved it

[slender wasp]

"really something" = good or bad?

[marble solar]

I think it's very good

[trail hemlock]

mhm

[slender wasp]

nice I'm just starting on it...

[trail hemlock]

i always say that to mean good, idk abt all yall

[marble solar]

I haven't really found an approach to Calc 3 that I'm a super fan of

I think Williamson & Trotter's Multivariable Mathematics comes closest

But they do linear algebra first, go figure

[molten mason]

As they should

I'm a big fan of Calc I and II -> LA -> Calc III but there's no real good or sensible way to do it except have some LA at the beginning of Calc III and then later or simultaneously do an actual LA class. Apostol has it mixed in both volumes and I appreciate that.

[molten mason]

I'll check this out

[crude sage]

A slightly silly question: what is the most challenging analysis book someone could hope to read after finishing Abbott?

[marble solar]

Try to get a first or second edition

[marble solar]

Papa Rudin?

[crude sage]

That's Real and Complex Analysis not PMA right?

[marble solar]

Rudin: Real & Complex Analysis is probably the most difficult one that you could try

Yeah

[crude sage]

Thanks 🙂

[marble solar]

That doesn't mean I recommend it!

[tribal crow]

i feel like LA and calc 1/2 can and should be taught at the same time

[modern ruin]

I think Calc3 still is in the realm of "you can do this with a video series a la professor leonard and POMN"

[crude sage]

I'm just looking for that feeling of just barely understanding something but still learning

[modern ruin]

and then learn the rest as you go

if you need more

like if you're doing some approach with differential forms

afterwards

[molten mason]

Apostol technically has it at the end of Volume I, so that's kinda like having it between Calc II and Calc III... but I mean as an instructor or someone who is doing self-study you could probably do it out of order, and hit those chapters sooner.

It's weird to me that in the US we kinda do this weird thing of introduction the very basics of LA in middle school, maybe high school, then we avoid it completely until Calc III after it's been forgotten about.

[tribal crow]

huh. thats not quite how its done here

[modern ruin]

just read folland or something

lol

[tribal crow]

none of LA is introduced until grade 12, and then you get exposed to the rest of it in first year uni

[modern ruin]

i mean idk what Abbott covers I have never read it

it's just like introductory RA? how does it compare to Tao

[finite gale]

I don't think there is very much learning going on if you barely understand it, unless I'm misunderstanding what you're saying

[crude sage]

Folland looks interesting, but I do wonder whether it's really self-contained for those fresh out of Abbott

[tribal crow]

can i read folland after having taken intro analysis

[modern ruin]

i mean idk depends

[finite gale]

probably depends what you learned in intro analysis

[tribal crow]

whatever i learned, it's not enough for folland. even i know that much

[modern ruin]

uh maybe like WZ measure and integral? idk, this is the book that the course that is the "next one harder" from my intro RA courses used

[tribal crow]

what i said was in jest

[modern ruin]

like do you want something like just "real analysis?" i really don't understand what you want the difficulty to be here

if you want to not understand something just pick out a hard book and read it'

[hallow oriole]

what do u think of shifrin

[modern ruin]

like you either understand it or you don't

I should probably be asking "what kind of flavor are you looking for?"

[crude sage]

I mean provided it's self contained I could theoretically understand everything with arbitrary time

[finite gale]

if you want to not understand something, just go on arxiv and pick a random article and read it i guess idk

[crude sage]

As best as I can figure out the problem with this is papers don't really define everything you need

The question is kind of underspecified I agree. It's just that the "typical" analysis progression seems to rehash the same things in very gradually increasing generality/conciseness (too gradually), and I'm wondering whether it can't be done faster

[modern ruin]

i mean just read folland if you're trying to be frustrated and still "learn" then. Are you interested in analysis (like platonically) or are you seriously just trying to do something "difficult"?

not that the last thing is "bad"

because folland will seriously test you to see if you know your shit

[crude sage]

I find analysis very fun, and I also enjoy suffering a bit (though whether I do any more than anyone who enjoys analysis is another question), put it that way

[modern ruin]

that is fine, seriously you should crack open folland and get back to me in like 3 weeks to tell us how it's going, maybe you'll really like it

if you find it too hard then just open like tao's analysis II (I think analysis I is too much of an overlap with abbott from what you're describing you want, and personally I think tao's analysis I and II are two of my favorites of all time)

[crude sage]

Yeah I already impulse borrowed it from the library haha

(I have many analysis books from the library rn, my intention going into this conversation was not trying to get people to say I should read folland or something)

[crimson leaf]

Alternatively if you think Folland is too hard you can try Royden I like it so far

[modern ruin]

yeah I suggested folland as a joke at first, but maybe your masochism makes you the perfect fit for it

[crude sage]

We'll see, maybe I'm just saying that because I don't know how hard things can get. Thanks for the recommendations all

[crude sage]

Going to have to look into that, thanks

[marble solar]

Shifrin is an interesting guy, and it's a decent book. It's close to the way I learned it as my undergrad prof. and Shifrin were office-mates in grad school (and shared an outlook on math education)

The biggest plus in Shifrin is that his lectures are online

Which make it easier to learn

[trail hemlock]

thoughts on Hubbard and Hubbard?

[molten mason]

Try Bass

[molten mason]

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

[marble solar]

Haven't read it. Can't say anything about it

[trail hemlock]

👍

[remote sparrow]

#book-recommendations message

https://eugeniacheng.com/wp-content/uploads/2017/02/cheng-morality.pdf

[remote sparrow]

https://measure.axler.net/

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

these are well-regarded too

[remote sparrow]

http://abstract.ups.edu/

was it this book?

[modern ruin]

yes

[remote sparrow]

pinter, judson, or aluffi's Algebra: Notes from the Underground (this book begins with rings first but that's okay)

[modern ruin]

i didn’t know how to work through books at the time, so i spent a lot a lot of time doing exercises

i did all the exercises in chapters 1-9

when i first read it

[marble solar]

https://www.math.toronto.edu/mccann/199/thurston.pdf

[remote sparrow]

https://djvelleman.github.io/HTPIwL/

This book is intended to accompany my book How To Prove It: A Structured Approach, 3rd edition (henceforth called HTPI), which is published by Cambridge University Press. Although this book is self-contained, we will sometimes have occasion to refer to passages in HTPI, so this book will be easiest to understand if you have a copy of HTPI available to you.

HTPI explains a systematic approach to constructing mathematical proofs. The purpose of this book is to show you how to use a computer software package called Lean to help you master the techniques presented in HTPI. Lean is free software that is available for Windows, MacOS, and Unix computers. To get the most out of this book, you will need to download and install Lean on your computer. We will explain how to do that below. An alternative is to run Lean on the web using Gitpod; we also explain how to do that below.

[molten mason]

Well that's cool

[void gazelle]

One reason I like recommending Stewart is that it covers in one book from precalc to Stokes theorem, any other books with similar coverage?

Cause if I read this chat right Stewart might not be the most recommendable book after all

[hallow oriole]

the only reason i would ever recommend stewart is if someone really needed to do a shit ton of exercises

[void gazelle]

Yeah I did Stewart front to back it took me two years

Well not all exercises

I meant from precalc to vector calc

[rigid flint]

Anyone know any good textbooks on multivariable calculus? I’m looking for a textbook with lots of questions which also covers a decent amount of theory.

[hallow oriole]

i like shifrin!

oh lots of questions

[remote sparrow]

https://matrixeditions.com/5thUnifiedApproach.html

https://www.amazon.com/Multivariable-Mathematics-Algebra-Calculus-Manifolds/dp/047152638X

[rigid flint]

Thank you!

[remote sparrow]

https://www-users.cse.umn.edu/~akhmedov/MATH4281.html

https://math.berkeley.edu/~gmelvin/math113su14/math113su14.html

https://math.dartmouth.edu/~m31x19/syllabus.php

https://faculty.uml.edu/dklain/algebra.html

here are some course websites that show which problems should be done in pinter (not related to the previous query)

[lunar junco]

I'm about to start engineering in 3 months. Want book recs on math that'll help me in engineering, but not undergrad level. It should be a level higher than high school level.

any help would be appreciated!

[remote sparrow]

did you take calculus in high school

what kind of engineering by the way

have you previously studied any kind of physics?

[lunar junco]

yep

[lunar junco]

not sure as of now, but inclined towards mechatronics

[lunar junco]

i am doing halliday resnick walker's fundamentals of physics

[remote sparrow]

is there a reason why you're specifying that you don't want undergraduate-level books?

can you explain a little more what you mean by that?

[earnest wolf]

any suggestions for probability?

probably (xD) I'm looking for two types of books:

1. rigorous theory: sigma-algebra, measure theory and so forth (but accessible to undergrads, since that's for an undergrad course)
2. algorithmic problems w/ solutions for calculating probabilities etc

[lunar junco]

i have had calc classes but i need to better understand the topics, so I want to brush up on differential and integral calculus, along with coordinate geometry and algebra

a book that will take me from a beginner level to a really good level

book or books

basically all my classes are over and my finals are coming up, those are pretty easy to do i have no issue doing those questions. i'll have a 3month gap before uni and i want to learn math well so that i don't have to go back to these topics ever again

[void gazelle]

What do you folks think of the McMullen workbooks?

[remote sparrow]

is your calculus book not good enough to do problems from again? and i feel like if you do well in calculus, you are already good at algebra, analytic geometry, and trigonometry

https://tutorial.math.lamar.edu/

use this website to review

[remote sparrow]

Introduction to Probability by blitzstein and hwang and Mathematical Statistics with Applications by wackerly, mendenhall, and scheaffer are good for criterion 2

good measure-theoretic probability books are not designed to be accessible to the average undergraduate

i mean, billingsley develops measure theory from scratch

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

i heard this might be suitable

[lunar junco]

im from india and the problems here are very non-creative as such. they follow a far more methodical and rigorous approach than the ones used internationally. i want to get used to the kind of problems done in other places to check myself and also to experience newer varities of problems

im going abroad for my studies in a year

[remote sparrow]

what do you mean by "methodical" and "rigorous?"

have you done lots of proofs?

[lunar junco]

look at the JEE Advanced questions, you'll get an idea

[lunar junco]

nope, we don't do proofs at all

[remote sparrow]

so you want more routine questions?

[lunar junco]

i mean whatever generally worked for you

[remote sparrow]

i learned calculus from stewart

there are also tons of workbooks available

[lunar junco]

i just want to see what kind of questions others did and challenge myself, if i don't get it i'll learn them

[lunar junco]

ah cool i'll go through that

[dusk wind]

you have the latest edition?

[remote sparrow]

stewart has plenty of routine drill problems and some more challenging problems in the problem-solving sections