book-recommendations

[sturdy shore]

yep

lol

[gray jungle]

[real veldt]

Oh that’s neat

[pine vine]

hey guys

i want to read a book about math

like uh

i dont know how to explain

a book with a story

[eager ermine]

Guys is there no one to help me?????

"

[gray gazelle]

instead of sullying someone should just report this guy... <@&268886789983436800>

[wispy pebble]

@eager ermine this aint the channel for math help

[eager ermine]

???????????//

i am new

i am old bye

leaving this server

[sturdy shore]

nooo don't leave

[gray gazelle]

Major loss

[fierce hedge]

sed

[slender crown]

im trying to learn calc ahread of uni (im in gr12)
i have stewarts early transcendental 9th edition
and aops calculus
i heard spivak and apostol are really good

any advice on the pros/cons of each?

[alpine rover]

What are some math books that you can read in bed?

[mystic orbit]

Nuuuu

What would we do without major slayer of discord#7750

Nuuuu

[gray gazelle]

The elitism of some authors or people is very unfun to deal with.

[gray jungle]

The Banach-Tarski paradox from cambridge

[gray gazelle]

The terms don't have neutral connotation. In my opinion there is implicit elitism in saying 'it is easy'. It can make it off putting for struggling students. Does a logical jump really have to be notated using the phrase 'it is easy'?

[gusty smelt]

I think its fine. Part of mathmetical maturity is understanding that "it is easy" doenst mean you should immediately see 100% of it, but that its something that should fall out easily from working it out.

although i see an arguement for not using it on like

intro books ig

for ppl new to math

[gray gazelle]

I don't like it. It has unnecessary connotation associated with it. In computer science "master slave" has specific meaning but they are still trying to phase it out.

[gusty smelt]

I mean these are pretty different things lol

[sturdy shore]

I disagree that putting words like "it is easy" is elitism, in fact I'd say it is closer to the opposite

I think what happens is that, those who are seasoned mathematicians have already been humbled thousands of times, it's really no big deal seeing the phrase "it is easy" in a proof and struggling a whole day to understand why it is so

but for beginners who haven't had these experiences, it will instead sap your motivation and make you feel insecure

so I'd agree that these phrases aren't appropriate for introductory books but appropriate for whatever that follows

[slender crown]

lmao meanwhile me tryna get advice on a calc book

my opinion though is that maybe they mean that certain thing is "easier" than the rest of the proof, and getting the idea of the big ideas is more important

[gray gazelle]

I'm not a seasoned mathematician. My analysis and topology and algebra and manifolds books all say that stupid shit and I get easily triggered because I have poor mental health. I think not giving a shit about mental health makes math worse.

[alpine rover]

can't tell if this is /s

[dense hamlet]

Is that the thing in the first 5 pages of folland

[sturdy shore]

I am not sure what you are looking for here, but even if phrases like "it is easy to see" are dropped, there will always be proofs in math books where the author leaves gaps to fill for the reader, either because the details are too technical or because the author wants the reader to figure it out on their own.

[gray gazelle]

I don't have a problem with gaps or glossing over details, just the pretentious language

[sturdy shore]

but I've explained to you it is not meant to be pretentious at all

I am all for trying to be accommodating, but if you know a phrase isn't meant to be insulting and yet you still find a way to get insulted, you should try working that out yourself

[heady ember]

I just laugh it off and move off lol

Lmao another "Trivial proof"

But in Enderton this doesn't really happen much

[stark stratus]

I mean the truth is the same with responding to a phrase “I dont care”

Or any phrase

[stark stratus]

Some people have personal psychological behaviors that arnt neurotypical tho, so this may be his natural way of being

[sturdy shore]

I don't buy the idea that this is not something you can work on yourself

and I think it is an inherently fruitful endeavor, it's not just for some phrases in a book

but I'll cut the discussion here

[gray jungle]

Whats /s

[gray gazelle]

sarcasm I think

people write /s to indicate they are being sarcastic

[gray gazelle]

Ive been in therapy and psychiatrists for my whole life. Fuck you.
Also claiming that the meaning of the phrase is completely decoupled from the colloquial dialect is something I think one should be very skeptical of, not the other way around. How do I know that it wasn't used historically to be demeaning and then people kept using the same language and 'gave it new interpretation'?
Elitism in math is super apparent in many ways and this is only one.

@gray jungle

[gray jungle]

Oh gotcha , no im not being sarcastic @alpine rover its a interesting book

Thanks for clarification

[gray gazelle]

Even if you think they deserve this, lets try to not be aggressive

I usually try to ignore people that annoy me

[alpine rover]

oh hello Blitz thanks for your help with alg geo in the other server

[gray gazelle]

Im upset because he just casually told me to 'work on' my mental illness

[gray gazelle]

no problem xd

I know nothing of alg geo so that was a new one for me

[real veldt]

In any case, those phrases will always be a thing, and something I’ll be incorporating in my mathematical explanations

[gray gazelle]

Yes I am aware I won't bring about change. But I get pissed and say shit to whoever whenever I hear it.

[gray jungle]

Im sorry for what you are going through , i can understand how these phrases can be annoying and indeed while some authors may use it as a elitism phrase , most of them are simply following standard practice of leaving details that the reader is capable to fill out with some effort

As opposed to possibly crucial proof ideas that can be really difficult to see without guidance at the end there has to be a balance in how much a book can hold the readers hand , and the term "it is easy" is in reference to perhaps a much more difficult and deep idea in the proof

Like the author wont write "its easy to verify" under tychonoffs theorem

But they might right it with certain small details

[stark stratus]

As Nietzche said, “He who fights with monsters should look to it that he himself does not become a monster.”

But lets end this conversation here

[gray gazelle]

I just wish they could say something else. Maybe "glossing over some details..."

[gray gazelle]

Fine

[gray gazelle]

insulting people is bad

[gray jungle]

Thats a good suggestion

But for now try to see these terms as the authors way of nicely keeping you on guard , even if thats not what some of them intended

[gray gazelle]

it's not easy to always withstand people so I understand you, but you should be less hot-headed next time - that'll just be better for you

I had many situations where I felt the other party to be really annoying or insulting, but I suffered through

generally try to assume good intentions

[gray gazelle]

[dull sedge]

I recommend Euclid and his elements

[gusty smelt]

hey anyone have any reccomendations for books they would like latex'd?

preferably in the 50-150 page range

[gray gazelle]

Is 500 okay?

[gusty smelt]

sure, we can do that one later

any recommendation is good

[gray gazelle]

Engelking's General topology and Dugundji's General topology

[gusty smelt]

I see, yeah a lot of the topology books are p old

ill note these

[gray gazelle]

By latex'd you meant that pdfs of them are scans for example, right?

I understood it that way

[gusty smelt]

like very badly typeset books that you would want to see in a new latex typesetting

[gray gazelle]

Oh, like the ones with bad font?

[gusty smelt]

yeah

[gray gazelle]

Then forget what I said

[gusty smelt]

oof

https://people.math.rochester.edu/faculty/doug/otherpapers/Adams-SHGH.pdf

this is what i think of when i think "bad" i guess lolz

[gray gazelle]

We're on the same frequency now

I had few books like this that I thought were cool. But I usually read a result or two and delete the pdf/djvu

[gusty smelt]

lol

[gray jungle]

Not a short book one but "Victoria Symposium on Nonstandard Analysis: University of Victoria 1972" had a really bad typset

[fickle bough]

I definitely agree with you that it was wrong to delay the construction of R until the ending, it's definitely one of the weaknesses of the book, I specifically mentioned "with no other reference", I think it's wrong to just take 1 book and only stick to that point of view since having multiple texts will cover the flaws of each other, but Rudin as your first text with no other reference unless you're already really good at writing proofs will take you an ungodly amount of time

[gusty smelt]

thats an interesting one, ill add it to our list

I considered applying to victoria they have C* people btw

[fickle bough]

and not only does he delay it he doesn't start from N if my memory isn't failing me

might be wrong on that one would have to check

but yeah if you don't have an instructor for that subject you should definitely have more than 1 reference

to be able to compare

[sturdy sail]

Atiyah's K Theory book

[finite crane]

Peter Constantin - Navier-Stokes equation

some profs recommend this book, but oh boi I sure as hell don't want to read it

[hazy elk]

Auslander, minimal flows and their extensions

[gusty smelt]

oh nice this is actually perfect for a project I had in mind in a way

[gusty smelt]

yeah we for sure plan to get to this at some point

although i have heard arguements to do botts book on the topic instead

should be interesting which one we pick lol

[gusty smelt]

this one looks good too, I will add to the list

(when i said looks good i mean it looks like shit hence good for the project lol)

[coral prawn]

mfw Navier Stokes

[cedar rain]

A book that explains Handle decomposition (Handle slide, cancellations, surgery) in detail for undergrads? I feel like every source I encountered assumes that you can visualize 4 dimensions and above so probably I am missing pre-reqs.

[fierce hedge]

sorry I thought I had replied. My question is, have you tried this book and vouch for it? Like do they have any kind of refund policy if I don't like it

Or any sort of demo version I can look at before buying

[grave thorn]

"Lectures on stochastic analysis: diffusion theory" by Stroock

[stuck tapir]

what are the best books for combinatorics

more specifically dearrangments in combinatorics

[finite crane]

what is a good resource on stationary measures on a Hilbert space like L^2(X) (where X is compact), from a Markov process on it? for reference the markov process is like just applying heat flow with some noise

[finite crane]

hmm, is the fancy name of this topic "the existence of stationary measures for stochastic evolution equations"

[proper harness]

anybody know a good source on the projective line?

I tried Hartshorne's book on Projective Geometry but it only mentions it briefly.

[still nebula]

Any good textbooks for an introduction to statistical modelling with the following topics

[stray veldt]

what do you want to know, the book should give you the tools to study it

[proper harness]

anything really, I can prove stuff on my own, just trying to get a sense of what is known and out there.

[stray veldt]

i mean its a really simple example of a projective space/an algebraic curve/wtv you want; there isnt too much interesting to say about it immediately

i guess there is something more interesting to say in specific cases like over the complex numbers, or maybe over some weird rings (?)

also wondering if there is a synthetic notion

[proper harness]

Riemann sphere also counts

but it is a bit weird how he skips immediately to the plane

[stray veldt]

you have the studying role

[wind trail]

Oh

,Iamnot dying

[hasty eagle]

Removed the studying! role from you.

[stray veldt]

well, projective planes are a field of active research (somewhat at least)

the projective line is very simple

there isnt much to say about it in general

[proper harness]

you might be surprised

[stray veldt]

try me 😛

[proper harness]

ok Wikipedia has an article that I didn't see before

[proper harness]

I mean
the empty set is very simple, but we can still learn new things about it. like who would have known that it can be used to represent logical negation? but in propositions as types that's a crucial observation.

[stray veldt]

the only interesting thing i could find is https://ncatlab.org/nlab/show/projective+line#synthetic_projective_lines

though this seems to list all examples

[proper harness]

hmm ok

[gray gazelle]

intro real analysis book which covers a lot of theorems and topics ... from basic level

[wind trail]

This one is awesome

And very well known

Starts from the very basics

[shadow forum]

@wind trail it gets tough really fast tho

i suggest abbott's understanding analysis. it just has analysis on the real line which makes it easy to understand the topological properties when u are learning for the first time.

[gray gazelle]

how is this

[distant spear]

very good

[gray gazelle]

um why

[distant spear]

i enjoyed it a lot

[gray gazelle]

is it good for learning real analysis the first time ?

[distant spear]

most ppl say no, but I found it not too difficult

abbott is usually the starter

try that then

[gray gazelle]

should abstract algebra be studied before real analysis ?

[shadow forum]

no

[gray gazelle]

so is it not useful ?

[oblique hatch]

They can be studied in either order, or in parallel
Except where you’re at a uni where one of those is your “intro to proofs” course

And not the other

[gray gazelle]

i am very new to proofs

[oblique hatch]

If you’re self studying, that part of my comment doesn’t matter, although doing some form of introduction to proofs may be useful

[gray gazelle]

do you recommend any youtube series on intro proof ?

[oblique hatch]

I don’t really know any
I don’t really use YouTube to learn new maths

[hazy elk]

Pugh can be read even without knowing how to write proofs, but it will be a difficult (yet fruitful) journey... You can also read Abbott's understanding analysis or Ross' analysis (I forgot the exact name but I remember the proofs in this book were very accessible) for a (slightly) gentler treatment

[gray gazelle]

i am so stressed about this subject ...

[hazy elk]

Its not that hard

You just need patience to get good at it

It's really not that difficult to get a handle of... you just need to put in a lot of effort

[gray gazelle]

a lot of effort..... more than calculus 3 ?

[hazy elk]

Eh you can't really compare the two

[hasty turret]

Alternatively you can start with a calculus book

Like spivak calculus

[gray gazelle]

why will i learn calculus again

i just finished it all

[hazy elk]

Yeah just learn analysis imo

Just get started, no need to be scared

[gray gazelle]

hmmm should i take a book which teaches it using metric spaces

[hazy elk]

Rudin and Pugh do metric spaces

[gray gazelle]

or something which teaches it seperately for 1D and 2D

which seems easier

i am a engineering major btw taking

it

[hazy elk]

You're really overthinking it

[gray gazelle]

cuz its in my course

[hazy elk]

You can't go wrong with Pugh/ Rudin/Abbott

[gray gazelle]

i finished all calculus and don't know Epsilon delta definitions .....i wish i over thought before starting calculus

[hazy elk]

Just try reading and then decide yourself

[hazy elk]

Actually most ppl who learn analysis for the first time don't know the epsilon delta defn

I mean at least in my country

[gray gazelle]

may the analysis god bless me

let me make a list'

Abbott's

ross

pugh

[hazy elk]

Rudin
Tao

[hasty turret]

What's your endgoal exactly

[hasty turret]

What's the difference tho?

[gray gazelle]

passing the test ....and become a engineer

[hasty turret]

Then like read the recommended textbooks?

[gray gazelle]

they didnt recommend me sny

any

[gray gazelle]

imma read 1st chapter of all those you sent and choose one wisely

[hasty turret]

Is it supposed to be like "rigorous calc*

[hazy elk]

Uh.. that sounds like a hugely inefficient plan

Math books take time to read, start with a book and it it doesn't work out for you, by all means change the book but if something works, there's no reason to try out all possible books before deciding

[fierce hedge]

Bartle and Sherbert is very good

[grave thorn]

iirc Hairer has notes on this

[finite crane]

Erdogic process something lecture notes right? I have it. But stochastic evolution on infinite dimensional L^2 is a bit trickier

[gray gazelle]

Guys, I'm taking a CS course and my math knowledge is not that good. I failed at differential calculus exam (it was about limits and derivatives) and as the 2nd semester came I started failing understanding the basic concepts of algorithms (big O notation, gamma and theta notations). I mean.. I understand them, but not in a mathematical way (couldn't understand the demonstrations).

I'm familiar with the concept of limit and function, but that's it, that's all. Everything else is like arab for me, I don't know trigonometry, I don't know how to deal with exponentials, I don't know anything.
That said, I always struggled with math as** I can't find it enjoyable**. While I really enjoy taking other courses and learning other things (boolean algebra, logic gates, assembly, programming etc) I really can't take myself to enjoy math. It almost feels like somebody's speaking another language and I have to find a meaning to what they say 😐 .

I also have an integral calculus course to attend this semester, and I'm already not understanding it xD (it was the 2nd lesson today). He started talking about series and successions (idk if that's the correct way to translate the arguments of today's lesson) and I couldn't understand anything basically 😐

And I really don't know where to start, what to do

I thought about starting by reading Carl Stitz "Pre-Calculus"

But I don't know

What would be your best suggestion for me? 😦

[wind trail]

Goodnotes op

[finite crane]

Read Tao's Analysis
Speedrun through what you already know.
But to be honest, you should have done this sooner. It may be too late. Or not. You may need to go to office hours and ask for personal tutoring

[gray gazelle]

Well, maybe it's too late, but I'll manage to do it anyway

In case I can't get to the moon, I'll still be floating through stars :3

[slender cargo]

What math classes have you taken? Discrete math, non-rigorous calculus? What CS course is being a problem?

Tao’s Analysis imo is at a higher level than you’re expected to know. You’re getting tripped up on basic high school math. Maybe going through a book like Lang’s Basic Mathematics would help. Seems like you’ll really need to slow down for a bit

Maybe go speak with your advisor also?

[finite crane]

it may be good advice to study precalc yes if you don't know how to calculate with trig / exp

and then you work through James Stewart's Calculus book (which provides practical first course on calculus without any proofs). Most likely Stewart is all you will need in your course.
And then if you want to understand why certain things work and others don't, you can read Tao's Analysis (after Stewart). I know that some people like to understand more than others.

don't read everything. you can skip around, and ask your professor / TA in office hours what you need to know

[crimson leaf]

https://tutorial.math.lamar.edu/Classes/CalcI/CalcI.aspx

Good resource especially the first section

[gray gazelle]

Well, before university I didn't learn that much math because I used to drop out of school at 15 and now I'm 25.
In the university we took Differential Calculus and another course that's literally called "Mathematical Methods for CS" that is basically discrete math and explains combinatorial calculus, functions, relations and logic (truth tables and stuff like that)

[wild fern]

Would you guys recommend Bartle & Sherbert's "Introduction to Real Analysis" or Tao's "Analysis I" as an introductory book on analysis?

[finite crane]

Bartle doesn't construct the real numbers or go into the depths of Tao's discussions. I imagine you can use it if you want to put off Tao and Rudin until later

The real value of reading Tao or Eli Stein however, is to hear their discussions. Intuition is a valuable thing. Try to prove the theorems yourself before reading the proofs, as much as possible

[faint nebula]

I recommend berserk
Nuff said

[sage python]

Does construction of R matter much?

[finite crane]

definitely won't matter for people who have just started calculus and have more practical concerns. They can just blackbox it. Matters when you try to understand things in a rigorous way.

[sage python]

I mean even from an analysis pov, feels like you just use ordered field with suprema

[finite crane]

I think completing a metric space is a more general concept, such as for p-adic numbers

[sage python]

That much is true yeah

[narrow relic]

I'm not sure if they have a refund policy. I learned a ton from the first chapter of that book but I didn't go onward. It's a very dry book but as far as I can tell it has a lot of the right content and it's all laid out pretty clearly. However, the dryness of the writing and the really boring typesetting and font make me not want to pick it up again. Now that I have the basics down, I'm planning to work on a more "exciting" abstract algebra book since I don't need the super-pedantic notation that the Cooperstein book has. I hope that's a helpful "review."

[narrow relic]

I thought the Bartle book was pretty good; I've never looked at the Tao book

[finite crane]

if you like chatting
sounds like you will like tao

[grave thorn]

If you want stochastic evolution equations in infinite dimensions, I can recommend "Stochastic differential equations in infinite dimensions" by Gawarecki and Mandrekar

[finite crane]

lol there's a book with nearly exact same name "Stochastic Equations in Infinite Dimensions"

[grave thorn]

LMAO

[finite crane]

da prato's book looks way lengthier

more fancy?

[inland elm]

im getting a reference AT book. hatcher is too handwavy so i was looking at spanier but i hear it's dated. is there anything similar in rigor and more modern? categorical would be nice

[finite crane]

either tom dieck or peter may

[gusty smelt]

Tom dieck is p good for reference I second

[inland elm]

i do like dieck
i also want to mention that looking at spanier it feels like hatcher but done right. am i not familiar enough with modern AT to notice its age, or is it not really that dated

i wish i could buy all of these

[cobalt phoenix]

Stewart's calculus books

no

Stwart's anything

RIP

[rigid shale]

Book recommendations for the major branches of math?

[grave thorn]

What level are you at

[rigid shale]

High school level

But I have a thing for analysis and higher level maths

I would like harder material

[chrome yacht]

Abbott for analysis, axler for lin alg, munkres for topology, enderton for set theory

[rigid shale]

Analysis is Terrance Tao for me

But I'll check the other author

[cobalt maple]

Try Michael artin algebra

Teaches you algebra and Lin alg together

I’m not a fan of a ler

[sage python]

I also don't recommend Axler, it's mostly fine but toward the end it gives you brainworms

[worthy chasm]

Some reading recommendation on estimation theory for someone who's done a basic level course in stats and is getting started with machine learning? (Online course recommendation wud do too) Also for a beginner level text in optimization?

[glacial crypt]

you mean the determinants bit? I was thinking of using it until determinants and then picking a diff book

[fervent mist]

I need a book for understanding the affine space :(

[heady ember]

Any nice fiction books to chill and relax with?

[foggy relic]

Dostokevsky

[orchid mortar]

Pick any from a top 50/100 novel list

[heady ember]

[orchid mortar]

Well, not all of them would be super chill (thinking is probably necessary for a book to be good, but this shouldn't be stressful thinking), but certainly worth to read. But I think still most are readable in a chill way.

[chilly yacht]

Hi, guys! Can someone recommend a good introduction to math logic?

[karmic thorn]

Leary, A Friendly Introduction to Mathematical Logic

[sturdy shore]

the part about determinants is fine, that is the last section
I believe he is talking about the section before that, where the characteristic polynomial for a real VS is introduced in an absolute ridiculous way just to keep not talking about determinants

I just don't get why he has to introduce them at the very end

[oblique hatch]

I think that’s kinda the point of the book
He’s trying to not use determinants, and teach LA

[sturdy shore]

yes but this is not a binary

[oblique hatch]

And the best way to do it is not to have them

[sturdy shore]

just because you are against introducing determinants early on and generally avoiding their use in proofs doesn't mean you have to introduce them at the very end

goes from a somewhat reasonable idea to a not very reasonable one

[grand thistle]

https://www.maa.org/sites/default/files/pdf/awards/Axler-Ford-1996.pdf

[sturdy shore]

I am aware of this paper

again, I broadly understand his intentions, I already said as much...

[pseudo forge]

Dostoevsky is barely even fiction tbh

his books are the definition of real

[indigo mesa]

You should go see someone if that is a depiction of reality for you

Pawnbrokers sweating right now

[viral cove]

i read ready player one again

[solemn rover]

I learned out of Spanier and it was not dated.

There are problems with it but it's not really that it's dated

the problem is more that it's too detailed and contains too many theorems that are of only technical interest.

You need somebody to tell you what the important theorems are so you don't spend two years reading it

you need to like, carefully read the opening paragraph of each section to figure out what the important theorems are, and then ignore the other 50%

Like the biggest problem is that it takes 150 pages to get to homology because he grinds out all these theorems on simplicial complexes and fibrations early on

[coral prawn]

Wha

[solemn rover]

Spanier would be a better book if you attacked it with a pair of scissors and got rid of 50% of the content

it's a compromise between a text and a reference but it doesn't balance them well. it just slowly turns from a textbook into a reference and before you realize it you're reading an encyclopedia of everything that's ever been figured out about singular cohomology

I also hate to say it but some intuition is lost with the formality.

The proof of poincare duality, i have no idea what the intuitive content of that is.

You have to supplement it with a book that explains the geometric content of theorems sometimes

[inland elm]

i did end up getting spanier because dieck was a bit more expensive and also out of stock where i looked. i’m hoping for more of a reference than anything so as long as it’s not dated i think i’ll be alright with it. i did like the formalism when i took a look yesterday

one day when i have a little more spending cash i might buy dieck or something but spanier will do the trick for now

[unborn hazel]

Never been through a mathematics book, how would one approach and learn from it?

[novel siren]

Best textbook for self-learning multivariable/vector calculus?

[sage python]

Do you want more theory, computations, physics intuition, what?

[novel siren]

Me?

[sage python]

Yeah

The recommendation might depend on that a little bit. For more proof-based stuff I'd probably recommend Shifrin's Multivariable Math, and tbh it does have some physical intuition and computational examples

So it's prob the best "well-rounded" book I know of

But for some people the proofs and theory are a distraction, in which case maybe I'd recommend other books

[novel siren]

Well i got done with single variable calculus and now eager to learn vector and multivariable calculus

Mainly because i want to learn more into vector spaces and fluid dynamics

And also because i want to get ahead before i actually take the equivalent of vector/multi calc in college

[sage python]

Did your single variable calculus prove theorems? E.g. did you guys prove the fundamental theorem of calculus? The man value theorem?

[novel siren]

I just did the regular calculus classes

[sage python]

And whatever your answer is to that, do you want to learn how to prove theorems? Or is your focus using the theorems to calculate and to do problems in engineering/physics?

[novel siren]

Honestly id like both im just very curious and i want to learn more of math and mathematical physics

[sage python]

Then read Shifrin

[novel siren]

Man these prices 😹

[sage python]

Ah true

Hmm

Let me find a cheaper one

[novel siren]

I mean i can probably find a second hand or whatever

[sage python]

Well let me look I have one book in mind

And if it's suitable I'll recommend since it's pretty cheap

[novel siren]

You think ill be alright understanding all this just from calculus?

[sturdy shore]

hubbard hubbard is touted as a cheaper shifrin generally

can buy from their website for a discount apparently

[sage python]

Hubbard-Hubbard has very fucky organization

Try "Advanced Calculus of Several Variables" by Edwards

[sturdy shore]

whether you are gonna follow shifrin's book or not, this playlist is a godsend https://www.youtube.com/playlist?list=PL5I-Eyk8l9FHdJUd9UujGcvumjCFPHbrd

[novel siren]

Thats more my price range

But you think ill be fine learning this by myself from regular single variable calculus foundation?

[sage python]

I didn't use this myself but the preface of the book suggests so

[novel siren]

Perfect thanks alot

[oblique hatch]

How much of Atiyah Macdonald needs Ext/Tor (and stuff that they only introduce using it)?

[remote sparrow]

not so much a discount as much as amazon sells hubbard and hubbard at a substantial markup

[heady ember]

There are... 'creative' ways you can get free PDFs of books online. Then you can print it out if you want

[glacial crypt]

first book of the bible library may have it

or last letter of the alphabet library

[hollow shore]

Round Ireland with a Fridge

[remote sparrow]

kingkiller chronicles

[cobalt maple]

How do you guys approach digital v. Physical books?

I kinda wanna start building up my library and I do feel like having a physical copy is good from a physiological standpoint, but 💰

[finite gale]

physical is nice but im not spending $100 on a textbook

[cobalt maple]

What about like monographs or something

[coral prawn]

tbh I'd definitely prefer physical over digital but

[cobalt maple]

Like let’s say you want serge langa algebra, which is 1k pages

[coral prawn]

as u pointed out, money
also, it can be a pain when they're so thick

[cobalt maple]

Id assume you’d use it so much you’d get your moneys worth

[coral prawn]

me reading serge lang linear alg XD

[cobalt maple]

Yeah fs…

[cobalt maple]

Didn’t know he had a lin algebra book

Need to check it out cause I didn’t enjoy axler

[coral prawn]

XD

[coral prawn]

https://tenor.com/view/kirby-gif-19542877

[cobalt maple]

If you spend that much, you have to read it

[finite gale]

on one hand, true; but on the other hand, sometimes it is nice to switch around between textbooks because one might explain something better than another

[cobalt maple]

Also true

But also

Struggling with a single textbook is healthy imo

[coral prawn]

me after reading George Shilov's lin alg and not understanding anyt and then moving to serge lang's lin alg:

[real veldt]

Physical textbooks would make a nice collection but sometimes it’s cool to just have exercises and definitions side by side

probably the only reason for me

[pseudo forge]

i usually use my notes as the go-to reference anyway so having a physical copy around isn't really necessary

and my notes are pretty much an abdridgement of the textbook

with solved questions

[alpine rover]

odd request, but are there any basic abstract algebra books that are written as if they were a high school calculus textbook?

something super standard like pearson

[grand thistle]

wdym, like just having a bunch of calculations?

[alpine rover]

maybe but not exactly

i'm thinking like stewart calculus

what is the stewart calculus of abstract algebra

very corporate feeling

clean but comprehensive summary

[grand thistle]

maybe dummit and foote

[alpine rover]

thanks

[karmic thorn]

Gallian comes very close

Oh also, Pinter's Abstract Algebra

These aren't exactly Stewart-esque but are introductory textbooks with a lot of chapter end exercises that range from routine computations to standard results

[alpine rover]

ohh nice thank you

both of those look great

[karmic thorn]

[grand thistle]

any opinions on shastri's "Elements of Differential Topology"?

[tawny copper]

libraries exist

[hidden elbow]

ong

[gray gazelle]

Invest in a kindle or buy second-hand

[narrow relic]

Did you like the Serge Lang Linear Algebra book? I had forgotten this but I worked through some of it a while ago and thought it was pretty clear/good

[remote sparrow]

physical technical lit just straight up beats ebooks. for fiction you can use an ipad or e-reader.

tabs or split screens aren't the same as having multiple books open at once to cross reference

[simple oak]

a mind for numbers

[dense plover]

why not?

[finite heath]

Does anyone know a book where I can find a proof that the Hurwitz integers are a maximal order in the quaternions?

[coral prawn]

Yep, found it to be a lot easier to understand. A lot easier to digest for those who have basic knowledge of set notation. That being said tho, the topics covered seem to be rather basic as compared to other books- so I'm looking to move on to others as soon as I grasp the fundamentals

[narrow relic]

Cool, yeah I had completely forgotten that I had worked through part of the book. I looked at it again and now remember why I stopped with it. It isn't that much more advanced than an introductory book like Poole and I had already learned a lot about basic linear algebra from that. So I realized I wanted something a bit more advanced and that covered more.

[potent pasture]

for advanced maths pls refer me a book

[finite gale]

what kind of book are you looking for

[uneven sundial]

hey guys im lookig for a book on analytical geometry of 3d space. i have no idea what kind of books there are so any rec will be helpful.

[swift dome]

I need a decent source for undergraduate students for discrete mathematics

[sage python]

@swift dome are these math majors?

[swift dome]

yea

[sage python]

So, one of my former calc students is mathematically pretty curious, focuses on applications of math but wanted to learn math on math's terms

He was a nuclear engineering major so I knew he'd take calc and linear algebra anyway. I was trying to find something in discrete math that was kinda... Simultaneously an intro to proofs, algebra, discrete math with some cool applications like error correcting codes and cryptography

The closest thing I could find was "Mathematics: A Discrete Introduction" by Scheinerman

[swift dome]

I appreciate the suggestion Daminark ty

[sage python]

Rosen is the most standard book, and Matousek-Nesetril is more sophisticated

[orchid mortar]

Oho Jiri Matousek?

That's nice, to see someone who wrote a fairly intro (and nice) book to LP

[sage python]

Yeah, "Invitation to Discrete Mathematics"

[remote sparrow]

concrete mathematics

[sage python]

I prefer the older edition called "Cement Mathematics"

[remote sparrow]

[inland rampart]

What is that

[livid ermine]

hmmm

aluff is like a book about algebra

and it has chapters, and subchapters.

and i made a list how how good each of the subchapters are

[dapper root]

Damn u read a lot of this book

[livid ermine]

yeah. i think that is the book I spent the most time of on any book

[dapper root]

Good book

The last 2 chapters r good

On homological algebra stuff

[livid ermine]

it was the first algebra book I got also, and I got it in HS when I didn't even know what a vector space was, so I had to re-read some of the stuff cuz i didn't understand it

[dapper root]

For a book on this level

Hopefully you didn’t get it as a companion to your highschool algebra class

[livid ermine]

hmmm. in my country it is actually standard to talk about spectral sequences and derived categories in HS algebra

[livid ermine]

its funny tho, there actually a reasonable number of people who do this.

some times I go to a university book store

and there is like a single copy of a book called like "basic algebra" or something

and its like a research monograph about topoi or something

and its a book thats been given there

@dapper root whats the book you spent the most time on of any book?

[dapper root]

Hartshorne

Or matsumura

[livid ermine]

Man that sounds hardcore

I want to learn algebraic geometry and also more commutative algebra.

[tropic thorn]

may i ask what country ?

[livid ermine]

hmm. its called obungabingbong in my language, I don't know the english word sorry..

[tropic thorn]

im algerian nice to meet you

[gray gazelle]

good book for alg K-theory?

[rigid shale]

A good book for abstract algebra?

Recommend both beginer books and books with more contents please

[remote sparrow]

Beginner books: A Book of Abstract Algebra by Pinter and Abstract Algebra: Theory and Applications by Thomas Judson
Books with more content: Dummit and Foote, Jacobson, and Lang

[finite gale]

Fraleigh is decent as well

[gray gazelle]

Abstract Algebra: An Introduction by Hungerford and Contemporary Abstract Algebra by Gallian,
for more depth you could probably stick with Hungerford and read Algebra

[plush saffron]

Does anyone know any good math books that goes in depth on the maths of quantum mechanics?

And any good advanced abstract algebra?

[heady ember]

Hm is this Jacobson's Basic Algebra I lol

I bought it around two months ago

Tho I knew what I was getting myself into

[glad folio]

Leon Takhtajan

[sand garden]

Any books about Mathematics related to Computer Science? Specifically about how it can also relate to Information security?

[torn crypt]

information theory

[livid ermine]

No. But it could've been.

One book like this that I bought was the book

[heady ember]

i see

[livid ermine]

DO you think jacobson is a good book?

[plush saffron]

thank you!!

[heady elbow]

what books would help me reach imo level

[noble kayak]

hello could someone please recommend me some books about alegbra i am in highschool so something beginner friendly

[foggy relic]

dont learn it till you need it tho

Aluffi based

[heady ember]

Haven't read it

[foggy relic]

Yeah it is good

part 2 covers some nice topics that arent found in a lot of similar books

[livid ermine]

is universal algebra useful?

[foggy relic]

like Birkhoff theorem stuff?

oh im pulling up jacobson toc rn

yeah this looks like fairly standard stuff

inverse limits, free groups

[river kindle]

Is "The Art of Problem Solving, Vol. 1: The Basics" by Rusczyk, a beginner-friendly book for maths problem solving?

[foggy relic]

yes.

[finite gale]

Many of the aops books are pretty beginner friendly

[alpine rover]

any good introductory analytic number theory books?

[hearty steppe]

This quantum theory for mathematicians book by Brian Hall is really hard but… quite motivating. There are some abstractions of concepts that go a little over my head but I’m still able to wrestle with it and I’m 3 chapters in. I’m still going to finish Griffiths QM book but this will make it an easier read.

[slim peak]

I don't have a lot a memories about it, but afair it was really good

[hearty steppe]

Do you have recommendations for other texts that may gloss over the concepts in better detail that certain chapters don’t cover very well?

[slim peak]

B.C.Hall's book is pretty detailed if I remember correctly

Maybe you should check for the pre-requirements books

[hazy elk]

Is the language Sesotho?

[gray gazelle]

a book on intuitionistic logic?

[remote sparrow]

it's cheap if you get it from dover if nothing else

[remote sparrow]

you could read shankar qm over griffiths

[hearty steppe]

I mean aren't they around the same level of exposition? I like griffiths so far. I am going through Hall for different reasons other than just learning QM

[remote sparrow]

shankar does more bra-ket and uses linear algebra more frequently. griffiths uses the schrodinger wave equation more

[gray gazelle]

which one more uses more math and less physicy stuff?

in QM u can have unsetly many vectors?

[hearty steppe]

Well if I find myself struggling too much with Hall or Griffiths, which... for now I'm doing alright... so I'll wait on reading shankar.

[shut cave]

I'm trying to find some open problems in real or complex analysis to work on over the summer. Does anyone have any recommendations for resources I can use to find such problems?

[remote sparrow]

they're both physics books for physics students

just shankar uses more linear algebra formalism and many people prefer this treatment over griffiths

[lean abyss]

power of five is a fun read, ending kinda smells a little but it’s a great read overall

is this like a maths book recommendation

[gray gazelle]

"Use this channel to ask for book recommendations. Tends to be mostly math but feel free to ask about other literature (YMMV)."

[gray gazelle]

no

[lean abyss]

oh ok lol

[coral prawn]

Recommended book(s) for analysis?

[sage kelp]

What’s your background @coral prawn

[coral prawn]

mostly doing calculus and linear algebra rn

[fierce sequoia]

book name-Glass Castle is a pretty good one

[gray jungle]

You can try tao's analysis 1

[coral prawn]

Tarrence tao had an analysis book? Pog

[gray gazelle]

yeah I heard they're good

[sage kelp]

You can also try Bartle and Sherbet, Pons, Abbott

[foggy relic]

Browder mathematical analysis, an introduction

[narrow relic]

This book is pretty hard-core, right?

if I remember right it covers a ton of material in very short order, does it gloss over the stuff or is it actually okay to follow?

[foggy relic]

Normal analysis book with no prerequisites

Yeah it's okay to follow

[narrow relic]

Cool thanks.

[finite crane]

proof-less calculus or proof-based calculus (analysis) ?

usually ppl go through the former before they get to latter

if you're doing proof-based then I second Tao's Analysis I & II. He's very chatty and informative so you can learn from his intuition. However, be sure to prove every theorem before reading the proofs (as much as you can, of course). And check errata on his blog
https://terrytao.wordpress.com/books/analysis-i/

[grand thistle]

you could also try spivak’s calculus if you want something slightly easier (though still difficult compared to normal calculus texts)

[coral prawn]

Thanks for all the responses guys

[coral prawn]

Tao the Chad as always

[gray gazelle]

What is a book recommendation that can help me understand calculus better

[swift dome]

Stewart calculus and you can see khan academy tutorials too.

[gray gazelle]

Since you said understand it ‘better’ I’m going to assume you’ve already seen some derivatives and integrals. I’m currently going through Apostol Calculus as a second course in Calculus and a gentle Analysis course.

Oh ok thank you for your help

[crimson leaf]

I would say probably an analysis book popular choices are: Abbot Understanding Analysis, Schroeder Mathematical Analysis, Browder Mathematical Analysis, Tao Analysis 1&2, and Bartle Introduction to Real Analysis

[coral prawn]

Wrong chat?

[opaque steppe]

woah sorry

[grand thistle]

you forgot the goat

[sage kelp]

I don’t think I’ve heard about this one. Will check it out

[wooden sparrow]

Hello, I'm looking for a book/course/ video recommendation for my first course in linear algebra.

I am looking for an engineering oriented book/course

[dapper root]

If engineering I think the book by Strang

[wooden sparrow]

Ok thanks

[remote sparrow]

Differential Equations and Linear Algebra by Goode and Annin has a complete treatment of linear algebra, plus ordinary differential equations (no boundary-value problems or PDE coverage).

[sage python]

I thought it was by Goode and Amin for a second

And was gonna be like yo this is actually the perfect book

[wooden sparrow]

Oh this sounds nice, I'll try this one

[foggy relic]

nobody is reading 900 pages for linalg

[remote sparrow]

only 312 pages are dedicated to linear algebra

can't really count the appendices either

in any case the linear algebra chapters stand completely on their own; you don't even need to read any of the differential equations chapters

[cedar ridge]

bit of a book hoarder but which real analysis books/problem books have qs harder than rudin

and where can you find assignment type qs in general

[grand thistle]

i mean that's still not really "only", that's longer than a lot of full length math textbooks

[grand thistle]

amann and escher's analysis books are difficult and abstract

covers much more content than rudin too

[heady ember]

A fellow book hoarder? I have more than 10 anal books in my totally legal collection lmao

[cedar ridge]

only 10? rookie numbers

[cedar ridge]

iirc amann is the three part series that is a rough ug course, and eschler got no topology

[heady ember]

Lmao how many (real) anal books do you have

[remote sparrow]

i'm pretty sure amann escher covers some topology

[heady ember]

Yeah in book II I think

[grand thistle]

amann escher has topology integrated within the analysis

[grand thistle]

no

it's in book 1

[heady ember]

Yeah just checked

[gray jungle]

What do you consider "real analysis" ?

[pallid hatch]

analysis of data structure

[sage kelp]

Serious question. In what year is Amann and Escher is used?

[dusk tapir]

My impression is that its the standard to cover the topics of the first book + beginning of the second book in the first semester over real/(complex) numbers.
In the coming second semester we introduce metric/normed spaces, revisit some topics from analysis 1 on these spaces and cover some new stuff.
So the contents are used in the first couple analysis courses (atleast my university has a mandatory analysis 1-3 progression) (probably less in depth and not defining e.g. sequences on metric spaces from the beginning) and I have seen the books in the recommended list of some analysis 1/2 courses online (many examples where they are not referenced too, e.g. my analysis 1 course).

Im just a first semester student btw, so maybe someone with more experience can chime in.

Also piggybacking on your question: Does anyone have a (german) analysis 1/2 lecture script from one of the authors or some other professor that based their course mostly on amann escher? I could not find any online.

[indigo mesa]

Yeah the mandatory analysis 1-3 progression is standard here afaik

Amann Escher aims to provide for exactly that, first, second and third semester

but of course covering things as in depth as in there is not really possible

[dusk tapir]

Did you read the books simultaneously to the lectures?
I started reading the first one now and it takes time working through it so im wondering how I should handle it when classes start again.

[indigo mesa]

i didn't have a lot of system behind it

[sage kelp]

Safest bet in the world I gather. Are you German? If so, can I DM you?

[indigo mesa]

I read stuff and did exercises whenever i found the time

[tulip saffron]

can anyone recommend me a linear algebra book for CS students?

I was recommended Friedberg Insel Spence's linear algebra book but I think it might contain too many unnecessary contents for a CS/engineering student

[remote sparrow]

#book-recommendations message

coding the matrix also exists

https://codingthematrix.com/

[wicked lagoon]

You guys know where I can find some PDFs on mental math tricks there was this book by a guy named arthur Benjamin I was thinking about buying but I want to dip my toes in before I buy a book like that

[narrow fiber]

idk about pdfs but that book was like

formative for me as a kid

I have an old copy in softcover but I'll let you know if I find a pdf

[gray gazelle]

Art and Craft of Problem Solving

[wicked lagoon]

Thx mates 👍

[narrow fiber]

the book I have is "secrets of mental math" by benjamin I'm pretty sure

[tulip saffron]

thank you!

[tulip saffron]

I thought you were all going to recommend Gilbert Strang's Introduction to linear algebra

[gray jungle]

Is learning proof based linear algebra really unnecessary ? I find that hard to believe, and i think the problem solving skills and mathematical thinking you'll build from doing friedberg is ultimately a investment worth considering.

[tulip saffron]

I dont know actually

thank you, I will try reading Friedberg's book

[sage python]

If you wanna see something proof-based written by a professor that's math cap CS

(Though perhaps not in final form)

http://people.cs.uchicago.edu/~laci/HANDOUTS/linalgbook.pdf

[subtle mango]

graduate level statistical theory books?

[fierce hedge]

Ohh, that's the graph isomorphism guy. I read his paper in my 2nd year internship

[sage python]

Yeah I first learned linear algebra from this guy

The notes are not quite in the same order in which he did things, he intertwined material of the first two parts more, and obv some stuff was based on peculiarities of our class (our first two days were taught by someone else whose approach to the material was different)

But yeah in a way the spirit is similar

[fierce hedge]

The books looks pretty good, will give it a try when I get free time

[tulip saffron]

Thank you!

The order of the book seems pretty different from other linear algebra books

[cobalt arch]

any axiomatic books for geometry?

[gray gazelle]

The foundations of geometry by David Hilbert

[broken meadow]

i hope you mean that as a joke

in any case it doesn't belong in this channel

(I hope you were not calling them childish or worse)

@boreal quiver

[fickle whale]

What's the opinion on Lay,Lay,McDonald Linear Algebra

[remote sparrow]

it's a pretty standard first course in linear algebra book

[dense hamlet]

Does anyone have a quick primer on Frechet differentiability and stuff related to Gateaux differentiability and similarly related topics on nvs

actually, here's just the list of topics I missed while sick for this lecture:

More on differentiation: Fréchet differentiability, derivative as a continuous linear map.
Why a linear map from a finite dimensional normed vector space is always continuous.
More on Fréchet differentiability: why it implies Gâteaux differentiability and continuity, how a directional derivative is computed from the Fréchet derivative.
Equivalent formulations of continuity of linear maps between arbitrary normed vector spaces, characterization in terms of "boundedness on bounded sets", definition of operator norm.

no official textbook for the class so I'm just trying to find the topics online rn

[gray jungle]

The options im aware of are :

Henri cartan "differential calculus" (most comprehensive book on the subject)

Coleman Rodney "Calculus on Normed Vector Spaces " (clean writing and comes with exercises unlike cartan)

[rapid lily]

Cartan's book has exercises as well.

[karmic thorn]

"Topics in Functional Analysis" by Teschl goes into these around the end, the keyword to look for is "nonlinear analysis". There's also a book by Kesavan called "Topics in Nonlinear Analysis", but I've never read it.

[grave thorn]

If you are interested in this kind of stuff, I'd recommend Bogachev "Differentiable measures"

[dense hamlet]

Thanks for the recommendations, I'll try to take a look at them when I'm less sleep deprived

[dense hamlet]

maybe one day with more math under my belt

[rapid lily]

I'm not aware of Cartan discussing directional derivatives. But Rodney's book does.

[cobalt arch]

Anything more modern?

[cobalt arch]

And more comprehensive

[cobalt arch]

Any books for set theoretical combinatorics? Not infinitary combinatorics but how you can describe combinatorial principles by using set theory.

[narrow relic]

What is the title of the course?

[slate pond]

any good introductions for projective geometry?

[alpine rover]

Introduction to Projective Geometry, C. R. Wylie, Jr.

[glossy schooner]

Hello, I’m studying the article of Burghelea « Cyclic homology of the group rings » and in the section I he speaks about cyclic sets associated to simplicial sets. I don’t understand the intuition behind this definition. Does someone has a good reference about cyclic sets with examples please ? Thank you 🙏.

[dreamy ibex]

Does anyone know of a resource that relates Stokes' theorem to maxwells equations in an intuitive way?

[gray gazelle]

if anyone could direct me to a text covering Markov chains and states ill be forever grateful

[orchid mortar]

Are you looking for an introduction or something advanced?

Many Markov Chain-focussed books I know essentially like to get advanced

[gray gazelle]

probably intro,but dump anything on me

[orchid mortar]

Should be good for intro:
https://www.statslab.cam.ac.uk/~james/Markov/
Should be good for more excitement:
https://pages.uoregon.edu/dlevin/MARKOV/

[gray gazelle]

tysm!

[orchid mortar]

Another one for excitement is Meyn Tweedie

[narrow relic]

Who is your pfp by the way?

[dreamy ibex]

Does anyone know of a resource that relates Stokes' theorem to maxwells equations in an intuitive way? I need to relate Stokes' theorem to maxwells equations for a project and I can mathematically show the relation but I'm not quite sure how to relate it intuitively as I haven't taken physics 2 yet any help would be appreciated

[gray gazelle]

Shinji from eva 😄

[narrow relic]

Oh nice 🙂 Didn't recognize him in that outfit

[wicked lagoon]

Here's a couple videos you can watch that might be helpful in your pursuits.
https://www.youtube.com/watch?v=rB83DpBJQsE
https://www.youtube.com/watch?v=9iaYNaENVH4

[dreamy ibex]

@wicked lagoon thank you so much I am reviewing these now

[wicked lagoon]

I hope they help 👍

[queen geode]

Any book recommendations for trigonometry and calculus?

[blissful island]

Calculus by L V Tarasov

[umbral peak]

The Humongous Book of Calculus Problems is one of my childhood favs

[runic sand]

Hello everyone, I am Chinese, I have a bachelor's degree in mathematics, I do not know much about the English world, do you have any recommended math blog or mathematician

[finite gale]

do you have any area that you are particularly interested in reading about

[runic sand]

Any field is fine, because I don't know any English math blogs yet

[steep badger]

Terence Tao's blog is pretty renowned.

[runic sand]

I'll do a search

I have followed him, he is very famous in China

[fluid skiff]

Is this channel also for making groups for reading books?

[glacial crypt]

I mean there already exist several reading groups around anyway

[runic sand]

I can't read his article at all, but his best function is to remind me of my ignorance hahaha

[upper orchid]

Any one who studied this Math Book for college algebra. I am going to take Course and i dont know if this is right book or not . Or which book is recommended for student

Stitz, C. & Zeager, J. (2011). Precalculus. Lakeland/Lorain, OH: Lakeland & Lorain Community Colleges.```

[cobalt arch]

Are there any books that start from very elementary proofs and build up from there? I want a book to learn proofs from. I want to learn how to prove elementary things and build up to more complicated and nuanced proofs.

[flat jackal]

Does anyone have the 2022 edexcel pure for revision

[gentle arrow]

book of proof by richard hammack
free pdf and hardcover is cheap, overall good and gentle book to start intro proofs

[marsh coral]

Hello, are there any pre-reqs to reading the book? I am also quite curious about proofs. Will high school math be enough?

[gentle arrow]

it has 0 prereqs

in fact if you give it to a motivated middle school student i wouldnt be suprised if they could do a good chunk of the book

[alpine rover]

Any good introductory analytic number theory books?

Other than Apostol

[tawny copper]

I have heard about Kowalski and Iwaniec, but not sure what's the level of that book @alpine rover

[alpine rover]

seems fairly advanced

[remote sparrow]

@sage python you should consider taking a look at meckes' Linear Algebra. it introduces the determinant as the unique alternating multilinear function that maps the identity matrix to 1. it's written as a first course in linear algebra.

[sage python]

Looks interesting, though mildly fucky organization

[narrow relic]

Some people might disagree with this but I recommend this book: http://logic.stanford.edu/intrologic/public/chapters.php , Chapters 1-8, and maybe even 9 and 10.

[inland elm]

want to get a homalg book for self study and reference. rotman looks good, but i hear weibel is more advanced (albeit riddled with errors?)

can anyone chime in whether that's still the case?

[inland elm]

it seems like rotman doesn't mention derived and triangulated categories either

[dapper root]

It’s far too, like, elementary for that

It depends on what you want tbh, if you want to do AT stuff, rotman should be sufficient

If you really want to know about derived stuff well… it doesn’t suffice

[marsh coral]

Ah, thank you very much for the info! I shall read it once my exams are over

[inland elm]

i think im going to go for weibel to have access to the category side. i do like how rotman writes however, and weibel does look a bit terse

[vital bane]

Is visual complex analysis (by tristan needham) a good book to learn pure math from? (like does it have all the theorems and proofs and lemmas) like for example alfhors is such a book, it's rigorous, but I'd imagine not as pedagogical as VCA

[heady ember]

Hi neam

[vital bane]

Hello grass 👋

[remote sparrow]

from what i've heard, although it claims to be a complete text, it's still a bit too handwavy. that isn't strictly a bad thing, provided you're able to formalize the handwaved parts yourself, but that's easier said than done. you can try looking at gamelin or bak and newman. brown and churchill has a more applied slant.

[sage kelp]

How to prove it by Velleman

[vital bane]

so then a VCA + alfhors combo would be good?

vca for explanations and alfhors for rigor and exercises

[glacial crypt]

they recommended gamelin

iirc you can check the book reviews or was it #books

[vital bane]

i read it as gremlin

[hearty steppe]

You guys are totally going to recommend the Princeton lecture series if I ask about a good in between text that talks about the math and physics behind the relevance of Fourier transforms I bet

I might just give that a go, never really read it yet but I figured I wouldn’t need to work through it since I’m not a mathematician or trying to become one

Stein Shakarchi I believe it is right?

Unless there is an easier book to read with less irrelevant rigor >.> but I do work through hard books

Motivation; better intuition for the wave function

Been bumping into Fourier transform a ton in Brian Hall’s quantum theory book so that’s why I’m asking

[undone heart]

cartoon guide to calculus

its pretty small so its not intimidating

but its a good intro to calculus

[narrow talon]

Is there a canonical book on nonlinear optimisation? Something a bit more modern than Nocedal Wright

[foggy fiber]

The Calculus Lifesaver by Banner is a pretty solid overview/intro.

[remote sparrow]

bak and newman has answers to most of the exercises in the back of their book btw

gamelin has some answers in the back of the book

[vital bane]

i see okay thanks!

[sturdy shore]

decided to check out bak newman, seems really good imo though I've read a small part of it

it starts with polynomials and power series

like marshall iirc

it definitely seems to motivate the theory better tbh

[vital bane]

how are the exercises?

[tame plaza]

huh didn't know Paul's Online Notes had free math books

here's one

[heady stag]

Is there a textbook that I can learn logarithm with practice and formulas?

[sturdy shore]

just checked the exercises of chapter 2, they seem good

mix of "computation" and proof

[vital bane]

noicee

[vital bane]

an entire books just for logarithms?

[heady stag]

and algebra may be?

[finite gale]

this may or may not be what you're looking for, but i think it's still a good resource for these sorts of things: try one of the art of problem solving books (whichever one does logarithms, idk which one)

[gray gazelle]

Like how chemists do with DOI articles
Get the PDF then printout the pages
Getting a printer that prints like a book is near impossible to my knowledge

[finite heath]

Is there any resource that gives a summary (even if it's handwavy) or motivation of abstract pure maths topics

Just something to help me make sense of stuff that is really abstract

[stray veldt]

the napkin

https://web.evanchen.cc/napkin.html

[finite heath]

Oh perfect, that's exactly what I'm looking for

[sick vector]

Does anyone have any combinatorics book recommendations for a beginner?
Btw, didn't we use to have a #resources channel?

Oh, wait?

Why is it hidden?

[remote sparrow]

it's not a free math book so much as it's all the notes compiled into a pdf

[remote sparrow]

a walk through combinatorics by miklos bona

[sick vector]

[hearty steppe]

So are there other texts for learning Fourier transforms other than Stein Shakarchi that are worth reading that are more application/physics focused and not too pure math?

[remote sparrow]

https://www.amazon.com/Fourier-Boundary-Value-Problems-Churchill/dp/007803597X

maybe this?

tolstov fourier series could work too

[hearty steppe]

@remote sparrow this one? https://www.amazon.com/Fourier-Dover-Mathematics-Georgi-Tolstov-ebook/dp/B008TVG4ES

[remote sparrow]

yeah

[mystic orbit]

how tf are you alive

[gusty jasper]

Hi, i'm looking for a book on the representation theory of the general linear lie algebras gl_2{C}, but I'm having a hard time finding relevant reading material, does anyone have any recommendations?

[marble solar]

I like Korner's book on Fourier Analysis

It's pretty math-y, just not typically like S.S., Brown, or Silverman's

[hearty steppe]

SS?

Getting bodied a little by Hall’s quantum theory book but I’m able to look up stuff on Quora and Reddit that helps clarify anything confusing

Oh right stein Shakarchi…

[remote sparrow]

korner has his fourier analysis book plus a separate companion exercises book

[hearty steppe]

Yea

[finite gale]

mse >> quora

quora is literally unreadable

[hearty steppe]

I think I bumped into Korner’s texts as a recommendation yesterday from Quora

[slender cargo]

I think he says in the preface that his book is designed for those who have had a course in functional analysis?

[remote sparrow]

https://www.amazon.com/What-Quantum-Field-Theory-Mathematicians/dp/1316510271

this is inspired by hall's book, but meant for undergraduates apparently

[slender cargo]

"Most of the text will be accessible to graduate students in mathematics
who have had a first course in real analysis, covering the basics of L2 spaces
and Hilbert spaces"

[hearty steppe]

The book is not foreign to me in terms of its exposition, just a bit terse and gets really carried away with the math rather than the theory

I am surviving working through the book. It’s not the hardest book I’ve tried to work through by far

spent a little bit of time in functional analysis land with kreyszig’s book so I was able to sift through the important bits, even if I get lost a bit in the proofs and the exposition

[marble solar]

Korner's book is a pleasure to read

It doesn't shy away from technical details, but it also gets into some interesting applications

Like age of the earth

[hearty steppe]

I like Hall’s book. It’s a good challenge for me.

But I’ll check these out

[finite crane]

believe it or not Hall is the easy book for quantum mech

compared to, say, Leon A. Takhtajan

[hearty steppe]

It really is one of the easier books I’ve found tbh you are correct

[finite crane]

Hall at least assumes you're new to everything

[hearty steppe]

I’m on chapter 6

[grave thorn]

ive tried to read through all of them, but they always lead me (someone more math minded than, say, a physicist) to question why something is true (eg. why is the Hamiltonian of this form etc); the position operator is obvious, but the others are not

@finite crane

[finite crane]

The philosophy of quantum mechanics is learned from its history, not textbooks

as for why things are done in certain ways you have to follow the history

#discussion message

[grave thorn]

ty

[forest sleet]

that might actually be covered in Takhtajan in the section on quantization (if I'm remembering the textbooks right)

at least if you're ok assuming classical mechanics and want to go from classical observables to quantum operators like the Hamiltonian

[forest sleet]

there is also Teschl Mathematical Methods in Quantum Mechanics which I thought was easier to read than the other books, though it is more focused on spectral theory

[forest sleet]

possibly also Zworski semiclassical analysis

[buoyant halo]

recommended beginner abstract algebra books?

for group theory

currently using Artin's Algebnra

[gray gazelle]

Basic abstract algebra by Bhatcharya etc

[grave thorn]

Ty

[hearty steppe]

Does anyone want to team up with me on Hall’s quantum theory? Would be cool to talk about some ideas presented here

[hearty steppe]

You guys ever heard of this book? https://books.google.com/books/about/Quantum_Mechanics.html?id=oaO6AQAAQBAJ&printsec=frontcover&source=kp_read_button&hl=en&newbks=1&newbks_redir=0&gboemv=1#v=onepage&q&f=false

Leonard Susskind

Is he kinda suss?

[karmic thorn]

Susskind has serious work and is a respectable professor, but he writes some stuff aimed at the general public/non-specialists

Which is of course not bad

Just that he does write stuff for that audiences, and you might want to check out the target audience before getting a copy

[hearty steppe]

@karmic thorn you recommend his playlists on YouTube?

[karmic thorn]

I only watched a bit of his theoretical minimum series and I'm not in a spot to vouch for them or say anything against them

That said they have a complementing book series

You can see if you find either interesting

[vital bane]

i think they'd be a very nice complement to a course you're taking or a book you're going through

[remote sparrow]

judson or pinter

[stray sentinel]

hello.
i have worked a lot around combinatorics for an olympiad i participated. i think i'm relatively advanced in combinatorics, but i'm not sure how much i actually know.
is there any book that goes over the topics of combinatorics concisely? note that i'm not familiar with the english phrases about combinatorics so i can't just look at the topics and i need a little explanation.

[crimson leaf]

Bona walkthrough combinatorics or guichard combinatorics

[hearty steppe]

Bona is hard but very good.

Apparently it’s notorious because nobody solved all the exercises in the book? What’s with that 😂

Those are probably some of the hardest math problems I’ve ever attempted. Combo is brutal

I think going through Bona and Resnick’s probability path is a nice combination read

[finite heath]

Does anyone have a copy of the book 'A First Course in Module Theory' by Keating? Or at least Chapters 7, 8 and 12?

[remote sparrow]

it definitely exists in a well-known place online

[wary compass]

Could anyone recommend a textbook on dimensional analysis? I'm getting confused by the definitions and our instructor did not provide a textbook.

[hasty turret]

Dimensional analysis as in the trick where you deduce dimensions of a thing?

[hasty eagle]

Delerik

[finite crane]

basically that's all what dimensional stuff boils down to

[stray sentinel]

thanks a lot.

[leaden cloud]

Any good books for number theory ?

[gray gazelle]

An introduction to number theory by Graham Everest and Thomas Ward is AWESOME

[leaden cloud]

Thnx

[remote sparrow]

Dudley or burton are good

[gray gazelle]

This is statistics thing I think

[gleaming turtle]

Suggest me a good book for class 11 advance math problems

[lament shell]

any book recommendations for abstract algebra?

[random jolt]

book recommendations for euclidean geometry with good problems banks? i'm looking for a book for competitive exams to cover 2d and euclidean geometry

[foggy relic]

for elementary, manin or ireland-rosen if you know some algebra

[heady ember]

Manan

[winter tiger]

needed a bit of advice: i have a problem, i have tons of books I open them all at once on chrome and keep jumping from one to other and end up doing no question in the end
with 3 hrs wasted
how do I stop this temptation(due to curiosity and passion) to open all books at once and stick to solving one first has been happening for long time and is affecting performance

[quartz mantle]

Get a hard copy book?

[karmic thorn]

Remind yourself consciously to stick to one source at a time, write down any problems/things you didn't understand and keep reading ahead. Once you're done with a reasonable goal of covering a section/some exercises, feel free to think more about what didn't make sense or look up other sources.

I even encourage not using Google search or similar in the middle because that in itself becomes a tempting rabbit hole, save it all for later.

[grand thistle]

opinions on pederson's "analysis now"?

[sleek python]

If you can go to the library, physical books may help with this

[winter tiger]

so setting pre determined goal helps?

[winter tiger]

i cannot be in library all the time

[karmic thorn]

Somewhat, yeah

As long as they are realistic

I'm not sure this is how everyone learns things, but it's worth giving a go

[remote sparrow]

you can check out books though

as in borrow them

like, to take home temporarily

[hollow shore]

Looking for a book on single variable calculus which is concise and efficient. Something on the thinner side I'd say.

[remote sparrow]

emphasis on proofs or computation

or mix

[hollow shore]

computation I'd say

mix? is that a thing?

okay I am interested in this mix category if there exists any cuz I don't know of any

[remote sparrow]

https://www.amazon.com/Calculus-Rigorous-Course-Aurora-Originals/dp/0486809366

only covers calc 1-2

but it should work fine

[hollow shore]

I think I should explain my situation a bit lol

[sturdy shore]

great book but very topological and also terse

which may be a positive or negative depending on your background idk

[hollow shore]

So I am learning analysis rn without a good calc background and so far I have progressed upto sequences and series. But before I do differentiation, I wanna get a concrete feel for it (a sort of less rigorous look).

same for integrals as well

[remote sparrow]

stewart

actually

[hollow shore]

I am looking for smth efficient

stewart is a 1000 page book lmao

[remote sparrow]

why not something like a calculus book that uses infinitesimals loosely

https://intellectualmathematics.com/calculus/

[hollow shore]

hmm interesting

[spiral inlet]

thomas calculus is great

[remote sparrow]

https://www.amazon.com/Calculus-Made-Easy-Silvanus-Thompson/dp/0312185480

[remote sparrow]

that's another long book

like stewart

[spiral inlet]

he can skip to main chapter

thats what i did very crystal clear book

[grand thistle]

what (analysis) background would you say is sufficient for this (perhaps in terms of folland chapters/sections if possible)
also, could you like motivate me to study this? as in like what applications or uses would learning functional analysis have?

[spiral inlet]

if u need the motivation to study how are you gonna compete with those who study no matter how they feel?

[grand thistle]

huh..? i don't really know what you're getting at but i'd much prefer studying with a purpose compared to blindly learning something that might not be that useful in the future

[spiral inlet]

it was a joke

[grand thistle]

that's funny i guess..

[sturdy shore]

it's hard to pinpoint some exact prereqs because funnily enough the book is essentially self contained (except linear algebra and baby rudin level analysis), as it does topology on section 1 and the rest builds upon that, but you do need a lot of mathematical maturity

as for applications, functional analysis is essentially the backbone of almost every applied analysis: think pdes, optimization, numerical analysis, probability etc

[grand thistle]

ooh yeah that does sound very appealing

maybe i'll work through like chapters 1-2 of folland at least

then maybe start looking at it more seriously

[sturdy shore]

so I think you should at least do up to L^p spaces in folland, preferably the topology too

[grand thistle]

especially since folland chapter 4 and pederson chapter 1 coincide

[sturdy shore]

yeah

[grand thistle]

so all of chapters 1-6?

[sturdy shore]

lemme see

yeah

again you don't need all that and there will be overlap with pedersen but it is safe to say seeing these concepts twice from two different books is better than seeing them once

unless you are a genius that understands every key functional analytic result instantly

[grand thistle]

haha yeah no

sounds good

i'll just continue with folland until i get more comfortable

with analysis

[spiral inlet]

topology is nasty

[sturdy shore]

sounds good

[grand thistle]

i'm kinda split on topology

[spiral inlet]

i couldnt solve any question on my first quiz of 10 marks

[grand thistle]

on one hand it's so useful and ubiquitous in analysis that you can't not see it but then it's also quite boring to study on its own

[spiral inlet]

absolutely flabbergasted

[grand thistle]

rip..

[south niche]

Books on problem solving mathematical and general
Also books like mathematical circles russian experience

[spiral inlet]

what exactly ur purpose is ? exact goal

[south niche]

Learning problem solving for fun

Till pre college stuff

[fierce hedge]

@sturdy shore how's it going with knapp?

[spiral inlet]

theres ton of books for problem solving

[spiral inlet]

http://www.salvemini.na.it/om/docs/engel.pdf

do this OG book i used this for my olympiads legendary book

[south niche]

Thanks

[sturdy shore]

the algebra knapp? haven't really advanced any further the past week, but since we began rings in my algebra course ig I'll be reading further pretty soon

[fierce hedge]

I see, how has it been so far including the linear algebra sections? As in would you recommend it

[sturdy shore]

personally yes

[gray gazelle]

[remote sparrow]

i guess zorich

https://www.maa.org/press/maa-reviews/mathematical-analysis-i-0

Weighing in at about 1300 pages, the present work is three times as long as Apostol and four times as long as Rudin. The extra length comes not from more topics or more depth, but because Zorich writes everything out in detail and because includes a large number of worked examples. It does cover some topics in greater-than-usual detail and does cover a few newer topics that are not in the classic works.

[heady ember]

Damn 1300 pages

[remote sparrow]

it's two volumes. volume 1 roughly corresponds to the first semester of analysis, while volume 2 has second semester stuff and a complete treatment of multivariable analysis.

[heady ember]

Yep just read the maa review

[narrow relic]

I don't like that it teaches what matrices are before linear transformations

[clever timber]

calculus for dummies

[remote sparrow]

does one need to read grimmett and stirzaker before a measure-theoretic probability book? assume the reader has only encountered basic calculus-based probability, but has measure theory background. also, does anyone have thoughts on schervish or shao's measure-theoretic statistics books?

[grand thistle]

probably not

unless ur like going into one that assumes probability already

but you can easily find books that introduce measure theoretic probability without assuming that you know everything in probability without measure theory already

ofc there are books that include everything for completeness but implicitly assume that you should be familiar with the results

something like jacod and protter's book is good

[sleek python]

Most intro books include a quick review of measure theory anyway

[grand thistle]

yeah, you could find any measure theoretic probability book and just try and read it while skipping the measure theory chapters

and see if you can understand

[narrow relic]

I remember not liking that probability book by the way

[narrow relic]

Schervish is a little above my level but I have a good impression of it.

[grand thistle]

what's wrong with it? just curious lol, i thought it looked pretty good

[remote sparrow]

is the companion exercises book interesting at least? problem books are cool

[grand thistle]

assuming ur talking about grimmett stirzaker

[narrow relic]

I'm trying to remember. I think the thing I didn't like about it was that it sort of claims to be rigorous but some of the presentation was not in the right order or something, I forgot

I think the problem book is probably fine. But you can learn about probability from a practical perspective in a better way I think

Like, a book that has a better narrative, they all have exercises.

[remote sparrow]

i have a copy of blitzstein's book

it pretty much serves that purpose for me

[narrow relic]

The Grimmett book might work for you since you are way more mathematically sophisticated than I was when I was learning non-measure theoretic probability

[narrow relic]

Oh cool, I haven't heard of that one

The Shao mathematical statistics book is used in some graduate programs, it's super detailed, I think I have looked up some things in it before

[remote sparrow]

i wasn't talking about myself when i said the reader had measure theoretic background

[narrow relic]

Well I meant in general 🙂 You seem to be pretty into math and well-read, you know about so many books and things

I was recommended a probability book you might want to look at, after I'd already learned it at that level, let me get the reference

https://openlibrary.org/works/OL11282060W/Probability_random_variables_and_stochastic_processes?edition=key%3A/books/OL22641107M#editions-list

[remote sparrow]

https://www.amazon.com/Mathematical-Statistics-Selected-Chapman-Statistical/dp/1498723802

volumes i and ii apparently give a non-measure-theoretic graduate treatment of statistics

[narrow relic]

It's not mentioned there but I think the edition of the Papoulis book I saw was the 1991 edition.

(Probably any edition is fine.)

[narrow relic]

This is a very nitty-gritty book. It has some results that aren't in other books of that level.

[grand thistle]

wasn't there a book that introduces probability from a functional analysis perspective?

i remember seeing it somewhere and thinking it was interesting

can't remember the author or what it was called though

[sturdy shore]

bobrowski?

[grand thistle]

ohh yeah that's it

[remote sparrow]

The website for the book is pinned in #probability-statistics

wrong message

i meant the blitzstein book

[remote sparrow]

^

[fierce hedge]

I don't see a big issue with that like one can think of matrices as a particular arrangement of numbers which although naive serves the purpose
Plus most of us would probably have seen matrices beforehand in hs already. Or do you have some issue with that in particular?

[rare pagoda]

If you are in grade 5 and you must be in Philippines, I would recommend to buy any math books like Soaring 21st century Mathematics grade 5.

[spiral inlet]

😂

[narrow relic]

I'm probably just weird.

[fierce hedge]

umm... like I am curious as to why would you have that issue. Even Artin does that

[narrow relic]

I take it all back

[fierce hedge]

I read all that and I think it's a bit of gate keeping for people who aren't that much into abstraction

[narrow relic]

I take it back because I forgot that there's something useful about matrices that doesn't fit into the linear transformations perspective so easily: the whole Gaussian elimination thing.

[fierce hedge]

Like you can always treat some things as blackbox and let it be like that. I don't know shit about the kernel that I'm using
All I know it that the newer version would be better

[narrow relic]

That's true too!

[fierce hedge]

oh yeah, that too

[narrow relic]

I'm not trying to be gatekeepy, I just like when people take the time to present stuff to me in a good sensible order so I try to keep that preference myself

[crimson leaf]

I also read your explanation but I see it the opposite way just learning about matrices is like learning about how to drive a car but you don't know how the car works all you know is that you can crank it up and drive places. Learning about linear transformations is like learning why a car drives how does it move what makes the car run

[narrow relic]

But it does make sense to present matrices before linear transformations since you can use them to solve systems of equations

[narrow relic]

I actually agree with your point.

[hasty turret]

I think matrices are useful because of Gaussian elimination and other tricks

[narrow relic]

I'm probably too focused on "one best way to do things" whereas in reality there probably isn't one ideal way

[hasty turret]

They are a useful structure to represent linear operators because of those tricks

[hasty turret]

So this is a consequence

[fierce hedge]

yeah sticking to one-fits-all is bad in general

[narrow relic]

What is a consequence of what?

[narrow relic]

I apologize

[hasty turret]

That matrices are a good structure to represent linear operators

[narrow relic]

But my point is that just looking at a system of equations doesn't necessarily have anything to do with operators.

[fierce hedge]

Don't apologise it's interesting to know how people think, I think it was a fruitful discussion

[narrow relic]

Like, you might just want to find how three planes intersect

[narrow relic]

Okay 🙂 It certainly is for me

[hasty turret]

Well I think linear operators are useful in general because they can be encoded as matrices

And matrix ops are very optimized

[narrow relic]

Well that's true too 🙂

[remote sparrow]

matrices have the advantage of being based on a very simple concept: systems of linear equations. also, matrix operations are a priori computable, while linear transformations are not before you learn about how every linear transformation can be represented by a matrix. however, matrix operations, especially multiplication, are admittedly unintuitive before understanding that it represents a composition of linear transformations. a crude, probably inaccurate analogy would be that matrices are to assembly code (or some other low-level programming language of choice) what the concept of linear transformations is to python (or some other high-level programming language of choice).

[hasty turret]

I think matrix multiplication became a thing because of elementary row operations

Like you can think of matrix multiplication as "how do I encode elementary row operations in a matrix"

Well it's no longer elementary

Why does that sound like lisp xd(ops represented as a data structure)

[remote sparrow]

that sounds like a historical question. was the definition of matrix multiplication originally conceived as a compact way to denote systems of linear equations, or was it defined specifically to make it work out to be a composition of linear transformations?