book-recommendations

[open storm]

Hi, I've already read Book of Proof and taken Calc 1, 2, and DE. What should I do next? I want to learn Linear Algebra but don't know what book to do. I'm a pure math major.

[remote sparrow]

#book-recommendations message

#book-recommendations message

[acoustic inlet]

Hi Sour Drop thanks a lot for replying, i will surely look into that suggestion 😃

Hi amukh1 that an amazing book, I read a few pages and its captivating

[jovial parrot]

Glad to hear it

[flat jackal]

What’s the best book out there for learning vector calculus

After I’ve finished this topic I’ll be starting calculus 3 so want to get stuck in a good book that isn’t to overwhelming and has a lot of problems+solutions

As well as applications I suppose

[halcyon trail]

Anyone have a reccomendation for a maths series for preparing for uni and undergrad itself

[frosty basin]

what are your goals

i have two options: hubbard hubbard or colley

don't use stewart tho for multivar

[flat jackal]

So I’m a year 12 right now

I’ve studied all of further and regular maths so I guess up to calculus 2 in the US so I’m planning on self studying all of calculus 3 this summer with a bit of linear algebra along the side to

Just need a book that isn’t overwhelming/difficult to read and with a lot of problems with solutions as well

Price doesn’t matter cause I’ll get a pdf

[subtle mango]

a pretty common calculus textbook is Thomas' Calculus

i liked it

idk if it has solutions in the textbook but it's common so there's solutions online

[flat jackal]

It is popular

I’ve heard of it but I don’t use it

[lavish void]

is there any book or website i can find problems with solutions for calc 1

[zenith eagle]

Has anyone read:
Algebra
From the Viewpoint of Galois Theory?

Is there a better book?

[delicate wagon]

Book recommendations for Dynamic Optimization and Optimal Control Theory? Thanks 🙂

[stuck zephyr]

There's a book called "Calculus Problems and Solutions" By Abraham Ginzburg from 2003 that has problems and solutions if that's what you are looking for

[finite gale]

Lang

D&F is too wordy and dry in everything it covers for a second reading imo

[crimson leaf]

If you read Lang Bergman has good notes on his website to go with it he helps fill in some gaps that Lang leaves or poor notation along with some really nice proofs.

[tulip glacier]

guys,
I will be starting uni (engineering) soon, and i have learnt single variable calculus before and i can solve a few problems, but i want to study it again, any good books for single variable and multi variable calculus.

thanks a lot

[finite gale]

I'm not really sure if I'd recommend spivak for someone going into engineering, sure it is kind of the natural thing to recommend for someone who has studied calc once in the past, but I'm not too sure if a proof based text is something you'd want for an engineering student

I agree, but I'm saying that I'm not sure if that is the content to recommend for someone going into engineering

Especially since calculus on manifolds requires a decent bit of linear algebra background

[jovial parrot]

What is calculus on manifolds

Arent manifolds the main topic of differential geometry ??

[sage python]

It's complicated

A manifold is a type of object you can study. They include curves and surfaces, and calc 3/"vector calc" classes often do study calculus on curves and surfaces

Calculus on manifolds would just do it but from the more sophisticated point of view

Differential topology studies topology of smooth manifolds, and differential geometry studies their geometry

Tricky thing is, manifolds don't have an automatic "geometry"

Saying something is a manifold tells you what it means for a function to be smooth

Knowing what smooth functions are tells me what the topology is

But it doesn't give you a notion of length or angle or anything geometric (rather than just topological)

So you need extra structure, usually a "connection"

So that's what diffgeo does

[rapid wave]

Does anyone know whether 'Topology' and 'Topology; A First Course' both by James R. Munkres are the same books?

[fierce hedge]

My guess is that the former is just the 2nd edition of the latter, I might be wrong

[chrome yacht]

read what you said again, but slowly

[gray gazelle]

The former is the second edition of the ladder

[fierce hedge]

Thanks pegSus

[calm latch]

Can someone recommend me a good geometry book ? I have just completed me school , going to join a college soon, btw i am from india

[tawny copper]

Evan Chen

[heady ember]

What sort of geometry

[tawny copper]

where can I learn integrals

[tawny bone]

Khan Academy is a great place tbh

[tawny copper]

so like to be able to solve MIT nitegration bee integrals

[tawny bone]

I know this is a book reccomendation channel but interactive ways are better to learn integration

[tawny bone]

MIT have their own integration course for free on EdX and MITOpenlearning

[safe wyvern]

You will need to learn upto calc 3 to be able to solve MIT integration bee questions I think?

[finite gale]

Take previous integral bees and practice doing those

[tawny copper]

im fine with that

[tawny copper]

yeah I have been doing similar stuff, but pretty sure there are some classic tricks Im not aware off and that I could just learn

[safe wyvern]

There are some tricks
Do you have your basics clear?

Like trigo, pre calc?

[tawny copper]

idk

but its irrelevant

[safe wyvern]

It is relevant though

[tawny copper]

well, then assume the asnwer is yes

[safe wyvern]

Good

Then carry on with Khan Academy's lectures then

[tawny copper]

I dont like khan academy

[safe wyvern]

Hmm

[tawny copper]

also their stuff is like introductory

[safe wyvern]

True

[tawny copper]

like the MIT integration thing was just an example, I just want to get good at integrals and so on

[tawny copper]

I found "Inside interesting integrals" by Paul Nahin. I think this will work fine for me, along with what I was already doing

[tawny crater]

im looking for a biography book on an influential figure from mathematics history, but focusing on their personal life not their mathematical or professional one

[trail yarrow]

From a friend: hey there, I’m doing some research (robotics/decision making related) involving metrics between probability distributions, and it seems like there’s lots of different divergences/metrics out there, and a lot of the math seems to have some relation to measure-theory and optimal transport. i just have a BS in EE, so a lot of this stuff is completely new to me. does anyone have any recommended sources for getting into the basics of measure theory and related subjects? i don’t know how relevant it all is to what I’m doing but i’m curious to learn more

Basically: is there a measure theory book that doesn’t need RA

[subtle mango]

Alan Hodgkin “Chance and Design”

[tawny crater]

thankee

[sage kelp]

Hey everyone, can anyone recommend me any textbooks that include algebraic and trascendental functions? It’s for a class I’m going to teach in high school

[wispy socket]

"Precalculus: Mathematics for Calculus" by James Stewart, Lothar Redlin, and Saleem Watson. This textbook covers algebraic, exponential, logarithmic, and trigonometric functions, as well as systems of equations and matrices.

"Calculus: Early Transcendentals" by James Stewart. This textbook covers algebraic, exponential, logarithmic, and trigonometric functions, as well as limits, differentiation, and integration.

"Algebra and Trigonometry" by Robert F. Blitzer. This textbook covers algebraic functions, systems of equations, inequalities, and matrices, as well as trigonometric functions and their applications.

"Functions Modeling Change: A Preparation for Calculus" by Eric Connally, Deborah Hughes-Hallett, and Andrew M. Gleason. This textbook covers algebraic, exponential, and logarithmic functions, as well as linear and nonlinear models and their applications.

[gray gazelle]

are the DeMystified books any good?

[flat jackal]

I’m at the stage where I have just finished all of calculus 2

Next should i: do calculus 3, read a linear algebra book or do real analysis?

[sage kelp]

Thanks, I will check them out

[austere oyster]

hi guys, can recommend me a textbooks to the career mechanic engineer? please

[halcyon trail]

Anyone have a reccomendation for a maths series for preparing for uni and undergrad itself

Basically a set of books for the next 5 years

Ja.

BSc

[hallow oriole]

there are two 'canonical' books for this

[halcyon trail]

Thank you! Quick one does the website present in the correct reading order?

[hallow oriole]

nahin's "inside interesting integrals" and valean's "almost impossible integrals, sums, and series"

[tawny copper]

lol yeah, I found the nahin book

enjoying it quite a lot actually

[hallow oriole]

keep in mind that valean's book is a very significant step up in difficulty

this is the first problem in it

which actually this one isnt bad

but compared to practically everything in nahin's it's still not easy

[tawny copper]

I have looked up a bit of valeans book. I think it was the second volume. I actually did not like it too much lol

like the sums and integrals are so random

as an example of what I mean

[hallow oriole]

bro i've read it

😭

[tawny copper]

its like everything in terms of weird ass functions

[hallow oriole]

?

are you talking abt polylogs

or like

[tawny copper]

yes

wtf

[hallow oriole]

weighted harmonics/

bruh

[tawny copper]

yes

bruh

[gray jungle]

This is a bit much no ?

[tawny copper]

like the harmonic things are present in the entire book

[gray jungle]

@halcyon trail What level of math are you studying rn

[hallow oriole]

polylogs are just a power series

[tawny copper]

but you would expect functions of weighted harmonics = something nice involving pi

but its like weird harmonics = weird harmonics

and also werid binomials and factorials

[tawny copper]

yeah I know, they are probably cool

[hallow oriole]

they're cool trust

it's like crack cocaine once you solve a particularly nice one

[tawny copper]

also like

tanh, sinh, cosh?

[hallow oriole]

like how can someone not like this?

[hallow oriole]

hyperbolic trig man cmonnn there's some of that in nahin's too

[tawny copper]

yeah I should learn how to use those, they are probably fun

the two volumes of valeans book are pretty much the same right?

[halcyon trail]

Year 12 UK

[flat jackal]

Do u guys read problem solving books

[hallow oriole]

i imagine

[tawny copper]

ye

but like there is no reading

[flat jackal]

Is there a really good book for it in mind

[tawny copper]

well mostly

[finite gale]

Have you studied calculus and if so to what extent

[gray jungle]

Have you seen calculus?

[flat jackal]

like tips,tricks in the books idk

[tawny copper]

Engel

[finite gale]

I think polya has a nice book also

[flat jackal]

Less have a look

[tawny copper]

what is Ti lol

[flat jackal]

I think I’ve done an integral like that from MIT 2010

U go for a tan substitution then kings rule

I think same applies here

[hallow oriole]

uhh

[tawny copper]

yeah but what is Ti

[hallow oriole]

im not quite that confident lol

[tawny copper]

in the book they dont define this special functions

[hallow oriole]

you need more

the integral you are thinking about has a = 1 and it's log(1+x)

it was a5 in 2005 putnam iirc

[flat jackal]

Was in the bee to

Hm

[hallow oriole]

the other easy way to do it is feynman's trick

[tawny copper]

yeah A5

[hallow oriole]

im not in college yet

[tawny copper]

acshually, some dude from the XIX century had already posted about that integral

[tawny copper]

lol u already mentioned a5, idk why I missed it

?? Im from the Roman Empire

bro respect

[flat jackal]

Why is this Putnam paper for multivariable on

is Putnam for undergraduates or seniors?

[tawny copper]

undergraduates

[hallow oriole]

at a guess it could be the trig integral for tangent

[flat jackal]

Damn

[halcyon trail]

Not yet in the course, it's slightly touched in further maths but not in depth.

[flat jackal]

I guess I can’t do this the nvm

[mystic orbit]

lang for algebra?

really?

[tawny copper]

I support that choice

[glad prairie]

extremely based analysis recs

[mystic orbit]

it's a very unpopular choice 😅

[hallow oriole]

$T(a) = \int_0^a \frac{\tan{x}}{x} \dd{x}$

[hasty eagle]

valley143

[glad prairie]

however definiely not necessary for someone preparing for uni

maybe good for someone trying to do analysis in grad school

[hallow oriole]

not sure what it means by the second tangent integral

[glad prairie]

lang for algebra is awful

[mystic orbit]

also wtf lol

[tawny copper]

look at this @hallow oriole like what is this dude smoking

[mystic orbit]

that's for a hs student??

[gray jungle]

@halcyon trail So going back to your message , in case you have not seen calculus yet then that is definitely what you want to be studying , if you have seen calculus then there is many maths you can take but i will list a bunch of topics i remember on the top of my head that you should be able to tackle with a bit of effort , then you can pick it up from there , the choice of books is up to you ofcourse.
(No order in particular)

1. Introduction to probability 2. Discrete math 3. Naive set theory 4. Linear algebra 5. Real analysis over R

[mystic orbit]

[tawny copper]

and there are many more like that

[hallow oriole]

nono trust there's a nice pattern

valean is my god

[tawny copper]

😤

[mystic orbit]

not unreadable
that's the very bare minimum

the point is, there are better options

[hallow oriole]

there's def worse tbh i have no idea why you're showing these

there's a horrific arctan one

[mystic orbit]

especially for a hs student

like artin

[hallow oriole]

that involves the 2nth derivative of a whole sum of polylogs

[tawny copper]

just randomly encountered. Im sure there are worse

[mystic orbit]

I meant to write artin lol

[finite gale]

Lang is certainly not ideal for a high school student, questionable for a first pass, probably fine for a second pass

[tawny copper]

oh yeah I do support artin over big lang

[mystic orbit]

I'm pretty sure it's stated in the preface of lang that it's meant for grad students

[tawny copper]

lang has one undergraduate algebra book, which might also be good btw

[mystic orbit]

same lmfao

I prefer aluffi

[gray jungle]

Artin

[mystic orbit]

I do understand why aluffi isn't for everyone lel

(aluffi is also meant for grad students for the record)

[tawny copper]

have you worked carefully through his books or you know him from other stuff too?

[mystic orbit]

also

wtf is jean pierre serre doing here?

[hallow oriole]

books!

[mystic orbit]

[hallow oriole]

i like integrals

[tawny copper]

yeah, Jean Pierre Serre is cringe as fuck

[flat jackal]

Is there a book for integrals only btw

Like a book to prep for integration bee

Like just purely integrals with tips and tricks along the way and formulas not taught?

[mystic orbit]

yes!

[tawny copper]

Nahin

we were talking about it like 5 mins ago

[mystic orbit]

what was it's name?

[mystic orbit]

yea this one

[tawny copper]

the dude is an engineer btw. And the crazy integrals one is Cornel Ioan Vălean

[flat jackal]

Less go

I love maths

[tawny copper]

🐒

monkemath

[flat jackal]

I’ve got Anna’s achieve

[mystic orbit]

anywho

[mystic orbit]

I suggest you don't look for such a list

[flat jackal]

Thank I

I’ll probably use this along side a multivariable calculus book to do this summer

[mystic orbit]

and instead you need only figure out the next 2 or 3 books you want to read

[flat jackal]

I had a look at Stewart’s calculus cause apparently it was good

Looked difficult to read for me ngl

[mystic orbit]

since you're almost certainly not going to follow through with any list you might find or compile yourself

[tawny copper]

isnt it 1000 pages

[flat jackal]

How am I meant to study that over the summer😭

[mystic orbit]

you don't have to 100% it lol

[sage python]

Stewart is 3 semesters of material isn't it?

Hmm? Calc 1, 2, 3, and what?

I see

[finite gale]

I think that the best approach to "preparing for uni" is knowing calculus well, and if you find yourself interested in the material you learn in calculus, you can read a bit of some of the topics susilian mentioned #book-recommendations message , but also I think it is important to also understand that burnout can also be a concern if you overwork yourself prior to starting uni

mans about to come back to like 5 individual pings

[mystic orbit]

lol

[flat jackal]

I’ve already done calculus 1 and 2

I self studied it during school this year

I only finished it about a month ago cause I forgot to do reduction formula

[halcyon trail]

Im not going to lie, I'd like to have a structured textbook list so I can know what's next

[mystic orbit]

a single textbook is structured enough imo

like, for each topic you're gonna find a couple dozen options

a bunch of those options are actually good

and each of those good options work better for different people

having a list of textbooks is just too restrictive and any effort spent compiling the list is ultimately counterproductive

I would understand if you had a hierarchy of topics you wanna learn first, but for anything more advanced than a semester or two of uni it largely comes down to just personal preference

and even your interests change over time

[flat jackal]

U know the trick where they did g(x)= even +odd and swapped the e^1/x on the denominator for some function d(x)

Can it be done on any integral

Cause they only showed 1 integral for this and there wasn’t like a name for the trick

[mystic orbit]

just trust me on this one lol

you need ony decide on the next couple textbooks

[mellow wren]

opa you are actually insane

do you realize this person is in HIGH SCHOOL

and you're telling them to go read folland

[mellow wren]

there's also Ron Gordon's book

https://link.springer.com/book/10.1007/978-3-031-24228-1

I like this one a lot

[mystic orbit]

reading folland in hs is the least insane part

[mellow wren]

that list is missing uhhh Serre's local fields clearly you should also give that since is important to also know coming into uni

I am sorry if that sounded mean but it just seems to me that you might have been a bit over ambitious when recommending books

[tawny copper]

nice. Thanks

[mellow wren]

also whoever came up with that list also seems kinda out of touch

[mystic orbit]

yea

sheafification is kind of a meme here lol

[gray gazelle]

what are some good books for algebra

Algebra I/II

it can be Algebra I and II in one or seperate books

do you know how beginner friendly that book is?

[fossil kraken]

I dont think they're books, it's websites that post online vids

[gray gazelle]

ahh, i see

[finite gale]

there are also books

if you mean aops

but khan academy is indeed just a website that has videos and practice problems

[fossil kraken]

https://artofproblemsolving.com/store oh yeah didnt see this

[flat jackal]

Is Stewart’s calculus the best calc book

Like 5e edition

[gray gazelle]

It's considered one of the best, yes. 5e is not the latest, though.

[flat jackal]

Which one is the latest

Just need a really good book that covers calculus 1-3 in depth😩

[gray gazelle]

The 9th edition

[gray gazelle]

It does that.

[quasi hare]

anyone

Anyone here

[limber carbon]

"Heya,!"

[flat jackal]

Nice nice thanks, have u read this one

[gray gazelle]

I read the 8th, the 9th was not out when I was studying calculus 3

not sure about geometry, but for number theory you could consult Elementary Number Theory by Burton

I've read a few chapters and it was good

But I have a feeling you're looking for something competition-oriented?

[quasi hare]

Yup

But pure number theory is fine

[flat jackal]

As long as it isn’t hard to read I’ll look into it

Cause some books are super heavy text and just hard to read

[gray gazelle]

It's very friendly and holds your hand for most of the journey

[tawny copper]

for number theory Modern Olympiad Number Theory, here's the pdf https://artofproblemsolving.com/community/c6h2344755

for geometry, do Evan Chen's book

I recently found the books of Everaise academy. It covers like algebra, nt, geometry, combinatorics, at basic level. So you might want to check that too for general stuff and as supplement (Im not sure if you will be able to find the pdf on google tho, the pdf is in the olympiad discord server)

[sick root]

i dont know if this channel is the best for this question but is there a list or place that has math textbooks which have solutuions for their exercises ? Or in general is there an easy way to check if there are solutions by someone of a book's exercises online ?

i want to start a book by myself but i want to know that there are solutions for the exercises it will have

[gentle arrow]

depends on your level

more advanced books tend to not have solutions at all

[hazy elk]

Idt theres a specific source for this, just googling solutions manual book name should mostly tell you if there is a solutions manual, you can probably try searching on websites that let you download books too

[sick root]

thank you

[sick root]

i am looking for an introduction book to knot theory

[hazy elk]

https://www.geneseo.edu/~johannes/knots.pdf has a partial solutions manual here: http://www.math.utah.edu/classes/4800/homework/homeworksolutions.pdf (although Id advise you to be careful since it was made by students)

[sick root]

nice, i will check it. Thanks again

[hazy elk]

Sorry, there is a mistake! it is not the correct solutions manual, just section 2 seemed matching, my bad!

[sick root]

oh ok dont worry. I will check it when i will be home and will search for more

[cobalt arch]

Any books on combinatorics that use multisets to define concepts?

[desert fern]

any recommendations for story books or novels? (the channel desc. stated that i can ask for other literature so yes)

[tawny bone]

They usually remove a course before they reupload it. The integration one should be starting again soon

Im waiting for it too

[stuck zephyr]

what topic

[desert fern]

Adventure or philosophical

[stuck zephyr]

do you have any specific book that you want to read?

[desert fern]

no but i did like the book "the alchemist" a lot

[stuck zephyr]

https://www.gutenberg.org/ebooks/4081 this?

[desert fern]

No, not this. i will send the link to the book

[stuck zephyr]

ok

[desert fern]

https://www.goodreads.com/en/book/show/18144590

I also liked this book, A LOT - https://www.goodreads.com/book/show/52529 This book and the alchemist are literally my most fav books

[stuck zephyr]

oh I see

but it says you need to buy it to read sadge. I mostly read some books on this website https://www.gutenberg.org/

[stuck zephyr]

thats very good book indeed

[desert fern]

oh, i didnt know abt gutenberg. i used to use zlib (got ceased but us court recently sadly) and i used to buy actual books but i guess i should try gutenburg, thanks

this isnt a book recommendation but it sure is a recommendation for an elibrary

[cedar flume]

Can anyone recommend a book please for introduction to measure theory with lebesgue measure

[stuck zephyr]

oop

welp I only know this

[stuck zephyr]

I know a book called an Introduction to measure theory by terence tao

[ocean mulch]

And you'll die. He included AC in the Foretext, iirc

[ocean mulch]

I used Princeton Lectures in Analysis, Book III

Best intro to measure theory I've seen so far. Detailed and intuitive.

[cedar flume]

Ok thank you, I’ll check them out

[gray jungle]

Royden is pretty good too

[prisma osprey]

this is a stretch but does anyone have a PDF copy of stability instability and chaos by Glendinning?

[orchid mortar]

Is Royden an introduction?

[prisma osprey]

no royden is definitely not introductory

[empty junco]

I think it is an introduction

very much so

[gray jungle]

I thought royden was on the pretty easy ends of measure theory books , it definitely felt introductory

[prisma osprey]

was trying to copy and paste the book into chat lmao

[empty junco]

heck it even defines functions

what could be more introductory than that

[prisma osprey]

so does mechanics for masochists

most books have an intro

[prisma osprey]

maybe we're speaking of different books

[gray jungle]

Real Analysis by royden

[empty junco]

if it isn't an introduction to measure theory then what measure theory does it assume knowledge of

heck it even looks like it wastes time doing things for the lebesgue measure first then doing them again

which I remember dami complaining about eons ago

[prisma osprey]

ah yeah

didn't notice that the first time lol

why have a chapter on uniform integratibility and have a 'preamble' on lebesgue integration of single valued functions??

[remote sparrow]

blitzstein and hwang

[gray gazelle]

The Myth of Sisyphus by Albert Camus. I can send you a pdf if you'd like, just DM me

[visual vapor]

🤓

[gray gazelle]

[desert fern]

thanks, I will read it and i also found a pdf from google. Thanks anyway!

[gray gazelle]

yep

[round pelican]

Does anyone have some good recommendations for mathematical logic books and abstract algebra books?

[crimson leaf]

For a first course in abstract algebra I reccomend "A First Course in Abstract Algebra" by Rotman though I suggest you have experience with linear algebra before abstract algebra

[round pelican]

Thank you I’ll look into that book

[crimson badge]

Anyone have a book for introduction to differentiation equations for self-study? Ideally, the book would be geared towards an honors level class.

Couple of nice to haves:
Solutions to exercises
Applications of the ODEs/PDEs
More Abstract(?)/More Theory based

Currently I am looking at elementary diffeqs and BVP by boyce, diprima and meade, but I am not sure if there is any better book for my needs.

(Please ping me if you do reply)

[finite gale]

arnold's text on ODEs is quite good i think

[crimson badge]

Thanks for the recommendation, do you know how it compares to the one I have right now?

[finite gale]

im not sure, though arnold is fairly rigorous i think

[crimson leaf]

Isn't Arnold marketed towards grad students?

The book Atunez mentioned is like a standard first course in ode book

[upbeat vine]

Eberhard Nonlinear functional analysis Volume I: Fixed-Point methods. Covers both of these things ODEs/PDEs and does everything in an abstract fashion. It should be accessible by a honors students.

[finite gale]

I don't know, but it seemed fine to me in undergrad

[fallow timber]

im really interested in learning some topology- i dont know much, just a bit from analysis, but that was mainly specific to R, so im looking for something very introductory

any good book recommendations for that?

[tribal sapphire]

anyone read the hobbit

or the lord of the rings

[fierce hedge]

Gamelin is recommended for very basic topology, there's also Topology without tears among easier ones. I haven't personally used gamelin except for first few pages so I can't comment much.

[glacial crypt]

lol, why not lee

[tawny copper]

where can I read about hyperbolic functions?

like sinh, cosh, tanh, etc

[flat jackal]

Best books for analysis?

[chrome yacht]

Amann Escher

[safe wyvern]

Rudin?

[flat jackal]

TL maths has a playlist for this on YouTube which is very helpful

I’ll have a look

I should do real before complex tho right?

[chrome yacht]

gamelin is pretty good

[chrome yacht]

yes, and the book i recommended to you develops basic ideas for complex analysis together with the reals (works over abstract fields and metric spaces).

[tawny copper]

I preffer book or small text

[tawny copper]

I have been going towards more "classical" analysis. Here, I got recommended the books of: Titchmarsh, Duren, Stromberg and Whittakker (four books). The last one I have not done a lot of it, the rest I have done some parts and I really liked them

[fierce hedge]

wdym by "classical" analysis and is there a "modern" analysis counterpart. Or are you talking about classical analysis textbooks?

[tawny copper]

the book of Duren is 2012, so I mean an analysis with a slightly different flavour, and not old books

my impression is that some analysis texts are more oriented towards analysis in more abstract spaces and stuff. And for example, special functions and formulas are almost entirely omitted

[fierce hedge]

I just checked the book, seems very interesting. Covers some unusual topics although not aimed for beginners

[tawny copper]

like for example

Titchmarsh's book has a chapter on Dirichlet series

which is pretty nice if you are interested in NT (like I am)

and Duren covers stuff like Tauberian theorems, summability etc. This topics I think are almost entirely forgotten in moder analysis texts

and again they are important for NT xD

Hardy has a book on divergent series

its probably one of the craziest books I ever picked lol. Its pretty hardcore

[fallow cypress]

I like William Wade's

[flat jackal]

Yeah ok I’ll have a look

cause I’ve done calculus 2 now

And I’m just debating whether to do analysis, linear algebra or calculus 3

I think analysis might be better idk

[fallow cypress]

Abbott's is good for beginners

Rudin is fun if you want less explanation and more "work it out on your own"

[gray gazelle]

Best linear algebra book

[flat jackal]

I can try and study them both at the same time🤷

I’m doing like further maths practice questions at the same time and integrations bees so I might not fit it in

Some books are just hard to read

I’ll probably use videos along side

[tawny copper]

wanna see a cool channel with a bunch of hardcore integrals?

https://www.youtube.com/@maths_505

[rapid spire]

so I just got out of high school and I would like to expand my knowledge about mathematics independently,, I covered most of the topics of calc 1 in school but now im not really sure what to do next

[finite gale]

If you liked calc, you could study the "rest" of it (calc 2 and 3)

Otherwise you could go in a different direction of say discrete math or logic or linear algebra

It really depends on what you are interested in doing

[rapid spire]

I really liked calculus but i wasnt really exposed to the logic/proof side of math so im not sure which one is more important

[rich sun]

Important for what? / What is your goal? If you intend to study math, learning about logic and proofs is indispensable.

[rapid spire]

I'm looking to either study math or physics in college so i wanna get a good head start. Do you know any good books to learn how to write proofs for beginners then?

[finite gale]

Books like that exist, but I think a better or more efficient approach is to do some proof based math, say spivak calculus or some proof based linalg text

A discrete text could work as well if you want more options

[rich sun]

You can look into #books-old, too, if you haven't already

[rapid spire]

thank you guys

[flat jackal]

I’ve seen this channel

I’ve only done some of the integrals with laplace transforms

I’ll look at some more

[fallow timber]

lee is grad level

i tried it and didnt get very far

[fallow timber]

100% abbott's "Understanding Analysis"

if this is your first time doing analysis i cannot recommend it enough

[rose pendant]

Hello I’d like some advice

Im almost a software engineer graduate, I want to specialize in AI but im rusty on the math side So I decided to learn math again (starting from algebra), any advice?

Any books you can recommend?

[fierce hedge]

In that way topology itself is grad level

[fallow timber]

is lee really meant to be introductory?

[empty junco]

do you mean point set topology

or topology topology

[chrome yacht]

If you find point set topology too abstract then you might be better off just doing metric spaces first and in that case Gamelin's is a pretty good book

[fallow timber]

to be honest i have no idea the difference

[empty junco]

lee is topology topology

[fierce hedge]

The first book is meant to advanced ug I think but yeah if that feels hard you should use gamelin

[fallow timber]

i just know a small amount of topology from lee chapter 1

[empty junco]

from what you said you knew I assumed you would want point set topology

[fallow timber]

but i mean i want to work with general topological spaces

[empty junco]

yeah so point set

[fallow timber]

again im curious the difference

[empty junco]

topology topology being like

[fierce hedge]

no one works with general topological spaces as they're usually too pathological to work with which is why we have manifolds which is what Lee does
If you strictly want point set then Munkres is a better bet

[empty junco]

algebraic stuff

manifolds

cw complexes

etc

[fierce hedge]

Or dugunji or willard (grad level)

[empty junco]

point set is "general topological spaces"

and is a largely utilitarian area

[fallow timber]

alright cool

so whats a good point set book

preferably not super long

[empty junco]

uh

do you know much about metric spaces

[chrome yacht]

if you wish to get a second look at analysis with metric spaces then you can go for Rudin i guess, many people do that

[fallow timber]

i am familiar with the definition, and i know how convergence works and stuff

i think

[empty junco]

yeah this is a good idea I'd say

[fallow timber]

i just finished analysis tho

well abbott i mean

i was wanting to do smth a bit different

[empty junco]

it will feel different

it'll feel more like point set topology than it would feel like any analysis without a focus on metric spaces

if that makes any sense

anyway if you just want to keep going with lee that's probably not a bad idea either

[fallow cypress]

Lee's intro to topological manifolds isn't a bad choice for this yeah

At least the first few chapters

[fallow timber]

i found the exercises kind of impenetrable

[wraith rampart]

Hey, hi, I need to find the pdf of the original book/or English translation of "Nine Chapters on the Mathematical Art". How can I find it?

[fierce hedge]

are there other options that do not do much point set and jump quickly to algebraic topology

[fallow cypress]

😭

Why do you hate point set

You could read Hatcher's point set topology notes, they are fairly short

[fierce hedge]

[fallow cypress]

Uh

[empty junco]

general topologists when they get a new separation axiom from their spouse

[fierce hedge]

Holy shit my comment gave you mod

anyway, jokes aside. I don't hate point set I just wanted a quick revision of it instead of whole book and yes Hatcher's notes should suffice

[sturdy shore]

I'm not sure if this is what you were trying to imply, but there are many spaces we want to work with that are not topological manifolds

[fierce hedge]

oh I was just taking one example where you have additional structure since we were on the subject of Lee's book which does topological manifolds so I just said that

[sturdy shore]

if you want to get into geometric topology as fast as possible, I'm not sure if it is advisable to go faster than Lee tbh

he does point set in like 100 pages?

maybe bredon who does it in 60 pages lol, but that book aint easy

[fierce hedge]

what about hatcher's notes? It's 53 pages I think but maybe that's too barebones idk

[sturdy shore]

I've never skimmed it, I'll do so now

[sturdy shore]

the notes are great but yeah, it really is written for the fastest introduction to geometric topology and is a lacking treatment of point set ignoring context

bredon/lee are considerably more general

like, one weird thing is that hatcher dedicates a page or two to normal spaces but only proves theorems of the form "spaces with x property are normal"

doesnt seem to mention any of the key theorems that make us care about this property

[fallow cypress]

It is fairly barebones yeah

For example Urysohn's lemma is missing

[sturdy shore]

yeah that is one key theorem

[fallow cypress]

Which I would expect any math undergrad that took a topology course to know

[sturdy shore]

no local compactness

[fallow cypress]

But it's an okay start if you just wanna learn algebraic topology

[sturdy shore]

dont think there is local path connectedness either

doesnt seem to have paracompactness etc

but although it is barebones, it is at least good coverage of the topics it does include (other than normal space)

nice examples etc

[hazy elk]

I really like the "toronto topology lecture notes"

[gray jungle]

an epsilon of room has a relatively quick review of topology , but not ideal if you want to actually study point set which you should lol

[hazy elk]

Very pedagogical and such a light read, you can blaze through them

The big list of problems are not bad too

[fierce hedge]

Uff, I'll try Lee then. There's also Runde's taste of topology which I heard it does just enough point set I'll see

[gray jungle]

folland has a cool chapter too

[fierce hedge]

oh yeah, I should try that, I have a copy of that and also one from U of Buffaloo

[hazy elk]

I think Stillwell's classical topology and combinatorial group theory would make a great intro to topology

Especially for freshmen if they have a great prof

No

It doesnt assume a GT background , just defns should be good enough for the most part

Yeah idt it is an easy book to wrap your head around

[fallow cypress]

numbpy's first topology book should be the list of topological counterexamples

:^)

[mellow wren]

euler mod

when

is this a meme?

[fallow cypress]

Yes

[crystal trellis]

does anyone have any book recommendations for getting started in differential geometry at the undergraduate level? i have some knowledge of analysis, topology and algebra.

i suppose i am interested in eventually studying differentiable manifolds

[gray gazelle]

does "undergraduate level" mean curve and surface geometry?

if you are interested in studying differentiable manifolds, tu's book an introduction to manifolds is a good read with your background

its exercises aren't great and it lacks some important content, so you should supplement it with a thorough book like lee's "introduction to smooth manifolds"

the reason i didn't recommend that at first is because it's way too long

if you just meant curve and surface geometry (i don't understand the "undergraduate level" comment) then do carmo's book (i forgot the title) is the classic

[crystal trellis]

okay thank you very much!

[restive falcon]

good intro difftop books?

[gray gazelle]

guillemin and pollack

which is basically the expanded version of milnor's classic 50 page long "topology from the differentiable viewpoint"

(also worth a read)

[mystic orbit]

what about someone with my background?

also do you remember my promise that I'd do diff geo within a year?

well a year has passed and we're doing diff geo soon™️

right after some AT

[gray gazelle]

i unfortunately do not remember that, but i am still proud of you for keeping the promise

very based of you!

[mystic orbit]

how about the book recc?

[gray gazelle]

haha

well i don't remember what you know too well

you could look at the appendices of lee and tu

if you're not completely lost in them then you can probably read them just fine

[gray jungle]

If you are looking for curves and surfaces diff geo then andrew pressley (2nd ed ) book "elementary diff geometry" is a lovely book

[crystal trellis]

thanks!

[mystic orbit]

yea I think I can keep up lol

thx!

[restive falcon]

the definition of manifold here feels weird

[gray gazelle]

every manifold embeds into euclidean space so for the sake of topology there's no reason not to assume they're already there

[restive falcon]

it feels unnecessary

[gray gazelle]

it's not terribly necessary but it does simplify a lot of things

[restive falcon]

hm

[gray gazelle]

you CAN do differential topology without it, but still:

1. whitney's embedding theorem is extremely important, and it needs to either be proven or assumed
2. a lot of proofs are going to start with "assume M is in R^n"

[restive falcon]

so this book is like
the non algebraic perspective

[gray gazelle]

it's about as elementary of a differential topology treatment as you can get

[restive falcon]

hm

[gray gazelle]

i don't know what an algebraic treatment of differential topology would look like

[restive falcon]

isn't most differential topology nowadays very much based in AT

[gray gazelle]

[mystic orbit]

maybe not at an introductory level

[gray gazelle]

i can see it but there is merit in doing things the elementary way

quite a lot of interesting differential topology can be done without any heavy AT

that is one objective of the guillemin and pollack book

i know you kids probably want a treatment of the stuff which says "infinity model category" or something every couple of lines but this is how we did it back in the day

[mystic orbit]

Lang

[remote sparrow]

do carmo's Differential Geometry of Curves and Surfaces is standard and is available as a cheap dover paperback. tapp's book by the same name, however, seems a lot nicer.

https://www.amazon.com/Differential-Geometry-Surfaces-Undergraduate-Mathematics/dp/3319397982

a lot of colorful pictures

which is nice for such a visual subject

[gray gazelle]

it’s worth looking at which theorems each book has that the other doesn’t

[candid creek]

Is Polya's how to solve it still worth reading as an undergrad student?

about to start a semester in Real Analysis

[finite gale]

it's a pretty short book too, so it's not like it will take much time

[fierce hedge]

@restive falcon, I think you've read Runde's topology book. How was it, I am thinking of reading it?

[fierce axle]

calc 2 book recommendations?

rn i have stewart's earlly transcendentals 9th edition and briggs/cochran/schulz early transcendentals

[restive falcon]

I've never heard of this book

sorry

[fierce hedge]

A taste of topology?

[restive falcon]

no

i used Hatcher's notes

[fierce hedge]

That's you right or am I mistaken?

[restive falcon]

oh likely i started it and quickly jumped ship

I don't remember any of it

[fierce hedge]

lmfao nw

[candid creek]

How long do you think it would take (assuming a reasonable pace, full time ~10 hrs a day)

trying to budget my time :3

would I need to take notes?

[finite gale]

no

[smoky zephyr]

10 hours a day

[crimson leaf]

A day but 10 hours is not reasonable lol

[heady ember]

Yeah 10 hours seems impractical/unsustainable

Not impossible but you get our point

[weak nest]

10 hours of productive study? is this possible?

are you going to lock yourself in an empty room with just the textbook and wait until the pain of boredom is worse

[hallow oriole]

honestly?

ten hours in a day is probably possible, assuming a few things

ten hours all together?

i genuinely doubt it

to keep it reasonable something like

3 breaks?

of at least an hour each

even then i'm not convinced it's sustainable for even medium periods of time

maybe if u have adhd/autism and you were hyperfixating on something you could do it

or just very dedicated

idk tho not sure anyone nowadays has that much discipline

yeah it does

for me personally i've spent over 16 hrs a day for weeks doing things

like i said that was all adhd tho and i don't do that anymore

thankfully

[weak nest]

after 8 hours of work (at my job) I can't bring myself to even open a text. I'll look at it and decide the pencil looks too heavy or something and then just do something else

[hallow oriole]

a three year long hyperfixation is crazy tho i could never

i wish

i'd be so fucking good at things

[weak nest]

huh?

[hallow oriole]

can confirm

i just finished high school

so summer

i had an internship last year and it was awful

9-5 is so tiring

i'd rather do something fun

no

not like software engineering

like skydiving

or

idk

stunt driving

that's the point

i need my fix yk?

there's no other job i know of that's relatively safe while still giving me adrenaline

can't live w/out it

[candid creek]

10 hours on average yeah

I have a routine if that helps

and no, it's not 10 hours in a row lol

[hallow oriole]

okay!

10 hours on average

[candid creek]

I think I'm pretty priviliedged in my position to be able to do this

[hallow oriole]

i'll assume 20~ pages a day

[candid creek]

yep yep

[hallow oriole]

which is a pretty low bound tbh so mabe more?

in any case

[candid creek]

ah, I try to read more than one book at once

[hallow oriole]

around 3 weeks

[candid creek]

to reduce the negative effects of cramming

[hallow oriole]

hmmm

sure

we can halve pages per day

it's a really low bound anyways

you'll be fine

probably around a month, maybe less, maybe more

i've never read it

im going off page count

that's all

is it easy?

oh, interesting

[gray gazelle]

I need to practice algebra 1 ( elementary algebra ) is there a good textbook that covers all the topics and has good practice exercises.

[turbid fulcrum]

good discrete math resources

[gray gazelle]

rock climbing?

like proffesional

you have to climb a lot to be a pro doe

[gray gazelle]

book that can help me with stochastic integration

[chilly yew]

gn berman

[half marlin]

does anyone have books to self study number theory

[stuck zephyr]

https://play.google.com/store/books/details/Tom_M_Apostol_Introduction_to_Analytic_Number_Theo?id=3yoBCAAAQBAJ

[stuck zephyr]

[topaz rune]

I am looking for a good resource on the greens function method for PDEs, as my lecture notes are quite bad. It does not necessarily need to be a book. Preferably some resource aimed at physicists

[shut haven]

Hello! I am looking for a few books, I'm starting off in college algebra and wanted to move to set theory proofs. Are there a few good books for that progression?

[remote sparrow]

Naive Set Theory by Halmos

[brazen yacht]

I jus realized that Munkres has a whole part on algebraic topology. Hatcher would be a more complete text though yes?

[gray crystal]

Where can I learn about nilpotent, solvable groups and some more advanced group theory (say Thompson or Frattini etc)?
Dummit Foote or Herstein barely cover anything about them
Non-rep theory stuff

do tag me when replying

[gray gazelle]

Is there any good book on olympic maths available in PDF?

[mossy flume]

Here's what I've been using for my REU

• Gorenstein - Finite Groups
• Issacs - Finite Group Theory
• Manz, Wolf - Representations of Solvable Groups
• Suprunenko - Soluble and Nilpotent Linear Groups

I haven't done a deep dive into any of those

but if I have questions about solvable groups, alot of it has been in there

Huppert also is really good but the first book is in German

[gray crystal]

Thanks!

[mossy flume]

(I have a partial translation but I don't know if I can share it)

[crimson leaf]

Gorenstein is the reference lang gives for solvable groups

[gray crystal]

I remember either Rotman or Farleigh or Hungerford or some famousish book covered this stuff

but i lost a lot of my pdfs

[crimson leaf]

It's at the end of the normal groups chapter

[gray jungle]

The theory of finite groups by kurzweil & stellmacher is lovely

used it for a 2nd course

doesnt cover TOO much

[mossy flume]

Oh that's also a good book

[hearty pollen]

Could anyone recommend a textbook or problem sets to accompany this playlist: https://www.youtube.com/watch?v=rG2q77qunSw&list=PLJHszsWbB6hrkmmq57lX8BV-o-YIOFsiG&index=8&ab_channel=eigenchris, tensors for beginners which has to do with covectors and tensor products

[gray gazelle]

Is PreCalculus: Mathematics for Calculus by James Stewart any good?

i dont think its only made by James Stewart but rather a few authors

[inland elm]

munkres is pretty thorough if you’re referring to elements
hatcher does homotopy theory, but i think munkres only covers the fundamental group in his original topology book

hatcher is a bit loose with how proofs though so do be wary

[brazen yacht]

gotcha, thank you!

[inland elm]

he actually does covering spaces and a bit more that hatcher does as well, but doesn't have as much homotopy theory as hatcher

so it just depends on your wants

[coarse arrow]

Is titu andreescu's linear algebra book good as an introductory book

[raw olive]

im grade 8 but study 10th and above math (ik quadratics, arith progressions, function, linear equations with two variables, trig) etc., so can i get a book recommendation helping me study further

[hasty turret]

Do Insel Friedberg(linear algebra)

And Spivak calculus

[gray jungle]

not a book but khan academy has plenty content to study what you need (subject will usually be called pre-calc)

[raw olive]

ok thanks

[gray jungle]

khan academy is a website btw

and no , dont read linear algebra its a bit above your level rn , and certainly not from a book like fridberg filled with proofs

[raw olive]

ik ik i have account

ok

[outer lynx]

what kind of maths would you like to study? xd

[raw olive]

idk

i need recommendation

for wt i shd learn too

[finite gale]

general recommendation would be to use khan academy to learn through precalc (and possibly calculus) then find some textbook to study calc out of (usually stewart)

[dense ore]

I want resources to learn the entire advanced trig

[minor nebula]

any non fiction and fiction books to read on the internet?

[dense ore]

I want resources to learn the entire advanced trig

[mystic orbit]

It would be less pedestrian, that's for sure

[mystic orbit]

Mofo is 13 lololol

[hasty turret]

idk it seemed like they were done with highschool math

So the next is the "lowest denomination of uni math"

I honestly don't get why people fear "proof based math"

FIS is as good, if not a better introduction to LA than Strang

Well if they wanted to do something like ML, Strang is probably what they want. For physics and math in general, FIS is probably better

[grand thistle]

proof based math is just when the writer is slightly condescending and annoying change my mind

[hasty turret]

Or Lazy

"Aw I don't want to spend all this time thinking about how multiplication and divison work with dedekind cuts, I will just leave it as an exercise"

[gray gazelle]

I have finished pre-algebra textbook from openstax what should I do next

[desert oriole]

hoffman or strang for lin alg?

[fallow cypress]

Depends on your purposes

If you want an advanced abstract book for mathematics majors then hoffman kunze is very good

If you just want to learn linear algebra to code or something, then Strang is very practical

[sudden kindle]

Erictao mod??

[ebon spire]

Hi can I get a reference book recommendation for calculus

Anything simple to complex level of problems

Now I am using amit m agarwal of Arihant but the solutions r too hard so can anybody pls reclmmend

Recommend*

[desert oriole]

oh ok thank you for the advice

[desert oriole]

when going through the contents, i noticed that stuff like rings and other abstract structures were mentioned. is abstract algebra a prerequisite for hoffman?

[fallow cypress]

No

You would learn them as you go

[desert oriole]

oh ok thank you

[undone finch]

friedberg/insel/spence is a good alternative to hoffman/kunze that i used before, i liked it

[heady ember]

My classmate said he's using HK (Heckler and Koch ) because its the hardest LA book to which I say

[desert oriole]

oh ok ill look that up

ty

[undone finch]

i haven't heard of that one

but shilov is pretty hard hitting

[heady ember]

I was joking about Heckler and Koch, I was referring to hoffman kunze

[undone finch]

oh lol

it sounded like legit names lmfao

[desert oriole]

ill try HK first

if its too difficult then ill prolly go for strang

[gray jungle]

Both HK and friedberg/insel are great books , HK is admittidly a bit more old styled

strang lectures are good too

[glacial crypt]

as we all know the harder the book the better it must be especially if you're a beginner

[gray jungle]

This is not about fearing "proof based math" its about recommending a proof based book to someone who is still learning early pre-calc lol

[grand thistle]

yeah obviously

anyone who doesnt use rudin as their first analysis book is a coward and doesnt deserve to learn math

[glacial crypt]

you're supposed to immediately use rudin rca

as we all know

[grand thistle]

imagine running away from lang for a first exposure to algebra just cuz he uses less words

sounds like a real skill issue to me

[crimson leaf]

I love when gun manufacturers write math books

[gray gazelle]

Best book for Odes?

[finite gale]

Arnold is nice if you have background in analysis, from my experience

[mystic orbit]

I would say the next step would prolly be "calculus"

[mystic orbit]

that's not the hardest LA book

lang is prolly harder

[crimson leaf]

Lang Linear Algebra?

[mystic orbit]

no his graduate algebra book

[crimson leaf]

Oh, yeah probably

His linear algebra book is pretty easy though if you've already done computational linear algebra

[desert oriole]

discrete math

not difficult and fun to do

[sage python]

I mean that's not really a fair comparison lol

[desert oriole]

😭

[wicked thunder]

What is the analogue to discrete math? Continuous math?

[sage python]

Pretty much

[mystic orbit]

use a stupid metric get a stupid answer

[sage python]

I mean in the context nobody was asking "What's the hardest book?" lol

[gray jungle]

Whats the hardest book?

[opal shoal]

thoughts on rosen discrete math book

???

[mellow wren]

I'm looking for a text that goes very in depth on group theory (ala group growth)

[subtle mango]

good

[mossy flume]

What is group growth?

[mellow wren]

I meant subgroup growth

[mossy flume]

I still don't know what that is

I don't think I'll have a book rec I'm just curious

[mellow wren]

it's the study of functions that talk abt how many subgroups there are of a given index

https://en.wikipedia.org/wiki/Subgroup_growth

[mellow wren]

could you link the books?

[crimson leaf]

I saw this in the same series might be of interest

https://link.springer.com/book/10.1007/978-3-030-88109-2

[mellow wren]

what abt the infinite groups one?

[mellow wren]

thanks!

[fallow cypress]

It's worth noting that there's a whole gradient of books between those two

I personally like Linear Algebra Done Wrong—it's well-written, relatively easy to read, but keeps the same proof-based spirit

[heady ember]

I said my classmate said it lol, not me.

[inland elm]

can anyone comment on "sets for mathematics" by lawvere

i heard they work on categories of sets in there. i wanted to read it to work within categories for a little to get intuition for more general CT

[mellow wren]

I feel like CT is already approachable enough if you're algebraically minded

[inland elm]

i've been trying and i'm progressing pretty slowly

i figured something more concrete would help build more intuition

[hoary kiln]

hi

[fierce pollen]

Yo is republic by plato or meditations by marcus aurelius better for a busier individual?

[mellow wren]

math server
philosophy
lmao

[fallow cypress]

The channel is for book recommendations of any kind

Although this question is weird lol

Neither is "better"

[wicked thunder]

Anyone read the manga guide to calculus

[remote sparrow]

yes

[opal shoal]

meditations is a very short read

iirc the republic is not a short read

[gray gazelle]

If you learned Perko, can u skip Arnold and go to Hartman?

[tawny crater]

No. They develop it for polynomial matrixes and for some extra subjects at the end. You can ignore the structures and read 95% of the book

[fierce hedge]

Egyptian stone tablets I guess

[brisk ice]

I see what you did there

[errant condor]

Hi

Recommend a book please

[valid monolith]

Why can't i post pics hold on

[valid monolith]

https://www.sfipress.org/books

David C Krakauer
Worlds Hidden in Plain Sight: The Evolving Idea of Complexity at the Santa Fe Institute, 1984-2019 (Compass)

[undone finch]

it's what we use in my uni and i have worked with it a lot as a TA. it's a good chunky boi for computer science students that want to learn the basics on the topic, very few prerequisites, but also pretty long. LOTS of exercises, which is good.
so yeah i can recommend it for first/second year CS students, but if you actually like the topics and want to get deeper into them i would recommend some more specific and focused books (i.e. for enumerative combinatorics, bruce sagan's book)

[opal shoal]

been tutoring a discrete math CS student that uses the book, i also used it myself as supplementary reading during my first proof-based math course

not sure what more specific and focused books i'd be into right now 🤔

[undone finch]

it depends on the topic, because rosen covers a LOT

for example idk, graph theory has a large number of very good resources, like bondy & murty, diestel, bollobas for the mature readers....

if you want to check out discrete probability on the other hand, idk which books are great but i'm sure you'll find plenty

[tawny crater]

im working on Knuth's concrete math which you should check out if you got intrigued by CS and discrete stuff

it's pretty fun and has a different angle

[undone finch]

i heard about that one, but didn't get to read it

i would say bruce sagan's combinatorics: the art of counting has been good for my self study on enumerative comb
(but if i'm going to be perfectly honest it's not a flawless book, the notation sometimes bothers me a little...)

[tawny crater]

so the philosophy of the book is instead of shying away from annoying details they reviel in it. They want to give the confidence to go into hairy discrete problems. and they make it fun and interesting.

[opal shoal]

discrete probability is probably more in line with my interests

rn im just working on linear algebra applications and trying to learn QM

trying griffiths intro qm

[thorn cloak]

how hard is baby rudin as an intro to proofs? (not self study). I am reading How to Prove It, but im only on chapter 3 and i dont believe i will be able to finish it before the semester. I have Abott to supplement too. Just wondering if it would be wise to focus more on Abbott or proof writing at this stage

[stray veldt]

i dont think your standard intro proofs texts help a lot with analysis

so i would suggest to focus your extra time on abbott to get some head start

[thorn cloak]

hmm alright. It does have a chapter on infinite sets. Should i at least complete that one first before moving on (as it seems it overlaps a bit with chap 1 of abott)?

[stray veldt]

i dont really know abbott, so 🤷 but you dont need to know a lot about this

if there is overlap, just do it once in abbott?

when it comes to proving things in analysis, its a lot more about juggling inequalities than whatever you do in how to prove it

[thorn cloak]

fair enough. Thanks !

[mystic orbit]

@glacial crypt this one is for you

[glacial crypt]

you probably won't need it

just get started with abbott

[thorn cloak]

👍

[glacial crypt]

maybe do the exercises where he does indexed families of sets

and whatnot

[thorn cloak]

alright, any thing else i should prob glance over?

[glacial crypt]

i'd say just have a look at 1.4, 1.5

are you familiar with induction

[thorn cloak]

a little bit if you asked me to explain why it works i couldn't

[glacial crypt]

i mean can you prove strong and weak induction are equivalent

probably good to go

[thorn cloak]

er idk if i can do that tbh

[hardy olive]

hi every1

i purchased oxford math dictionary

by richard earl and james nicholson

any opinion how tu use it

[finite gale]

You don't

You only use those kinds of things when you've already learned the material before and just need a quick lookup to remember what things are

You honestly could just use Google

[hardy olive]

ohk

[wicked thunder]

Reincarnation of the strongest sword god is pretty good
https://www.webnovel.com/book/reincarnation-of-the-strongest-sword-god_8527113906000305/starting-over_30630056514606255

[flat jackal]

Best books for difficult integrals and learning new tricks and techniques for integration?

[sage python]

Hmm, not sure if this is exactly what you're looking for but I've heard of a book called "A Garden of Integrals" which you might enjoy

[warm creek]

almost impossible integrals

[grand thistle]

what are yalls opinions on schlag's complex analysis book?

[grand thistle]

@sage python i heard you're familiar with the book, how was it?

[crimson leaf]

Idk if you've seen but Dami has some of their opinions in the pins

[sage python]

I know it a bit but I am more familiar with Schlag the person than his book

Schlag taught the class based on grad complex analysis at Chicago

Now, first year grad students there take a full year of algebra, topology/geometry, and analysis

Complex analysis is the third quarter of analysis. So by the time the students get to that class, they've done measure theory and functional analysis

Also algebraic and differential topology

[grand thistle]

ah i see

assuming one does have the prereqs, how is it as a book on its own?

cuz ive done measure theory and have seen a bit of functional analysis, and am learning some algebraic topology rn

[sage python]

My impression is that it's good based on Schlag being a kickass prof

[grand thistle]

cool cool got it

thanks

[gray gazelle]

Any suggestions for calculus ?

I need to solve more exercises but my book doesn't have enough (Pearson tenth edition)

[fleet bramble]

Zorich?

[orchid bridge]

Anyone knows of any online resources(notes,lecture series,..) for intro to discrete math? Im starting uni soon and the textbook my school will be using is "• Main Textbook – Discrete Mathematics with Applications, Susanna S. Epp, Thomson Brooks,
4th Edition. ISBN 9780495391326" but I am just looking for a more brief overview of content since the textbook itself is like a 1000 pages long.

[mystic orbit]

What's you guys' favourite manga?

[fierce hedge]

Pluto and Liar Game

[topaz rune]

Is there a nice book introduction to calculus of variations that starts with some functional analysis? When I got it taught, it was rather informal in that respect

[gray gazelle]

Can someone tell me a good algebra book I just finished a pre-algebra book

[rich sun]

Tsubasa: RESERVoir CHRoNiCLE

[sudden vale]

Wrong channel

[heady ember]

Any books are allowed here

[peak ledge]

Anyone know a good book about learning to solve hard reccurence relations?

[paper tangle]

Uhh this maybe
https://books.google.co.in/books/about/Recurrent_Sequences.html?id=s9X-DwAAQBAJ&source=kp_book_description&redir_esc=y

Anyone knows problem books in mathematics with a lot of prove or disprove kind of problems (ask to find counterexamples or so) with subjects like analysis, topology , algebra

[mystic orbit]

That's where you're wrong, Jimbo

[mystic orbit]

Why is the title sarcastic? Lol

[rich sun]

What's sarcastic about that?

[fierce hedge]

what's this about?

[mystic orbit]

It's an internet thing where if you capitalize letters randomly you're implying a sarcastic tone

[rich sun]

It's about a group of people traveling across parallel universes / dimensions to retrieve the lost memories of one of the main characters. The series has a lot of crossovers from many of the author's (Clamp) previous works, including Card Captor Sakura if you're familiar with that.

[ornate saddle]

Can anyone recommend me an introductory statistics book with formula derivations in it and explaining things concisely?

[heady glacier]

Does anyone know a book with good exercises in stable homotopy theory?

[fossil arch]

alg top books that aren’t hatcher

go

(not a response to cammacmahon)

emphasis on analytic applications (if there are any, like homotopy stuff in complex analysis idk lol) would be cool

[inland lichen]

Bredon Topology and Geometry

Lee's first book in the trio is also sufficient in the later chapters

[fallow cypress]

rotman

[fossil arch]

I really like the analytic flavor to this

Just wish it was formatted better

And it doesn’t seem very alg topy LOL just building up to manifold theory

[inland lichen]

Only chapter 2 because it’s relevant, the rest is actual algebraic topology

Chapter 1 and 2 are preliminaries to an extent

But this book is also a bit deeper and detailed than Hatcher

If you look at Lee’s introduction to top manifolds the last chapters are alg top stuff like cw complexes, fundamental groups, covering spaces etc

[glacial crypt]

you mean literally like most of the book

is alg top

[inland lichen]

Now that I look at it you are right haha. I did munkres for basic top then hatcher for alg top but it seems the first four of Lee is basic topology and the other 9 are algebraic topology

[glacial crypt]

yep

[grand thistle]

fulton

[keen mountain]

are there any books directed to visual learners?

im myself get lost in most of the formulas and expressions in books and feel like they're not explicit enough

or maybe should i be using desmos as a crutch in order to learn steward's book?

[heady glacier]

@fossil arch you can try Bott and Tu, that book is pretty analytic

[fossil arch]

I thought that was more adv alg top

[fossil arch]

Desmos is excellent when learning calculus

[heady glacier]

A book that is less advanced but of a similar flavor (at least in the first few chapters) is "From Calculus to Cohomology"

[fossil arch]

Check out 3B1B’s Essence of Calculus series on YT too

Oh I’ve heard of that!

[heady glacier]

Its definitely very analytic

But can get pretty advanced in the later chapters

My favorite book for learning smooth manifolds as well as jumping right into differential forms and the De Rham complex is Tu's smooth manifolds

But I wouldn't call it an exclusively alg top book

[inland lichen]

i would call this differential topology

[remote sparrow]

wackerly, mendenhall, and scheaffer

[keen mountain]

but yeah, i know this sounds a bit like heresy but is brilliant my go to whenever i get done with 3b1b?

i'm really curious about the service but im not sure if i can make the most of its potential

[fossil arch]

Why pay money when there’s such high quality education on the internet for free?

You can learn just as much for free if you know where to look

[heady glacier]

Just briefly once again since the question was buried: does anyone know a good source for exercises in stable homotopy theory?

[patent trail]

What is a good resource to start studying differential geometry

[crimson leaf]

What level

[patent trail]

Beginner

Thats why i said start studying

[inland elm]

what is your background in topology and algebra

[patent trail]

I didnt take topology yet, i know differential geometry requires parametrization from line integral and stuff

In my country line integral anf surface integral parameteization is in analysis IV

Which i just finished this semester

[stray veldt]

if you want to learn topology first, introduction to topological manifolds is an intro with a view towards diff geo

otherwise, you can try Tu

[patent trail]

Topology is only available in year 4 , and differential geometry comes before that which is in year 3

[patent trail]

So topology is a must before differential geometry?

[stray veldt]

Tu "Introduction to Manifolds"

[inland elm]

cyrenux when you say “differential geometry,” are you referring to studying smooth manifolds, or the classical surfaces, curves, etc. in R^3?

[wicked thunder]

Who cares when it's available. Just learn it yourself.

[stray veldt]

you can learn both at the same time

[patent trail]

I think so

[inland elm]

to which one

[patent trail]

I have seen name of those but not sure if all

I have seen "curves"

As a title

First title in fact

[inland elm]

have you heard of a “smooth manifold” before

[stray veldt]

actually looking at Tu again, it also requires topology, so nvm me i guess

[patent trail]

Let me see, i didnt take it in english

[inland elm]

i’m asking because it’s common to refer to differential geometry for two different things

perhaps what you want to study could be referred to as gaussian geometry

which i’m not familiar with any books about, but could help others point you in the right direction

[patent trail]

Yeah no, i havent seen this "smooth manifold"

[inland elm]

http://alpha.math.uga.edu/~shifrin/ShifrinDiffGeo.pdf
these are some good notes on the content. let me know if that looks like what you want to study

[patent trail]

Yeah this is exactly what i asked for