book-recommendations

[grand thistle]

didn't even have that much experience with proofs going in

[frosty girder]

we all hate axler here

[grand thistle]

i havent used axler at all so like take what i say with a grain of salt

but determinants were pretty cool

idk how u do eigen stuff without determinants tho

[hasty turret]

Read Down with Determinants to find out

[gray gazelle]

determinants are for the weak

[heady ember]

Friedberg, Insel, Spence gang

[hasty turret]

axler is a ok guy

[fervent lava]

I am starting to like hoffman and kunze. I could read rudin without me complaining but for hoffman and kunze initially I could not get into it even with my linear algebra background from ladw. Then I told myself to stop being a little bitch and read it. Liking it so far.

[smoky zephyr]

[frosty girder]

based

[wispy owl]

Does someone knows a book or a paper on random variable taking values in cartesian product of sets, such as $\mathbb{R}^2$, $\mathbb{C}^2$, or more generally in $\mathbb{R}^n$ ?

[hasty eagle]

TimourX

[wispy owl]

I struggle with the properties of random variable like this

[cursive orbit]

So a random vector?

[wispy owl]

Yes

I was looking for the name

[gray gazelle]

I work in a 3-2 alternating cycle.

For a given week, 3 days for book 1, 2 days for book 2. Next week 3 days for book 2, 2 days for book 1. Just continue doing that.

[sterile remnant]

Is Loring Tu a good first book on manifolds? No prior knowledge regarding differential geometry or topology

Should I do Lee's Topological Manifolds on parallel?

[fluid skiff]

First do spivak calculus on manifolds

[earnest fable]

loring tu refers to two books one of which is good with no prior knowledge the other is impossibl

i liked his introduction to manifolds book

whereas lee seems to go on and on about topology which im sure is necessary at some point but it takes a while to get to the interesting material

[sterile remnant]

I'm talking about his An Introduction to Manifolds book

[earnest fable]

yeah i read that as a first introduction but it didn't click for me until i was reading sean carolls intro to his relativity book discussing motivations behind it. There's a lot of weird constructions that just seem like they are over complicating it at first

thats differential geometry though, youll get that with all books

would just say look for multiple perspectives

so yeah maybe lee

[sterile remnant]

I don't mind if Lee talks about topology a lot since basic point-set/general topology is also a subject I'd like to get familiar with. But I'm not sure if it'd be better to get a separate intro to topology before diving into Lee

[earnest fable]

lee has a book that introduces all the topology needed for manifolds lemme see if i can find it

yeah intro to topological manifolds

[regal wasp]

You can’t go wrong with Lee or Tu but I usually recommend Lee since he’s a little less straight to the point which helps which intuition

[slow roost]

I'm reading Tu's differential geometry book now

which the manifolds one is prerequisite for

it's really crisp

might be more readable than Lee's

maybe not for a first intro though

good to have both

[gray gazelle]

what are the most important pure maths modules a pure maths major takes, and what books would you recommend for them, respectively?

(excluding analysis I and II)

[slow roost]

I would argue the most important subjects for a pure math major are linear algebra, abstract algebra, and real and complex analysis

[gray gazelle]

complex analysis
important

[slow roost]

followed closely behind by topology

[sturdy sail]

Come on TTerra

It is important for some Kahler Geometry memery tho

[lime sapphire]

TTerra really TTerrarising

[sturdy sail]

Which is pretty nice DG

[slow roost]

yeah, the subject behind the most pressing millennium problem is unimportant, ok

[gray gazelle]

does anyone know a good algebra book that teaches algebra 1 e.g. algebra basics?

[sturdy sail]

TTerra is meming tho

[lime sapphire]

I like to call them millennium puzzles just for yugioh sake

[gray gazelle]

am i?

[sturdy sail]

[gray gazelle]

someone answer me plz? ^^

[lime sapphire]

You can use the openstax algebra book

[slow roost]

all algebra 1 books are fine

[regal wasp]

I’ve never take a linear algebra course as a pure math and physics major

Very easy and intuitive to pick up after analysis in R^d, manifolds, and a course on rings/modules/fields

I guess the latter course was basically linear algebra

[gray gazelle]

doing analysis rn, finished linear algebra; could you recommend a book for CA and abstract algebra?

I might be missing some pre requisites because I am still in school, so if there are any for CA or abstract algebra then kindly lmk

[slow roost]

I really like Visual Complex Analysis by Needham, but it's not as formal and rigorous and comprehensive as other books

but it's just beautiful

for algebra I like Dummit and Foote

[gray gazelle]

which one is more noob friendly?

[quiet forge]

Michael Artin's abstract algebra book is great.

It even has pictures.

[gray gazelle]

I'm guessing this offers more geometric interpretations right?

[gray gazelle]

ty! will check it out

[slow roost]

yeah, it's full of pictures

[gray gazelle]

ahlfors is old but good. stein and shakarchi is modern and very analysis-focused. gamelin has a lot of yummy geometry

for complex analysis

[slow roost]

it can be a bit loose with proving things

[quiet forge]

I used Gamelin as an undergrad.

I can vouch for it.

[gray gazelle]

Gamelin for CA?

[quiet forge]

Yes.

Ahlfors is better for a graduate course in Complex Analysis, IMO.

[gray gazelle]

what would the pre reqs be?

real analysis?

[quiet forge]

Yes.

That would be fine.

[gray gazelle]

and may I ask what you used for Abstract Algebra?

[quiet forge]

Apostol's analysis covers both real and complex analysis.

[gray gazelle]

if you did it

[quiet forge]

As an undergraduate? Hungerford's undergraduate book.

But I wouldn't recommend that.

[gray gazelle]

oh did you take two separate courses (grad + undergrad)?

in abstract algebra?

[quiet forge]

Yes.

That's standard.

[gray gazelle]

ah

[gray gazelle]

you'd recommend Artin?

[quiet forge]

Absolutely.

It's a wonderful book.

[gray gazelle]

is it noob friendly?

[quiet forge]

But of course.

[gray gazelle]

what pre reqs would I need?

[quiet forge]

None.

If you can do even half of Baby Rudin, you'll be fine.

[gray gazelle]

thank you! I'll check all of these out

[quiet forge]

Generally, with books, you want to layer things.

[gray gazelle]

is there anything else apart from CA and AA you would recommend studying?

I'm planning on doing a lot of math over the summer

[quiet forge]

Do easy books first, so that you can get a handle of the main ideas.

More advanced books tend to leave much more unsaid.

[gray gazelle]

(for a prospective math major)

[quiet forge]

For example, they expect you to understand and appreciate the significance and applicability of various theorems.

[gray gazelle]

yeah.. I noticed that in Tao's analysis II

[quiet forge]

Gamelin & Greene's Introduction to Topology.

There's a lot of overlap with it and the point-set topology in Rudin, but it takes things further, being a topology book.

The Stein-Starkarchi (sp?) books are all nice.

[gray gazelle]

will check that out too, ty again

[quiet forge]

No problem.

Another really fun book, though a little specialized, is Steven Strogatz's book on non-linear dynamics.

https://www.amazon.com/gp/product/0738204536/ref=dbs_a_def_rwt_bibl_vppi_i7

This is the kind of book you can actually read like an ordinary book.

It's by no means "core content", but it's totally worth reading.

[gray gazelle]

will add that to my reading list!

[frosty girder]

😌

[vital bane]

does it cover real analysis in general metric spaces or only in R^n?

[frosty girder]

General metric spaces

afaik

[misty wyvern]

I should actually check out Rudin RCA's take on complex, I just stop reading it when the real analysis stops.

[junior mantle]

I have a massive gap in my knowledge when it comes to geometry and trig, can someone recommend me some resources please?

[compact crypt]

do you need problem solving skills

or just the concepts

[junior mantle]

Im most interested in the theoretical part but problems help me understand concepts usually

[compact crypt]

tbh I'd recommend for dummies series

if you do not need it explicitly for school exams or thigns like that

if you need it explicitly for school exams then I'd recommend precalculus by stewart or openstax textbook on precalc

has anyone here read freitag's complex analysis btw?

https://www.amazon.com/Complex-Analysis-Universitext-Eberhard-Freitag/dp/3540939822

the book says that this should not be the first exposure to complex/topology on complex

so I am wandering what are the prereqs

[junior mantle]

Precalc by Stewart sounds good

Ill find it online

[junior mantle]

Also

Where do you guys find cheap books?

Like

All of these textbooks are so expensive

Ive heard you could get them use for a few dollars but even used theyre expensive

[stray veldt]

i think abebooks is good

[heady ember]

Just find a copy online

[junior mantle]

Yeah but i feel like i dont learn as well from a screen

Idky why

[heady ember]

Hm I see

Well one solution is

Printing out your "totally legal" copies of the books

[hasty turret]

Assuming the printing doesn't cost more than the actual book itself

[heady ember]

Well yeah

[fluid skiff]

But people are printing illegally

Nothing can stop it

[runic hatch]

Do you not have access to a university library?

If you're not a student you can try sneaking in and using a physical copy during the day

[junior mantle]

That was exactly my idea

Are xerox companies ok with it?

Lol

Well Im Romania anyways so nobody cares

https://tenor.com/view/yakuza-majima-trashcan-trash-can-majima-romania-gif-23653182

[lime sapphire]

Printing the book is legal as long as you don't distribute it or use it for commercial use

[frosty girder]

well try seeing if there are some companies that print out these books for u, its usually cheaper to get them printed that way

[junior mantle]

[compact crypt]

in my country i haven't had troubles with it

the problem is cost though

I advise you to download some type of pdf editing software and remove things like answer keys index or units that u don't need

[quiet forge]

Both

[vital bane]

niceeee

[compact crypt]

my friend recommended me to just go to manifolds directly

as soon as learning ift

that way is easier

at least thats what he said

btw is hubbard& hubbard's appendix rigorous/well written enough as a alternative for spivak or rudin?

[lime sapphire]

i mean can you really use an appendix as a substitute for whole textbooks?

[compact crypt]

it states in intro that

it could be used as an analysis textbook

since the proof in the book already are on spivak calculus level+appendix is more than 150 pages

but since I've never heard of somebody actually reading appendix I asked here

[junior mantle]

Oh yeah thats a good idea

Thx

[marble solar]

Used book stores

[junior mantle]

Ill try

[smoky zephyr]

the internet

[junior mantle]

https://tenor.com/view/jump-scare-gif-24401793

[misty wyvern]

I learned on this server that you can use your institutional access to Springer to just DL textbooks for free

Legally.

Springer has so many books that in all likelihood you can get something on any topic you want.

[lime sapphire]

DL?

[misty wyvern]

deez luts

[lime sapphire]

are you fr

[smoky zephyr]

no

it’s download

[gray gazelle]

I've learned this from my topology prof

Not that I need it

[manic cairn]

I'd make sure that you know a good deal of topology first, though

[forest sleet]

you can also save on some print costs by printing 2 pages side by side per page, as long as the book is a normal small-ish size book so the font is still big enough to read (so 4 pages per sheet after double siding). you can even go ahead and bind the printed pages yourself if you want. Surprisingly the "gold standard" of sewn book bindings is also the easiest to do by hand at home if you have enough patience

[slow matrix]

depends on where you live

I actually do this a lot, since the difference between original copies and "totally legal" printed copies cost is about you save at least half the cost, or even more.

it's in 3rd world tho, also be sure to print it in special printing service since some printing service in 3rd world don't use special printing machine that lower the cost, actually might inflate the cost instead

also the bookbinding might not be as good as special printing ones

[slow matrix]

I feel like this one depends on where you live

[timber mesa]

true about the binding by hand at home

it's a good hobby

[slow matrix]

what's sewn book binding

[timber mesa]

the bit about printing in e.g. half-letter is also true, I actually usually print each chapter that way when I can't buy the book

[timber mesa]

basically, the way most commercial books are made

[slow matrix]

oh this mean booklet option printing in ms office right?

[timber mesa]

a bunch of small brochures sewn together

[slow matrix]

I think this is equivalent of A5, if the default (often used) paper is A4.

[timber mesa]

yep

depending on your country either letter or A4 will be the standard, though usually you can buy both

[slow matrix]

yeah

[timber mesa]

see e.g. https://www.ibookbinding.com/blog/sewing-the-book/

there are a lot of online tutorials

[slow matrix]

the annoying things with printing service is figuring out the terms, also maybe editing the pdf out yourself since, at least in my place, they only accept "print only no editing"

[timber mesa]

true

[slow matrix]

wew I'm always shet at handicraft

[slow matrix]

editing pdf is surprisingly annoying lol

[timber mesa]

yeah it can be lol

[slow matrix]

from my experience, adobe acrobat is gold standard I think. Its feature is fairly complete and quite accessible.

I tried other pdf editor, but the experience really isn't as pleasant

or some things even flat out can't do

[timber mesa]

I use a (totally legally acquired >.> <.<) program named PDF XChange Editor

but adobe acrobat is good too

[slow matrix]

I think I tried that one too, but couldn't get it to work for my purpose lol

[timber mesa]

basically I like how it has an option to print as booklet

[slow matrix]

-adding and cropping whitespace margin
-changing ratio

[timber mesa]

here's Hatcher's pointset topo notes printed as a half-letter booklet

[forest sleet]

pdfjam will output pdf in booklet form even with signatures

[timber mesa]

adding whitespace isn't always easy in my program but I eventually figured it out

[forest sleet]

i'm trying pdfcrop but it seems to be a bit buggy

[slow matrix]

yeah lol, I had quite a pain with that too

[forest sleet]

either that or my pdf from springer is buggy

[slow matrix]

hatcher is nice, tho from my pdf copy, I would maybe clip a bit more of the margin

[lime sapphire]

Is white space needed cus otherwise the text on the inner side would be obstructed?

[slow matrix]

tho my most serious problem is one where the book have different left and right margin for odd and even pages

[timber mesa]

yes, I'd say some margin space is important

[forest sleet]

if you do sewn binding there is essentially no inner text obstruction

but having margins makes it easier to read

[slow matrix]

yea some whitespace margin is important

[forest sleet]

if you just do booklet form without checking you might get uneven margins which looks bad

[timber mesa]

yeah, it's important not just for binding but for design and practical reasons

[slow matrix]

for standard printing I guess, springer truepdf is the gold standard

[timber mesa]

(particularly if you want, well, space to write margin notes)

[slow matrix]

springer ones, at least from my experience, just order to print and forget lol

but not all the best books (but a lot, maybe most?, of math ones seem) are published by springer so

[timber mesa]

there's cambridge U press, AMS, Dover etc

[slow matrix]

I feel like one of these got the left and right margin odd-even pages difference problem.

It's a pain figuring out how it will come out depending on the printing service

[forest sleet]

AMS books are nice

they are sewn

[timber mesa]

probably, it's usual to have these even in some LaTeX templates

[forest sleet]

a lot of springer ones are not sewn any more

[lime sapphire]

Oxf U press

[timber mesa]

doesn't adobe acrobat let you apply certain changes to even/odd pages only?

my program certainly does

[slow matrix]

I mean theoretically the seem nice, it's just ordering to print them at printing service can be quite a pain to get it right

[lime sapphire]

Yea it does

[timber mesa]

though it can be a pain if you have e.g. a pdf that has the blank pages removed

[forest sleet]

I think the more popular/standard springer books are still good quality, but the print on the demand ones vary a lot

[slow matrix]

maybe I haven't tried hard enough

but it does seem they do have that option

[lime sapphire]

If you provide a book pdf to a printing service, do they adjust margins for you?

[slow matrix]

this too, I needed to manually add "blank pages here" pages

[slow matrix]

maybe, but the one I'm having is no nonsense just print it out kind

it's a pain to switch to new one who you don't know well enough yet

at least with this one, I know where the pitfalls might be and how to handle them

[lime sapphire]

Fairs

I have yet to find a printable spivak copy

[slow matrix]

what's your best copy look like?

[lime sapphire]

Its just

[slow matrix]

screens?

[lime sapphire]

The text is so very thin

[slow matrix]

ah it's calculus and not the one on manifold?

[lime sapphire]

Yea

[timber mesa]

he's better known for his calculus book rather than CoM lmao

[lime sapphire]

Not the manifolds one

[slow matrix]

yeah I think for small letters you gotta have to bite and print it on big sized paper lol, like A4

or letter

and not do booklet printing

[timber mesa]

iirc that Calculus book is typeset for a larger page size

as many calculus books are really

[lime sapphire]

Hmm true

[slow matrix]

didn't know that

[timber mesa]

larger than half-letter or A5 I mean

you can usually find the book's size in e.g. Amazon

[slow matrix]

yeah, books titled calcullus are usually for intro course, and these tend to be large in content for breadth

[timber mesa]

this is mostly due to the amount of pages I guess

[slow matrix]

so just gotta bite it and print it on large paper size

[timber mesa]

when you have a 600> page book it's best to use a larger page size for better reading and maybe even to save paper

[slow matrix]

^this

that or split it in 2

actually my concern is more on the bookbinding lol

600 pages with B5 size, feels a bit weird

[timber mesa]

for instance this says it's 10 x 9.2 inches, which is slightly smaller (edit: actually, about the same area but in a square ratio) than A4 but bigger than A5: https://www.amazon.com/Calculus-4th-Michael-Spivak/dp/0914098918

[forest sleet]

for anyone looking for an easy cropping/margin script, this one appears to work well: https://tex.stackexchange.com/a/42259

then for reorganizing into booklet form with signatures of a given size there is: https://askubuntu.com/a/833534 edit: the number 40 in the example is the number of pages per signature, for standard 20lb printer paper 16 or 20 is probably a good number

I recall pdfjam also runs on windows

[fervent lava]

If I am looking for a good website for printing/binding pdfs what do you guys recommend?

[forest sleet]

local print shop?

you can also take a look at their past bindings probably

for doing it yourself I just found some videos on youtube

[slow matrix]

yeah local print shop, I'm in 3rd world so can't really recommend people here

[fervent lava]

I didn't think about local print shops. Thanks.

First time hearing of it actually.

[slow matrix]

in my case it's not really local, since it's hundred kms away tho , but technically local since it's still one country

[forest sleet]

if the local print shop does bindings too, then they should handle all the booklet/signature thing

since it varies depending on what binding method they use

[slow matrix]

btw what's signatures?

[forest sleet]

if you're in the US local print shops should exist, especially near universities since people have to bind thesis

for a sewn hardcover book, signature = group of pages that you fold and sew together. Then you make a bunch of signatures and sew the signatures together

[lime sapphire]

You'll usually find these shops are called "studios" or "printing press" or "printing services"

[slow matrix]

yeah near university seems like good option to see if there's good local printing service

[lime sapphire]

Or smth along those lines

[fervent lava]

I see thanks.

[slow matrix]

seems like binding thesis is universal thing in higher ed lol

[lime sapphire]

Whats the biggest book youve sewn

[forest sleet]

I only started recently, so I've only done one book

[lime sapphire]

Uh huh

[forest sleet]

but the signatures are roughly the same size regardless of book length

so you just make more signatures and continue stitching them together

in a pile

[lime sapphire]

I see

I'm gonna go llok at diy book binding vids now

[slow matrix]

nice GL

[forest sleet]

good luck! It is kinda fun and now I'm planning to do this for a few sets of long lecture notes

it is very nice because with sewn binding, the books lay flat

so you can make a paperback that actually lays flat. or you can make it into a hardcover but that is a bit more work

[slow matrix]

https://www.bibguru.com/g/harvard-youtube-video-citation/

I wonder how acceptable is youtube video of a scientific conference for citation purpose.

like these days especially during and post pandemic, some conference moved online, many of them are in youtube, on official channel

[runic hatch]

What’s this for

[slow matrix]

just wondering

like say you want to cite the corollary here https://www.youtube.com/watch?v=4CBFUojXoq4&t=286s for your thesis or smth

tho acceptability of citation source seems depend strongly on your thesis defense judge and advisor.

at least for nontraditional source (non published in book form)

[forest sleet]

I've seen someone cite an ICM talk

not for like a theorem

but for a perspective, idea, or observation

if it is for an actual theorem statement, probably the author has a preliminary version that you can contact them about

[quick hornet]

i'd probably phrase it as citing the talk instead of citing the video

but include a link to the video if one exists

[gray gazelle]

book for probability (I'm a 12th grader)

[solemn rover]

i have no idea if it would be appropriate for your level but when i was a college sophomore I think I was taught out of the book by Hogg, Tanis and Zimmerman

Probability and Statistical Inference

[gray gazelle]

k

[halcyon garden]

If one wanted to study manifolds(to get into geometry) after Pugh's analysis, is it a good idea to do Munkres analysis on manifolds before jumping into other standard books?

[compact crypt]

I plan on going directly into manifolds

instead of r^n manifolds

my friends told me that is easier

but I think you should know inverse function theorem

[halcyon garden]

Oh, any idea why that is so?

[compact crypt]

they told me that stokes theorem proof on R^N is very complicated with painstaking detials

but its proof on manifolds are much smoother

[halcyon garden]

I see

[timber mesa]

doesn't Pugh's analysis cover multivariable calculus already

I think reading e.g. Lee's topo. manifolds book after that might be feasible

[compact crypt]

https://www.amazon.com/Problems-Mathematical-Analysis-Student-Library/dp/0821820508

is this book good to use as problem book for analysis

since my textbooks does not have solutions

[halcyon garden]

Yup, but not in great depth.

[finite thorn]

Found this in my local library, but it says it assumes I know field theory and whatnot, which I don't. Should I use it anyway?

My only other option is to use ebooks (ew) or print a pdf for artin's algebra

[night prism]

Artin’s algebra really is a dream text. I’m with you and much prefer physical copies, but that one looks more like specialized topic coverage

[finite thorn]

Gotcha

So ig I'll print myself the pdf

Especially since the hardcover is going for like 400 bucks in Amazon for my country

[night prism]

Yeah it’s kinda crazy here too for that particular book

[finite thorn]

Wait, I found the first edition of that series

Which covers basic algebraic structures

There is no part 2 (unless it's the linear algebra one)

[sage python]

Jacobson is weird

There's the three volume "Lectures in Abstract Algebra"

And then there's the newer two volume "Basic Algebra"

[heady ember]

Hi Sloths

[finite thorn]

I found the three volume thing

Ya still reckon it works sloths?

[sage python]

I'm not super familiar with the three volume series, try it and see if you like it.

What's up grass

[gray gazelle]

I've read the first one

It tries to be general and doesn't go on a lot of tangents

It also covers lattices and Boolean algebras a little, which is curious

The notation is bad fraktur everywhere

There's better series of lectures out there

I also read a little of the second one about linear algebra, but I don't like it. Idk, maybe it's the topic itself, or maybe the presentation

[finite thorn]

Yeah I see the notation isn't stellar, but it's preferable to printing my own copy

[night prism]

Dover has some nice algebra books; they’re not D&F, but the price is right snd there are some quality pieces they offer (with regular sales if you subscribe to their emails).

[modern stone]

Is Pinter a good book to get into AA or should I begin with something like Artin or D&F?

[flint forge]

Pinter is nice for a leisurely first pass

i recommend it often to people who are self learning

but its not ideal for e.g. an actual class

[night prism]

That’s a really good take, actually

His set theory is probably likewise, which I have a copy of

He’s very good at breaking things down in beginner-friendly ways

[slow roost]

Pinter is very beginner friendly

a lot of the exposition happens in guided exercises which is a nice approach

[hearty steppe]

Yea but I prefer more exposition in the chapter leading to the exercises. It’s an interesting approach

Def gona look more at it

I was recommended another abstract algebra book I haven’t looked at yet

[compact crypt]

is herstein topics in algebra beginner friendly?

[timber mesa]

I don't particularly like it (bit dated, weird notation) but I've seen it used as an intro text

[subtle mango]

prereqs of Advanced Modern Algebra by Rotman? (besides lin alg)

[slow roost]

it's a bit old school but well written. I would recommend supplementing it with a more recent text

[eager sandal]

hi, where are 'linear algebra done right' solutions?

[timber mesa]

I don't think there's any official solution manual but there's a few unofficial ones made by students. A quick search yields
https://linearalgebras.com/
https://github.com/celiopassos/linear-algebra-done-right-solutions
https://toanqpham.github.io/notes/linear_al_done_right_note.pdf

(also TIL Axler offers a free copy of LADR with a small catch: there's no proofs, examples nor exercises so it's basically just for review https://linear.axler.net/LinearAbridged.html)

[lime sapphire]

people hate on axler's book but i have to admit that his typesetting certainly is sexy

[pale scarab]

I like that pinter forces you do the exercises and all solutions are online so it's ideal for self study. It's one of the best budget books I own I highly recommend a copy. I would get something like Artin or DF also as reference and it goes further than pinter.

[gray gazelle]

Is Rotman's introduction to homological algebra a good book

[cursive orbit]

ye his typesetting makes the typical definition, example, theorem, proof structure significantly more palatable to the eye

[lime sapphire]

If only we had more aesthetic higher math books

[primal summit]

I think rotman is an amazing author and a fantastic pedagogue and I'd highly recommend anything he writes. I've read a few chapters of the book and they were great as always but I can't comment on the later material, though I have no reason to believe it's not presented in a good fashion

Well, was. He passed away a few years ago

[subtle mango]

i hear conflicted opinions on Tao Analysis I and II, and ditto for Baby Rudin. If not one of those two, then which book should I use for Real Analysis?

[gray gazelle]

Alright. I like it as well so far.
I think I'm going to learn from it, it's probably my favourite part of algebra

[primal summit]

Homalg is pretty cool

One gripe for me is the exercises are a bit easy

You can find exercises in weibel. Tho

That's the other big homalg book

The chapter ordering is different tho

[night prism]

I initially thought you wrote “Roman” and was going to say he is definitely alive and well

The same goes for him, though, I’d say

[lime sapphire]

Go with an author you like the style of

Every book has its haters

[night prism]

True; I remember loving the first couple chapters of Tao the first time I picked it up

[sage kelp]

What kind of real analysis book do you want? Like something introductory, second round?

[subtle mango]

this would be my first go through of real analysis but ideally something thorough

maybe a bit unrealistic but something that i can just read and it would suffice

suffice as in not have to read another real analysis textbook afterwards

[sage kelp]

I see. I mean, I would say it depends on one's background, motivation and what not. I can only speak for myself of course, and the experience I just had last year. I think I checked tons of RA books to see what was a better fit for me.. For example, I read Bartle & Sherbet and found it an excellent book. I tried Tao, and while I enjoyed a lot his exposition, I was not so sure about his problem sets. Personally I felt like the exercises didn't match the chapter itself (Tao also has very few exercises). Baby Rudin is tough, tbh I only read the first chapter, it was mind blowing and I loved the ellegance of his proofs, so I hope I can read the whole book later, but like half of the exercises killed me

[brittle breach]

undergrad book

[night prism]

Hoffman’s analysis is underrated, I always say

[runic hatch]

Apostol’s analysis is also an option

[night prism]

I have that and it’s good too; haven’t made it far yet but was a fan of his style

[brittle breach]

Rudin PMA is the standard, first 8 chapters

[subtle mango]

i see, thanks

[subtle mango]

what should i read after the first 8?

[brittle breach]

what ever interests you

[subtle mango]

ty

[gray gazelle]

just finished single variable calculus, any recommended books into building good intuitive understanding for the next few stages of math, no particular topic planned out but i would like to learn stuff to compete into integration bees finales and more

[junior merlin]

"all the math you missed but need to know for graduate school" and "the princeton companion to mathematics" are good for getting an overview of a lot of math

after single variable calculus you'll probably do multi variable calculus and linear algebra

[gray gazelle]

i see isee

[compact crypt]

is zorich's mathematical analysis good book for learning undergraduate analysis?

for first time self learner

I plan on using it with lang's analysis for problems with solutions to check myself

[heady ember]

Heard Apostol is good

[compact crypt]

how's apostol?

is it as terse as rudin

?

[runic hatch]

it's got quite a bit more detail than rudin

[compact crypt]

also why are there so many analysis books btw

loomis, buck, rudin, zorich, lang, apostol, abbott, ross, spivak, kolmogorov, simmons, etc

[heady ember]

Spivak???

He has an analysis book?

I only heard of his calculus book and his calculus on manifolds book

[compact crypt]

spivak's calculus is basically analysis

at least in my opinion

[heady ember]

Its actually quite far off from real analysis, more like in between normal calculus and anal, from what I have heard

[compact crypt]

I haven't read the whole book

but I found it to be harder than ross's textbook

and more thorough

[heady ember]

I mean...

Spivak is known to be a challenging book and more rigorous than most calculus books so of course

[compact crypt]

btw are there any analysis textbooks that you'd recommend?

preferably with solutions to at least some problems

[heady ember]

Im not the guy to ask

[compact crypt]

at least the book you used?

[heady ember]

Im doing Spivak's Calculus right now bruh

[compact crypt]

oh

you must be in very demanding college

[heady ember]

I just suggested Apostol cos I have heard its a good analysis book and since you asked about book recs on RA, I thought I'd bring it to your attention

[sick ledge]

book recommendations for general problem solving and insight

like for example, preparing for the IMO needs you to get insight

[heady ember]

Self-studying for fun lol, still in highschool

[hollow shore]

The Art and Craft of Problem Solving by Paul Zeitz

[sick ledge]

[sick ledge]

Thanks, it might help me :D

[gray gazelle]

arnold recommended it, so it must be good!

[gray gazelle]

This is #book-recommendations

[heady ember]

A h y e s this is a book recommedation

[sick ledge]

?

that's a problem, not a book

[heady ember]

exactly bruh

You literally asked a question in #book-recommendations

[sick ledge]

oh wait

sorry

I forgot the channel

😂

sorry

I thought I was in #discussion

[heady ember]

#❓how-to-get-help

[hollow shore]

it's okay bruh

[lime sapphire]

if this is the case, have a look at garling's A Course in Mathematical Analysis volumes or Amann and Escher's analysis volumes

[rancid ivy]

Hey guys do you know any book for vectors in the level of 10th grade and more ?

TO train my level to its full potential.

[tardy walrus]

Wat

And what do you mean by vectors? Do you want linear algebra books or books on HS vector geometry?

[gray gazelle]

Same interest here.
Need more like a Principia for dummies 😂

[tardy walrus]

Wat

[runic hatch]

That not really vectors lol

[tardy walrus]

Principia was written to rigorously prove like foundations, I think a principia for dummies would totally ruin the point of principia. I don’t think such a thing exists.
What exactly do you want?
You say “same interest here” but I was asking what the interest was

[runic hatch]

Have you tried Khan Academy?

Or the vector section of Paul’s Online Notes

[gray gazelle]

https://eric.ed.gov/?id=ED184834 will this help? Quote: “This volume is an experimental edition for a high school course in the theory of matrices and vectors. One of the basic aims is to demonstrate the structure of mathematics. Another criterion is to provide some tools that will be useful in the student's transition from school to college”

It says its an ‘experimental edition’ so that may or may not be desirable, but it does sound intriguing definitely!

Its also aimed at high schoolers so theres that

Ohh its a preliminary edition

Download it and take a look at the preface to see what the author wanted with the book id say

I'm looking at both versions of Rotman's into to hom algebra, and it's pretty surprising how much content was added

not sure which version I prefer though, the first one was pretty simplistic

[carmine musk]

"Humble pi" very good book

[rancid ivy]

Yes, more or less

[rancid ivy]

Thanks

[coarse frost]

its great

[atomic hound]

well i know this is math server, but you guys have book that teaches you all about mechanics?

newtonian mechanchs

[night prism]

Feynman’s lectures Vol 1 are the best, in my opinion. It makes you feel like you’re in a solo silent lecture

[gray gazelle]

take a look at kleppner and kolenkow's an introduction to mechanics. could be what youre looking for

[subtle mango]

taylor is a well known book for mechanics

though i think it's more towards a second course in mechanics

[waxen sorrel]

anyone have a recommendation for maths books that are inspiring / ignite the flame for math?

[slow roost]

Mathematics: A Very Short Introduction by Timothy Gowers

[quick hornet]

https://www.youtube.com/watch?v=uxizZPWhzu8

[broken meadow]

qhT

whsat**

[modern stone]

Burn Math Class and Reinvent Mathematics for Yourself, by Jason Wilkes

[gray gazelle]

This is a channel about any book recommendations, physics included

[tight crag]

Is this book actually good?

[waxen sorrel]

ill check it out, thanks

[coarse frost]

[modern stone]

It depends on what are your expectations

[quick hornet]

ima be honest i meant to post that in #chill

and didnt notice it was in #book-recommendations till now

[broken meadow]

ah

its fine

[gusty smelt]

no its not fine! what an unforgivable mistake

[coarse frost]

[hasty marsh]

Hey, anyone know of a book like N piskunov differential and integral calculus? (or even better if someone knows if that thing has any solution manual)

[tepid prairie]

Consider the book Ordinary Differential Equations by Morris Tenenbaum. The books are written at a similar time and cover many of the same things in surprisingly similar ways (can even use both).
Solutions can be found for this entire book too.

[hasty marsh]

Let me check it out!

[tepid prairie]

When I found Piskunov's book I literally compared the two and they use the same terminology and everything.

[hasty marsh]

This book does not have Partial differentiations?

I am kinda done with ODE's already. Needed something along the lines of PDE's and using maxima and minima and taylor series. And then geometrical integration (double integrals and all). Piskunov have these a lot

and honestly, questions in piskunov are so good (it's not like evrything is hard, but it keeps rewarding you with easy questions so the motivation is always up)

such an intuitive way to space questions imho

[tepid prairie]

I see. I'm not sure the book was/is popular enough to have many solutions. Chegg doesn't seem to have them. I'm not sure what to recommend now. :'(

[hasty marsh]

Well you know any book which has lots of limits problems? (of indeterminate forms)

[tepid prairie]

Advanced Calculus by David V. Widder.

[hasty marsh]

Alrightyy

[hasty marsh]

This is exactly what I need!

It has PDE and it's applications and multiple integrals and everything!

[tepid prairie]

I love this book. It's currently what I'm studying. I hope you enjoy it as much as I do. :)

[hasty marsh]

waiit, it there a solution manual thing for this?

I don't wanna spend 30 mins finding an answer

[tepid prairie]

No, sadly. This book is probably the least talked about book I've personally ever seen.

Answers are in the back though. Sometimes the questions are linked so the answer is actually there but it's almost like a two part question.

[hasty marsh]

[tepid prairie]

I'd imagine you only need the worked answers in the material to do the problems though.

[hasty marsh]

Well I'll just ask you if I get stuck upon a problem for a particularly long time

apart from that, I guess it's good to spend a few 10 mins on a question

[tepid prairie]

I'll try not to discuss too much further here but I won't be able to do those problems as I'm on chapter 5.

[gray gazelle]

abstract algebra book in the same style as rudin.

[gray gazelle]

maybe lang

[proven wedge]

any recommendations for an absolute beginner in trigonometry?

[gray gazelle]

khan academy.

[hollow drum]

What should I read to learn about any of these topics tropical geometry, enumerative geometry, Schubert calculus, and intersection theory.

I have seen those terms and suspect they are vaguely related but not sure how. I'd like recommendations of historical papers or problems or textbooks. I apologize that this is such an open ended question.

If there happened to be a casual read on any of these topics I would also appreciate that

[manic cairn]

i love lang

but hate rudin

maybe it's just because I don't like analysis

[gray gazelle]

there are no prerequisits for learning LA right?

[manic cairn]

i've only heard of intersection theory, and if you want to learn that, I recommend you read Lang (Algebra, Undergraduate Algebra), Munkres (Topology), Mac Lane (Categories for the Working Mathematician), Hartshorne (Algebraic Geometry), and Fulton (Intersection Theory). You'll also probably want to pick up matsumura or eisenbud for commutative algebra if you didn't read all of Lang's algebra Part I, II, and IV.

actually, pick up matsumura either way

[manic cairn]

depends on what type of linear algebra you're doing

[gray gazelle]

lang

[manic cairn]

lang's introduction to linear algebra, or lang linear algebra

[gray gazelle]

just LA

[manic cairn]

neither really have prerequisites, although you'll want some experience writing proofs for LA.

[gray gazelle]

and where would I learn that?

[manic cairn]

but that just comes with time

[manic cairn]

just by doing la

or abstract algebra, or analysis, or logic

[gray gazelle]

what is the difference between thos 2 books

[manic cairn]

one doesn't have any proofs, and is targeted towards a more general audience

the other one emphasizes linear maps, jordan normal form, etc.

[gray gazelle]

what would be the equivlant of first year LA

[manic cairn]

either, but more common is "introduction to linear algebra"

[gray gazelle]

so should i read the entire book (LA)

[manic cairn]

i would recommend reading the entire book

[gray gazelle]

Ok thanks

[gray gazelle]

have you ever read a book not by lang?

[gusty smelt]

lang is actually a horrible writer lol

[gray gazelle]

I have never ever read a book

[gray gazelle]

how come?

[gusty smelt]

just read anything he has written, its not written with pedagogy in mind

i read his famous algebra book for some exposition and his algebraic number theory book

[fluid skiff]

Do math grad books are written with pedagogy in mind?

[gusty smelt]

depends on the book.

i mean its written with pedagogy thats appropriate for grad students in mind

ig

[queen beacon]

great books to learn linear algebra?

[brittle breach]

https://www.math.ubc.ca/~carrell/NB.pdf

[queen beacon]

ty

[brittle breach]

np

[warm glen]

im reading his linear algebra book rn actually (the proof based one) and it's very easy to understand, and i barely have any background in computational linear algebra

so at the very least i wouldn't discount that book of his

[glad arch]

Can someone give me a recommendation for an analysis book?

[brittle breach]

Rudin PMA (baby rudin)

Abbot Understanding Analysis

I personally prefer rudin

[glad arch]

oh okay thx c:

[heady ember]

You can try rudin, but its renowned for its difficulty as well. So you might want to try Apostol also, then see which you like best

[junior mantle]

is geometry for dummies good if i want to learn geometry?

im most interested in the theory

but i wanna be able to solve some problems

[grand osprey]

Does anybody have any book recommendations on an introduction to hyperbolic geometry/spaces; and more specifically on non Euclidean crystallographic groups of the hyperbolic plane?

[livid ermine]

What is the difference between Miranda Algebraic Curves and Riemann Surfaces and Fulton's Algebraic Curves. Is there a lot of overlap between the two books?

I know one covers Algebraic Curves from a complex analytic pov.

But does this mean if I read Fulton's book, Miranda's will be less interesting afterwards?

The Miranda book seems to go more in depth. Covering sheaves, more complex analytic stuff and diff geo. However. I really like the way Fulton is organised with very short sections of text followed by 5-10 problems.

[gaunt bobcat]

A good book for “proofs and logic”?

[compact crypt]

book on proof

https://www.amazon.com/Book-Proof-Richard-Hammack/dp/0989472124

I found this book to be more consistent/organized than how to prove it by velleman

[modern stone]

Here’s a pdf of it

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

[compact crypt]

does anyone have recommendation on topology book with solutions?

any book would do because I am looking for problems to test myself

[south valve]

The one with steve warner is pretty good

I liked it

[compact crypt]

https://www.amazon.com/Topology-Beginners-Introduction-Metrizability-Connectedness-ebook/dp/B07R5PQL3K

this?

[karmic thorn]

Any recommendations (preferably an expository article, lecture notes, or a compact textbook) that roughly talks about propositional logic, boolean algebras and Stone representation theorem?

[compact crypt]

are there any set theory textbooks

with bare minimum content that is necessary for studying other subjects?

rather than covering all the way through axiomatic set theory?

[runic hatch]

Naive Set Theory by Halmos should suffice

[gaunt bobcat]

Thx

[compact crypt]

how long do you expect to take me to cove rit

I wouldn't want to spend a lot of time for it

[atomic hound]

two books, one for calc2 and other for cal3

[brittle breach]

book of proofs or
how to prove it

[compact crypt]

hmm is the content there really enough?

[stray veldt]

to do mathematics? yes

there is an even shorter intro (written by me) pinned in #proofs-and-logic and i am of the opinion that this suffices to do more stuff (given a sufficiently beginner friendly book)

[lusty perch]

Cheaper alternative to Basic Mathematics by Serge Lang? Or just generally a alternative?
ping when replying

[manic cairn]

munkres and axler

oh yeah, and mendelson's logic book

[main void]

any nice books on network flows/integer programming? I know about bertsimas & tsitsikilis but would really like another reference

bonus points if its more of a “mathyish” book, ie. with a greater focus on theory rather than concrete applications

[unreal elm]

I dunno if its any good but recently got this pop math book where a mathematician talks about his work on the langlands project

[sudden kindle]

https://youtu.be/3SfoeFUi24E

Very interesting nonstandard reccomendation

[subtle mango]

interesting

i will use this when i do aa

[sudden kindle]

Harold M Edward's Galois Theory not just as a recommendation for Galois Theory, but for an introduction to Abstract Algebra in general

[subtle mango]

this would ideally be followed with a more rigorous aa book, i assume?

[sudden kindle]

Yeah , thats what he says

[subtle mango]

kk

[fading goblet]

Hello, everyone.

Is there anyone here that have a fair amount of experience in dealing with Fermi-Pasta-Ulam-Tsingou problem? If so, could you recommend me resources for starting studying these phenomena?

Most of my background are Dynamical Systems and Hamiltonian Systems from perspectives of mathematics. If there is any physics prerequisites that I need studied first, feel free to tell me..

[slow roost]

that galois theory book looks super interesting, thanks for the rec nyamin

[livid ermine]

What is the difference between Miranda Algebraic Curves and Riemann Surfaces and Fulton's Algebraic Curves. Is there a lot of overlap between the two books?I know one covers Algebraic Curves from a complex analytic pov.But does this mean if I read Fulton's book, Miranda's will be less interesting afterwards?The Miranda book seems to go more in depth. Covering sheaves, more complex analytic stuff and diff geo. However. I really like the way Fulton is organised with very short sections of text followed by 5-10 problems.

[gray gazelle]

Hey , i am 20 year old and i wanna start algebra from scratch . I researched some book ( according to my budget ) and i finalized these two book from which i wanna pick one .

1.  Elementary Algebra For Schools
   

2. Algebra For Beginners

From these two books which should i choose , it will be great help 👍🏻

LINKS : 1) Elementary Algebra For Schools = https://www.amazon.in/Elementary-Algebra-Schools-H-S-Hall/dp/9350943255/ref=sr_1_1?qid=1652854284&refinements=p_27%3AS.R.+Knight&s=books&sr=1-1

2. Algebra For Beginners = https://www.amazon.in/Algebra-Beginners-Hall/dp/9350943204/ref=pd_bxgy_img_sccl_1/259-1965674-7376029?pd_rd_w=MxuXn&pf_rd_p=0ead3825-c5eb-49e5-97ec-968efd0ae7aa&pf_rd_r=41QK26GACPJ086GEGJ3T&pd_rd_r=b30d8bcd-6b39-4956-97c9-1dd4e9b12572&pd_rd_wg=5PO2D&pd_rd_i=9350943204&psc=1

help me please !

[modern stone]

You can also check Khan Academy if you haven’t done already. It has videos and exercises from pre-algebra to calculus and it’s all free

[vivid bridge]

https://artofproblemsolving.com/community/c5h2847328p25234767 An Integration Article

[gray gazelle]

Can someone recommend a book?

[fervent lava]

Water Is wet by Penny Pollock

[gray gazelle]

Thanks

[vapid harbor]

Has anyone read "Basic Mathematics" by Serge Lang, and would you recommend it?

[obtuse prairie]

https://freenode-math.fandom.com/wiki/Book_List

[gray gazelle]

its a great pre-calculus text-- in the literal sense of the stuff you should know before studying calculus (not the strange assortments of topics in a standard american precalculus course). It hints at the axiomatic way of thinking about math which is excellent imo. Strongly recommended if you are interested in eventually studying math more seriously, lays a great foundation for a more mature studying of single variable calculus.

can double as an intro to proofs book imo if you really get everything out of it

only complaint is that it doesnt treat topics like injectivity surjectivity etc

but that can easily be covered when studying calc

[vapid harbor]

alright, thank you! I'm currently in high school at the moment and I really enjoy math so I'm just trying to pursue it more and find some good resources. I was using Khan academy for a while but it just feels odd learning with it sometimes.

[frosty carbon]

Anyone have a recommendation for graph theory and probability? My discrete math course kicked my butt in those topics

[gray gazelle]

killer textbook

[gray gazelle]

i self studied this, all 800 pages and I was able to pass 4th grade!

this looks very hard

owl is scary compared to racoon

yk

[gray gazelle]

i might try out the aops prealgebra or introductory algebra textbooks if i were you

let me try to pull up the table of contens

books look like these btw

even though it says prealgebra or intro algebra these books go very in depth into certain topics which helps you gain a solid intuition for what you are doing

https://s3.amazonaws.com/aops-cdn.artofproblemsolving.com/products/intro-algebra/toc.pdf

Intro Algebra table of contents

https://s3.amazonaws.com/aops-cdn.artofproblemsolving.com/products/prealgebra/toc.pdf

Prealgebra table of contents

i would lean more towards the intro to algebra book as i don't think they go too fast

the aops (art of problem solving) books and website as a whole are very well known for making a lot of high school mathematicians truly excellent.

like this isn't necessary but just to show how in depth the aops books are this is from the table of contents of the intermediate probability book which has graph theory generating functions, and all this crazy stuff which is very advanced but these books are able to explain it in such a seemless way where too many ideas are not thrown at you at once

[gray gazelle]

thanks for telling , gonna look at both books! 👍🏻

[gray gazelle]

Is Calculus by Apostol(volume I) good for beginners?

[gray gazelle]

MIt OCW >>>

?

[gray gazelle]

mit open courseware has past MIT lectures including calculus lectures that are very thorough and are likely a better subsitute than a textbook

[gray gazelle]

Where can I get them?

[gray gazelle]

just search her up

her

*here

https://ocw.mit.edu/courses/18-01-single-variable-calculus-fall-2006/

here is one for multi as well

https://ocw.mit.edu/courses/18-02-multivariable-calculus-fall-2007/

@gray gazellei dont agree

they are hs level at best

[gray gazelle]

its a good intro tho

u can go deeper if u want '

for calculus ? yes

for analysis ? no

oh they asked for an analysis textbook?

shoot

they asked if it aposotl's calculus is good

they asked for a beginers book no?

[gray gazelle]

oh ..

i gtg

[runic hatch]

Apostol’s calc series seems pretty decent

It’s like intro analysis (similar to spivak)

[compact crypt]

its a great book

but is very long and has many topics

[gray gazelle]

thx

[waxen badge]

Could anybody recommend any entry level books/material for any of these subjects? (doesn't need to cover all)

Starting my CompSci degree after the summer so I'd like to get a little head start because my math isn't the best

[mild cedar]

I have been learning calculus 1 recently and I have learned linear algebra long time ago.. As a highschooler, I can't use pdf books cuz, I can't take my phone or pc to school. So I want a hardcopy of books. I was learning calculus 1 from the "calculus for dummies" book printing all pages with my printer. But I am not sure if I can afford doing this for every book I want to read. So, I want a book that comprehensively include necessary math's concepts for AI and machine learning. Is this book worth it?

[gray gazelle]

after a brief look through the textbook you should certainly have studied calc 1,2,3 and linear algebra before reading it. probably probability theory and some discrete math course as well

[gray gazelle]

take a discrete math class at a comm college?

[mild cedar]

Hmm... I thought the book has included linear algebra and probability.

[waxen badge]

I'm in the UK we don't have that choice sadly

[gray gazelle]

i am trying to look for this book

this is a good one

[vapid harbor]

I'm considering getting a few books from The art of problem solving but I'm not sure where to start. Considering their prices and whatnot I'm not sure. I would say I have a pretty good understanding of all the core math concepts but I'm not sure how they structure the content. I'm currently in highschool so should I start from intro to pre algebra or would I be fine with jumping into something like Vol.1 The Basics?

[gray gazelle]

what are your goals? if u are trying to go the comp math route what have you accomplished.

[vapid harbor]

Well mainly just to study more math, I find it enjoyable and also because of computer science and how it's kind of limiting me not knowing a lot of mathematical topics.

[lime sapphire]

A concise introduction to pure mathetics by Liebeck looks good for students just finishing A levels

[waxen badge]

I didn't take maths at A Level, I do have basic knowledge of differentiation and integration though. Would you still recommend?

[lime sapphire]

Yea of course

Is your algebra up to scratch?

If so you should be fine with the book

[waxen badge]

I think my algebra is pretty good and I can always refresh if not, thank you I'll give it a read

[gray gazelle]

oh my bad i kinda just assume people who mention aops are from comp math 😅 . Vol 1 is more geared towards competiiton math specficalyl and has practice problems from comp math.

maybe try intermediate alg, it may be a bit of a strech the intermediate books are somewhat harrd

i think the most interesting book for a cs person would be intermediate counting and prob bc it starts to get into recursion and stuff like that

oh wait you haven't done prealg yet

i don't think that taking aops prealg is a necessity and i will recomend intro alg

its not that diffiicult and goes in depth

[vapid harbor]

I should have mentioned it, but I've already taken trig. Though in our school we haven't learned things such as Series and Summations yet so its quite odd. I was mainly just looking into the Vol. 1 book because it has a ton of topics, not sure how much more condensed the information would be vs other books that might explain it better such as their pre calc book or the intermediate algebra.

[gray gazelle]

i mean

aops vol 1 is very broad

and is geared more towards competition techniques

do you want to learn algebra?

you talked about the prealg book

hmm

i think volume 1 can do the trick for you

but this may also be a good intro to math competitions

it sets you up for sucsess

[vapid harbor]

you mentioned earlier that people asking about aops are usally comp math. Are the other books also pushing towards competition in a slow manner or is it just for general learning?

Im just going to read the Intro to Algebra one I think, that way I can have a more solid foundation and come back to the Vol.1 eventually

Thanks Gabreil

[gray gazelle]

👍

[gray gazelle]

it pushes towards competition stuff in a slow manner

but i think you should have general intuition in the topics that lead up to those results

comp math is more about using and weaponizing the tools and thereoms at your disposal rather than deriving and understanding them

mad respect if u decide to do intermediate alg

it will definitely be possible but you may have to put a lot of effort that may not be worth it

[vapid harbor]

I might jump straight to the intermediate one to be honest, the only thing I'm worried about missing in the intro to algebra book is the self-symmetry and the information towards the end, but luckily most, if not all of that is included in the intermediate

[gray gazelle]

wdym self symetry

[vapid harbor]

Ive never read any of the art of problem solving books so im not sure what the content will look like

1 sec

[gray gazelle]

im gonna look at this

lol

[vapid harbor]

oh sorry, self-similarity

[gray gazelle]

hmm

ok

can i give you a problem

[vapid harbor]

sure

[gray gazelle]

one second

log (x+4) - log(x) = log(x+2)

this is a harder problem

but if u can do this u are def ready

if you don't know log propertie don't worry

u will learn it in intermediate alg

[vapid harbor]

alright, ill try it out

[gray gazelle]

ok

good luck

[vapid harbor]

I got 2

log(x) = 2

yeah i dont think thats right'

[gray gazelle]

hmm

let's go through this problem

do you know that log(a) + log(b) = log(ab) ?

[vapid harbor]

yeah

[gray gazelle]

ok

explain why

the intuition behind these things are important

[vapid harbor]

Its just one of the properties, I'm not entirely sure what the reason behind it is besides making a proof or something

[gray gazelle]

like i wouldn't say i remmeber a lot of formulas but intuition with these things definitely saves a lot of effort

ok

so basically

you know that 10^(log(x)) = x right

[vapid harbor]

yup

[gray gazelle]

ok

now

10^(log(x)+log(y)) = what

[vapid harbor]

xy

[gray gazelle]

ok

[vapid harbor]

or would it be x+y?

[gray gazelle]

one second

10^(log(x)+log(y)) = 10^log(x) * 10^log(y)

this is by breaking up the exponents

logx+logy=logxy

[gray gazelle]

i'm trying to explain to him/her/them why it works

[vapid harbor]

that makes sense\

then the base of the log is canceled out and you are left with x*y

[gray gazelle]

yep

and you can trace back your steps and basically you get what you want which is logx+logy=logxy

so my verdict as of now is that you can prob do the intermediate alg book but you would get so much more if you understand the derivations/proofs of the things you are doing. It gives a much much deeper understanding

[vapid harbor]

how well do the books explain them? Do they show proofs etc or something of the sort like you did? Or just descriptions

[gray gazelle]

yep they do things the way i like em

they don't just give you a formula to remember they give you a proof

and they make you understand that

like i absolutely did not take effort memorizing that "proof"

but it just comes naturally to you

i think those books really helps you conceptualize these ideas and help you use them effectively

this in turn makes more advanced topics and harder problems much much easier imo

[vapid harbor]

alright thanks Gabriel. You helped me a ton, I guess I'll see how it goes when I start reading it

[gray gazelle]

ok

i just wanted to show you the sharp contrast of being able to think on your feet that you will learn versus remembering formulas and grinding uninspired practice problems (which thankfully you will not see in this book)

this book does increase in difficulty near the second hald

in the first half i would say that some of the stuff (50%) is standard stuff you will see in a hard high school class

then there is def a difficulty curve that you will have to get over

lol was just looking at this

and they have a section called when formulas fail

but these books are amazing and really thrusts you into truly interesting topics imo

https://data.artofproblemsolving.com//products/diagnostics/intermediate-algebra-posttest.pdf

[vapid harbor]

yeah I think its really interesting, things like telescoping etc.

[gray gazelle]

here is a link to questions that you will learn how to solve by reading the book

and if you are able to survive this book i highly recomend checking math competitions out

[vapid harbor]

alright, will do. Sounds pretty fun actually

[gray gazelle]

no problem

good luck with everything

there is also a class for this book on the aops website

that costs a bit of money + its online and is easy to get distracted

but it is still a pheonomenal book

[vapid harbor]

yeah I like paper books more mainly just because I can travel with them and not get distracted etc. Also taking them to school etc

[warped kayak]

If I wanted to get a rigorous understanding of Gödel's Incompleteness theorem, what books/math topics would be a prerequisite?

[mild cedar]

I have been learning calculus 1 recently and I have learned linear algebra long time ago.. As a highschooler, I can't use pdf books cuz, I can't take my phone or pc to school. So I want a hardcopy of books. I was learning calculus 1 from the "calculus for dummies" book printing all pages with my printer. But I am not sure if I can afford doing this for every book I want to read. So, I want a book that comprehensively include the necessary math's concepts for AI and machine learning. Is this book worth it?

[quick hornet]

you might have better luck asking in a place more catered to CS; i'm not sure many mathematics students would have read a book targeted at programmers

(and my impression is that "the necessary math concepts" depends heavily on what you want to do/how far you want to go with the theory)

[mild cedar]

I want to go with the theory but I will also do practical ml sometimes

[hollow lark]

Hey guys I want to study the philosophical and conceptual side of mathematics, What are the best books in that regard?

[quick hornet]

a cute intro text to philosophy of math is shapiro's thinking about mathematics

it's more like a particularly in-depth survey than a proper source on anything it talks about

but it's good

[hollow lark]

Okay that was fast

thank you I will read it

@quick hornet what about this book?

[quick hornet]

unfamiliar with it.

[hollow lark]

well it's the first thing that popped up on google so i thought it was quite famous lol

[hasty turret]

Well, It's Springer. So probably good

[quick hornet]

seems less like a philosophical text and more like a survey text of various fields intended to build mathematical maturity?

but im not entirely sure

[hollow lark]

Probably introductions to concepts?

[quick hornet]

just going based off the toc

yeah

[hollow lark]

Quite the timing

Alright lemme check the one you recommended

[quick hornet]

kinda reminds me of the princeton companion

[hollow lark]

That's what I'm reading currently

but it is so broad however I can just search specific books for specific subjects for detailed In-depth study

[compact crypt]

https://www.amazon.com/Complex-Analysis-Universitext-Eberhard-Freitag/dp/3540939822

does anybody here have experience with this book?

[sudden kindle]

Looks good

[stray veldt]

i used this and liked it a lot

there is also a second part about riemann surfaces

[compact crypt]

how difficult is this book in your opinion? like is it approachable for undergrads?

[stray veldt]

yes, i used it in undergrad

standard intro to complex analysis (after 2 semesters of real analysis)

tbf we covered roughly the first 4 chapters

[compact crypt]

by 2 semesters of real analysis

can you specify which topic you covered?

[stray veldt]

uhh

everything up to riemann integral and then some multivariable stuff

[compact crypt]

oh okay

[stray veldt]

sequences and series, metric space stuff, topology of R, continuity and differentiability, riemann integral, differentiability in higher dimensions, implicit function theorem

[compact crypt]

would you recommend it as a self study book?

[stray veldt]

maybe

i took a class roughly based on this and then used it for review a year or so later

it worked well for that

[compact crypt]

okay

thanks for answering

[compact crypt]

one last question: how would you rank the level of difficulty of the exercises/problems

[stray veldt]

i dont think i have a useful answer to that

its the only complex analysis book i know, but they were easier than the ones in my class

but that might just be because i had spent more time with the subject by then

[compact crypt]

oh okay

[livid ermine]

What is the difference between Miranda Algebraic Curves and Riemann Surfaces and Fulton's Algebraic Curves. Is there a lot of overlap between the two books?I know one covers Algebraic Curves from a complex analytic pov.But does this mean if I read Fulton's book, Miranda's will be less interesting afterwards?The Miranda book seems to go more in depth. Covering sheaves, more complex analytic stuff and diff geo. However. I really like the way Fulton is organised with very short sections of text followed by 5-10 problems.

[marble solar]

I don't think that it's one or the other yoohoo

I really liked Fulton's text, but I only got up to the proof of bezout's

I didn't take the class that was based on Miranda's book during my grad program because it conflicted with other commitments

but many of my friends took both, and they said the two point of views were helpful

[slow roost]

https://en.m.wikipedia.org/wiki/Mathematics,_Form_and_Function#:~:text=Mathematics%2C Form and Function is,American mathematician Saunders Mac Lane.

[sage python]

@livid ermine Not a lot of overlap iirc. Fulton's more like

Mostly an intro to affine/projective varieties over an algebraically closed field

The main content that's specific to curves is a bit on intersection multiplicity, Bezout's theorem, resolution of singularities, and some chit chat about divisors

Miranda goes more into the analysis, talks about cohomology, and does a lot more with divisors/Riemann-Roch

[hollow lark]

this is a buried treasure thank you very much

[drifting elm]

a perfect place to start. https://www.logicmatters.net/resources/pdfs/LogicStudyGuide.pdf

godels incompleteness theorem simply states that any system of axioms will be either inconsistent (some paradox can be made in that system) or it is incomplete (there will exist some true statement for which a proof can not exist).

but it is also important to know that godel did much more than the incompleteness theorem.

I have this book https://www.amazon.com/Axiomatic-Theory-Dover-Books-Mathematics/dp/0486616304/

which is basically a book about zermelo frankel with the axiom of choice. ZF or ZFC as it is named. This is the most widely used system of axioms today in mathematics. The book is actually very difficult to understand if it is your only book on the subject. There are better books on first order logic. I think it runs through things too fast. not enough examples. all the references in the book you need to pull from other sources.

[subtle mango]

goldrei set theory is also a good text

[drifting elm]

I happen to have this axiomatic set theory with me at all times. I'm finally at the level where I can understand the book after going through 10 other books to prepare.

[warped kayak]

@drifting elm and @subtle mango thank you so much for your thoughts! I truly appreciate it!

[mild cedar]

Is there any book you recommend for calculus. I want the book to have calculus 1, 2 and 3 as well as some pre-requisite chatpers for calculus 3.

Calculus 2 and 3 only also works for me

[hasty marsh]

N Piskunov differential and integral calculus

for pure mathematics btw

[mild cedar]

ohok. thank you let me have a look at it

[mild cedar]

Oh. This book has all pre-requisites lol

Is there just a calculus book?

By pre-requisites I mean, forexample for calculus 3, just about vectors and matrices...

[hasty marsh]

Calculus by Spivak

[hasty marsh]

You can just skip the pre-requisites really for the starting things.

[mild cedar]

Yeah. I actually want a hardcopy book.. and with all those useless pre-requisites, it will be expensive for me.

[hasty marsh]

well there is calculus by spivak which will be more expensive than N piskunov vol 1 and 2 combined

[mild cedar]

hmm

[mild cedar]

I am actually trying to grind through calculus and all other machine learning pre-requisites. I think, I better start with practical machine learning and I will learn the math on my way. Since, I am just a grade 10 student, I will have a lot of time in the future.

[hasty marsh]

You definitely don't need calculus textbooks for that. Try going over some basic calculus course and that should be about it.

Machine learning does not really need much maths at all to be honest. (personal experience on OpenCV)

[mild cedar]

I am already getting done with the calculus for dummies book.. but I feel lost now. So, I will stop it 😅

[hasty marsh]

Yeah, that should be about it. If there is something you don't understand, you can ask in help or wherever. You don't need that much calc to get started in machine learning.

[mild cedar]

Yeah. I did train some models in summer. I just wanted to learn the math cuz, I like to go low level most of the time.

[mild cedar]

I am just realizing that these days. Thanks anyway 👍

[misty current]

Any book recommendations to develop good intuition of the mathematics behind econometrics?

Preferably grad level + prerequisite to see if I am at the appropriate level

[west bramble]

Ayo

I need book recommendations to my friend abt sequences

arithmetic/geometric progressions/ sequences in general/ limits/ sums/recurrence relations/series

[heady ember]

Spivak's Calculus for maximum pain and suffering

[mossy portal]

are there any prerequisites for getting into multivariable calculus?(except real analysis) and if so which books would u recommend for a highschool student…☺️

[cursive gust]

For the spanish speaking people here, one of baldor's books. They are more like testbooks but yeah same thing. They range from arithmetic to geometry and trigonometry, basically precalculus.

sorry if bad english

I haven't invested enough time into multivariable calculus, sorry I couldn't help.

[mossy portal]

no worries!

[coarse frost]

u dont need real analysis for multivariate

[mossy portal]

well ive done analysis and thats abt it

[coarse frost]

u can try pauls online notes

[mossy portal]

ill try them out

[coarse frost]

i was also recced this book

[hearty steppe]

What is that?

Is that an analysis book

[coarse frost]

its a multivariable book from the looks of it

[hallow oriole]

^

im using it

[coarse frost]

oo

valley u are doing multivariate?

[hallow oriole]

self studying

still v early

[coarse frost]

dayum

no worries about exams?

[hallow oriole]

well

technically

i still have to worry abt my single variable calc exams lmfao

[coarse frost]

[hallow oriole]

my final is on monday 👀

[coarse frost]

are u not giving any entrances?

wait really?

thats nice

[hallow oriole]

yeppp

the issue is

im v sick rn lmao

so i might not be able to go

[coarse frost]

oof