book-recommendations

[heady ember]

(Because I haven't seen any new recs here that seem interesting)

[remote sparrow]

there are books from all sorts of subjects

doesn't have to be math

could be fiction as well

[heady ember]

Ah well I don't really read fiction much

[fierce hedge]

@gentle arrow Artin log where?

[swift dome]

I need recommendation for statistics books for undergrad

[orchid mortar]

What is 'stats book'

[main void]

One introductory book I really liked is statistics for mathematicians by victor panaretos, it presupposes a basic course in probability theory though

[gray gazelle]

Any good books for Year 9/10 In the au curriculum focusing on mathematics?

[fervent bolt]

FIITJEE package + PYQs(Mains + Advanced) + Reference books (HCV,NA,MSC) Can get you up to how much rank in JEE Mains and advanced?

[lime sapphire]

there's a book by chiswell and hodges on mathematical logic and i thought it looked pretty out of the ordinary, would like people's opinion on it

out of the ordinary in the sense that it communicates ideas quite differently as compared to other books i've looked over

[remote sparrow]

https://www.logicmatters.net/tyl/booknotes/chiswellandhodges/

[fossil arch]

Are there any light-reading introductory number theory papers (not books, just up to like 40 pages or wtv) giving a quick look/introduction at various flavors or major results of the subject?

Something I can just skim through to get excited about math I haven’t seen before without having to dedicate much brain power to it

[heavy pelican]

why number theory lol

[fossil arch]

Idk I haven’t learned much about it and I want something new

[heavy pelican]

oh well

[finite gale]

Random Keith Conrad notes?

[topaz haven]

R.D. Sharma>>>>

[limber flicker]

Guys I want to learn about the following topics:

Advanced Algebra, Basic and Intermediate Trigonometry, How to deal with imaginary numbers and Euclidean Geometry can y'all recommend some easy-to-read books that I can begin with (I am gonna start High School from June)

[gray gazelle]

good book for uni physics?

[gray gazelle]

rensick haliday's one

its too expensive in my country 😭

there are cheaper ways to get your hands on it

[hasty turret]

Pray to god of genesis

[gray gazelle]

😉

[limber flicker]

guys respond to my message up there

[gray gazelle]

read george poyla's book

[gray gazelle]

o-oh

[gray gazelle]

and by cheap I mean 0 cost

[hasty turret]

The god of genesis has graciously provided us with libraries

[gray gazelle]

i prefer physical copies

[hasty turret]

And that's how Hotaro got banned

[limber flicker]

Hey which one excactly

[gray gazelle]

I forgot the name

Google it

[limber flicker]

I have there are several books in there

[gray gazelle]

How to prove it

no wait

"How to solve it"

[limber flicker]

oh thanks a lot dude

[gray gazelle]

Np

[gray gazelle]

you're in 8th grade??

[limber flicker]

ye ggonna go in ninth next week

[gray gazelle]

yo im in ninth

(india)

#discussion

[limber flicker]

same

[heady ember]

I mean you can print the PDF(s)

Of course after you have legally purchased them

[finite gale]

i would recommend that you don't print 500 page textbooks

[gray gazelle]

it's a 1500 page text 💀

[heady ember]

So its not 500 page

[slim bramble]

print small chunks
you'll probably need some time to finish x number of pages so print each month a chunk and that would be your goal

[grizzled drum]

Looking for graph theory resources

[cerulean cypress]

are there any other books for vector+multiavariable calculus that are better than stewart? excluding apostol's calculus

[hollow shore]

I have started a basic Real Analysis reading group where we work through Abbott. DM me if any of you guys are interested in joining.

[fierce hedge]

I'd join but I'm already in chapter 2 mid

[hollow shore]

feel free to join!

[smoky zephyr]

what chapter are you on?

[hollow shore]

2

[hollow shore]

and I am speaking for myself here btw

the reading group hasn't officially begun

[fierce hedge]

If you want to you can also message modmail for a server wise announcement

Maybe we can get some honourables to do the honour of being TA

[timber falcon]

Any book suggestions for linear algebra or complex analysis?

[flint forge]

Conways complex analysis is pretty good

and I like linear algebra done wrong

[remote sparrow]

is this your first time taking linear algebra?

[timber falcon]

Yeah

I'm really a math virgin, highest level is basic differentiation

after complex analysis I'm tryna do multivar along with Griffiths electrdynamics book then QM with linear algebra

but rn I'm just sticking with Lagrangian mechanics and complex analysis

Physics math duo

[marble solar]

I prefer Marshall's Complex Analysis book. There's also stein and shakarchi volume 2 which is excellent

[flint forge]

oh wait i rescind my recommendations completely

if you don't have any proof based math background don't read conway

LADW is probably still doable

but might not be what ur looking for if you just wanna learn how to work w matricies and such

[remote sparrow]

so you haven't finished your calculus sequence yet?

[ocean mulch]

this is your last chance to turn back and retain your innocence sanity

[vast raptor]

Opinions on Wasserman's All of statistics?

[timber falcon]

yeah I heard good things abut Axler for Lin Alg and “Complex Variables” by Ablowitz

[marble solar]

If you can't read and write basic proofs on your own, it's going to be rough going

[timber falcon]

oh yeah especially since im weak w calc

ig

[timber falcon]

no lmao some people told me me to just jump to line alg directly anyway

[timber falcon]

1. e4

[remote sparrow]

you can do linear algebra early but why worry about complex analysis when you haven't even finished calculus?

[timber falcon]

someone said it was super interesting

also single var calc feels like a drag

[flint forge]

i strongly recommend against axlers book tbh

esp if you are not used to proof based math and are looking for a computationally flavored linalg book

[timber falcon]

mitocw might have good courses

but don't i need multivar for lin alg or sm?

[remote sparrow]

#book-recommendations message

[timber falcon]

thx

[remote sparrow]

no, multivariable calculus depends on linear algebra

[flint forge]

other way around

[remote sparrow]

although it's generally taught before linear algebra

[flint forge]

multivariable calculus is best understood after a course in linear algebra

[timber falcon]

oh

[flint forge]

its insane that most schools reverse the order

[timber falcon]

thought it was single var alone 🤦‍♂️

[timber falcon]

yeah i noticed i was wondering

[remote sparrow]

some schools teach an integrated course in linear algebra and multivariable calculus using books like shifrin or hubbard

[flint forge]

If you think of derivatives as approximating a one-variable function via a linear map mx+b (usually you only consider the slope for the derivative but the intercept is secretly there) then linear algebra studies linear maps between vector spaces, which is the correct multi-variable analog

so differential multivariable calculus is studying approximates to mulivariable functions by linear ones

[timber falcon]

oh i see

was about comment that those are gradients

k thx, ill look into the books

[hallow oriole]

do you know a book that does both appropriately?

like

linalg and mvc

[flint forge]

i would suggest two books

[hallow oriole]

and develops them tgt in the best manner

[flint forge]

there no reason to do it in one book

[hallow oriole]

oh that works too

[heavy pelican]

Shifrin, “Multivariable Mathematics” is my suggestion

[hallow oriole]

what're your suggestions

[hallow oriole]

dami likes this one

[flint forge]

I like LADW for linear algebra

and i have no suggestion for multivar

i've never actually taken a course on multivar lmao

[hallow oriole]

how?

im required

[flint forge]

i took a proof based calc course

[hallow oriole]

i asked to skip but they said i couldn't skip it

[flint forge]

and we never got that far

bc it was proof based

[hallow oriole]

OH

LMAO

[flint forge]

i did do multivariable analysis

but not quite the same

like i have no idea what greens theorem is

or div

or curl

[hallow oriole]

me too bro

[vast raptor]

Bump

[gray gazelle]

Hello, I am looking to self study linear algebra, and am wondering what books are good for that. I'm leaning towards Elementary LA by Anton, with the Schaum's as a supplement right now.

[remote sparrow]

#book-recommendations message

[heady ember]

Also look in pinned for Dami's recs

[queen cairn]

Is there anything comprehensive I can read before starting my bachelors in math, I just finished Cegep and I have taken stats, linear, calculus 1,2

Just want something higher level that covers a bit of everything

[fierce hedge]

Max how do you have honourable when you joined yesterday

[smoky zephyr]

they rejoined yesterday

[fierce hedge]

Oh, wait is it that same Max who once roamed #point-set-topology ?

[smoky zephyr]

probably

[fierce hedge]

Use this channel to ask for book recommendations. Tends to be mostly math but feel free to ask about other literature (YMMV).
no issues

[cerulean cypress]

zill vs morris vs boyce

which ode book would you recommend?

[gray gazelle]

I've only used Boyce and it was more than good enough for what I wanted to learn

[gray gazelle]

any good books on algebra review? I'm going into trig and I feel like I'm lacking in algebra.

[shadow hedge]

Can anyone tell me whether book of proof by hammack and how to think like a mathematician by Kevin Houston contain the same content. If so which book should I read?

[cerulean cypress]

there might be some differences but it isn't going to matter. just pick one book and it should be enough

what you are trying to get here is proof skills

[shadow hedge]

I would like to add that I am starting my math bachelor in Europe and would like to prepare beforehand.

[cerulean cypress]

i'd recommend you book of proof by hammack though

i've used the book and found it effective

haven't used the other one but I can tell you that book of proof is a great book

[shadow hedge]

I have one last question. Would I be able to solve questions like these (https://postimg.cc/qzsBFssp) after I have studied the book of proof by hammack?

[cerulean cypress]

yes

don't get intimidated by the appearance

[shadow hedge]

Thank you

[cinder quiver]

I need a prealgebra, algebra 1 and 2, and a trigonometry book

For revision

Before I finish calculus 2

If those topics are explained comprehensively in a general maths book, then send those as well

Thank you

[woeful pollen]

What book is recommended to study fourier series? I need to study it for a signals and systems course

[desert oriole]

aops

books

[cinder quiver]

What's this

[desert oriole]

artofproblemsolving

[cinder quiver]

What's there

There

Tgwr

Thwr

Thst

Man.

What is that

[sterile harness]

It’s a website

[cinder quiver]

Oh wow

Yeah I'm looking at it rn

[fierce hedge]

Affe probably means the books sold by aops community/website

[coral prawn]

the books on the website tend to be cheaper from amazon but you can always get it online

[cinder quiver]

I got it

Thanks guys

[desert oriole]

yea the books sold by them
||just ... them and save money||

[desert oriole]

i think the aops books sold on amazon arent actually from the aops team, and just individuals who want to make some money

[coral prawn]

Ye

I compared the price, in my country its literally double on amazon

[desert oriole]

oh i remember the prices on amazon being something like 20% of the original price

[coral prawn]

Tho that being said ofc there's other countries where amazon products may be cheaper

[desert oriole]

ah

[coral prawn]

Yeah it tends to be higher cuz yknow profit

[gray gazelle]

I used: Fourier Analysis and it's Applications by Vretblad

Worked pretty well for me but it might be overkill if you just want to learn it as a tool to solve PDEs

[woeful pollen]

I like overkill

[gray gazelle]

Go off king

[woeful pollen]

tho maybe I won't have the time for that

[gray gazelle]

You can def skip a lot of the unnecessary stuff like Z transform and L2 theory

[sage python]

😦

[gray gazelle]

Z transform does objectively have the best name of anything in mathematics tho so maybe you want to learn it just because

Legit sounds like a dbz power up

[gentle zealot]

Z transform will be needed for signals and systems. But for that class, knowing the form of Fourier Series and it's coefficients is all you need. A book focused on Fourier Series is overkill

[gray gazelle]

Huh that's interesting, when my friend who was taking that course asked me for help it didn't look like he ever needed to use them

[orchid mortar]

I would assume Signals needs Z Transform

[gray gazelle]

Fair enough though maybe it's just my university

My class was a pure math class and we only had Z transform as an optional extra topic which I gave a cursory glance

Just assumed it wasn't that important since it wasn't used later on in the book

[gentle zealot]

My course had fourier, discrete and continuous, and Laplace and Z

This was an undergrad EE course

[orchid mortar]

Makes sense

[woeful pollen]

I actually need to learn Z transforms

[gray gazelle]

Well that's in there too

The book covers laplace, z, and Fourier transforms along with Fourier series

With discrete as an appendix

[remote sparrow]

Presumably you're an electrical engineering student. I once saw a book online that was free, but I forgot the name of it. I think it had a lot of applications for your field though. There is also another book that I happened to stumble on online: https://www.ece.uvic.ca/~frodo/sigsysbook/downloads/signals_and_systems-3.0.pdf.

[woeful pollen]

Thanks! I am using Oppenheim for signals and systems

[remote sparrow]

For more mathematical treatments, Brown and Churchill has one, though the main application is PDEs, and not so much on transforms. Stein and Shakarchi or Tolstov are also good choices for a rigorous treatment, though again they may lack direct treatment of topics relevant to signals and systems.

[orchid mortar]

Most recent version of the book is 5.0

[remote sparrow]

Good to know! Can you link it for Alacris?

[orchid mortar]

Same url just changed from 3.0 to 5.0
https://ece.engr.uvic.ca/~frodo/sigsysbook/downloads/signals_and_systems-5.0.pdf

No clue on changes

But presumably later = better

[gentle zealot]

Oppenheim is painfully verbose if one is used to math books

This one looks better

[woeful pollen]

"painfully verbose" sums it up but still way better than my collge recced book and lectures

[gentle zealot]

Oppenheim has lectures up on mit ocw/youtube if you want his view on things

[woeful pollen]

This is helpful to know. I was using IIT Bombay lectures on edX so far

[remote sparrow]

http://www.dspguide.com/pdfbook.htm

@woeful pollen found the book i forgot about

https://www.math.ucdavis.edu/~saito/courses/Fourier/books.html

i also found these recs

[woeful pollen]

Thanks!

[quartz coral]

hello

i just read the book "how to solve it" and i am looking for other books on heuristics

can anyone recommend me some?

[peak crater]

hi, is Basic Mathematics by Serge Lang a good book for people that wants to start math from scratch ?

[desert oxide]

||m||

[maiden halo]

I think it's pretty good, but it's not comprehensive. It barely touches trigonometry, for example

[final sluice]

has anybody here worked through klenke's probability theory?

(or is currently working through)

[gray gazelle]

does anyone knows a good textbook for improper integrals and series , i need a lot of examples and exercises

[still saddle]

Have a look at "Art and Craft of Problem Solving" by Paul Zeitz [googling will give a free pdf]

[prime oak]

googling will give a free pdf
when does it not

[slim bramble]

when the book is new 🙁

[glossy saddle]

any good books on trig?

[prime oak]

be the pioneer; put it on the front page

[cerulean cypress]

ordinary differential equations by morris tenenbaum must be one of the best books that i've ever read

[cerulean cypress]

isn't stewart or thomas enough?

[tepid prairie]

It is amazing.

[cerulean cypress]

the only downside is not having solutions manual

but tbh i should be thankful that it gives out answers

i plan on using the book for explanation along with zill

[tepid prairie]

True! Answers to every question was helpful.

[gray gazelle]

what are good introductory books for philosophy?

[hasty turret]

Can you not

[tender river]

<@&268886789983436800>

[maiden flume]

sorry it was a joke

[acoustic cliff]

The trigonometry section in Simmons’ PreCalc in a Nutshell is enough tbh

But if you want an entire book there is Corral’s trigonometry

http://www.mecmath.net/trig/index.html

Most of the regular calc books assume no trig experience and teach it to you themselves so a trig focused book isn’t really a necessity

[coral prawn]

Ehhh. I'd doubt that considering how trigonometry is a thing in pre calculus

[stoic nova]

I started with 'The Story of Philosophy' by Will Durant and then branched to other books from there.

[dapper root]

Waaaooowwwww red diamond

[coarse arrow]

I want to study topology what prerequisites should I know?

[flint forge]

Some people recommend familiarity with metric spaces at the level of eg Rudin

But honestly you can kind of just jump in formally, it’s only intuition that you might be lacking

[dense pumice]

I'd say knowing some Real Analysis is worthwhile, at least for Point-set Topology

Might not need a full course, but at least some understanding of sequences, open/closed sets, and continuous functions

[ocean mulch]

Strictly speaking, basic set theory, and know how to do proofs.

What's very, very helpful, is Real Analysis. Not a prereq, but it helps a lot, and it is a prereq in most uni.

Multivariable analysis and linear algebra, for the same reason.

[sage python]

The parts of multivariable analysis/linear algebra that are in the vein of, topology of R^n, sure they can help

The calculus stuff is largely orthogonal

[ocean mulch]

It's good to know for example, closed unit ball in Hilbert space is not compact.

Topology breaks one's initial intuition. Examples like that, which mostly come from analysis/linear alg, help a lot.

[sturdy shore]

in infinite dimensions*

[velvet gyro]

Perhaps not exactly pure math, but does anyone know any good introduction to information theory?

[hallow oriole]

fwiw i heard shannon's thesis isn't bad

cannot confirm and would also like recs tho pls

[dusty trench]

Hello, I am trying to practice more with problems like this one, involving 3D dimensions and using concepts like, trigonometric ratios with right angle triangles and sine and cosine law. Does anyone know where I can find challenging problems like these? https://cdn.discordapp.com/attachments/903463353417072641/1114318505945354261/859187052b80f2a0c62fa345b9e89d0d.png

[gray gazelle]

what are some good books touching topics in algebra 1

[thorn quiver]

If you mean abstract algebra, then Judson and artin are good

If you mean HS algebra, then give hall and knight a try

[thorn cloak]

i would recommend khan academy for anything calc 1 and before tbh. Books might a bit overkill

[flint forge]

did somebody say higher algebra

Sorry that was an extremely niche joke for like 10 people

(Jacob Lurie has a book called higher algebra which is very much not applicable in this context)

[thorn quiver]

They have two textbooks I think, you can look at whatever suits you better

[thorn cloak]

they are fairly standard books

if you dont like them though no harm in checking out a different book

just cuz a book is liked doesn't mean its perfect for everyone or the best book for you

[gentle arrow]

i guess it depends on what you are majoring in

[thorn cloak]

(i personally found them to be a bit unsatisfactory and very computational)

[gentle arrow]

stewart is pretty good if you do not necessarily require extremely heavy theory

but if you're doing something like pure mathematics as your major i would not call it ideal

[thorn cloak]

^ Shiffrin or Hubbard are good for theory based MVC

[gentle arrow]

id probably recommend spivak then

very good book but also difficult

[thorn cloak]

yeah i heard this book is pretty good for intro calc for math majors

[gentle arrow]

stewart has some pretty interesting exercises

at least towards the end of each section

[thorn cloak]

^ in the problem plus section

ye

or the hard problems in thomas

whatever they are called

[gentle arrow]

where are you in math right now

have you done like intro calc

like calc 1

calc 2

[thorn cloak]

hmm then probably no use in relearning it IMO (other than theory). intro calc is mostly formulaic which isn't really learning past a certain point. Maybe you can jump into multi-var or analysis.

did you not learn them in intro calc?

[grand thistle]

if you learnt the material before it should be a breeze

[thorn cloak]

its normal to forget but i took mvc 3 years after calc bc in hs and was fine

[grand thistle]

review for like a week or so

then calc 3 would also be pretty easy

[gentle arrow]

<@&268886789983436800>

[grand thistle]

[thorn cloak]

yeah if you learned basic calc concepts before you will prolly be fine. if not then yeah you should know limits, derivates, integrals and series, though series arent very important for calc 3

[flint forge]

series are extremely important for the general circle of ideas tho

[thorn cloak]

yeah i wouldnt skip

[quick hornet]

when do you actually need to compute an antiderivative

that sounds like a shitpost but its semi-serious

antiderivatives come up so rarely in applications outside the obvious FTC application

series come up everywhere

[flint forge]

Are you telling me i spent days of my life studying residue integrals for no reason nami

how dare u

[quick hornet]

max you got a math degree

[flint forge]

actually now that i think about it you never compute an antiderivative

[quick hornet]

what did you think you were signing up for

[flint forge]

not that

ur right tho

one of my many gripes w calc courses

[elder stratus]

maybe in fourier analysis

[flint forge]

is how much time is spent on computing increasingly inane antiderivatives

like an entire week on recognizing the antiderivatives that use inverse trig functions

[quick hornet]

yeah idk, if an antiderivative isnt likely to come up in a stats course i dont think its worth spending much effort on

[flint forge]

what a waste

and all the volume integrals

i hate them so much

the students are always confused and im always annoyed and no one is happy on rotational volumes week

[quick hornet]

especially since a mathematically mature individual can look up an integral method and figure it out themself in a fraction of the time it takes to teach in a calc course

but thats more a symptom of intro courses being slow as shit in general ig

[flint forge]

yeah i am convinced you could teach most of a conceptual calc course in like 1 quarter

and certainly in 2

i guess differential calc doesnt really need to be simplified much

[crimson leaf]

I use integrals all the time in my ug research to get generating functions but it's more like I punch them into a calculator if they're not easy lol

[elder stratus]

at the very least I can confirm trigonometric integrals come up very often. So atleast those need to be covered

[flint forge]

when

i mean the basic ones are fine ig, and the ones that are just regrouping + some easy identities are whatever

typically i recommend khan academy for anything below calc

[crimson leaf]

The most I've used anything below multivariable was in my ode course

[deep forge]

good intro stats book

[sudden kindle]

Id like to learn about arithmetic groups

Any recommendations?

@slim nacelle @gilded lagoon

[slim nacelle]

do you have any particular applications in mind?

[sudden kindle]

No

[slim nacelle]

do you want to do cohomology of arithmetic groups or something else?

Harder recently sorta finished his book project on Eisenstein cohomology and the cohomology of arithmetic groups, it's pretty self contained, it's just fucking impossible to read lmao

but that is maybe the most complete reference for some of this stuff

but let's see more generally

you might also like Morris's introduction to arithmetic groups

also kinda long

here is the most recent version of Harder's book https://www.math.uni-bonn.de/people/harder/Manuscripts/buch/Volume-III-07.-08.-2022v3.pdf

[sudden kindle]

Oh cool

[slim nacelle]

imo Harder's book is probably the best source on this stuff and it's where the most interesting research directions are in this area

although I'm kinda biased towards this stuff lol

I guess there's also a decision you have to make about like, do you want to learn about arithmetic groups in the classical language or the adelic language

Harder's book starts in the classical language and then eventually uses the adelic language

[sage python]

Oh he's basically done?

So there are at most finitely many typos?

[hallow oriole]

Perhaps not exactly pure math, but does anyone know any good introduction to information theory?

[hasty turret]

Coding and Information theory by rotman seems like a good introduction

[hallow oriole]

will check out

🫡

@velvet gyro

[velvet gyro]

Are you certain it’s by rotman?

I think it’s… roman?

[gray gazelle]

yellow

[hasty turret]

mb it is roman

[velvet gyro]

oki, thank you!

[tender river]

https://dontasktoask.com/

[coral prawn]

Ask whatever you have

[marble pagoda]

What are some good books for learning dynamic systems?

[hazy elk]

If you want to get your feet wet with the "pure" side of things, theres a book in the AMS library called "Dynamics done with your bare hands" It has relatively low prereqs but is a do it yourself book so not a light read. You can also try Devaney's introduction to chaotic dynamics/Holmgren's discrete state dynamics which are kinda easy to read for a mid level undergrad but can give you the wrong impression of what dynamics is because it is a very vast field. If you know measure theory there is a lecture series and notes by Stefano Luzzatto on ergodic theory on yt. Notes available on his site. Theres also Tao's lecture notes on ergodic theory (a bit sophisticated). Then there's Viana's Foundations of ergodic theory which is a good text. One modern reference for a huge chunk of dynamics is Katok Hasselblatt's "Introduction to the modern theory of dynamical systems". If the more proof heavy part is not what appeals to you, its hard to beat Strogatz's Non-linear dynamics (and his lecture series) for an intro. Just a disclaimer, since dynamics is very vast, you should probably take my suggestions with a grain of salt because there is so much more flavours and paths that I haven't mentioned! I have just suggested material that I have experience with.

Oh and Stefano also has another series of lectures covering content similar to that in Devaney's book but focusing on certain aspects way more since it is a course

[finite gale]

<@&268886789983436800>

[primal summit]

ty

[subtle mango]

why does hartshorne get the weird spotlight it has?

i honestly can't tell whether people think it's a good or bad textbook

is it like the rudin of alg geo?

[dapper root]

Hartshorne

[sage python]

So, Hartshorne is one of the older books on algebraic geometry, so a lot of people did learn it from there and go back to it, even see it borderline as a "rite of passage"

That said, it does seem somewhat concise, and a lot of important material is relegated to exercises so you'll have to do most of them (and there are many). Also, it does make some demands on your commutative algebra background.

My AG prof actually feels like its pov aged somewhat poorly, as it seems to emphasize the functorial pov less than eg The Red Book. Also, it seems to throw around the Noetherian hypothesis more than some arithmetic types would prefer.

Finally, I've heard the complain levied that you can spend a year doing Hartshorne without learning much "actual geometry". This seems strange at first, since Hartshorne's own bias is geometric: that's why he starts with a chapter on varieties instead of jumping right to schemes and cohomology, and spends the last two chapters applying that material. That said, the core of the book (chapters 2-3) is pretty technical, and if you read just those two (which is perhaps possible, if all-advised) you may see less geometry

[gray gazelle]

So I'm going to be self studying algebraic structures for the next year or so (currently haven't fully decided between Judson and Artin, starting with Judson for now because the pdf was legally free).
But I just finished a course on elementary number theory and loved it, so I was wondering if it'd be a good idea to jump into some algebraic number theory alongside the algebra.
Is this a good idea? If so, any recommendations on books for algebraic number theory?

[sage python]

Disclaimer: I am not an algebraic geometer, nor have I worked through much of Hartshorne or done many problems, this is mostly osmosis

[remote sparrow]

getting into algebraic number theory is ill-advised, but A Classical Introduction to Modern Number Theory by ireland and rosen is a standard graduate text that only assumes some algebra

[gray gazelle]

Mans name is literally Ireland

Ty

[gray gazelle]

Just out of curiosity though, is the reason you don't recommend algebraic number theory simply because it would be too early?

[finite gale]

I think you'd need to at least be comfortable with some galois theory to get into alg nt

[gray gazelle]

Makes sense, I'll see if I end up dabbling in it by the end of my self study, the last chapter in Judson's book does seem to cover it

I don't think my university has a course that treats with galois theory though

I'll have to ask my counselor

[flint forge]

Normally an undergraduate algebra sequence will have a few weeks of Galois theory

[remote sparrow]

it's also taught in early graduate courses

talk to your counselor if you can petition such a course after finishing undergraduate algebra

[gray gazelle]

What course would galois theory typically be contained in?

From what I can tell we used to have a course on solely galois theory like 10 years ago but not any more

[remote sparrow]

at higher tier universities, the last quarter of an algebra sequence

or the second semester

[gray gazelle]

And when I look at the syllabi for all the algebra courses I can find I can't find it

[remote sparrow]

in undergrad

[gray gazelle]

Hmmm

[remote sparrow]

in lower tier universities, early graduate

[gray gazelle]

We don't really have an "algebra sequence" as far as I can tell

[remote sparrow]

so it's just one semester or two quarters?

[gray gazelle]

You can take a pretty wide variety of courses but you aren't really required to take them in order so long as you have the 1 or 2 prerequisite classes

[remote sparrow]

i'm generally a fan of teaching less but more thoroughly imo

[gray gazelle]

We have 2 half semester courses on just "algebra" but in reality the first half semester course is more of a regular college algebra class and the second is basically just a ring theory class

Then there's 3 half semester classes of linear algebra

And the requirements for all of these are all pretty low

[remote sparrow]

college algebra is usually reserved for basic precalculus algebra

we use the terms abstract algebra or modern algebra instead

[gray gazelle]

Then there's a full semester of algebraic structures which I'm pretty sure would be equivalent to a modern algebra course in the states

But without the ring theory

There's also a course I could take simultaneously as that called "modules and homological algebra" but it seems pretty hardcore 💀

Nowhere in here do can I find any galois though

[remote sparrow]

modules are a generalization of vector spaces, in which a field of scalars is replaced by a ring

[gray gazelle]

I'll probably end up taking it one day

But for now I'll just inquire about where the hell I should go to learn galois theory lol

[remote sparrow]

you should focus on mastering the basic facts about groups and rings

[gray gazelle]

Rings I am very comfortable with

[remote sparrow]

pretty sure dummit and foote treats galois theory

[gray gazelle]

Come to think of it

[flint forge]

Abstract algebra

[gray gazelle]

Do you have any recommendations for someone who just wants to learn about groups?

Books I mean

[flint forge]

Dummit and Foote

It’s dry as hell but it’s the standard for a reason

[gray gazelle]

More or less dry than Munkres?

[remote sparrow]

i think rotman has a book on just groups but i haven't really looked at it

might be too advanced

[flint forge]

The subject matter is less dry

The exposition is similar

[gray gazelle]

I think I can deal then

[flint forge]

Honestly it’s not even munkres fault really

Point set is probably the driest subject in an undergrad

[gray gazelle]

I partially blame my instructor too

0 motivation for anything the entire class

[flint forge]

I genuinely don’t think anyone can make it exciting

[gray gazelle]

I don't ask for it to be exciting

[flint forge]

And the only real motivation is metric spaces for most people

[gray gazelle]

I just want to know why

[flint forge]

And once you study spaces that are pathological there’s really nothing you can compare to

I think point set is a really hard class to teach honestly

[gray gazelle]

To be honest the only reason I took the course was because it was supposed to be applicable to knot theory which I am really interested in

[flint forge]

It is

I mean it’s the like foundation of it

[gray gazelle]

But what I learned about just felt completely removed from anything

It just felt like spicy set theory

[flint forge]

That’s just the truth lol

Like that is what it is

[gray gazelle]

I passed the class with a B and still don't feel like I understood like half the concepts

[flint forge]

A huge amount of a point set course is typically spent on spaces that are totally separated from things people have seen before

[gray gazelle]

Esp ones that are supposed to be important like compactness and especially local compactness

[flint forge]

Bc honestly the nice spaces are very easy and simple

Oh

Those one hopefully does understand

Locally compact is weirder

Compact is probably something you want a feel for

[gray gazelle]

I mean I "understand" them on a baseline level

[flint forge]

Compactness is probably one of the most important notions in topology

[gray gazelle]

Like I know the definitions

But I don't know why those are the definitions

And I definitely don't know why they're important

[flint forge]

Do you know the various ways to equivalently reformulate them for metric spaces?

[flint forge]

This will come when you see topology applied in other fields

By itself it’s incredibly dry and unmotivated

[gray gazelle]

Apart from Urysohn metrization theorem I can't recall

Unless I just didn't really understand your question properly

[flint forge]

I mean like, there are ways to talk about compactness that feels more motivated when you assume all your spaces are metric spaces

[gray gazelle]

Apart from that and the whole "closed and bounded" stuff (which I kinda get why is important but not really) we didn't really do much with compactness

[flint forge]

This is what I meant basically

[gray gazelle]

Ok then yeah I guess

There's a short paragraph in munkres that talks about why metric spaces are important

But so far it's really just been on faith lol

And now that I'm going on an exchange for a year and won't be studying anything topology related I don't have much faith in myself to remember much about stuff that I hardly understood

[subtle mango]

ahhh i see

whats the "red book" in question?

[flint forge]

You can probably pick it up again

[sage python]

Mumford Red Book of Varieties and Schemes. Not as comprehensive/doesn't do cohomology

[subtle mango]

oh it's literally called "red book" lol, thought it was a nickname

[gray gazelle]

I def can but I wonder how much of a pain it'll be

[flint forge]

Substantially less than the first time around

[gray gazelle]

Ig lol

Thanks

[sage python]

But its take on raw scheme theory aged better

[subtle mango]

in reference to red book or hartshorne?

[sage python]

Red Book, or so my AG prof said

[subtle mango]

gotcha thanks

i will keep this in mind

[marble pagoda]

Thanks a lot

[thorn quiver]

Coming up with a definition of compactness was itself a huge deal for last century mathematicians, it is an important concept. It is understandable that it isn’t intuitive

You should look at many expository articles on compactness online, I think Terence tao wrote one too. Compactness is important for analysis, so you’ll have to go through some of that to really appreciate the notion

This link https://math.stackexchange.com/questions/371928/what-should-be-the-intuition-when-working-with-compactness helped me a lot

[gray gazelle]

Yeah I guess I've just ended up taking things in the wrong order possibly

[thorn quiver]

Finally you’ll have to get used to compactness, for that I think baby Rudin chapter 2 is great

[gray gazelle]

I have little to no experience in analysis

[thorn quiver]

That is unfortunate

[gray gazelle]

I've just been more drawn towards the algebra based courses

I'll end up taking real/complex analysis in a year or two

But for now I'll just be satisfied knowing that my exposure to topology won't go to waste later on

[thorn quiver]

So I guess you wanted to study algebraic topology when you took the course?

[gray gazelle]

Pretty much

I wanted to study knot theory and category theory

And so my advisor was like "ok you need to take this"

And so I did lol

[thorn quiver]

If you have some time, I’d say go through baby Rudin chapter 2. It did wonders for me for topology

[gray gazelle]

I'll end up doing it anyways when I take real analysis

But for now I guess I'll give it a cursory glance if I get particularly interested

Thanks for the advice

[thorn quiver]

That depends actually, not all analysis courses deal with metric spaces in general

But as long as you are taking an Honors or graduate course they should

[gray gazelle]

I mean the real analysis course at my university has baby rudin as the only listed course literature

So I assume I'll be going through it one way or another lol

[thorn quiver]

Yep that sounds good

All the best!

[heady ember]

Set theory is interesting

[gray gazelle]

what's up guys, do you know books for high school mathematics? i am studying for the hardest exam in my country and now i am searching other books to learn math. the level exam is a little bit easier from jee main

[timid schooner]

hello

[thorn quiver]

Educative JEE is a pretty good book

[undone jacinth]

Most of my textbooks are pretty big, I fly a couple of times a year and would like a backpack friendly / pane seat tray friendly sized book with exercises, any recommendations?

Proof based / Undergrad level*

[gusty smelt]

I usually read on my ipad on planes, so maybe a better investment here is like a reading tablet or something. I think they fit the size of the tray pretty well

because I can set it to an upright position

on the other hand even smaller books are a bit hard to manage on it imo, if you plan to annotate on it with a pen or w/e

as for topics, atleast for me the plane is an unideal environment to think too hard oof, so I usually read expisatory/survey type of things. So maybe download a book or paper that introduces some field you have heard about and then like, read the first chapter. I think this should be doable as a UG for many topics. You can also try reading papers from the Uchicago REU, usually pretty good for the parameters I said, an introduction to some topic

@undone jacinth

thats my 2 cents on this, but this is ofc how I personally work so maybe this isnt what you are looking for

[flint forge]

fwiw i feel like most textbooks fit the size specifications

maybe not the huge ones

[gusty smelt]

I feel like If I am using a pen to annotate it gets kinda hard when the book is like, laying down on a tray

my arms threaten to bump into my seatmates oof

[flint forge]

I dont usually use the tray

i just keep it on my lap

[gusty smelt]

fair

[undone jacinth]

Hi John, I realised, as I type this on my iPad mini at the airport, that you are right. I just like physical books.

For programming there’s a very short cool book: Exercises for Programmers: 57 Challenges to Develop Your Coding Skills by Brian P. Hogan https://www.goodreads.com/book/show/26489826-exercises-for-programmers

What’s great about that book is it’s language agnostic so you can pick up toy languages and play around, a bit like the concept of “code katas”.

I was hoping for something similar to that.

[flint forge]

Oh for sure if you already have the ipad you should do that haha

[flint forge]

probably difficult to find something like this, most mathematics requires careful development and treatment, so you can't really do a mishmash like this

[hasty turret]

Similar in what aspect exactly?

[flint forge]

unless you assume your audience already knows everything

I would just download a ton of stuff to the ipad and then mess around once youre on the plane

see what interests you and what doesnt

[hasty turret]

If it's about being easy to pick up, just like read any (intro) cs book ever

[flint forge]

dont feel too tied to any particular book

[gusty smelt]

yeah thats probably a good idea

[undone jacinth]

I suppose naive set theory is “little” enough to fit my definition https://www.goodreads.com/book/show/558194

[gusty smelt]

I still vote for reading some like, Uchicago reu papers

choose a topic that sounds interesting

and dive in

[undone jacinth]

Oh what is that?

[gusty smelt]

REU are research expereince for ugs, I have found that the papers out of the uchicago are like, very good exposition on whatever topic at a low level

ofc this is just a easy source for them, you can find tons of good expository papers/survey papers from other sources too!

but maybe the uchicago REU one is more UG friendly

oh btw most of my flights are like, 3 hrs so its appropriate for me to read some survey papers oof

maybe thats not what you want if you are on like a long intl flight

[remote sparrow]

can you tell us what you've already done so we don't give redundant recommendations?

[undone jacinth]

I’ve covered the engineering version of many courses up to diff eq,linear algebra, Fourier,Laplace, wavelets etc,

but I’m self teaching the proof based versions one might cover in a mathematics degree to build what mathematicians call “mathematical maturity”.

Books I’m working on at the moment are:

Proofs a long form text book by jay cummings
https://www.goodreads.com/book/show/56895723

And
Basic mathematics by Serge Lang
https://www.goodreads.com/book/show/79781

[remote sparrow]

jay cummings has also written a book on real analysis, but it's also quite big (mainly since it's a low-cost paperback)

small books that you might find interesting are burton or dudley's books on elementary number theory

miklos bona has a book on combinatorics that's fairly small

hrbacek and jech or enderton are small books on set theory

Understanding Analysis by abbott is a small book

most books past calculus and ODEs are not 1400-page doorstops

gamelin's complex analysis book is generally regarded to have very minimal requirements

[undone jacinth]

Thanks for the recommendations!

[remote sparrow]

axler is a small book for a second course in linear algebra

judson and pinter are small books on abstract algebra

[undone jacinth]

Do you mean linear algebra done right by sheldon axler or another book?

[remote sparrow]

yes, LADR

[remote sparrow]

The Cauchy-Schwarz Master Class is a problem book dedicated to learning how to use inequalities and prove things about them

nice prep for analysis, but optional

beckenbach and bellman have co-written two books on inequalities, one introductory and one advanced

hoffman and kunze is another rigorous treatment of linear algebra

garcia and horn have co-written a linear algebra textbook that is strongly slanted to matrix theory

[ocean mulch]

Lang has a readable book? Impossible

Ironically I think most of the inequality tricks are found in Olympiad problems, if that's something you want to dive into

[fierce hedge]

Are there any proper Olympiad books which actually teach rather than just giving a hard asf problem

Olympiad problems feel like banging your head against a wall till you have some epiphany

[coral prawn]

Right, I've given it a look, pretty interesting so far

[ocean mulch]

There are plenty

I only remember Engel for Combinatorics, but there are a ton of them for each topic. You gotta ask someone who is doing or just did Olympiads

[ocean mulch]

Tbh, so is (math) research 😄 you bang your head long enough until either you die or the wall breaks.

[chrome yacht]

the person that recommended you that book must be so cool, i wonder who it is

[coral prawn]

totally not pegasus

[coral prawn]

[heady ember]

Imagine kmm sticking to one book/resource
||imagine harder||

[coral prawn]

Screw yo-

[cinder quiver]

Math is hard

But I'm harder

[coral prawn]

#chill

[dapper root]

They’re saying they go hard 💪

[lapis sundial]

Fr

[candid creek]

Does anyone have any good math books for practising inequalities?

I'm finding that several of the questions/proofs that I have trouble with in my classes very often involve proving some inequality

since I find that they are less direct, and sometimes rely on intuition to derive certain intermediate results to prove the final inequality

[crimson leaf]

#book-recommendations message

[thorn quiver]

there is also a book by hardy-littlewood-polya, but this is more advanced than the book mentioned just above

[coral prawn]

So I've heard of 2 ODE books:
Elementary differential equations with boundary problem values, and a first course in differential equations. Any recommendations on which to use?

[tender river]

nagle saff snider anyday baby

[inland elm]

im reading through weibel's homological algebra book and wanted a quick review on R-modules
anyone have any good books/resources that go through R-modules and the major results quickly?

almost like something to keep as a reference as i read

[remote sparrow]

this book has no exercises, though, right?

[remote sparrow]

can you give authors? ODE books tend to be titled similarly

[thorn quiver]

like most hardy textbooks, it does not

[coral prawn]

XD now that I had a look, yeah mb.

First one is by William F. Trench
2nd by Dennis G. Zill

[warped canopy]

hello

[remote sparrow]

i looked through trench a bit when i was having trouble understanding boyce and diprima

it helped clarify some things

bonus is it's free online

[coral prawn]

anything is free online if you tried hard enough wtf??? Based author

[remote sparrow]

sadly his hard copy is out-of-print

[coral prawn]

Oof...

That's unfortunate kinda curious tho how does this "out of print" stuff happen? Like, the publishers just choose not to reprint after a certain number?

[remote sparrow]

could be an unpopular book

sometimes authors choose not to renew contracts with publishers

[coral prawn]

Icic...

[covert spindle]

i recommend “How to touch grass

especially for gamers

[cobalt arch]

Any books that exhaust most of the properties of functions? Like for example that a function has a left inverse iff it is injective, etc. I know there are a lot of books for function theory but I specifically want something that exhausts most of the theory of functions and covers all of the basic and some of the advanced properties.

[fossil arch]

Well the issue is there’s lots of different types of functions

“The theory of functions” is pretty meaningless imo

Any modern real analysis textbook will cover the very basics of functions, then depending on what field of math you’re interested in you’ll learn about specific types of functions with very nice properties

“Function” as a term is just so general that there’s not much meaningful stuff you can say until you look at specific classes of functions

[gray gazelle]

What you are looking for might us Aluffi: Algebra Chapter 0. It covers the basic properties of functions as well as discusses monomorphisms, epimorphisms, and showing how they are equivalent datum to injection and surjection.

There are many different ways to look at functions, which you will encounter as you climb mathematics. You should just learn something else and you will eventually come to new ways at looking at functions.

One interesting route after exhausting undergraduate Algebra is #category-theory, which is essentially the theory of morphisms of objects. You might find this interesting, personally I find it dry, and boring, but to each their own.

[rigid barn]

What are some examples of books that are entirely dedicated to a single problem, i.e. pick a certain problem, develop a theory for it, and solve it completely (or as much as is possible)? Two examples I know are Cox's "Primes of the form x^2+ny^2" and Schoof's "Catalan's Conjecture". I'm really interested in these types of books. The subject matter is not that relevant, but algebraic stuff is preferred.

[gray gazelle]

Well what is more Algebraic than Fermat Last Theorem, which contains 300 years of Algebra by the best Algebraists of our species. Diamond, Darmon, and Taylor Fermat Last Theorem, Coates Yau Elliptic Curves, Modular Forms, and Fermat Last Theorem, and more are places that build a lot of theory to elucidate Wiles' proof

[rigid barn]

True, thanks. Anything else? Maybe something in analysis?

[gray gazelle]

Morgan/Tián, Ricci flow and the Poincaré conjecture

[hallow oriole]

not a problem per se but the cauchy swartz inequality book

(there's actually more than cauchy swartz but still)

[rigid barn]

Familiar with it, cool book.

[hallow oriole]

also def not a problem but there's a book called 'mathematical induction: a powerful and elegant method of proof' which is also vvvv good

it's a book on induction!

[gray gazelle]

An entire book on induction?

I guess it builds up to things at the (eg.) Putnam level?

[hallow oriole]

you want the pdf?

[gray gazelle]

Sure

[rigid barn]

same (if it's less than 25 mb)

[hallow oriole]

it is almost exactly 25 mb

26k kb

[gray gazelle]

It's by Andresscu so I expect it to be good, yeah

[hallow oriole]

oh it's a bit too big

i'll js dm the links

[gray gazelle]

Likely has to do with competition math

[slim bramble]

can i get one too please🙂

[hallow oriole]

fwiw i recommend buying the book if you like it! it's vv good

[rigid barn]

then it's probably the libgen version

[hallow oriole]

yup!

if you check the link i sent you it's a libgen mirror

[gray gazelle]

Thanks for the book rec

[hallow oriole]

ofc

[rigid barn]

If anyone wants a properly paginated and cropped version of this, lemme know, I modified the libgen version just now. No bookmarks tho, didn't feel like going through that.

[hallow oriole]

send me one?

seems nice to have

[rigid barn]

I wonder how one shares to libgen. Over the years I've cropped, paginated, and bookmarked so many books (that I'd gotten there) and I'd love to give back to them, considered all they've done for me.

[hallow oriole]

i sent u a link

[crimson leaf]

Not a book about one problem but about one thing is Stanley's book Catalan Numbers. Also sorta related but maybe not exactly is Fermat's Last Theorem: A genetic introduction to algebraic number theory. Also relevant is The Travelling Salesman Problem: A Computational Study.

[rigid barn]

Did you mean this (https://people.math.wisc.edu/~nboston/ddt.pdf) and this (https://books.google.de/books/about/Elliptic_Curves_Modular_Forms_Fermat_s_L.html?id=nxTvAAAAMAAJ&redir_esc=y )?

[fierce hedge]

I wanted to till I had a look at th book, it's way beyond my level at least for now

[gray gazelle]

It contians the proof of a millenium prize after all

[fierce hedge]

Yeah but I thought it might just provide the intuition of something which is correct and idk if that's the whole proof but it's actually math heavy.

[gray gazelle]

Yeah, it contains the full proof (in fact even more than the full proof) (cf. https://arxiv.org/abs/math/0607607)

[fierce hedge]

If this free pdf already exists, is the book even more expanded version of it?

[gray gazelle]

The book has 100 pages more content, so I assume so

though that might just be print size

i will check later

[fierce hedge]

Noice, onw to the second (late) coming of Peter Scholze

[gray gazelle]

ou you mean like how he backlearned for flt

i guess this is not as huge a project as flt

you need strong riemannina geometry and geometric analysis

then you can learn it ig

Fermat is so much theory , it would take atleast 3 years of nonstop grinding

[rigid barn]

the grind never stops, brotha

[hallow oriole]

learning enough math to understand flt proof might take three years but lets be real understanding enough math for that is at least five years

which actually sounds like a decent way to spend it

hm

[fierce hedge]

Ehh... I am not very interested in FLT atm

[finite gale]

I remember the lecture my algebra prof gave on "a 5 minute summary of proof of flt" that turned into 40 minutes which was pretty much "f is very nice so it doesn't exist"

[turbid mural]

book recommendations for commutative algebra

[remote sparrow]

atiyah and eisenbud were the first results i found on google

[turbid mural]

ok

[wispy bison]

Do you remember the title

[tawny copper]

what are books on elementary differential equations that are focused on problem solving?

[ocean mulch]

Yeah, it was essentially the proof, yes

If a^n + b^n = c^n, consider the elliptic curve y^3 = (x + a^n)(x + b^n) = x^2 + c^n x + (ab)^n

Then after a shit ton of math, ppl show that this curve cannot admit a corresponding modular form

[tawny copper]

modularity is crazy

[ocean mulch]

math is crazy

[tawny copper]

that is not the curve I think? no one writes elliptic curves like that

from the wikipedia article

[ocean mulch]

Oh yes, I forgot the exact form 😄

I just remembered it was something along those lines

[tawny copper]

idk but Im feeling very motivated to keep going in my NT journey 🐒

[fierce hedge]

I forgot who showed this, this wasn't done by wiles right

[tawny copper]

it was frey I think actually

wait no

ribet

[ocean mulch]

Some ppl still believe in conspiracy that FLT is false, and mathematicians are just hiding it from us under a ton of formality.

[ocean mulch]

Frey showed that it might be possible iirc. He didn't show the whole thing, but he pointed out how there could be a relation

Other followed suit since there were mainly technicalites. The epsilon conjecture was the final nail on the coffin

[fierce hedge]

I want to act surprised but flat earthers and anti vaxxers still exist

[tawny copper]

tbh most people (including me at the present tbh) dont really know why flt is so hard, like these cranks trying to solve fermat by elementary means dont even know how to solve much easier equations

[ocean mulch]

Ribet suffered with epsilon conjecture for months 😄 and then he found a way in a coffee meeting with a colleague 😄

The guy just said "Oh, you're almost there! Just add another singularity and you're done!". Well, that alone was worth a Master thesis, but the two guys were the best experts in the world at the time. He came back, did some computations, and verified intuition was correct

Or at least that's what I could recall. I read a book about the whole history of it 5 years ago

[ocean mulch]

Try n=7 and you'll see why it's so complicated 😄

[tawny copper]

ok n=7 case is related to the Klein quartic

[ocean mulch]

Ppl did it with infinite descent back in 1800s, but it was horribly complicated

[tawny copper]

there is this article of Noam Elkies on Kleins quartic that explains n=7, tho I have not read the proof

[sudden kindle]

What about Klein quarti

[sudden kindle]

Can u link it

[ocean mulch]

http://library.msri.org/books/Book35/files/elkies.pdf

This one maybe

[tawny copper]

there is an obvious isomorphism

[ocean mulch]

"obvious"

[coral prawn]

Andrew wiles in 1993, then corrected his proof in 1995 yee

[tawny copper]

no its completely elementary, Kleins quartic is just x^3y+y^3z+z^3x=0

[coral prawn]

Mfw other people actually care abt it without understanding it

[ocean mulch]

Nah, we were talking about the correspondence between Taniyama-Shimura and FLT

[tawny copper]

but its fun because its the simplest Hurwitz curve

[ocean mulch]

Frey pointed out the relation, Serre did most of the work, and Ribet hit the last nail with epsilon conjecture

[coral prawn]

Smash

[sudden kindle]

Thsts really cool

[tawny copper]

http://library.msri.org/books/Book35/contents.html this is from this collection of articles

[ocean mulch]

Well... we have vaccine, string theory, quantum mechanics, GR, ML, etc. It's not the first time.

[sudden kindle]

Thanks

[coral prawn]

Fair enough......

[tawny copper]

the article of Murray Macbeath on Hurwitz groups was very easy to read, and very useful to me. I have not read any other articles, but they all seem pretty nice

[ocean mulch]

Idk why ppl like FLT so much when it takes a PhD to even begin to understand it.

Catalan's conjecture was no less beautiful but far more accessible

[tawny copper]

it serves as a nice motivation

[coral prawn]

I honestly just looked for the proof of wiki "surely it's just some highschool algebraic fucking around?"

Oh man little did I know....

[ocean mulch]

The proof of FLT?

[coral prawn]

Yeah

[ocean mulch]

I think I can still recall the general outline

[sudden kindle]

Idk about FT

FLT

I care about Riemanm surfaces with many automorphisms

[tawny copper]

shiit I like that too

[sudden kindle]

Like Klein quartic and Fricke-Macbeath curve

[tawny copper]

which is what the articles above are about mainly

[coral prawn]

Me in an exam when having to prove a³+b³ = c³ has no int sols:

"This is a special case of FLT. As such, the proof is trivial."

[ocean mulch]

the case n=3 is a very nice elementary NT problem

I think I saw it once in some random math olympiads

[tawny copper]

Problem: Show that 2^(1/n) is irrational for n>=3.
Me, an expert: Towards a contradiction, suppose that 2^(1/n)=a/b with a,b integers. Then b^n+b^n=a^n in integers for n>=3 and ab!=0, contradicting Fermat's Last Theorem. QED.

[tawny copper]

highly doubt it

[ocean mulch]

With a ton of smaller questions to give hints, of course

[tawny copper]

what kind of math olympiad exam gives hints

[ocean mulch]

not hints, but a bunch of smaller questions leading to the final proof

you can kinda guess how it should go from the questions alone

[coral prawn]

Ye happens

time to memorise and vomit FLT proof so that I can use it no matter what n they use

[ocean mulch]

every once in a while I see some random elementary proof of FLT

Almost always in badly formatted Microsoft Docs

[tawny copper]

its hilarious when they dont use latex

and like they introduce functions and name them after themselves

[ocean mulch]

If anyone wants to be taken seriously, at least learn latex, or handwrite decently

MS Docs is insulting to the the readers

[coral prawn]

💀💀

[coral prawn]

NAH WHAT

THAT ACTUALLY HAPPENS?

[tawny copper]

yeah

like I saw this from a dude crying on Terence Tao blog

[coral prawn]

Oh?

[tawny copper]

(on the comments I mean)

he proved the Riemann hypothesis of course

[coral prawn]

<- the guy

[ocean mulch]

Of course, what else can it be

[tawny copper]

and like the references only included Riemann's paper and maybe some standard analytic NT text like Apostol xDD

[ocean mulch]

It's always either FLT, RH, Collatz, P vs NP.

Maybe some Bael, Catalan, if you dig deep enough.

[coral prawn]

Damn golbach survived the slander?

[ocean mulch]

Ppl usually "prove" Euler's version

Goldbach got almost forgotten, unfortunately

[coral prawn]

[ocean mulch]

There's also Erdos' conjecture on 1/n

That one was quite popular for a while

[tawny copper]

you mean the AP one?

[ocean mulch]

No, the one about reciprocals

[tawny copper]

like if sum{n in A} 1/n diverges then A contains arbitrarily long APs

[ocean mulch]

https://en.wikipedia.org/wiki/Erdős–Straus_conjecture

[coral prawn]

"Oh that, surely I could prove it with partial fractions no? Wait wdym I can't?"

[tawny copper]

this and bunyakovsky conjecture are my two favourite conjectures UwU

[coral prawn]

OwO

[ocean mulch]

I hate that I know these problems as "open problems".

It feels easier to solve something first then know it's open

Knowing something is open already limits mindset

[tawny copper]

depends on the person I think

but it also helps to know what people tried before you, so you dont lose time in naive things

[ocean mulch]

It might or might not help. I like to use this kind of resource very carefully.

A lot of times it's just a matter of viewpoints. Maybe someone with a different viewpoint can continue the attack. Something that was tried before doesn't mean it's not a good path.

[tawny copper]

yeah right

[hallow oriole]

regrettably fermat's last theorem is too weak to prove that the square root of two is irrational :/

[rigid barn]

Is it just me or are djvus somehow comfier to read than pdfs, even when the scan quality is a little poorer? It's like the djvus display text "softer" somehow.

[finite gale]

I prefer the pdfs for the bookmarks though

[tawny copper]

what reader do you use?

[rigid barn]

good ol' windjview, i'm on Windows

[rigid barn]

many djvus have bookmarks, although i haven't yet learned how to add ones yourself

[tawny copper]

I just use sumatra pdf reader (also on windows), never noticed a difference between djvu and pdf

but I prefer pdf generally, because the reader I use on by tablet only supports pdf

[rigid barn]

is it good? i've been using acrobat and windjview since forever, combining the two would make life easier.

[hallow oriole]

big fan of sumatra

[tawny copper]

I think its really good, yes

the main advantage its that its fast

[hallow oriole]

lightweight and displatys pdf quick

plus the customization is pretty

[tawny copper]

and you can add night mode easily if you need to

[hallow oriole]

look at it!

sumatra is great

[tawny copper]

mf change the name of the pdf when you download straight from libgen

[hallow oriole]

no

im a monster

[tawny copper]

shit I skeemed some parts of the almost impossible series text

[tender river]

lmao

[tawny copper]

I did one or two problems, Ill probably be coming back from time to time

[tender river]

finding books in your giant collection becomes hell without proper naming trust me

[ocean mulch]

Me trying to find my way through all the papers I downloaded when I had to actually write the thesis and put references

[hallow oriole]

nahhhhh

trust

it'll be fine

[rigid barn]

does sumatra have editing capabilities for either format? i use foxit for pdf, don't have an option for djvus

[hallow oriole]

i have them separated into "math" and "not math"

[tender river]

narrator: it wasn't fine

[tawny copper]

no

sumatra is just reader, thats why is fast, because its just reader

if I want to add bookmarks to a pdf I use jpdfbookmarks. If I want to make minor edits, like delete a page or something, Ill go to ilovepdf (online site)

[rigid barn]

seems like a hassle, foxit is easier imo

[tawny copper]

Id like to automate the process of adding bookmarks to a pdf actually

[rigid barn]

how charming

[tender river]

lol okular >>

wait windows?

[tawny copper]

I think Ill change to linux eventually

[tender river]

oh okular works in windows too

[rigid barn]

i did for a while, it was much better in some ways, but i eventually switched back for gaming. now that i'm tired of gaming thinking of switching again

[remote sparrow]

apparently the term is descriptive geometry, not projective geometry. sorry. but coxeter has a book on projective geometry.

[sudden kindle]

My system for storing papers is to

...

I dont have a system

[tender river]

i don't store papers

[gusty smelt]

zotero.

[sudden kindle]

You recomend that?

I keep track of papers I read/encounter fir future reference in a personal discord server like this

[tender river]

zotero way better than doing this

but again i only have like 10 books in my zotero

[gusty smelt]

yes zotero is p good imo

its one press to get it on to it

and if you have the ipad app it also stores the pdf

so you can like, transition between computer and ipad v easily

which is v convenient for me

[sudden kindle]

Ohh

That is very convenient

[finite gale]

Zotero

[gusty smelt]

(there is limited storage w/o pay tho for zotero so be wary of that oof)

[tender river]

and if you have the ipad app it also stores the pdf
and if you have the ipad app it also stores the
and if you have the ipad app it also stores
and if you have the ipad app it also
and if you have the ipad app it
and if you have the ipad app
and if you have the ipad

[gusty smelt]

bro

my dad got an ipad 10 for like 260$ somehow, some wild discount

im jelly lol

[warped wave]

Where do people stand on Rotman for Abstract Algebra for beginners?

I know absolutely nothing of the topic

[fierce hedge]

why not dual boot?

[stray veldt]

gaming on linux is mostly fine now too

[fierce hedge]

I know indie games work but what about AAA titles

Tbh, with the current state of unoptimised gaming, it'd a flex to get something up and running in linux

[stray veldt]

https://www.protondb.com/ you can always check
the last AAA game i remember is hogwarts legacy and that one runs fine for example

[bold moss]

Is their any book which goes from basic algebra till college calculus and have rigorous problems ?

[tiny spire]

MIT lectures by Gilbert strang along with his own book of algebra is all you need.
And they are also available for free on Youtube

[bold moss]

I think they directly start from college algebra

[tiny spire]

No the start is very basic. Not that much advance

[gray gazelle]

I wish I had this when I started algebra. If you have classes (not selfstudying) I would say this is the best book to have. It will also certainly be useful for more than just one course on algebra.

[fallow cypress]

I've been reading montanari and mezard's book on informaiton, physics, and computation, and the first chapter is on information theory

[foggy relic]

someone probably already said this but https://people.math.harvard.edu/~ctm/home/text/others/shannon/entropy/entropy.pdf

[fierce hedge]

What would be a better recommendation for abstract algebra, Rotman or knapp for someone not new to it (I have done a bit of group theory from Judson). Rotman seems more comphresive (talking about the 3rd edition) while knapp has linear algebra which seems like a bonus?
I am not used to the rings first way of learning while knapp has exercises towards the end only. Delerik recommended rotman while lems has shilled knapp.
Anyone who has tried them and can comment more is welcome to do so.

(sorry for the ghost ping delerik)

[finite crane]

That's my recommendation. But I will also be the first to point out that there is a great overlap between the tail end of "basic algebra" and specialized algebra topics. Like when you learn commutative algebra you will be relearning stuff at the end of Rotman. Perhaps it's just better to jump into the more specialized topics which usually have more focused exposition

[fierce hedge]

by basic algebra you mean the book "basic algebra" or you mean "basic" algebra?

[fierce hedge]

I am a bit confused with what tail end of "basic algebra" means? Does it mean fields and Galois theory?

[finite crane]

to define it in a cheap way it's whatever you will see again in more specialized topics

like for instance Lebesgue integrals are often dropped into the tail end of basic analysis (like in Tao vol 2) but it will be covered again properly in real analysis

which is also why I'm not too overly concerned with learning any topic 100%
Because they will get treated again somewhere else

also a good reason why I prefer lecture notes to reference books for more advanced topics. Because they will pick the most useful topics rather than the esoteric. Learn the most useful first and dive into references later.

[fierce hedge]

I mean quite frequently books were initially in the form of notes that were taught which later expanded to books right? Is there a big difference between the two then?

Also in that case do you have any abstract algebra notes? Most I found were either too brief or too specific

[finite crane]

well I specified advanced topics. Basic algebra or analysis books can easily be read in full or nearly full, and often PhD courses tend to make you do so.

Rotman 3rd edition vol 2 does go into a bunch of things that obviously can be safely skipped, such as K-theory

[fierce hedge]

K-theory, interesting. Thanks for your input delerik!

[warped wave]

Is Rotman not recommended for self studying?

[gray gazelle]

I'm not sure what the usual recommendations are, but I would be worried that it has a bit too much info ... if you know exactly what you want to study than I suppose its good, but you can quickly start doing something more advanced before even studying the standard basic material, if you're just following the structure of the book

[warped wave]

ah i see, but it serves well as a first exposure to Abstract Algebra, yes?

in terms of explanations and clarity

[gray gazelle]

I would say so yes, it's very thorough, has good explanations, plenty of exercises, and it will definitely make you really really good at algebra

[warped wave]

gotcha

thank you!

[remote sparrow]

rotman has an undergraduate introduction and a graduate text

[gusty verge]

I am currently self studying Kevin Murphy's Probabilistic Machine Learning, right now I am reading the chapter about Probability of Multivariate Models, I feel stuck on a topic called Linear Gaussian Model/Systems. I am looking for a book(which covers Linear Gaussian Models/System and Multivariate Models) that I can use for reference.

[gray gazelle]

Hey Guys,
I'm a student who's gonna start Btech in CS. Any math book recommendations?

[scarlet steeple]

you're actually evil

[hallow oriole]

qill check out tyty

[hallow oriole]

❤️ tyy

[foggy relic]

For people who've bought from springer before via pro-forma do they normally give you shipping information like UPS numbers and stuff?

[rigid barn]

Addison-Wesley had the best looking books (typeface, layout, everything), change my mind.

[lime sapphire]

all books should be typed up in computer modern, change my mind.

[heady ember]

ah yes iirc nami’s PhD was on this

[sage python]

This Rotman book is on drugs lmfao

[remote sparrow]

which one?

also 2nd ed. graduate text is very different from 3rd ed.

[sage python]

3rd edition of "Advanced Modern Algebra"

Organization is all over the place lol

[crimson leaf]

I think the second ed one makes more sense

Also 3rd edition being two books is wild

[remote sparrow]

2nd ed. is super expensive on amazon now sadly

[coral prawn]

"I prefer the 3rd Ed because the cover page looks modern" (don't beat me up pls)

[ivory jasper]

does anyone know where i can find free math textbooks online? specifically looking for Calculus: Early Transcendentals Single Variable (4th edition or newer) Jon Rogawski

[coral prawn]

could I dm you? We aren't allowed to openly discuss what I'm gonna share

[fierce hedge]

The secret ingredient is crime

[shadow hedge]

Do I need to brush up my pre calculus/algebra before starting the book of proof by Hammack?

[orchid mortar]

Yup, true moral crime committed by the publishers to deny proliferation of knowledge

[hollow shore]

I think you can jump right in

if you find yourself not being able to recall a concept you can look it up at the same time

[gray gazelle]

GUYS

waht do you think about grags diary

[tawny copper]

what are books on elementary differential equations that are focused on problem solving?

[karmic thorn]

Boyce-DiPrima might fit the bill

[fierce hedge]

why can't I sully react the above message above Chaigenvalue's?

[orchid mortar]

Let's not troll good faith askers

[sturdy shore]

...and it is not focused on problem solving at all, and is not "elementary" differential equations

are you going to deny that was a troll answer

[worthy venture]

Any recommendations for an actuarial sciences book

I want student to help me. I like his personality

[remote sparrow]

Tenenbaum and Pollard is also another good choice. It lacks treatment of boundary value problems, though, unlike Boyce and DiPrima. If modeling, qualitative analyses, and graphical analyses also count as problem-solving, Blanchard, Devaney, and Hall is good.

[winged meadow]

Is the HoTT book worth it ?

((Homotopy Type Theory)

[cunning forge]

Speaking of which, how does Olver’s book compare with Arnold’s Mathematical Methods of Classical Mechanics? They seem to cover pretty similar material (and have similar goals, that is, study dynamical systems via diff geo).

[solemn rover]

i think that is probably relative to your expectations and what you're trying to get out of it. It's been hyped up a little bit beyond what it really is. But it's an interesting area of mathematics. The book is more expository than technical and they don't force you to deal with technicalities such as a formal model of an infinity category.

I don't recommend it as a first introduction to type theory or homotopy theory

[foggy relic]

bump

[fossil arch]

Galois theory books go

I like authors who exposit a lot and write more thorough and explanatory proofs

[karmic thorn]

Message so based even Discord stops you from sullying it

Why the objection to Boyce-Diprima though? I think it's the Thomas' Calculus equivalent of differential equations

[remote sparrow]

he's talking about Student's message

[karmic thorn]

Oh

[fierce hedge]

Yeah the one with 20 sullies

My guess is that this person blocked me for some reason

[coral prawn]

Same

[remote sparrow]

i just saw the sully count on Student's message go to 21

[hallow oriole]

that was me

[remote sparrow]

then go back down to 20

[hallow oriole]

i just wanted to see if i could or not

[coral prawn]

LOL

[hallow oriole]

im not qualified to weigh in so im not gonna sully lmao

[remote sparrow]

you don't have to know anything

just basic research skills

[coral prawn]

aw geez person was literally asking for elementary ODEs and then this guy recommends lie algebras and PDEs?

[remote sparrow]

evans is entirely devoted to PDE, but the requester wanted elementary (ordinary) DEs

[coral prawn]

[hallow oriole]

i think its adorbs yall thought i read it 😭

if i see

clerk

disagree w someone

well ive never seen clerk be wrong

so clearly no further research is needed

[remote sparrow]

that leads me to wonder, what's the most sullied message on this server ever? or what's the message with the most reactions?

the most recent pin in this channel seems pretty competitive

[coral prawn]

Yeah if only discord has a search feature for reacts

[fierce hedge]

I haven't seen something more reacted at least in the pins

[crimson leaf]

#book-recommendations message

Maybe this one

A great moment for sure

[remote sparrow]

yeah, i mentioned that one

"most recent pin in this channel"

[crimson leaf]

I forgot it was pinned lol

Threw me off cause the person deleted their account