book-recommendations

[remote sparrow]

yeah lol

[upper orchid]

Next semester I'll be having discrete mathematics which book would you recommend? My goal in future is to be quant.

Also some books related to quant that I can read

[sage python]

Hard to say if there's a book that's particularly zoomed in at future quants, other than you'll probably want a good amount of probability

[spark shale]

Thomas calculus vs James stewert calculus
Which one has better explanations and exercises?

[gray gazelle]

Idk i think for discrete maths especially I'm not a fan of books... it's a subject that really differs from course to course, I think the best possible thing would be notes from class... as I remember our professor suggested a different book for every topic we did, but i never really looked at any of them

[upper orchid]

I understand I didn't knew this thanks 🙏

[coral prawn]

Are you open to other suggestions? What do you intend to learn calculus for? Do u intend to study analysis?

[gray gazelle]

I used Stewart for calc 1 and 2. The problem sets are fantastic, especially in the section "integration techniques". But don't go looking for anything formal, both books are very basic introductions to calculus

That being said, if you don't care too much about the "why" of things, they're fine texts

[coral prawn]

#bots

[coral prawn]

.

._.

do it in bots

and remove the quotes

[ocean mulch]

Galois' original memoir

After all, he wrote it when he was 18. How hard can it possibly be?

[gray gazelle]

who?

[coral prawn]

Oh dw it was someone earlier

[gray gazelle]

oh ok

Thought you were talking about the quotes I used

Not sure if it's proper use so

[spark shale]

Yes I plan on studying real analysis, need to study calc 3 and multi var calc

[coral prawn]

Then I'd recommend Spivak instead. He does both calculus and a bit of intro to analysis

[spark shale]

Well I think they don't cover multi var calc 😔

[spark shale]

Ahh thanks a lot

[coral prawn]

and as for calc 3/MVC, I've heard people vouch for Shifrin, which teaches basic Differential forms, MVC + LA in his book. I never read it though, perhaps someone who did could give more insight

[ocean mulch]

There's Calculus on Manifolds

although it goes pretty deep, more than you'd need for multi var calc

[kind rover]

Does anyone have book recommendations on precalc that also focuses on proofs and a lil bit of vectors?

[coral prawn]

What subjects do it cover? Heard that it's 160pages lmao

[ocean mulch]

Differential, Jacobian, Hermitian, bla bla (I think). Then it goes to differential forms

and ends with divergent theorem, Green's theorem, Stokes' theorem, etc

[coral prawn]

Damn

[ocean mulch]

That one, or Munkres' Analysis on Manifolds (though I doubt, that one is shorter)

I grinded both during Christmas break of my sophomore

Understood shit

And still understood shit till today

[coral prawn]

Pity

[spark shale]

Ty

By spivak right

[safe barn]

Yes

[scarlet sandal]

Hello, I want to find a book over tesselations, anyone know one good book to start ?

[gray gazelle]

has anyone worked through concrete mathematics? can i skip chapter 1 of the book, cause its so tedious to work through every page in that chapter.

[narrow relic]

For multivariable calculus there's a nice book called Functions of Several Real Variables by Moskowitz and Paliogiannis (review: https://www.maa.org/press/maa-reviews/functions-of-several-real-variables).

[oblique river]

Anyone have a book that’s good for aime prep?

[hallow oriole]

i have heard the art of problem solving books are good for this

[hallow oriole]

skip whatever you want, and if you find something you don't know just go back and figure it out

[wintry quartz]

guys thoughts on tao's analysis books?

Are they a softer intro than rudin?

[finite gale]

yes

[wintry quartz]

are they a good intro tho?

[finite gale]

i didn't use them too too much, but i think they're decent yeah

[smoky zephyr]

someone here with a phd always recommends that exact book so i would say yes

[wintry quartz]

ight

ok thank you guys

[fierce hedge]

The first few chapters are a bit slow but rest are good

[wintry quartz]

I was mainly reading it for the Analysis II

I finished spivak recently

and I kinda wanted to learn about lebesgue integration

[fierce hedge]

Why not pick a grad analysis book then?

[wintry quartz]

idk seems very intimidating

and I dont know if I'm ready for that

have any recommandations?

[fierce hedge]

easiest to read is folland I think

[finite gale]

there's a pinned post in this channel for measure theory books also

[wintry quartz]

yeah no, I'm defintiely not ready for folland

[loud cradle]

do you want an approach that uses concrete lebesgue measure or do you want to go straight to an abstract treatment?

[sage python]

The correct answer is the latter

[loud cradle]

i agree, but both types exist

[wintry quartz]

I would agree with the latter

[sage python]

The sad thing is, Royden immediately follows up Spivak

[loud cradle]

i think cohn's "measure theory" (2nd edition) is the cleanest version of the latter

[sage python]

But it wastes time doing measure theory twice

[wintry quartz]

wdym "follows up Spivak"?

[fierce hedge]

I think carothers also does measure theory but I haven't read it

[sage python]

As in, Royden does the metric topology that Rudin does, along with measure theory and functional analysis

While eg Folland wants you to know the metric spaces stuff before you open the book

[loud cradle]

iirc, carothers is more focused on function spaces and less (if at all) on measure and integration

[wintry quartz]

ngl this kinda sounds like the right thing for me atm

So then whats the difference between rudin and royden?

[sage python]

Rudin kinda duplicates some Spivak material

[wintry quartz]

(this is baby rudin we are talking about right?)

[sage python]

Yeah

Like if you read Rudin... Maybe chapter 1 is good because Spivak does that stuff in a very scattered way. Chapter 2 is new, chapter 3 has some new stuff such as convergence in metric spaces but also series tests

[loud cradle]

rudin also gonna waste your time with riemann-stieltjes integration, which is pointless if your goal is lebesgue integration

[sage python]

Chapter 4 will be new with some ideas repeated

Chapter 5 will be known, chapter 6 will be "known" but it extends to Stieltjes which has limited use

Chapter 7, the def of uniform convergence and maybe how it plays with integration will be known, most will be new

[wintry quartz]

I mean, its the summer, I just wanna learn new things, I recently saw lebesgue integrals come up in one of my projects, so I thought that I might as well learn it

[sage python]

Chapter 8 is kinda gimmicky, chapter 9 is questionable (tries to half ass the bare minimum amount of linear algebra needed to do stuff)

Chapter 10 is proof that Walter Rudin does not understand differential forms

[wintry quartz]

this sounds like the most rudin thing ever lol

[wintry quartz]

LMAO

[coral prawn]

LMFAOOOOOOOO

I CAN'T

[sage python]

And chapter 11 is just "Let's do some measure theory at the end so we can say we did measure theory"

[loud cradle]

it will serve you well, it's the only integral you want to use for anything serious

[coral prawn]

LADR on determinants be like (ok well at least they didn't outright claim that they "did determinants"

[wintry quartz]

rudin keeps using the term "k-cell" I dont really know what that is lmao

[loud cradle]

haha, at least rudin doesn't define the lebesgue integral in such a jacked up way as axler does determinants

[wintry quartz]

is this a standard name for something?

[sage python]

k-dim box in R^k

[loud cradle]

isn't that just a k-dimensional rectangle?

[wintry quartz]

why can't he just say that then

[loud cradle]

normal authors woud probably just say "rectangle"

[sage python]

Because he's not like other girls

[coral prawn]

The words Rudin and normal do not click.

[wintry quartz]

I thought they were differential forms and I got so fucking confused

he uses them in the whole book

and defines them for the first time in chapter 10

LMAO

[coral prawn]

NAHHHHHHHHH

[sage python]

Wait huh

[coral prawn]

💀💀

[sage python]

I thought he defines them in chapter 2

[fierce hedge]

yes, he uses k-cell to prove heine borel theorem

[wintry quartz]

thats where I first say the word

[loud cradle]

2.17

[fierce hedge]

it's defined few pages back

[wintry quartz]

I seem to have completely missed that

its also def 10.1

my computer is tweaking so I can't paste the image

[fierce hedge]

you gotta go really slow with Rudin

especially chapter 2 which is the most dense

[coral prawn]

https://tenor.com/view/malcolm-tucker-the-thick-of-it-dense-hes-so-dense-lights-bends-around-him-gif-17375190

[wintry quartz]

tbh I was studying for an exam and didn't have much time, so I was just going through proofs and theorems

[fierce hedge]

kmm stop with the reactions and gif

[loud cradle]

10.1 appears to be a (rather disgusting) definition of a multivariable integral

[sage python]

He's only defining iterated integrals since in the next chapter he'll do measure theory

[wintry quartz]

whats the best resource for calc on manifolds, like spivak level stuff that isn't spivak, folland or munkres? My background is that I know 0 multivariable calc

[sage python]

Which begs the question

Why not just like

Do measure theory first

[loud cradle]

swap those two chapters?

yea

[wintry quartz]

yeah I saw, its one of the most vile things I have seen ever

[sage python]

But uh here's the real problem with chapter 10

[fierce hedge]

Browder does it much more nicely, even probably Schroder

[sage python]

A differential form is defined as a linear functional on surfaces with a global parametrization by that formula

Like I'm sorry but what

If I'm giving an oral exam and a student says that I will find a way to expel them from college

[loud cradle]

in a better world, baby rudin ends after chapter 8

[wintry quartz]

honestly, understandable

[sturdy shore]

jesus christ what is that

[smoky zephyr]

i wonder if that looks worse when you actually understand what it’s saying

[sage python]

It is bad

[sturdy shore]

this is an insult to cartan personally

[wintry quartz]

better than munkres tho

[sage python]

I heard Munkres Analysis on Manifolds is pretty atrocious but I cannot imagine it being worse than this

Like my brother in Thurston what are you saying

[wintry quartz]

ok, its not worse, but still

[wintry quartz]

this is why I asked this

[sage python]

How's your linear algebra?

[loud cradle]

ugh chapter 11 is horrible too, look at how he defines lebesgue measurable sets

[wintry quartz]

also the reason I ask this is cuz my uni jumps from "Analysis I" to "Analysis II" where we do " Differential forms. Manifolds in R^n; integration on manifolds; Stokes' theorem for differential forms and classical versions. "

[wintry quartz]

its not bad

[sage python]

So if you wanna do both measure theory and multivariable calculus at the same time

Which you should

Then try "Functions of Several Variables" by Fleming

It uses measure theory to do calculus on R^n, so you get that proof of Fubini and of change of variables

[sturdy shore]

gerard walschap's multivariable calc book might be what you want

[sage python]

Rather than wasting time with Riemann integration on R^n

[wintry quartz]

ok lemme see if my uni gives it on springer

[finite gale]

i looked back through my notes on differential forms and found that i wrote in the margins that munkres never defined differential k-forms(?)

that doesn't seem right though

[sage python]

See here's what honors analysis needs to do, idk why nobody has cracked the formula yet for that class

[wintry quartz]

page 249 has the words "elementary k-forms"

[finite gale]

well first thing they need to do is give that class to someone who can actually teach the class

[wintry quartz]

the forms $\tilde{\psi}_{I}$ are called the elementary $k$-forms on $\mathbb{R}^{n}$

[hasty eagle]

ForJoke

[sage python]

First quarter you do metric topology, normed spaces/a bit of functional analysis (consequences of Baire category theorem, Hilbert spaces, but no weak topology or spectral theory yet), differentiation

Second quarter should be measure theory

[remote sparrow]

axler has a measure theory textbook

[hasty turret]

Are differential forms multilinear forms

[sage python]

And third quarter you do calc on manifolds using measure theory (this can get interesting, almost GMTish) for a while, then maybe weak topology/spectral theorem/ODEs

[finite gale]

i don't think we did any spectral theory in first quarter, but we also just skipped BCT and arzela–ascoli

[hallow oriole]

gmt?

"general manifold theoy"

[sage python]

Yeah that's because you guys did linear algebra, my friend who TAd the class last year said that now linear algebra class is a prereq for 208

[hallow oriole]

"gauss' melliflous tones"

what does gmt mean

[sage python]

Geometric measure theory

[hallow oriole]

ohhhh

[finite gale]

it was also the first quarter where they cut a week off

[sage python]

Oh right

Fuckin stupid

[finite gale]

but linalg being a requirement for honors analysis should have always just been a thing

[sage python]

I mean it's tricky because

You either expect people to double up on math first year, or you say at least make it concurrent with 207 as they do now (which means on paper you can't rely super hard on it until 208, kinda suboptimal), or do it in 207 and squeeze for time

My year they just had extra psets each week on LA which was... Not great the way Soug did it

[finite gale]

ok yeah i meant at least concurrent

but doubling math first year isn't too too bad either though

[sage python]

That's fine but I don't think it's fair to expect it

[finite gale]

since otherwise you're just doing whatever garbage classes anyway

also how would you rank the honors analysis quarters for enjoyment your year?

[sage python]

209 > 208 > 207

[finite gale]

oh

i think mine was 209 > 207 >>> 208

[sage python]

Our years were different

Also let's migrate to a different channel it's no longer about books

[worn steeple]

Hello, do u have any recommendation for me , i would like a book about algorithm and another about like the history of the evolution of maths ? Thx in advance

[gritty gale]

for that second one, what sort of level do you want?

bc the universe in zero words is decent if you want pop history sort of level

[worn steeple]

A mid-level

[worn steeple]

Oh i will check thx i appreciate

Thx i love the book i will buy it !!! I appreciate ! @gritty gale

[ocean mulch]

If you're Peter Scholze, yes

Uh...

If you study at Bonn or Princeton, yes

But if you're so committed to being tortured, there are always other paths toward suffering

Wait, wdym you wanna go to Bonn, lol. Aren't you grad student?

Lmao, don't pick Lang

It's infamous, not famous

[chrome yacht]

in any event you would want a good combination of computational problems coupled with several challenging proof based ones, i don't think lang even has that does it?

probably not the ideal first pick

[ocean mulch]

It wil be helpful when you prepare to do a PhD

Lang only has super preplexing proof-based problems

Bible? Pff

It's the Red Book

2nd edition has red cover

I think it's the most popular one in libraries

It's really an overkill. I know some students who still don't understand a lot of things in that book.

[cerulean cypress]

i've heard that lang's algebra book is a masterpiece

that is intended for people who already know algebra

i wonder if there are any people who have done every single problem from taht book

i doubt whether even serge lang himself had solved all the problems there

[vital bane]

hm

[foggy relic]

it dosent assume any (abstract) algbera

[balmy canopy]

Hello guys! I'm new here. I want to learn how to solve math but I don't know how to start😭 , can you recommended me, What book should I start to learn?

[ocean mulch]

Polya's How to solve it

[analog lava]

paul zeits

worked better form e 😄

[fierce hedge]

I was thinking of starting an abstract algebra study group using knapp. Note that knapp isn't completely beginner level. He does linear algebra first, then group theory, then some multi-linear algebra and so on. Kinda like Artin but slightly more advanced. DM me if anyone is interested. Also, mods can I use modmail for this?

[hollow shore]

there is a knapp reading group already which started not so long ago

in the reading group server

[fierce hedge]

Wait, what!? Point to it

[fierce hedge]

Ummm.... What's that?

[hollow shore]

a server where math peeps advertise reading groups

I don't have access for an invite

wait

dmed ya

[dapper root]

Sometimes you just can’t fix stupid

[smoky zephyr]

can you dm it to me?

[fierce hedge]

That server is a bit dead though. Maybe we can have a different server where people actually participate.

[royal smelt]

Can someone recommend some good course/books for stochastic calculus, if preparing for quant firms

[gray gazelle]

what are some good books on fractal geometry?

[ocean mulch]

Maybe the one by mandelbrot?

I heard good things about it, but I'm no expert

[crimson leaf]

Edgar has a book that a former professor at my school liked called "Measure, Topology, and Fractal Geometry"

[grave thorn]

do you know measure theory?

[graceful lynx]

hey guys - is casealla berger really the holy bible of inferential statistics?

personally, i use amazon reviews to get a feel for the book and peoples experiences with it. Then i use laplaces rule to determine if my experience will be a good one. There is a great video from 3 blue 1 brown explaining it. but pretty much, i let the amazon search engine / recommendations do the heavy lifting for me and then i will ask my peers or come on here. im not very active but i will be now that im in exam mode

[ocean mulch]

Search the topic, and find some recommendations. Then find the pdf, and read the first chapter to see if you like it

If the level is alright, the style fits you, the content, etc.

Ppl can recommend stuff, but each has their own preference. It boils down to trial and error actually, to find your own taste. After a while, you'll know which book suits you best

[leaden cliff]

Hii, can anyone recommend textbook to learn adomian decomposition and Homotopy perturbation method of solving ordinary differential equation?

[oak pecan]

depends on what you mean by "quant firms" - decide on the target firms, find their past interview questions and if they include stoch calc (which, big if, unless you're looking sell side), pick up an interview book that includes those problems.; that's the approach i'd take. if you insist wanting to learn kind of relevant stoch calc in a textbook form, pick up Shreve, or if you care less about proofs and want a quick intro to the concepts, Baxter&Rennie.

[abstract nimbus]

A good formal explanation about infinitesimals the "d" operator ( e.g. why df(x)=f(x+dx)-f(x) ) that does not involve hyperreals because that is the only formal I get. If dx is not a real number which it obviously isn't (cuz (dx)^2=0) how can we justify plugging into a r->r function etc... Much appricied (doesn't have to be a book any reading material)

[fossil arch]

You’ll need to learn differential geometry to learn about the exterior derivative (the d operator)

[graceful lynx]

say that 10 times fast. jk

[graceful lynx]

frequently asked questions in quant finance by paul wilmott is a good one. im currently doing my masters in quant methods for finance. My only main class with stochastic calc was in asset pricing.

[oak pecan]

as i remember it, that's not very structured and jumps from one topic to another, but i guess if you like the style

[graceful lynx]

my prof said not to try and master it because your time is better spent elsewhere in terms of quant finance. just my two cents here man take it as you want

Paul Wilmott also has a triology on mathematical finance if i remember correctly.

idk your background but my course is designed as followed:
mathematics
inferential stats
coding - mainly in matlab but this was a foundation class
derivatives
financial market models
time series
financial econometrics
investment banking
big data
advanced risk in portfolio managment
credit risk
empirical banking
asset pricing
securities regulations (EU)

just offering the layout of what ive been on the last year and a half. im still trying to get a handle on this myself. sorry, i just realized i didnt even answer your question about stochastic calc. i will shut up now

[oak pecan]

also it wasn't me asking the question, i answered the question and you pinged me.

[graceful lynx]

its the vodka. its 1:30am in Rome. my bad man

@royal smelt check my previous messages. I pinged the wrong person

[west arch]

Can someone recommend a good beginner book to learn maths? I'm currently in 9th grade and want to learn more but I honestly don't know where to start.

[crude wagon]

Mathematics: A Very Short Introduction by Timothy Gowers is nice

You can also checkout cambridge math reading list for other books

[fast gull]

yeah this is good advice

[meager socket]

Does anyone have a recommendation for a book after college algebra that isn’t trig or calc? I don’t know if there is anymore advanced algebra that doesn’t require calc

[sage python]

You could learn a bit of discrete math?

[meager socket]

Does most algebra from this point onward have some other pre req?

[wintry quartz]

Depends on what you mean by “algebra”

[sage python]

Yeah, there's a subject math majors take called algebra

[wintry quartz]

Do you mean abstract algebra?

[sage python]

But it's kinda another story entirely more than a continuation of what you've seen

[meager socket]

I’m just getting bored with college algebra but don’t want to start on calc quite yet so I want to explore some other subjects

[tender river]

#book-recommendations message for discrete wonder if this is any good

[wintry quartz]

how comfortable are you with proof writing?

[meager socket]

My school just doesn’t teach proof writing in my class so I would need to learn it some more

[wintry quartz]

so you might wanna pick up a book on that?

[meager socket]

Like a book on basic logic proofs and sets to prepare me for more advanced subjects?

[hallow oriole]

i doubt

i would stick with the well known discrete math books

[wintry quartz]

yeah somehing like that

[hallow oriole]

Discrete Mathematics and Its Applications - Rosen
https://www.amazon.com/Discrete-Mathematics-Applications-Kenneth-author/dp/1260091996/ref=sr_1_1?crid=K1Q37HJYZCBK&keywords=rosen+math&qid=1685307660&s=books&sprefix=rosen+math%2Cstripbooks%2C95&sr=1-1&ufe=app_do%3Aamzn1.fos.006c50ae-5d4c-4777-9bc0-4513d670b6bc

Discrete Mathematics with Applications - Epp
https://www.amazon.com/Discrete-Mathematics-Applications-Susanna-Epp/dp/0534944469/ref=sr_1_1?crid=2C8LJ5Z2SEDDM&keywords=epp+math&qid=1685307692&s=books&sprefix=eppmath%2Cstripbooks%2C96&sr=1-1

are what i've seen recommended

epp is supposed to be more approachable than rosen

obviously if you're pretty advanced you'll want to do concrete mathematics by knuth

[meager socket]

Is there any proof logic set sorta book for a beginner?

[hallow oriole]

sure

book of proof by hammack is free online legally

skip the calculus section

[wintry quartz]

I found book of proof to be a little dry ngl

[tender river]

Knuth has weird typesetting so ig ill give Rosen a look sometime, i've seen some interesting problems from it posted in the help channels lately

[hallow oriole]

how to prove it by velleman is also a thing

[sage python]

@meager socket I should ask, as far as you can tell at least

What do you wanna do "in life"?

[meager socket]

Either computer engineering or electrical engineering
But I also just like doing math

[sage python]

Yeah I think you'd enjoy basic proofs/discrete math then

[wintry quartz]

agreed

proofs help understand topics further and discrete math finds its use in weird/unexpected places ngl

[sage python]

And discrete math is a great way to learn proofs, easier then calculus tbh

At some point I was looking for a discrete math book to recommend to one of my calc students

He was a nuclear engineer who still wanted to learn more math beyond what was required for his major, the idea being that if he knows math that most other people in his area don't, maybe he can find cool connections

And he also wanted to learn from the theory side. Was very happy to just hear my rant about random shit lol

[wintry quartz]

this i would disagree lol, discrete math is very unintuitive me to at least, again this is only my experience

[sage python]

Anyway so, what I was looking for was a book which:

• Was reasonably gentle at introducing one to proofs
• At least hinted at the basics of abstract algebra
• Covered cool applications/CSy topics, such as cryptography and coding theory

While this doesn't cover coding theory, the best one I've found in that regard is "Mathematics: A Discrete Introduction" by Edward R. Scheinerman

[gray gazelle]

Pls recommend some physics books for a total amateur

[inner token]

How's your Calculus @gray gazelle

I can recommend "Classical Mechanics " by Kibble and Berkshire

[vagrant mason]

So question: should I do algebra + trigonometry or pre calc before calculus? This is if I have no knowledge of any other maths besides lets say algebra 1 and 2. So I havent touched trig or geometry.

[coral prawn]

absolutely

[worthy venture]

https://www.amazon.ca/Manga-Guide-Linear-Algebra/dp/1593274130/ref=asc_df_1593274130/?tag=googlemobshop-20&linkCode=df0&hvadid=312857309014&hvpos=&hvnetw=g&hvrand=5030058992341815715&hvpone=&hvptwo=&hvqmt=&hvdev=m&hvdvcmdl=&hvlocint=&hvlocphy=9001316&hvtargid=pla-334293747018&psc=1

🤨

[ocean mulch]

Do one, and go to the other if you find troubles

Idealy you do all at the same time

[ocean mulch]

Feynman's lectures are quite alright

You have to be stubborn a bit to swim through the math, but he's a master in explaining stuff

[young moat]

does anyone have any recommendations for a problem book for number theory / analytic or elementary

I know of the one by murty and pollack

and the one by sierpinsky

I'm wondering if theys more since I see a lot for other fields

[tawny copper]

kinda nonsensical question. Do you need more or you dont like those? Because what you mention include tons of problems/exercises already.

NT is thousands years old, of course there are many problem books on NT, elementary or more advanced.

for elementary, Andreescus book is pretty nice. But there are many more, you can find tons of good problems in math competitions. For more advanced stuff, besides what you mentioned, you can just go to standard texts (eg, Apostol).

to cope with more advanced ideas, it is good practice to try to come up with your own examples, so that will keep you busy too

Unrelated to the above: Does anyone have/know where to find Knuths concrete mathematics book with bookmarks? (Actually, Id also like to have his art of programming series).

Disclaimer: Asking this is fine with discord rules probably, if you google "concrete mathematics Knuth", you will find pdfs available from universities.

[tawny copper]

^

[gray gazelle]

why not bookmark them yourself

[gray gazelle]

i am learning real analysis but have not learned calculus

[coral prawn]

Based

[outer nova]

Can someone recommend a math and trigonometry book? I'm a little good at math, but not so good at trigonometry.

[remote sparrow]

why is trig considered separate from math?

anyway, james stewart's precalculus book is good

[tight glen]

You can honestly go straight to calc if you understand alg 2 well

[trail yarrow]

For anyone who has read Stein and Shakarchi Book 3 (measure theory), do you have any recommended exercises for self studying at least chapters 1-3?

[woeful ravine]

If you want a real difficult problem book in NT, try Unsolved Problems in Number Theory by Richard Guy ;)

[woeful ravine]

But seriously, for elementary number theory, I would recommend looking at competition problems and there are plenty of books that catalog them (e.g. The USSR Olympiad Problem Book, which has 360 problems or so with a solid range of difficultly). I have Murty's book as well and have done some problems in it and it is great, albeit much more advanced than the problems you would find in almost any competition.

[flat moat]

does it matter whether i get the third or fourth edition of "Mathematical Proofs: A Transition to Advanced Mathematics" by Chartrand Pollmeni and Zhang?

The 4th edition only comes in a hardback and costs 160 usd, and i can get the third edition in paperback for 60 dollars

[acoustic cliff]

The 4th edition has an additional Combinatorics chapter which apparently the 3rd lacks

You can also sail the Seven Seas and get either edition for 0 dollars

[flat moat]

unfortunately i'm incapable of learning from a book unless its right infront of me

[acoustic cliff]

I see

The main differences then are the aforementioned Combinatorics chapter, a chapter that reviews all the proof techniques thus learned, and more exercises

Whether this is worth an additional $100 is up to you to decide

[tough tapir]

does anyone know any authoritative book publishing ''the devil speaks''

[hasty turret]

What does that mean

[tough tapir]

who are you talking to??!

[hasty turret]

What does "the devil speaks" mean

[tough tapir]

it's a book

[hasty turret]

Ah I thought it was some weird satanist stuff

[fierce hedge]

the devil speaks seems like a tv series instead of book

[tough tapir]

The beauty of this book is that it touches on hidden but sensitive matters

[fierce hedge]

It might have if the book were real, the closest I could find was 'satan speaks'

[tough tapir]

i think so 'cause it is translated into my language so i don't know how it is called in ur language i mean english

[fierce hedge]

makes sense

[tough tapir]

this is into my language https://www.google.com/url?sa=i&url=https%3A%2F%2Fwww.goodreads.com%2Fbook%2Fshow%2F92250360&psig=AOvVaw2y02Yds_v3gVT1VzyZHAZ5&ust=1686674503822000&source=images&cd=vfe&ved=0CBEQjRxqFwoTCPiX36aWvv8CFQAAAAAdAAAAABAE

[weary cape]

Same situation here but I feel like a kindle might work for me and I was thinking about buying one just for reading but have you considered that? I def cannot read pdfs on a computer screen it just doesn't work for me and I get distracted easily.

[coral prawn]

relatable

[remote sparrow]

i heard the binding for the fourth edition sucks

[thorn cloak]

you guys' books are binded?? 😢 all mine are glue and dont stay open for first 100 pages

[remote sparrow]

?

binding just refers to how all the pages are held together

[thorn cloak]

oh i meant stiched

im dumb

[remote sparrow]

it could be glue or sewn

[thorn cloak]

ignore me

ye

sewn

[remote sparrow]

many older books are sewn

but newer books tend to be perfect bound (i.e. bound with glue)

[thorn cloak]

sad

sewn is so much better i think

i wish my baby rudin was sewn

[remote sparrow]

if you buy a used copy, you can

used copies of that book are expensive though

[thorn cloak]

yeah i got new.. for like 150...

no fun

[remote sparrow]

[thorn cloak]

it wasnt even that great quality

[remote sparrow]

you should have spent that money on a used copy instead

[thorn cloak]

yeah but im a bit of like a... hmmm whats the right word

purist?

idk i just like the feeling of a new book and save them so i can build a stack with them lol

[remote sparrow]

some used books are barely touched

[thorn cloak]

true

[rigid barn]

I recently bought a German textbook from the 80s/90s that's out of print from an antiquarian and it was quite literally like new, absolutely nothing about it suggests use aside from bookmark stickers at the beginning of each chapter. Couldn't believe my luck.

[blissful pulsar]

any step by step book that even starts from substracting? I meant most beginning friendy. Explain all the rules etc..

[untold obsidian]

Any recomandation for a integral book?

[thorn cloak]

use khan academy

[hallow oriole]

inside interesting integrals by nahin

[thorn cloak]

though i must ask, how old are you?

[hallow oriole]

if anyone tells you anything else they're insane

[blissful pulsar]

I heard that khan academy is worst.. Like W3 schools..

[blissful pulsar]

me?

[thorn cloak]

yeah

[blissful pulsar]

17

[thorn cloak]

its fairly good for anything before uni level math

[blissful pulsar]

I don't go to uni

I left high school

[thorn cloak]

right which is why khan is good

[blissful pulsar]

just a role I picked probably...

I'm looking for straightforward rich and best practise content

[thorn cloak]

you can prob just find problems online

a book might be a bit excessive for arithmetic

[blissful pulsar]

are u Greece?

[thorn cloak]

am i greek? i am from the united states but my dad is half greek coincidentally

why?

[blissful pulsar]

your about is greece I think nevermind..

[thorn cloak]

ah its not greek per se but it uses some greek symbols

[blissful pulsar]

I had found some fundamental books that starts from four basic arithmetic operations which one is "DOE fundamental handbook" and a few them. Seems pretty good and detailed..

Also

"Basic Mathematics" by Serge Lang

[worthy venture]

Paul’s notes

[blissful pulsar]

noted

[fast gull]

Hi im reading baxter and rennie rn

you are completely correct

are you currently studying financial math?

[bronze marsh]

95. We rotate the following isosceles triangle around side 6. What is the volume of the resulting figure? (T = 3)
    192 (1
    288 (2
    48 3
    96 (4

please do this for me

and send answer

for me

[coarse frost]

Firstly there is no figure, secondly we arent gonna give you an answer here

ask in the right place

#❓how-to-get-help

[thorn cloak]

i dont think youre allowed to ask for links here

[hallow oriole]

they're not

@left lynx delete it and also dm me

[ripe root]

using what textbook does proffesor leonard teatch calculus 3 with?

[oak pecan]

no, working

how did you end up replying to a message i wrote months ago?

[fast gull]

i lurk

[gray gazelle]

Schaums outlines

[snow torrent]

hey guys, what grade are you all in?

[tidal kraken]

Yo c: I wanna read concrete maths by Graham/Knuth/Patashnik in order to prepare for TAOCP, what books and previous knowledge would you recommend me before i do? o:

[latent remnant]

It depends on your current knowledge; a good course in discrete mathematics should be more than enough. Have you taken any calculus and/or linear algebra? If you have all three, you are ready to go. If not, I would suggest some basic calculus and very basic linear algebra, and some combinatorics study. CM does revise all of these, but its pace requires some mathematical maturity.

[tidal kraken]

im still in precalc

thanks for your response c:

y e s

[hasty turret]

Concrete math is a funny book

[tidal kraken]

bc my programming teacher mentioned that our career program didn't have algorithm analysis

[hasty turret]

For the first 5 chapters, it's fine

[tidal kraken]

and we have the first book of the taocp

[hasty turret]

Then it goes completely crazy in the middle of 6th chapter with hypergeometric functions

[tidal kraken]

in the uni library

[coral prawn]

nani

time to read it

[hasty turret]

You do not need taocp to learn how to analyse algorithms lmao

Just like use Skiena

Or udi Manber if you want a proper mathy experience

You might also find CLRS useful

[tidal kraken]

i mean, i wanna learn the math too lol

i wanna learn many things, and i have so little energy

[coral prawn]

relatable

[finite gale]

I mean realistically, algorithms can definitely be taught in high school

Oh wait the guy deleted message

[hasty turret]

Algorithms can be taught in pre school

[coral prawn]

what is CLRS

[finite gale]

The only possible issue I can see is having some familiarity with proof writing

[tidal kraken]

hands tower of hanoi to 4yo

[finite gale]

But that's fairly minor

[hasty turret]

I mean a 4 yo could actually figure out tower of Hanoi

[coral prawn]

yeah

[smoky zephyr]

really hard algorithms book

[coral prawn]

oh my have u seen how many HS people do their absolute best to avoid writing formal proofs

[hasty turret]

Really hard because it's hard to parse

It's like the negative clone of DnF

[coral prawn]

[tidal kraken]

why prove things

just be confident

[coral prawn]

pride comes before the fall of man

[tidal kraken]

i can't fall, im on bed

[hasty turret]

Pride comes before fall

[coral prawn]

time to make your bed collapse

[hasty turret]

What if there is an earthquake and your bed falls

[tidal kraken]

im fascinated by the fact that we have a latex bot

i wanna learn latex just to do math shitpost

[coral prawn]

"be confident that there will not be an earthquake "

[hasty turret]

I have a strong feeling TAOCP would be an exercise in parsing

rather than math

Like "what does this algorithm really do? What are the invariants this algorithm has to satisfy?"

And "why does it work"

[lime vessel]

Learn gilles castel latexing skillz and be pro math hacker

[coral prawn]

[tidal kraken]

i gotta confess, i finished school back in 2013

then i did 3 years of music and lost support, then i started working and now im back at uni

and when i went for the first time to the uni library and found the first volume of taocp

[coral prawn]

zamn

[tidal kraken]

i tried following it

and got stuck at the first algorithm

bc i didnt knew how to divide

LOL

and i had to teach myself how to do it

bc legit i never used math.

[coral prawn]

[tidal kraken]

surpsisingly im one of the few that are doing ok in both math courses lol (precalc divided in 2 subjects but i still dont understand how are they divided bc even tho i have one course called "Algebra" ive learn more algebra in the "Math" course lol)

not good, but enough to be passing

even tho most of my classmates come straight from HS with fresh math knowledge

it's so weird to have classmates 10 year younger than me

but i've tried to adapt

[hasty turret]

I imagine divison must have been pretty important in music

[tidal kraken]

i mean ye, fractions

but we didnt use the division algoritm at all

btw, sorry for using this channel to talk stuff, moving to one of the discussion ones c:

and thanks for the help ❤️

[gray gazelle]

In Axler's Lin Algebra, he said that his book only deals with R and C. Then will I miss out anything using Axler's? Do other LA books work on other fields?

[inland elm]

most introductory linear algebra i’ve seen is over R or C for clarity, and uses arbitrary fields when results allow for it. i don’t think you’ll miss much unless you specifically want to work with, e.g., finite fields

[ocean mulch]

Children's Light Reading for Summer

[ocean mulch]

Chap 1 of CLRS gives a fairy good intro. It has amortised complexity and some Master theorem iirc. In general complexity analysis is not the worst thing in the world to learn on demand

[ocean mulch]

The only part I've seen where specific fields come into play is quadratic forms, where you have another theory for fields of characteristic 2, iirc.

Other than that, you won't miss out anything.

[gray gazelle]

I used blitzer a bit quite good imo

[quartz verge]

is there a book on mathematical shitpost

[gray jungle]

define "mathematical shitpost"

[quartz verge]

a deliberately provocative or off-topic comment posted on a math textbook, typically in order to upset or distract from the main conversation

id love to read a math book w such a theme

expository + shitposting

FUN

[rancid hollow]

I have a conjecture about math textbook PDFs. I think >90% of books which aren't page-adjusted to match with the book numbering are off by 13-17 pages. the sample size I have to support this is small but it hasn't failed me

[flint forge]

I think such a thing would be unlikely to be written given the time cost of doing so and the probably small market for a book like that

[quartz verge]

YOO Max

welcome back!

[flint forge]

thanks haha

[quartz verge]

we dont talk about that here

[rancid hollow]

OK done

[brisk copper]

y does this server seriously have nowhere to socialize

[dapper root]

The discussion channels???

Oh

Go to #bots and type
,iamnot studying

@brisk copper

You have the studying role which blocks social channels

[brisk copper]

[gusty verge]

I struggle at proofs(undergrad level prob and stats). What should I read?

[dapper root]

Problems

Prove more stuff

The only way to improve is to read proofs, write proofs

[gusty verge]

Yeah but how do I prove stuff? Also any proofs based Stats book?

[rigid barn]

Any good intro to elliptic curves books that don't assume knowledge of algebraic geometry? Knowledge of algebra at ~Lang level is fine.

[dapper root]

Look at Silverman’s book

Arithmetic of elliptic curves

Or something

[rigid barn]

Muchas gracias

[brave lotus]

i am looking for a book to learn about more advanced probability, coming from

• almost finished reading ross 1
• limited knowledge of analysis... chap 7 of baby rudin

[sage python]

@brave lotus if you're doing analysis I'm guessing you're interested enough in a theory pov to do measure theoretic probability?

[brave lotus]

yes 🫡, though im interested to hear recs for both applied and theoretical treatments of probability

[sage python]

Hmm, idk much about the applied side exactly to say much there

I mean obv there's prob less of a barrier between pure and applied in this case, but I'm guessing that's where you get close to statistics range. Lawler has a book on stochastic processes which is what I was thinking of as "another direction" one could go rather than spending time on measure theory

Durrett I know of as the standard in measure theoretic probability, also check out the course notes from http://galton.uchicago.edu/~lalley/Courses/381/index.html and http://galton.uchicago.edu/~lalley/Courses/383/index.html

[brave lotus]

Does one need a foundation in analysis and topology to study measure theoretic probability or is the analysis-y stuff less relevant

[sage python]

I mean, the foundation in analysis is what you've done + measure theory, and I think Durrett is self-contained wrt the measure theory

[brave lotus]

okay thanks so much! i will check it out 😄

[gray gazelle]

hm we've used some topology in our probability and statistics course, but it wasn't even measure theoretic... i suppose it depends on the specific course (mostly we needed it when discussing types of convergences)

[hidden bough]

How Not to be Wrong: The Power of Mathematical Thinking by Jordan Ellenberg
It's a really good book

[quartz verge]

wrong is necessity

i need wrong

[indigo relic]

any books recommendation about stochastic processes and markov chaines

[sage python]

Try "Introduction to Stochastic Processes" by Lawler?

[stoic zealot]

anyone know good source/ book on Hilbert spaces and infinite dimensional spaces?

[indigo relic]

thank you

if you still know some other books

tell me please

[gray gazelle]

"analysis now" by pedersen

[heavy pelican]

jordan?

[gusty smelt]

Second pederson, goated book.

[stoic zealot]

Is there also a solution manual

Or do i just pray that i am right

When i solve it

Excercises i mean

Thanks for the recommandation it looks like a fun book

[quartz verge]

him #chill message

[gray gazelle]

if you have to ask then i'm not sure if it's the book for you

there isn't

you should know when your solution is correct

[tender river]

Being active in #advanced-analysis \implies no solution manuals needed.

[stoic zealot]

You guys are so reliable thank youuuuu

This makes my day

[tender river]

although you should probably still not use that book :kek:

[stoic zealot]

Owh ill use it as an aid with the book my Professor made

Or book

I mean course

[tender river]

Oh then that's fine

[stoic zealot]

they have it at my library

[quartz verge]

damn

you own a full fledged library??

[safe barn]

Yes

[stoic zealot]

You dont?

[quartz verge]

[stoic zealot]

One day you will i believe

[quartz verge]

even my breads look like that

[nova jungle]

any books for tensors , for a beginner

[reef cosmos]

Daniel Fleisch's book "A Student's Guide to Vectors and Tensors" has good reviews. Fleisch is a physicist and I believe he writes in a way aimed towards physics students

"Vector and Tensor Analysis With Applications" by Borisenko and Tarapov is a little more old school and has a bit harder to understand notation but I like it

[nova jungle]

alright , ill look into that

thanks

and do i need any presequites before studying the book ?

asking cuz im a highschooler so i havent taken any official university classes

[karmic thorn]

David Kay's book on tensor calculus is also okay

I am simply not a fan of presenting tensors in the physics setting

(Kay's book does that too, but you can understand the computational tedium)

[nova jungle]

ohk , ill try that

thanks

[spark shale]

Need book recommendations for vectors and complex numbers
Preferably at an undergraduate level, where it explains basic topics as well

Maybe a heavy complex numbers/analysis book, with an introduction to vectors

[reef cosmos]

Idk how much math you've had in high school but I think to approach tensors you should have a good understanding of linear algebra. So vector spaces, linear transformations, bases, eigenvalues/eigenvectors, etc.

And if you want to do tensor calc then multivariable/vector calculus. Calc 3 if you are in the US

[nova jungle]

Oh ok ok

I have self studied them so I think I should be fine

[fossil bison]

Complex analysis by snider and saff

Is the one i used in school

[spark shale]

thanks

[fossil bison]

Look at chapter 1

[rocky coral]

anyone in here who enjoys dostoevsky?

[heavy pelican]

i do

quite a bit actually

[rocky coral]

which book did you read?

[heavy pelican]

basically everything except brothers karamazov

[rocky coral]

very nice
actually i didn't read brothers karamazov too

[heavy pelican]

its quite long, i have two volumes lying around on my shelf

ill get around to it someday

my personal favorite is Demons

[rocky coral]

yes its quite a long novel
my favorite is white nights because it was the first novel of my life

[heavy pelican]

white nights is beautiful

more optimistic than ever from Dostoyevsky though

i think the first novella by Dostoyevsky i read was The Gambler

i was hooked afterwards

[rocky coral]

white nights is like literally me of novels XD
i didnt understand the gambler but it was a nice novel that like just wanted to say
DO NOT GAMBLE

[heavy pelican]

lol

i liked how feverish it felt while reading it

in nearly all of dostoyevskis novels the characters rant until they go into a fever pitch and a spiral rabbithole of self introspection and self deprecation and then emerge out of the other end either dead or a christian

very intense stuff

[rocky coral]

yeah dostoyesky was very good at writing characters

and he was suffering depression and other mental problems so maybe thats the reason too

[heavy pelican]

dostoyevsky was always wack out of it

but he did get exiled in siberia and then almost got shot in the firing range

and he had epilepsy

and gambling problems

and drinking problems

and………

[rocky coral]

and he was so many years in prison

as you said

[heavy pelican]

siberia, yeah. its prison but open air and harsh conditions

literally in the middle of a marshland

gotta built your own home and so forth

live like a nomad

[rocky coral]

and his wife and child died in an accident

[heavy pelican]

i think he married thrice, i could be wrong

[rocky coral]

yeah i think so

[heavy pelican]

what a man

wack, but still one of the visionaries.

[rocky coral]

yeah

[gray gazelle]

YO I FOUND A FIRE BOOk

The Pythagorean Theorem: The Story of its Power and Beauty

A lot of interesting stuff on the Pythagorean Theorem and Pythagorean Triples

[cosmic yoke]

It’s not that fire but it’s good

[gray gazelle]

Depends on what youe interests are... if you want the physical approach to tensors then Tensors, differential forms and variational principles from David Lovelock. If you are interested in tensors as in tensor products of module etc. then some abstract algebra book would do the trick, i would personally recommend Rotman: Advanced modern algebra

[hollow shore]

@heavy pelican what is a good book to get into dostoevsky?

like an ideal starting point

[nova jungle]

I just want to learn tensors for physics XD

[gray gazelle]

Ok hahah then i would advise lovelocks book

[gray gazelle]

guys please mention me or add me if u want to answer this , i am a 19 years old after studying cs for like 2 years i learned alot of things (webdev(html css js php sql i like it and i want to learn 3d web design) python i learned alot about algorithms sorting resistivity pyqt i like problem solving ) i feel like idk what do in university because i am not good at anything like i am just decently good can you guys please suggest any free courses or advise to excel my programming skills or roadmaps i should take and thanks in advance (edited)

[gusty verge]

Pick any. Most people suggest Crime and Punishment, but I highly recommend reading The Karamzov Brothers first. The Karamzov Brothers is arguably his best.

[worthy glen]

This is probably a bad idea to ask a bunch of strangers on the internet, on a scale from 1-10 where would you rate Tomas & Finney's 9th edition "Calculus and Analytic Geometry"?

[heavy pelican]

probably Notes from The Underground

[worthy glen]

whoever gets around to answering my question just go ahead and ping me

[slim bramble]

not a bad idea since that's really what the purpose of this channel is

[worthy glen]

That's true, I don't want to sound rude but this did not answer my question.

I guess it would take someone who has the book and has read it to give me an answer to the question I asked

[slim bramble]

yup

[lapis sundial]

hm are there any good sources of hom alg exercises

I don't remember Weibel having much when I was working through it

[gray gazelle]

im thinking about going trough james stewart calculus as a complementary book with exercises but i have doubts that it may not be good for that, do you guys know other similiar calculus books not focused on proofs?

[viral moth]

what would be a good continuation from abbott's understanding analysis? i'm thinking of tao ii

[coarse arrow]

Introductory book on multivariable calculus both rigorous and physically intuitive (I want to do it for physics as well)

[karmic thorn]

Hubbard

[tame marsh]

for multivariable calculus?

[remote sparrow]

carothers

[kind elm]

well, yea? It does cover it

its an unconvential take on multivariable calc but not necessarily a bad one

its suitable for someone who took calc 1,2 and wants a more 'serious' look into multivariable calc

[blazing canopy]

I'm looking for a basic (undergraduate-level) overview of image processing. I mostly want to just know what are even the fundamental breakdown of topics that people care about, details I can find later from more advanced texts. Any recommendations appreciated.

[foggy relic]

Lang, Gelfand-Manin

I like the latter

[ocean mulch]

Munkres

I like his cus they are more accessible and meant to be exercises, not some theorems left as exercises

[lapis sundial]

That's cool thank you both!

[final sluice]

has anybody here worked through/is working through "galois theory through exercises"

[analog lava]

yea me

my fav math moments

[final sluice]

do you think it's pretty comprehensive/fine to work through after a brief exposure to galois theory in say, fraleigh's first course in abstract algebra text

galois theory seems cool idk

[analog lava]

how brief

was your exposure

i know u from #groups-rings-fields

u know like first half of the chapters cuz it first talks about splitting fields

field extensions

irred polynomials..

algebraic extension etc

[indigo hollow]

What's the best book about both Calculus + Analytical Geometry in one?

[final sluice]

ye

[final sluice]

well i'm still working through that, but it goes through separable extensions, inseparable extensions, galois groups, insolvability of the quintic etc

and i plan to work through that

[cold halo]

I never made too much logic's in sense of mathemathics, what is the best book to learn it from start (English prefered or Polish) ? It may contain something also with proofs but I will go from this year to a politechnical school as a enginieer prolly electrotechnical enginieering or something like Electronics and Telecomunication externaly... Now I am lacking a bit of examples how to prove something . Book that I have "Elements of logic and set theory in tasks by J.Onyszkiewicz" is great alot of tasks but no explanations only pure tasks(unsolved) and I am missing alot of expirience, need to learn at least basics to be able to proceed with basic algorithms in programming etc that I will prolly have in comp. science subjects and introduction to calculus starting from october. For example I have such simple tasks and kinda empty head how to solve it. (did saw tables of truth etc for other tasks):

1.5
Prove that with help of alternative and coniunction it is not possible to define implication and disjunction.
1.6
Prove that equivalence and negation cannot define an alternative or a conjunction.
etc
some functor proving tasks, lots of proving in chapter 1. Need examples etc to gain expierience otherwise I wont do nothing xD Yes didnt done much proving. Anyone would tip me from what to start, prefered free books online or anything easy to get not spending alot of $. This is kinda abandoned topic at pre-university stage. They start to explain it from university a bit, but I start from october and wanted to self learn something usefull from this topic and start the journey.

[karmic thorn]

Yes

[rotund yew]

I want to learn about data science. I am studying at university but they dont teach it well enough, is there any book you guys recommend?

[dusk tapir]

Our lecture notes (First course in Abstract Algebra) are pretty bare bones.
Any recommendations for a book where the section on field theory onwards is particulary nice?
We did groups, rings, Ideals, UFD, polynomial stuff, ((Ir)reducibility and now field extensions, minimal polynomial and ultimately working towards Galois theory.

I guess im looking for something that is suited for a first course in tandem to my lecture notes, so rather more explanations/examples/friendlier than being very concise.

[ocean mulch]

Herstein 2nd ed is great about field theory

but that's the only algebra book I've ever used 😄

[prisma osprey]

karamazov brothers is waaay too long if you don't already read

[tawny copper]

Dummit and Foote part IV and/or Isaacs

or Lang

[gray gazelle]

I think Brešar: undergraduate algebra is amazing for just this and very underrated

[gray gazelle]

I like algebra chapter 0 by Aluffi

[dusk tapir]

Thanks, i'll check all options out

[rigid barn]

Isaacs has the nicest sections on field theory of any intro algebra book I've seen. Just look at this bad boy, he fits in almost an entire field/Galois theory course. His exposition is fantastic and he has good exercises, but his book's a little tougher than e.g. DummitFoote or Aluffi.

[loud cradle]

that's a nice book, isaacs was my prof for graduate algebra back in the day so i've read most of it 😀

his "finite group theory" book is even better imo

[rigid barn]

Lucky man right here! What was the course like, did you get to take anything else with him?

[loud cradle]

nope, just the first year algebra sequence, i took a finite group theory course from another prof who used completely different notes/topics than isaacs

the algebra sequence was very similar to his book's exposition, problem sets were similar, qual was fortunately also similar haha

i was also one of his TA's for calc 2, so i got to see him in action there as well, very good lecturer at that level too

[rigid barn]

Good stuff, man

[clear mist]

Hey guys, i'm looking for a book as my introduction to complex numbers, my current capabilities are calculus (learned from calculus by james stewart) and some high school topics, i heard book about complex analysis is good but someone said it is too brief, so can you guys recommend me something that is not brief but not unnecessary long, and if possible with proof of the theorem if exist?

[finite gale]

First off, if you want to study complex analysis, you should study some real analysis

[clear mist]

I just wanna learn about the complex numbers

[finite gale]

Second, I'm not really sure what you mean by "the theorem"

Also generally intro complex numbers is covered in precalc

[clear mist]

The theorem that exist in the book, like if f(a) is derivable at a then it is continous at a

[bright galleon]

I think he means whenever there's a theorem, he wants to see the proof

[remote sparrow]

gamelin supposedly has very minimal requirements

at first anyway

you can look for complex variables books as well

generally more oriented to scientists and engineers

i guess brown and churchill might be accessible to someone with only a calculus background

[clear mist]

Hmmm, okay then i think i'm gonna try with brown and churchill first, thanks guys

[strange sorrel]

hello y'all, i am looking for a good and rigorous (ideally all the math stuff in first order predicate logic) book on axiomatic set theory, any recommendations?

[heady ember]

If you have mathematical maturity then baby Jech (Hrbáček and Jech) is a common ug choice

Otherwise Enderton('s Elements of Set Theory) is a gentle intro to axiomatic set theory

Btw "all the math stuff in fol" isn't very specific though so you might wanna elaborate a bit.

Oh Goldrei might be worth checking out too as a gentle intro

[strange sorrel]

The books i found online often have the axioms written out in english which i kinda dislike, for instance extensionality is just explained as "sets with the same elements are identical" instead of having a clean definition in first order predicate logic etc.

[heady ember]

Are you sure you weren't looking at naive set theory books

[strange sorrel]

or the idea that all "things" you can talk about in ZF are sets and nothing else ist just brushed aside.

[heady ember]

Sounds like you weren't looking at axiomatic set theory

[strange sorrel]

they did talk about the ZF axioms just not very rigorously

but thank you very much for the recommendations, ima look at them 🙂

[heady ember]

Np

In my experience, Enderton is great if you have zero mathematical maturity (like me when I started reading it). But once you gain some basic level of mathematical maturity many of his exercises are quite lacking in difficulty.

[strange sorrel]

i found enderton online, it seems pretty verbose, i usually prefer a more terse style

[heady ember]

Ah yeah Enderton says a lot more. Sounds like you might enjoy Hrbáček and Jech more

[strange sorrel]

just found a pdf of thomas jech set theory online, looks pretty much like what i was looking for, thanks again for the help

[coarse arrow]

Has anyone studied excursion through elementary mathematics by Muniz neto

[heady ember]

Beware, Hrbacek and Jech is ug intro set theory but Jech's 3rd millennium edition is grad level and very heavy/dense.

[strange sorrel]

Yeah the latter is the one i found, but it looks manageable

[heady ember]

Uhh probably not a good idea unless you have knowledge on par with like a late undergrad.

As with these graduate set theory texts, and especially Jech, they expect you to know elementary set theory (on par with smt like Hrbacek and Jech) and will only cover those basics very briefly. Prerequisites wise you should have learnt 'basic' fol probably up to like Godel's Thms and stuff. And you should have some 'basic' ug level knowledge of anal, top and alg. Anal/alg stuff is used quite often. Even in baby Jech, in some sections I believe you are assumed to know some basic measure theory and algebra. As well as topology for stuff like Borel sets and Baire something.
(I certainly haven't learnt this stuff yet but I'm just trying to warn you that grad Jech might be more challenging to read than you're anticipating)

Or well, just ask the guys in #foundations who are much more qualified than me to talk about big Jech.

[rigid barn]

what's a good book on representation theory that instead of the ad hoc takes the "modules over K[G]" approach?

[gray gazelle]

@heady ember jech 3rd millenium is an awesome awesome awesome book with tons of epic shit. i hate when ppl get gatekeepy over books for some dumb reason.
Also I hate this "high school level/ug level/grad level" leveling system which is dumb. I remember trying to learn shit like calculus n shit and searching/asking for "most rigorous ... book" to try and understand whatever the fuck they were trying to explain, and eventually figuring out what I actually wanted was just called "graduate level" for like every subject.

[gray gazelle]

also this baby/papa/grandpa naming scheme for books is not only gatekeepy, its also mildly misogynistic

[orchid mortar]

That's like, your opinion.

[gray gazelle]

correct

[vernal sigil]

hey y'all.
i'm looking for some good trigonometry books. i have sl loney's plane trig and hs hall's elementary trig. i plan on finishing sl loney's part 1 and part 2. will these 2 suffice?

[rigid barn]

Is this meant to be ironic?

[gray gazelle]

No

[rigid barn]

in what way is it gatekeepy, exactly?

[gray jungle]

well the leveling system is sorta needed because some books do require more background

so by saying a book is "grad level" just means that you are expected to know some stuff going in yknow

[gray gazelle]

Theres a book called 'advanced trigonometry' by durell and robson

[gray jungle]

otherwise you might be putting effort understanding a topic you dont have the tools to go into

[crimson leaf]

You were looking for measure theory and functional analysis and asking for calculus?

[gray jungle]

take for example someone looking for a real analysis book and he goes to read the graduate book rudin Real and complex analysis , if i go read it while not having done real analysis and then im just met with some heavy measure theory right off the bat and i will most likely just drop it soon afterwards because it turns out the book i need was probably tao analysis or rudin pma etc which is the "undergrad book"

its just a way to keep track of your progress as a student

undergrad usually will refer to introductory material

[gray gazelle]

For instance 'baby rudin' compared to 'papa rudin'. The names of 'baby' vs 'papa' and 'grandpa' imply that the book is the 'childish' version of the other 2 books.

[finite gale]

What

[gray jungle]

i think you are thinking too deep into this

[rigid barn]

least autistic discord user

[gray jungle]

lets refrain from this language ocean

everyone has there reasons to think that way

[chrome yacht]

so many sulliable things said here, just another usual day

[gray gazelle]

Ya lets say ur in a high school statistics class and u don't understand how probability distribution works because how does one even think about continuous probability? Well you need measure theory. So yes, I was.

[gray gazelle]

I can use my other reply to explain this one too, if you wanted to learn continuous probability you can jump into this book and start learning borel sets without even needing the vast majority of the first book

[crimson leaf]

I mean you can teach it without measure in fact many courses do and I don't think throwing measure at people who've never seen proofs before or any kind of rigorous math is a bad idea (source: my probability professor tried this and gave up.)

[gray jungle]

was about to say this , the reason grad books are difficult for hs student is not just the topic its the presentation .

[finite gale]

My probability professor gave a very aside on measure and left it at that

[gray gazelle]

Lame answer. As a student not a teacher I didn't understand how it works without measure even after reading. I wanted a better explanation and I had to find it myself.

[gray jungle]

Its similar to going from intro learning a subject to reading a research paper, the way its presented is just gonna be really difficult to keep up with

because in the latter , the target audience is professional mathematicians , just like grad books are targetting a graduate level math student

[finite gale]

I'm not really sure this discussion even belongs on this channel at this point also

[gray jungle]

well its technically discussing "books" but i agree

[crimson leaf]

This is true yes

[gray gazelle]

Yes I agree. Thats why the material/topics shouldn't be confined to just 'graduate' books

[gray jungle]

as gomez would say , i resign sad and brad 0-1 you win

[chrome yacht]

whether you like it or not some categorization of maths textbooks will always be needed, as it turns out some textbooks are intended for more mature audiences compared to others

[gusty smelt]

<@&268886789983436800>

[crimson leaf]

Graduate also typically refers to what the thing is demanding you already know. For instance my graduate optimization course was labeled as such because the professor will frequently reference results from linear algebra and analysis without describing what those results are and expect you to fill in the blanks on your own or prove it rigorously in the homeworks.

[gray gazelle]

You can categorize something without calling it 'baby', 'papa' or 'grandpa'. And 'graduate material' could be put inside of a book meant for less mature audience

[coral prawn]

it's honestly just naming conventions no? I don't see why we have to pick a fuss over these petty things

[gray gazelle]

Because they are gatekeepy

[chrome yacht]

hallo jung welt

wie geht's?

[coral prawn]

"gatekeppy"? Wdym? it's not like just because we named it differently/ say it's more "advanced", you can't read it

[gray gazelle]

But, that means the optimisation book first off assumes you are in a graduate math program and that you learned those 2 subjects in undergrad.

[coral prawn]

gut, danke, und dir?

[chrome yacht]

ich bin gut

[gray gazelle]

It's gatekeepy because by calling the book 'baby' vs 'papa' and 'grandpa' implies that the book is more childish. Urban dictionary says gatekeeping is "A word used to describe when someone sets a standard/limit on what someone must do to call themselves a 'true fan' of something/someone." So when you call the book 'baby rudin' it is implying that the reader hasn't met the standard to move beyond 'baby level' of math enjoyer.

[coral prawn]

... that's just semantics/terminology. It has nothing and doesn't affect the content nor the implications, I think you're overthinking. Heck I bet if u told someone u could do baby rudin they'll be impressed a ton, given it's... reputation

[gray gazelle]

I'm not talking about the actual books. Im saying the terminology of calling books 'baby' vs 'papa' and 'grandpa' is gatekeepy.

[heady ember]

I'm not saying its bad but if one doesn't have enough prerequisite knowledge and mathematical maturity, I think its practically undeniable that reading big Jech is a bad idea. Like imagine a student just learning arithmetic trying to learn calculus...

[crimson leaf]

I mean yeah that's how prerequisites tend to work? I'm a bit confused on the end of this statement my schools math grad program has plenty of courses that suppose you know analysis or algebra so the courses will expect that and if you don't they'll have you sit in the undergrad courses for a semester to learn them.

[coral prawn]

we only call them baby, grandpa and papa to differentiate them (+a bit if humour), and also because they tend to be "prerequisites" in a sense to each other. It has no intended meaning nor implications to critizcise/filter/distinguish a "superior" person to an "inferior" one.

[gray gazelle]

If it has no intended meaning nor implications of superior vs inferior, then what does (+a bit of humor) refer to then?

[coral prawn]

it's simply a way we classify the series, relating it to a family chain.

they call it baby Rudin because it's a series and baby rudin is a prereq to his main book which is rca

._.

[merry sphinx]

Theyre just nicknames for books in a series lol, theyve been around forever so they're bound to have some weird names

[gray gazelle]

I liked jech 3rd millennium more than for instance halmos because halmos doesn't go into detail about forcing for instance

[coral prawn]

I think grass's point is not that Jech is bad, but that it's unsuitable for people who don't have the mathematical maturity for it?

[gray gazelle]

YES. THIS. It's outdated terminology

[glacial crypt]

arguing in book recs

[heady ember]

I mean... obviously these have very different target audiences? So of course halmos wouldn't have forcing

If you wanna learn forcing you wouldn't be picking up halmos, probably

[merry sphinx]

Outdated? Idk, I haven't seen anyone else have a problem with it

[heady ember]

Personally I use that terminology as a shorthand

[mystic orbit]

wat

[heady ember]

Do I recall off the top of my head how to spell Hebreak? No so I used baby Jech as a shorthand

[coral prawn]

get out while you can gently leads DarQ to safety

[gray gazelle]

Idk when I was trying to understand real numbers, a natural question may be 'why is there no set with cardinality between cardinality of naturals and cardinality of reals?' well I needed forcing to help with the answer

[gray gazelle]

How come every other book series I've ever heard of doesn't do this?

[heady ember]

Wait aren't you assuming the continuum hypothesis here? Even if forcing could help one better understand the reals and the person in question does want to satiate this curiosity, forcing would still require significant prerequisites to learn, does it not?

[coral prawn]

because rudin is

1. Infamous
2. old
3. it's a series
   and otehr reasons which I have no idea of, if they exist

[sudden kindle]

There are lots of natural questions you could ask which require advanced machinery to answer. Doesnt mean its appropriate to learn for a beginner

[heady ember]

Exactly my point

[tender river]

in any case, to understand that advanced concept wouldn't you need to have covered the material in a textbook designed for a first course anyway

also maybe just move this to #math-discussion now or whatever

[orchid mortar]

I have seen exactly 0 recommendations for Talagrand in this channel. Does this mean no one in this channel reads Talagrand

[gray gazelle]

@sudden kindle I want to end the discussion here with my problem isn't with the fact that some material requires prerequisite knowledge, it is the inappropriate naming conventions. If more people want to argue with me then don't continue this conversation in this channel.

[fierce hedge]

No way my man quoted Urban dictionary while trying to be serious

[gray gazelle]

You guys tell me to not reply/defend myself to keep this channel clean, and then turn around and shit on me some more in this channel.

[tawny copper]

I skimmed a bit of those, the exercises seemed shit to me, so I didnt look them ever again. There are much better books for elementary mathematics + these books are long as fuck. Eg, if you want to learn geometry, just go to Evan Chen's geometry book

[tawny copper]

are you into set theory/logic or you read Jech just to get some knowledge on these topics, but not being your priority? Just curious

[gray gazelle]

currently reading set theory and logic by robert stoll and can really recommend it

very articulate prose and stuff

the list of topics is also incredible

[gray gazelle]

Second one. Jech has random cool stuff like baire sets and baire spaces for instance

[tawny copper]

ah ok

I wanted to read the section on descriptive set theory

but I got bored real quick xD

they were doing it over some weird spaces for the sake of generality, and not just over R

[gray gazelle]

Book_AlgebreCommutative

[deep summit]

https://www.forgottenbooks.com/de/download/TheTheoryofEquations_10455554.pdf

what level is this book ??

undergrad post grad or grad

what is it about ??

[tawny copper]

look up the contents and the introduction?

[deep summit]

intro does not state that

plus idk theory of equation was a chapter in 9th grade

it can be of any level

tell me

[tawny copper]

well you asked two questions

what is it about and the level

the first question is very

the second might be a fair question

this is like stuff from field theory, which is undergraduate material

[deep summit]

field theory ?

[tawny copper]

some stuff is also high school level tho, or could be studied by high-schoolers

[tawny copper]

theory of polynomials ig

but this book is very weird

[deep summit]

why

it tells us all methods of solving polynomials right ??

or does it prove all polynomial related theorems ???

and its properties ??

[tawny copper]

have you heard about Galois?

[deep summit]

abstract algebra ??

[tawny copper]

Galois is a person

[deep summit]

ok

[tawny copper]

like the unsolvability of polynomial equations of degree >=5

[deep summit]

yes

[tawny copper]

so field theory is about that kind of things

[deep summit]

but is this book about methods of solving equation or proving their properties

or like methods of solving some specific equations of higher degree

why did you call it weird ???

[tawny copper]

both I guess

[deep summit]

is this book like theory of differential equations ??

but methods of solving them are different book

some methods work on specific DEs

[tawny copper]

but if you want to learn about that, just pick a standard book on field/Galois theory, you will learn more

[deep summit]

what are prerequisites of it

[tawny copper]

none really

[deep summit]

whhhaaat

not group theory and abstract and what not

category theory

[tawny copper]

no, not category theory

category theory is just for weird people

[deep summit]

lol

there are so many fields and subfields in math i get so confused

[tawny copper]

group theory goes hand in hand with field theory, at a basic level at least

[deep summit]

may i ask what level is galois theory why cant i find it in undergrad math courses ??

[tawny copper]

galois theory = field theory

galois theory is about polynomials

and permuting their roots

[deep summit]

is it msc level ?

[tawny copper]

its undergraduate, every undergraduate program has a course in that

there is a book by a guy named Judson on algebra (groups, fields), it is very accessible. You can find it online for free

if you want to know about this stuff

[deep summit]

why was that book weird ??

[gray gazelle]

Maybe look at Brešar: Undergraduate algebra

Its for an introductory abstract algebra course

And ends with galois theory

Its very chatty and intuitive

[deep summit]

it has so many weird newton methods

[gray gazelle]

With no prerequisites

[deep summit]

weird

[tawny copper]

there is no one alive on Earth that has read that book

[deep summit]

lol

u mean math drama ?

[chrome yacht]

how old are you Negwa?

<@&268886789983436800>

[finite gale]

?

[deep summit]

?

[heady ember]

tis

tos*

[chrome yacht]

please come back once you are 13 Negwa

[indigo mesa]

discord is 13+ and we have to enforce tos

[chrome yacht]

since like forever haha

[rigid barn]

does one have to state one's age when registering for Discord or are servers themselves 13+?

[finite gale]

Why would you ask that and then why would they answer that

[deep summit]

cuz that book has unique content of theory of polynomials which no one studies in that depth ??

[finite gale]

It's discord tos

[tawny copper]

why do you keep asking questions about that book

[deep summit]

answer me

my relative wrote it

[tawny copper]

bruh I was gonna suggest that 💀

[deep summit]

can i ask last question

[deep summit]

Abott vs bartle vs rudin ?

Real analysis

[tender river]

abbott and garling any day

[deep summit]

Whats the differences between them

Which is more complete and which has harder problems

What about jay commings

[remote sparrow]

#book-recommendations message

[remote sparrow]

rudin has more coverage and harder problems

doesn't make it the ideal book for self-study

[orchid mortar]

Why is a probabilist doing QFT

Actually thinking about it, it might make sense...

[gentle seal]

has anyone here read Daniel J.'s how to prove it?

[remote sparrow]

velleman's book? yeah i have

[deep summit]

Jay cummings is lengthy and intuitive with lots of text explanations is it good ?

I can go through rudin with ease after that

[remote sparrow]

it's good

abbott is also good

[deep summit]

Recommend me a short and easy proofs book ..... Not a order

[tender river]

sounds like an order

[deep summit]

Ok

[subtle mango]

any discrete math textbook

probably has a chapter on logic and proofs

[crimson leaf]

#proofs-and-logic message

[flat jackal]

Anyone got any good problem solving books

Just to get better at problem solving

[gray gazelle]

yeah

whoops, i forgot it's not a book

[tawny copper]

Engels book

Gowers has a playlist where he live solves problems from that book, so that can be helpful too

[gray gazelle]

Good books for learning Mathematical Analysis, Linear Algebra, and Abstract Algebra?

[subtle mango]

see #books-old

[sly sandal]

Google linear algebra and end the line with pdf. I guarantee you, no matter what subject you search, you will always find free books when pdf is in the search.

[loud cradle]

"linear algebra done wrong" is a good choice, it's even legally free

[native fractal]

Good recommendations in improving Euclidean Geometry?

[sage kelp]

Great book

[mossy comet]

Hey everyone! I'm looking for recommendations on the best probability books out there. Any suggestions?

[ocean mulch]

Kolmogorov's?

hand down one of the most important books, but idk how acccessible it is

[tender river]

depends on the kind of probability text you're looking for, just calculus based? sheldon ross first course in probability is a good one, measure theory based? idk about that one

[tulip hearth]

Any place where I can find a free pdf version of a book I wanna try?

[gray gazelle]

oh yes

Doesn't mean you should. If you use libgen then u could get potentially get arrested so don't use libgen. I do not advocate for the use of libgen.

[tawny copper]

what are you talking about

[gray gazelle]

yo who just posted anime shit

and deleted it

[tawny copper]

[gray jungle]

he is talking about the illegal website libgen that can get you a free pdf of many books you want to try , which people should avoid using.

[tulip hearth]

||I was trying to find a book an old teacher once recommend, cause his teacher wrote it. I thought of giving it a try, beach costs more then a gaming console 💀
Why do u think I need the book for?||

[gray gazelle]

yeah bro Im saying don't use libgen, the free pdf site

[tawny copper]

I know what that is, but how are you gonna get arrested? Also, why people should avoid using it? Furthermore, it is against discord rules to talk about piracy