book-recommendations

[flint forge]

not really

[golden bear]

yes it is

[flint forge]

its almost too numbers based at time lol

[willow pecan]

There is a degree of randomness

[tulip blade]

It can be a little random but you dont randomly get in to a top school

[golden bear]

Explain how I got into a program with 2.95?

[willow pecan]

It is not entirely random

[golden bear]

with TA ship

[tulip blade]

Thats masters tho

[sage python]

A couple of us had gotten hyped about calculus and basically asked our teacher to do it asap since we thought it was cool (we were physics people at the time), she wanted to do the group theory but decided against it since she felt our class wasn't good enough with proofs for that

[tulip blade]

Im saying funded phd

[sage python]

So yeah idk we did the topics in a weird order

[tulip blade]

There is some randomness but they dont choose just anyone.

[golden bear]

But very small programs offer masters TA ship. Still hard and random

[sage python]

Nah

Randomness in grad admissions is as a result of, there are more qualified people than there are spots

[tulip blade]

My point was he wouldve likely been overlooked if they required the gre

[karmic thorn]

Seems fairly standard except for discrete math and groups. By discrete math, do you mean basic combinatorics?

[sage python]

Funded masters isn't common but also I don't think a lot of people are even looking at them

So it's a weird niche

[golden bear]

because is not top named programs

[gray gazelle]

How do you not forget the previous math you've learned?

[tulip blade]

Uh

[sage python]

That and also, the more common thing is to either go for PhD

[golden bear]

practice

[tulip blade]

I forget all the time

[karmic thorn]

By seeing it being used in different contexts, some ideas just stick as you do more math.

[sage python]

Or if you feel like you need more practice you do a masters, it's sometimes considered almost "remedial"

[karmic thorn]

But it's not bad to review/refresh anyway.

[storm sleet]

If you can get into a PhD program

[sage python]

I don't want to use the term in the loaded way but

Let's say idk somebody goes to a school without as many resources or started in physics or something

[golden bear]

I consider masters like a "community college degree" that prepares you for PhD

[storm sleet]

That’s why my route is to get into an “early” masters in CS and moving into a PhD

[sage python]

Then yeah that's where you're looking most at masters. But I think if you're at that point you probably just accept that you'll likely pay

[golden bear]

NYU masters is consider a cash cow.

[tulip blade]

Why masters first?

[golden bear]

After my masters, I am literally going to take a break. Probably 1-2 years.

[storm sleet]

Our college lets you get into grad school through some weird channels before you graduate

[manic fox]

consider tteppa during that break.

[storm sleet]

And our CS dept let’s you move from a masters to a PhD, without the GRE

[tulip blade]

Oh ok nice.

[storm sleet]

Ideally I’d do a masters in CS and a PhD in math

[sage python]

Good luck

[golden bear]

Good luck.

[broken meadow]

Luck.

[sage python]

Here we have a paid masters you can get to prep for PhD (a lot of people do it and get accepted back, also some schools have a program where their last year of undergrad at their home school is the first year of masters at UW Madison)

[gray gazelle]

I'm doing cs but imma be a developer for some company

[sage python]

Then there's a masters you can get on the way to a PhD

[golden bear]

i was planning to apply for a PhD program but all the deadlines were already passed.

[gray gazelle]

Tough

What u do then?

[golden bear]

I applied to two masters program. One of them was unfunded and the other was funded.

[gray gazelle]

Did u pick the funded one?

[golden bear]

Yea

[gray gazelle]

Does a masters specialize?

[golden bear]

They have a thesis and non-thesis option. Pure and applied courses are offered

[gray gazelle]

R u doing thesis?

[golden bear]

I'm unsure yet. I have a year decide

[gray gazelle]

R u doing pure or applied?

[golden bear]

Unsure about that too. As of now I am mixed with pure and applied

[gray gazelle]

Is there any specific field u like?

[golden bear]

I like Analysis

With ODE

[sage python]

Analysis is good stuff

[gray gazelle]

I thought analysis was undergrad

[golden bear]

Analysis a research interest

[sage python]

Analysis is an area of math

[golden bear]

^

[sage python]

You start learning it in undergrad but there's still current work being done

[golden bear]

There are five areas of math: Topology, Algebra, Stats, Geometry, and Analysis. Not sure If I am missing but these are the ones I know

[sage python]

Hard to really delineate like that

[flint forge]

youre missing a few hahah

[gray gazelle]

Algebra still requires research

[flint forge]

logic, combinatorics, etv

etc

[willow pecan]

Number theory is an area

[flint forge]

graph theory

TCS

[sage python]

I actually think stats is kind of its own subject since idk if there's an axiomatic characterization of the objects of study. And then like, a lot of stuff doesn't really fit under these boundaries cleanly

[golden bear]

From what I hear analysis is a somewhat like a dead area. Unless I am hearing wrong. I know complex analysis which is something I want to do is not an active area. However, Several variables complex analysis is starting to become popular

[sage python]

You're hearing very wrong

[willow pecan]

[sage python]

Analysis is arguably the most active field of math

[willow pecan]

No one likes SCV

[sage python]

And yeah SCV... idk maybe it's growing now but it's not nearly as prominent as most other things

[golden bear]

SCV is hard from what I hear.

[flint forge]

also complex analysis isnt dead

[sage python]

Are you just an incorrect statements bot?

[golden bear]

Well whenever I say I want to do complex analysis research they say is dead.

[sage python]

I mean

Idk if much research is being done in single variable stuff

But SCV is def a thing

[flint forge]

also tons of complex analytic techniques are still popular

[golden bear]

Yea SCV is probably something I want to look at and see if its for me after I take complex this Fall

[sage python]

Complex geometry as well

[tulip blade]

Stats isnt math

[sage python]

But also there's a ton of analysis that's not complex analysis

Microlocal analysis PDE, harmonic analysis

[tulip blade]

Functional analysis is huge

Is that not analysis anymore lol

[willow pecan]

Dynamics

[sage python]

I mean

[tulip blade]

Operator theory

[willow pecan]

C* algebras

[sage python]

There's the usefulness of a subject

And then there's the research activity

[willow pecan]

Functional analysis is mostly complete

The outstanding questions are all bad

[golden bear]

https://math.cornell.edu/probability-and-statistics

[sage python]

I feel like functional is very useful but idk if there's a lot of current research I'd classify as "straight functional analysis"

[tulip blade]

Wow awesome👍🏻

[sage python]

Like the theory of Banach/Hilbert spaces

[flint forge]

uh

what about that stuff jan does

[willow pecan]

Functional analysis was solved with a hundred adjectives describing different types of Banach spaces

[flint forge]

thats like 50/50 functional and model thh

thy

[sage python]

There are like, 5 people who work in that

I think this isn't an exaggeration

[flint forge]

hey thats all u need

[sage python]

Killer sometimes they group them up in a department but philosophically I don't think stats is a subset of math if only because your basic objects of study are not axiomatically defined

Like what's the definition of data?

[flint forge]

it already feels like only 5 people know my subject

so who cares

[sage python]

So stats at the core strikes me as being more empirical than math. That's my take at least. Obviously it's a very quantitative subject but it does differ from most math in that regard (I do consider probability to be part of math tho)

[tulip blade]

Probability is math

[golden bear]

Well Stats is applied math if you think about it

[tulip blade]

Its basically analysis

[sage python]

I thought about it

[golden bear]

if you combined stats and probabilty

[broken meadow]

i think stats has enough unique practices to distinguish it

[sage python]

It's quantitative and it does apply a lot of tools from math but again, I think it kinda is its own thing a bit

Like that's not trashing it at all

[tulip blade]

Stats isnt math

[sage python]

It's quantitative and has applications

[golden bear]

Stats is math but with data. So is really not math

[sage python]

But the basic objects are just different, and I think the methodology is a different style

[tulip blade]

Basically all quantitative fields are math + something

fields can have overlap with math and not be math.

[sage python]

But yeah within analysis I'd wager PDE microlocal analysis is the biggest

Also harmonic analysis

[tulip blade]

Probability ?

[willow pecan]

PDE is the biggest in analysis

The outstanding questions in harmonic analysis are too difficult

[sage python]

Probability tru

Dynamics is active

[tulip blade]

PDEs is hugr

[gray gazelle]

I was wondering if there are any cute girls in any of ur classes who's a math major?

[tulip blade]

When i said functional analysis is big i just mean that i see a lot ppl with functional analysis/operator theory as interests idk anything about those fields tho

[willow pecan]

Dynamics isn't analysis

[tulip blade]

Bru

[sage python]

I think there are some people who are into it just not a lot

[golden bear]

jeez

[sage python]

My department is very big on harmonic analysis

[gray gazelle]

Bro it would be nice finding a partner with similar interest

[willow pecan]

This is so cringe

[gray gazelle]

🤣

[tulip blade]

@gray gazelle Thats subjective but im sure youll find someoen in math if you want

[gray gazelle]

I realize that

[sage python]

human if I'm gonna attempt to keep a straight face while answering you

[golden bear]

you said cute girls. Could have just said "Any girls"

[willow pecan]

[sage python]

The further you go in math the more male dominated things become

[willow pecan]

They're all lesbians

[gray gazelle]

Bro I would need to be attacted to the person

[tulip blade]

Cant comment on that

[willow pecan]

Because the straight women were all driven away by straight horny men

[sage python]

Now beauty is in the eye of the beholder and I don't know if I'm too fond of talking at large about the beauty of women in math

Like let's just not with that conversation topic lol

[gray gazelle]

Well is there anyone most ppl would be into in?

[flint forge]

my girlfriend is hot and does math

so

[gray gazelle]

Ur right that beauty is in the eye of the beholder but im sure we all can agree Ariana grande is hot

[sage python]

I have met people I consider very attractive in math, same as outside of math lol. I'm not gonna attempt to speak for anyone beyond myself or do statistical stuff because that's weird

[gray gazelle]

That's lit

[sage python]

Like ah n% of the girls in math are good

So yeah that's what I'll say

[cursive zinc]

pics or it didn't happen

[willow pecan]

Ariana Grande is problematic

[sage python]

That's... creepy

Please don't say that even as a joke lol

It just pushes the atmosphere in a bad direction

[gray gazelle]

My bad lol

[gray gazelle]

Wym?

[flint forge]

im not doxing my own girlfriend you creep

[gray gazelle]

I was just joking but idk about him

[flint forge]

im only referring to onenine

[golden bear]

human are you sure a 12th grader (17 or 18)?

[sage python]

Max didn't even you see you say anything human you deleted first

[gray gazelle]

17

Wbu?

[golden bear]

25

[gray gazelle]

Dam u old

No offense

[willow pecan]

✨ gay dead ✨

[golden bear]

once you hit 18. time will fly

[gray gazelle]

I'm glad it will

[sage python]

Yeah college was the best time of my life

Grad school was tbh set up to be almost as good but

Covid 🙃

[flint forge]

i lost 25% of college

[gray gazelle]

What was best part about college for u?

[flint forge]

i guess you lost 20% of gradschool

college is just more fun in basically every way

than hs

[sage python]

More interesting classes, way better social life

[gray gazelle]

Being able to wake up later would be nice

[golden bear]

I would say sophomore year then first half of junior year. Second half of junior was starting to be the best

[gray gazelle]

For hs gotta wake up at 6

[flint forge]

more freedom, more parties, better classes, better friends, substances if thats ur thing

[gray gazelle]

Worst part

[sage python]

Meeting interesting people

It's just better™️

[karmic thorn]

I haven't seen uni yet, in person.

[flint forge]

lmao in my first year of college

i slept till noon

every day

[gray gazelle]

Oh yea uni has people from all over the state and even country so there must be plenty of interesting people

[sage python]

Damn you had no morning classes?

/you missed them?

[karmic thorn]

I'll finish my first year in August, would probably not get to see it till then.

[flint forge]

nope i just scheduled well

[gray gazelle]

That's amazing

[sage python]

Nice

[flint forge]

all my classes were 12:30 to 4

[gray gazelle]

I actually wanna wake up around 9-10 that sounds like the best time

[flint forge]

yeah its too late for me now

[sage python]

I'm doing this analysis summer school and my classes are at 9 which s u c k s but they record so I just tell myself I'll watch the recording later

[flint forge]

ironically inwake up at like 7 or 8

[willow pecan]

(Dami never does)

[gray gazelle]

Do u actually watch the recordings

I tried that for one of my online classes and Id rather go to the class

[flint forge]

i never watch recordings

i dont think anyone ever has

[gray gazelle]

Same It's awful

[sage python]

Yeah I need to like

Drink a bottle of soda and just watch them on 2x speed

[flint forge]

there arent a lot of people i can suggest coffee to and improve their health

[willow pecan]

[hearty steppe]

thank you max, I can't even suggest coffee to myself more than once a week.

my nerves can't handle it

[tulip blade]

I drink multiple cups a day

how do you stay awake

[willow pecan]

By being a well adjusted person

[broken meadow]

i absorb my energy from the universe

Directly.

i do not need coffe

[willow pecan]

coffe

[broken meadow]

nor tea

cofe

[willow pecan]

Ok mitil

[broken meadow]

mutil

MUTIL

[flint forge]

i drink yerba matte

its all u need

[tulip blade]

Loll

[manic fox]

erb

[void sable]

is the whole link between this and throat cancer probably just due to people consuming it before it cools down

[viral hill]

it depends at what temperature you drink it lol, but, you normally want to cebar mate with water cooler than 75°C, because higher temps can ruin the yerba (kinda similar to tea leaves I guess), I have read that when most people consume mate it's around 37 -55 C, so it's safe, but nothing stops you from drinking an hotter infusion lol

[pale scarab]

That would have been great. Ah the joy of having to work near 40 hours a week with school in order to live.

[misty flax]

good book for set theory from the basics?

[storm harness]

Do you already know first order logic?

[velvet briar]

Levin's discrete mathematics is free online, is a good read, and one of the easiest intros to logic and sets I've ever seen

[gray gazelle]

Good comic books or books like diary of a wimpy kid with slight pictures in every page now and then

What suggestions?

[manic fox]

hartshorne has a great series

Look up "Hartshorne GTM book" for more

Great book

[hasty turret]

Isn't that only one book?

How is that a series

[manic fox]

Yeah but it's very long

They originated as a series which he later compiled into his book

[storm harness]

So like, compiled from storytelling sessions at universities?

[manic fox]

yeah

i hear he was around universities a lot

[storm harness]

Man children's books' authors have got it easy

[manic fox]

[karmic thorn]

I suggest action thriller Analysis by Amann-Escher. 3 volumes so far.

[hasty turret]

I suggest baby rudin

It's written for babies

[manic fox]

he could have done so much more if he wasn't into the self destructive shit he was into

He spent his days doing something he called "algebraic geometry"

it's depressing really

[storm harness]

How to waste a life

[manic fox]

truly a tormented genius. He was a great comedian but a little insane

i feel for his family.

[gray gazelle]

test 1 to see if i message this in a channel it will get active again

[west sedge]

Hello, does anyone recommend a book that contains measure theory and functional analysis together for a beginner?

[undone pine]

Are there any books speaking about riemann convergence theorems (in particular about the monotone convergence theorem) on "basic" analysis level? I mean without measures, lebesgue and so on..

[gray gazelle]

Check out Rudin

[timber mesa]

if by "monotone convergence theorem" for the Riemann integral you mean https://en.wikipedia.org/wiki/Dini's_theorem + the fact that uniform convergence lets you switch integral and limit, any introductory analysis book should be good. Baby Rudin treats this in Chapter 7, specifically Dini's theorem is Thm. 7.13

[undone pine]

@timber mesa By monotone convergence theorem I mean the following statement: if the sequence of functions f_n is increasing and riemann integrable and f_n-> f pointwise (f is Riemann integrable as well) then lim integral f_n = integral f

without the hypothesis that each f_n is continuois

so I can't apply Dini's theorem in this case

And i can't find the proof anywhere. In all articles that I found the proof involves measures

[timber mesa]

ah alright. I'm not sure if any book proves that without using the Lebesgue integral (which frankly, is probably the easier way)

[undone pine]

hm alright, thank you. I have this as exercice and I just wanted to check if my proof holds.

[gray gazelle]

riemann convergence theorems are a waste of time

i hate that stein shakarchi uses riemann integration for their fourier book

[tulip blade]

Isnt it the first course in the series?

[gray gazelle]

Any good books for geometry

[timber mesa]

it is and probably shouldn't

[gray gazelle]

yeah it's the first book so there's a fair bit of stuff that could either be generalized or proved faster

[gray gazelle]

do carmo

[sudden kindle]

any book recs to learn about riemann surfaces ?

[gray gazelle]

guys, do you recommend any supplement for Abbott's R. Analysis?

[storm sleet]

I’ve seen people recommend Miranda’s book

[obsidian valley]

for model theory: Marker or Chang & Keisler or little Hodges

i have decided to buy a book so I can treat it as the light at the end of the tunnel that is aluffi

pls ping cause ever since they moved this channel I dont read it thx

[obsidian valley]

@sweet lotus when you have a moment

apparently I'm not the only one who pretends this channel doesn't exist anymore

What are the possible goals

my goal atm is to learn model theory

I don't really have an end game for it

[hearty steppe]

Bruh, as much as I like Abbott, it will only take you so far on its own in understanding math

its really like a broken down first semester analysis course book

does its job well, but if you are serious about math you gotta pick up a more dense analysis book

[obsidian valley]

little hodges or big hodges?

I have heard lots of good things about the little one on MO

👍

okay I will purchase it then

thank you

[gray gazelle]

Don't you dare.

Don't say Rudin.

:D

Thanks Bruh.

[hearty steppe]

I was like that for a while but you'll understand why people say Rudin when you are ready to become a mathematician.

it is frustratingly hard to get through but I think I'm getting the gist of why people recommend it and why people strategize using supplementary material like Abbott to get thru it

having my second go with it now. The first time I tried reading it, I was too overwhelmed and obviously had to work a little on my proofs background. Spent my time doing that and easing myself into it.

I am starting to understanding that there is a certain tier of note taking and learning that goes into getting through Rudin. Each page and a half has you solving riddles that eventually has some pattern to build on.

and in a sense, it becomes engaging in a fun and eventually intuitive way, when you use supplementary material to your advantage every page you get stuck on

[narrow talon]

With all that

Do Rudin

[hearty steppe]

and mind you when I first openned Rudin, I didn't hate it, I just didn't understand how to get through it, and thats what frustrated me.

but I gave it another go last night, and I think im getting the hang of it and see why people recommend it so much

[narrow talon]

I’m working through it now, feel free to join

[hearty steppe]

how far are you in it Jason?

[narrow talon]

Err, at a fast pace mind you

Just first chapter, starting second tomorrow or overmarrow

Wait, Real and Complex right?

[hearty steppe]

oh no

lmao

not there yet

[narrow talon]

Oops 😬

[hearty steppe]

im still a pure newb

what do you call someone new to theoretical math? That's still where im at

[narrow talon]

I prefer Johnsonbaugh and Pfaffenberger. Not a popular book, but honestly better than Rudin as both a textbook and reference

[marble solar]

I've heard good things

[hearty steppe]

Pfaffenberger? What kind of name is that

[marble solar]

German

I used johnsonbaugh for discrete math and it was ok

Hopefully the real one is better

[narrow talon]

It is good! Basically the same level as Rudin, but with different organization and imo puts the emphasis in better places

It’s not excellent, but no real book is

[marble solar]

Stein and Shakarchi volume 3 is excellent

imo

[hearty steppe]

yea but S and S is after baby rudin tho?

[narrow talon]

Eh, that’s the one that can’t decide if it’s for grad students or undergrads right?

[marble solar]

Yeah ~ it's between the two

[narrow talon]

Err, I suppose that’s all of the S&S books

[marble solar]

The 4th volume is decidedly graduate

the 3rd volume depends where you're at

[narrow talon]

I’d honestly prefer just reading big Stein at that point

[marble solar]

At most schools it's graduate

at top schools it's undergrad

[marble solar]

That's what I thought

but the notation and the exposition is clearer in Functional

[narrow talon]

We did big Rudin at that point during undergrad

[marble solar]

Where was that?

[narrow talon]

And Brezis, 3rd book is functional or measure theory? I can’t remember

NYU

[marble solar]

I didn't take grad real at UCLA, I did grad complex

I did grad real at CSULB, and we used S&S since CSULB is a weaker program

[narrow talon]

I only did grad functional

[marble solar]

I thought it was good

[narrow talon]

Was a joke after the undergrad analysis 2 course ngl

[marble solar]

3rd is real, 4th is functional

[narrow talon]

Jeez, UCLA to anything is a downgrade for analysis no?

[marble solar]

The "functional" book is more a hodge-podge of random stuff

[narrow talon]

Ah

I am a huge fan of Brezis

[marble solar]

Well all of my analysis profs at CSULB did their PhDs at UCLA

[narrow talon]

Fell in love with that book a long time ago

[marble solar]

Since it's so close - we largely used the same books, or same style

[narrow talon]

Gotcha

[marble solar]

It was an upgrade in teaching quality

a downgrade in how much we covered

[narrow talon]

I’m just familiar with some of the lecture notes from ucla and they’re pretty great

[narrow talon]

To be expected

[marble solar]

e.g. my pure analysis prof didn't cover a whole lot

[narrow talon]

But motivation is important

[marble solar]

but my PDE prof covered more than what was possible at UCLA

Cuz of semester system

[narrow talon]

We covered nothing in functional, but I got a much deeper appreciation than I would’ve if a more “serious “ prof taught it

[marble solar]

The functional I took was an Applied Functional Analysis class

so we just did Green's functions, boundary value problems

[narrow talon]

I really need to improve my pdes

A lot

[marble solar]

and compact operators

[narrow talon]

Sounds really fun though

[marble solar]

I ended up skipping first semester PDEs at LB, and just took second semester PDEs

[narrow talon]

At least as someone who really likes the applied part of functional

[narrow talon]

Makes total sense

Common thing at NYU too

[marble solar]

That was a crazy class

[narrow talon]

First semester PDEs won’t mention sobolev spaces at all

Which is sad

[marble solar]

Yeah, day 1 was sobolev spaces

[narrow talon]

Makes sense

[marble solar]

We did a lot of regularity theory stuff

[narrow talon]

Encode your shit into the space and then use FA to solve your problems

[marble solar]

I had only seen basic wave equation or heat equation in like 1 or two dimensions

[narrow talon]

That’s the stuff that scares me

[marble solar]

it was my first time seeing n-dimensional PDE stuff, I was the best student in the class at it

Despite not doing first semester PDE

[narrow talon]

I need only Laplace and heat going forward (hyperbolic operators don’t come up often in probability)

[marble solar]

Yeah, the only thing I used in my research was the heat equation

[narrow talon]

Err, equations? I really haven’t encountered nonlinear pdes tbh

[marble solar]

Heat equation is

u_xx - u_t = 0

Or something

[narrow talon]

My PhD program covers way less pde than I anticipated, only optimal transport as an elective

[marble solar]

Are you doing your doctorate at NYU?

[narrow talon]

Err, heat equation is nonlinear wtf?

[marble solar]

badly non-linear

[narrow talon]

I really know jack about pdes

[narrow talon]

Oxford

[marble solar]

Ohhh fancy

[narrow talon]

Specialized program in probability and stats

[willow pecan]

[narrow talon]

Got in primarily because I’m interested in some bizarre applications

But of course you need PDE for probability

[marble solar]

Yeah, that's what my research was in

PDE & Probability stuff

[narrow talon]

So I'm spending my summer reviewing my basics and learning more about PDEs and SDEs

[marble solar]

I knew nothing about PDEs, and I still know nothing about probability

[narrow talon]

Vibe

[marble solar]

The only probability class I took was Random Matrix Theory

[narrow talon]

I aced the final but bombed the rest of my stochastic analysis class

[marble solar]

From the same guy that taught sobolev spaces

Which had as a pre-requisite grad probability

but he just kinda let me in

[narrow talon]

But really need a lot more comfort with some of the naughty measureability bullshit

Which is really a bit sad for a prob PhD student. I really did not do well my first semester post covid and need to review a lot of the technical details of fundamental probability

Though it's not too hard

[marble solar]

Are you a first year?

[narrow talon]

I really wish there was a better book on path-space oriented stochastic analysis, but every one I've found is really quite awful

[narrow talon]

Yes, still scoping out my research area, likely in IPSs or deep learning (depth separation or optimization landscapes of NNs)

Oxford has three research groups I'm really interested in, FA, Stochastic, and DS

Stochastic is a given, but FA leans more towards nonlinear PDE

which I know very little about

[marble solar]

Try to keep an open mind! no need to shoe horn yourself into a topic just yet

[narrow talon]

Yeah, that’s just where I’m leaning towards

But at Oxford you only get one semester to choose an advisor

So I’m exploring (especially DL) now in more depth

Depth separation is a lot of FA, but really investigated largely by someone at NYU, not Oxford

[marble solar]

Jesus

That is scary

[small garden]

and you don't get anymore chances?

like that's it?

[narrow talon]

So I’m leaning towards James Martin or one of the two DL people

[narrow talon]

Pretty much, you have to finish choosing in your second semester

But there’s lots of opportunities to interact with them

I may very well end up with someone in the math department and stats department

Just because my research interests don’t fall cleanly into a single person at Oxford

There’s also a lot of people who are firmly analytic focused probability, like Terry Lyons

[small garden]

and what is it that you want to study?

[narrow talon]

IPS based deep learning likely

So loss landscapes and such

[pine flicker]

no im jason

[narrow talon]

Pretty heavily dependent on analysis and statistical physics

As well as deep learning

[small garden]

do you think AI will 'destroy music'? (meaning AI is capable of making better music than us)

[narrow talon]

(Pretty heavily inspired by my mentors at NYU, Ben Arous did cowrite The paper relating the Hamiltonian of spin glasses to the geometry of loss functions of NNs)

[narrow talon]

Not for a while I think

But this is why I got into math actually, came from music to work in AI assisted music production

Now I don’t care quite as much about it

[small garden]

really, I did something very similar actually

do you think it'll even matter when AI near equals us in composing?

[narrow talon]

Eh, cultural context is hard to really adapt to, definitely a far cry from where we are now

[small garden]

that's the main I think that'll keep it a stalemate for a long time

the bedroom musicians are f*cked 😂 but the most talented musicians will have a job

[narrow talon]

Bedroom musicians have been fucked long before sample RNN

[small garden]

ghostwriters 👌 👌 😎

[small garden]

HOLY SHIT I JUST REALIZED

what's the best book on group theory???

idc how technical it is I'll just use other resources to understand as I go

[velvet briar]

I mean different books for different points of view

Fraleigh is really easy but still is a proof based book

[sage python]

Rotman's got a good group theory book

[velvet briar]

A lot of people look to Chapter 0 because it includes category theory

Dummit and Foote is good for when you have trouble sleeping

[marble solar]

A primer on mapping class groups

Heh

[small garden]

thank you

[small garden]

it would've taken forever for a future version of myself to look back and wish I knew about stuff like that earlier

@sage python @velvet briar thank you for your suggestions

[manic fox]

its best to learn from different sources

always try to keep an eye on wikipedia for what ur learning too

the "standard" development of a topic is usually there

[gray gazelle]

Susanna S. Epp's Discrete is also good.

I'd say for both math majors and cs majors.

It'll make you dip your toe in the water.

[tiny elk]

Hey guys! Do you think Apostol is a good choice for an EE indergrad?

*undergrad

[karmic thorn]

Apostol's calculus V1 has mixed reviews, you can skim a bit to see if it works for you. V2 has better reviews, and his analysis book is encyclopedic.

[manic fox]

very dry book

just going to put that in there

[tiny elk]

I see

Any good book rigorous books that aid both math and engineering and physics?

[manic fox]

try paul's online notes for calc.

[tiny elk]

Calculus that is

[manic fox]

categories in context by riehl bro

[tiny elk]

I've seen some of them. They are good

[tiny elk]

Is that a texbook?

[karmic thorn]

Not a serious suggestion

[manic fox]

meme recommendation

[karmic thorn]

But Paul's Online Math Notes should do the trick. You can also look at MIT OCW single variable calculus course.

The website has notes and PSets, as well as recorded video lectures.

[tiny elk]

I appreciate your recommendations, but I'm in search for textbook

[karmic thorn]

Then you could try Thomas' Calculus

Can you share your curriculum, in any case?

[tiny elk]

I heard Thomas' Calc is watered down

At least the new editions

Is that true

[karmic thorn]

Well, I can't tell without looking at what your curriculum covers

But for any non-proofs course in calculus

It should be good

[tiny elk]

I don't have my curriculum yet, I'm about to join college this year

[karmic thorn]

Ah

Okay

Then you could check out a few books and pick whichever you like?

[tiny elk]

I see

[karmic thorn]

Spivak is the standard rec for proper calculus

[tiny elk]

Of course

[karmic thorn]

Thomas' mostly for those not intending to major in math

[tiny elk]

A good prereq for Spivak that covers applications would be?

[karmic thorn]

You don't really need to know calculus going in

[tiny elk]

Oh

[karmic thorn]

But the book itself will take time to digest

[tiny elk]

I see

[karmic thorn]

That is a consequence of inherent difficulty, don't get bogged down

You can always ask for help if you're stuck on a certain problem, in accordance with #❓how-to-get-help

[tiny elk]

Alright

[karmic thorn]

Yeah, I suppose its alright at what it's supposed to do

[tiny elk]

What about courant?

[karmic thorn]

Never tried it

In any case

Skim through the first few pages

And see what floats your boat

[tiny elk]

Right

Good advice

Thanks man

[karmic thorn]

No worries. Goodluck!

[narrow talon]

Friend of mine, also in EE, used courant and loved it

[undone pine]

Does someone know a good book on real analysis counter examples?

I know this one

[manic fox]

ur brain

[wintry lotus]

Hello

Does anyone know of books or papers strictly concerned with the concept of dimensionality in fractal geometry/geometric measure theory?

[heavy pebble]

Hi does anyone know where I can get Thomas' Calculus, 14th Edition solutions?

[prisma snow]

In your brain :)

[heavy pebble]

I'm trying to practice as much I could but idk how to check my answers to see whether Im doing it right

[prisma snow]

Send the ones you are unsure about here

It's better to have someone individually check it and give feedback anyway

[static crest]

don't mention that on this server

[karmic thorn]

@crude iris We cannot endorse piracy in any form here due to Discord ToS. :(

[heavy pebble]

Sorry bout that

[karmic thorn]

It's alright, just be careful in future.

[heavy pebble]

Will do, thanks

[heavy pebble]

Sure. cheers

[karmic thorn]

[past storm]

hey i'm in 11th grade rn and i'd like to advance a bit on maths to get a head start for uni and stuff. What maths books do you guys recommend in general?

[willow pecan]

What sort of math do you know?

[marble solar]

Spivak's Calculus is good

[gray gazelle]

where do I find solutions to the exercises in bourbaki?

go outside to an open field

sit down with your legs out in front of you, and reach and grab your feet

then scream at the top of your lungs until someone calls the cops on you

[flint forge]

your best bet is google and failing that asking here whether your proof is fine

[gray gazelle]

alright thanks

[civic carbon]

I have more than once had to cite an exercise in a text in a paper

[willow pecan]

This is not the channel for math help

[wintry lotus]

Sorry, I missed the title

[vagrant sedge]

Hi... Is there a book that is sort of like "the algebra a numerical analyst needs" (but focused on stuff mostly other than linear algebra)?

[willow pecan]

Depending on what sort of numerical analysis you want to do, none to a lot

No satisfactory answer, I'm afraid

[vagrant sedge]

Seriously? I could be a lot? That is actually very much surprising to me.

[willow pecan]

For example, people working in numerical methods for odes/pdes use very little algebra

[vagrant sedge]

I was expecting "Nahh... it's mostly linear algebra"

[willow pecan]

Algorithm optimization in numerical linear algebra touches a bit on analysis on locally compact abelian groups

You have Fourier transforms which can be viewed algebraically

Nonlinear algebra/geometric programming relies very heavily on algebraic geometry

[vagrant sedge]

Cool. Any recommendations on the subject of geometric programming?

[past storm]

calc 1, a bit of linear algebra, bit of complex analysis

not too much outside of the standard curriculum

[willow pecan]

Ideals, Varities, and Algorithms by Cox, O'Shea, and Little is a classic

Sturmfels also has an Invitation to Nonlinear Algebra

You should learn more linear algebra

Try Friedburg

[past storm]

Thanks a lot!

[vagrant sedge]

Thank you

[dapper root]

Bruh what are you recommending this to an 11th grader??

[obsidian valley]

perfect time to start Hartshorne I think

[broken meadow]

lol

[dapper root]

Or was that a recc to phao?

[willow pecan]

It was for phao

Friedburg was recommended to Alvaro0

[dapper root]

Okay lmao

[willow pecan]

Admittedly, two book requests were resolved at the same time

But I think it was clear from context

[prisma snow]

But things need to be made extra clear to chmonkey :/

[sacred swan]

linear algebra and elementary proofs are a good way to get a bit of a head start. But I also recommend you just kinda explore around and see what interests you

As far as books go, "Book of Proof" is free online by the author and I've heard good things about "Linear Algebra and it's Applications" being pretty decent but haven't read it myself

[livid ermine]

i'm reading combinatorics through discovery and I really like it

I don't think it contains anything that couldnt be done or appreciated by an 11th grader

its a pretty natural playground to practice more general techniques like proof by induction as well

.

that reminds me, I wanted to ask if anyone knows a good second intro combinatorics book, if that is a category that exists lol

i looked at combinatorics and graph theory by harris and a walk through combinatorics by bona

are those good?

[warm glen]

i dont know about the two you mentioned but it seems like "bijective combinatorics" by loehr qualifies as a second intro book

it goes more into the direction of enumerative and algebraic combinatorics

actually i do know bona, that is indeed a good and widely used book

also i agree about combinatorics thru discovery, i disliked that book too

[broken meadow]

well

[true veldt]

wtf

[broken meadow]

this is one way to do it

[willow pecan]

[glad prairie]

when you find out #book-recommendations is a top

[tulip blade]

A walk through combinatorics is good and contains a lot more material than could be covered in a semester.

[gray gazelle]

If you know Calculus I and II, Hubbard and Hubbard’s Vector Calculus, Linear Algebra, and Differential Forms: A Unified Approach is really nice

[outer olive]

Any books for abstract algebra

[broken meadow]

#book-recommendations message

[gray gazelle]

Fraleigh is a nice introduction, but probably a bit basic? I’m not through with it yet

[tulip blade]

Fraleigh is fine

Id use a different book though

Exercises in fraleigh are easy

[crude iris]

https://g.co/kgs/gyJ5Rv

I found this book it briefly introduces the topic and gives recommended books for further reading in each topic

[willow pecan]

[uncut zealot]

Pinter is good for a first introduction.

[tulip blade]

Aluffi ch.0

[static crest]

no

[gray gazelle]

Godement's algebra

[velvet briar]

@sage python
I see you've said Knapp looks promising. Have you changed your opinion on it in the last year?

[sage kelp]

What is a good introductory book for number theory? My goal is to develop math maturity

[tulip blade]

If youre an econ guy maybe analysis would be better

[gray gazelle]

Weil's book

[sage kelp]

I actually started reading Abbott's analysis book, but it's crazy. Been enjoying it a lot actually, but maybe thought I could benefit more gaining some maturity first

[timber mesa]

I liked Burton's Elementary Number Theory, is good is you're just starting with proofs and the such

[sage kelp]

So would it be better to start with number theory before approaching real analysis?

[karmic thorn]

Depends on your background, most places still use analysis and linear algebra as a first proof-based math course. I think it would be equally okay to start with introductory analysis.

[sage python]

I haven't looked at it more, I still think it's good?

[karmic thorn]

Yeah, Abbott seems great for an introduction.

[tulip blade]

No im not sure why itd be better to do number theory first

[sage python]

Oh I was responding to Kaynex about Knapp

@velvet briar

The thing I like personally is that it does some noncommutative algebra

[sage kelp]

I don't have that much rigorous math backgroud. I just finished Velleman's book, but that's it. Just trying to figure out whether I should continue with number theory or real analysis

[karmic thorn]

See what works out better for you. Both are fine subjects for learning proofs in context.

(I would say analysis is inherently difficult as a subject too, but that's just how math is)

So even if you can't figure out ideas in the beginning, it's alright, you can ask for help here in accordance with #❓how-to-get-help .

[sage kelp]

I am looking something readable where I can learn proofs in context

[tulip blade]

Just pick a book tbh all the ones suggested are probably fine

Reading math isnt like a novel youll have to struggle with the material to gain understanding and mathematical maturity

[solemn mantle]

How is Lang for grad level algebra

I see the pins but I can’t decide between him and the others

[willow pecan]

I've heard some people talk about Lang

[solemn mantle]

Does he cover everything thoroughly and al that

[willow pecan]

And they weren't saying anything good

[solemn mantle]

Rly?

Oh

[willow pecan]

Apparently lots of skipped details in proofs

[sage python]

Lang I've used for exactly one thing

Namely when I was like "Wait how does 'raw' field theory work? Stuff like existence of algebraic closure etc"

[solemn mantle]

What is a solid book that covers everything completely (is that even a thing?)

Ohh I see

[sage python]

The local impression I got is that it's pretty clean

But he used a piece of terminology that pissed me off

I don't remember what offhand

[willow pecan]

D&F is a comprehensive book

[solemn mantle]

Yeah he seems to have some strange terminology

Ok

Anything that’s like, not dry but also thorough?

[willow pecan]

D&F may be dry, but only because it is too thorough

[solemn mantle]

Ah

[sage python]

Try Jacobson or Knapp

[solemn mantle]

Is it true that the choice of book doesn’t really matter long term (as long as you don’t choose an absolutely terrible one) bc you’ll just learn everything anyway

Or does book choice matter a lot

[solemn mantle]

Alright

[sage python]

People here seem to like Rotman but idk it

[velvet briar]

I like how it's called "basic algebra" and the last chapter is modules over non-commutative rings oof

Book looks pretty cool though I'll read a bit of it

[storm harness]

In what way (if any) is workingmacat outdated if I wanna learn cat thy?

I've read 3 chapters and I like how it's written

Are there some important things that he doesn't cover? Then could I read those separately for riehl?

Talking about mac lane

[willow pecan]

It should be fine

[storm harness]

Ty

[gray gazelle]

all algebra books r dry

[broken meadow]

certainly not

if you toss a print version of artin in the ocean

it will become very not dry

[sage python]

That's my boy

[broken meadow]

learning from the best

[karmic thorn]

Artin is so dry, it could soak up the ocean and still be dry.

[broken meadow]

lmao

badlands chugs the ocean vibes

[solemn mantle]

Lol check out Weil’s “Basic Number Theory”. Part I (“Elementary Theory”) starts with a chapter on locally compact fields, and proceeds to discuss adeles, zeta functions and the Riemann-Roch theorem

[sacred swan]

I know Mathematical Philosophy is technically a branch of philosophy, but does anyone have any recommendations for an introduction to this topic?

[livid ermine]

why did you dislike it? or did you misspeak?

[gray gazelle]

Ask a philosophy discord server?

[warm glen]

oh my bad i misread not misspoke

[warm glen]

i did dislike it and i thought u said u did too woops

[livid ermine]

what did you dislike about it?

the only problem I have with it is that I think it could restate core results once in a while. often after a question it will say "you've just proved the xyz-formula!", and you'll feel like "hmmm, have i? are you sure?"

which is slightly frustrating as it makes you second guess yourself a lot

[warm glen]

ah it's nothing that specific for me i just didn't enjoy reading/working thru it at all so i didn't get very far before stopping

not that math books are particularly enjoyable but this one was just less enjoyable than average somehow

[livid ermine]

thats interesting

what is a book you think is above average?

[raw pawn]

guys what should i read after apostol calculus volumes 1 and 2?

[gray gazelle]

What's your goal?

[raw pawn]

just increase overall mathematical knowledge

think im going to go with Rudins analysis textbook

[lament sparrow]

What are some good introductory books on proof writing?

I'm trying to learn Trigonometry and Linear Algebra which would involve Calculus and got recommended that I start with proof writing...

I have no idea what proof writing is all about.

Unless its the same as what I was taught in Geometry class in High School (Hence Proved?), I assume that this would be more in general.

Background:-
The most bare basic High School math (no Calc), flunked Trig because I was unable to cram all the identities, also probably forgot most of the things so going through Khan Academy (currently Halfway through Algebra 1, hath been a smooth sailing ride)

A little bit of sequential logic, introductory set and graph theory (which isn't much I think).

[glossy grove]

There is that nice thing, called "Book of Proof", that's free on the internet. You could read a little into that, and it basically assumes no prior knowledge at all.

[gray gazelle]

Book of Proof, Hammack.

How to Prove It by velleman

[glossy grove]

http://www.people.vcu.edu/~rhammack/BookOfProof/BookOfProof.pdf

[gray gazelle]

this book looks really good

yeah velleman is too wordy

hammack is better

its not too wordy

well i saw so

[lament sparrow]

Should I finish off Compound Statements before starting this?

[glossy grove]

I have no idea what that is, sorry, my English is just too great.

Ahh, it's just logic.

That's introduced in the book, too.

[sage kelp]

Velleman’s book How To Prove It is excellent

[buoyant crater]

hammocks book is rlly good

[lament sparrow]

Alright thanks for all the responses.

[marble solar]

🤮

I don't understand the introduction to proof books

Just like, start reading math and trying it

[livid ermine]

most intro to proof books cover logic, set theory, basic discrete maths as well as proof techniques. i think its very useful

[marble solar]

Yeah, but why not just start with linear algebra or real analysis

Just try to pick up as you go along

[manic fox]

proof books are literally a waste of time

[sage kelp]

I disagree. Those intro books just give you the tools to understand the structure of a proof. I think that once you have that, then you can adventure yourself in math and start learning by doing

[glossy grove]

If you read a proof though, you figure out the structure of a proof as well.

[manic fox]

proofs are intuitive tho

i never used a proof book and well

[livid ermine]

you could say that about anything tho, like "why do real analysis or linear algebra, just learn differential geometry and pick up what you need as you go along"

[manic fox]

im doing just fine

[manic fox]

learning proofs is not that big of a step. You don't need all the bigger theorems and definitions down.

But real analysis and lin alg do have big theorems you need to do stuff in diff geo, so you can't really pick it up along the way. Tho really i guess you could, it just wouldn't be very efficient

[tulip blade]

that isnt the same

[manic fox]

[livid ermine]

really neither of you is gonna say how they're not the same?

[manic fox]

.

[tulip blade]

you need to know analysis before you start doing analysis on manifolds

I dont think proof books are necessary but if you need it then do it. I did take one and thought it was a waste I wish it wasnt required at my school/

[manic fox]

You can very definitely nose around wrt proofs and follow what you think is right

My only intro to proofs was lke the first 5 pages of apostol's book

the material needed to do proofs is not very lengthy, you need just to develop some good intuition and a nose for solving problems. You do this by actually solving problems in nature and not spamming artificial ENT problems in a proof book

[livid ermine]

i guess its a difference in degree. but like i said, most proof books go over other things than just proof techniques, like logic, set theory, languages, graph theory, combinatorics etc. Stuff it will make it a lot easier to work with in other contexts, if you've seen them before.

I think the fact that the problems are artificial is good.

This might just be me, but personally, I often found it quite hard to know exactly which "resolution" to spell out a proof in. I think this is the case for a lot of newbie math people

[tulip blade]

I wouldnt really look at the graph theory and stuff in those books

[manic fox]

Like look

[livid ermine]

in a book like vellmans, there is no such ambiguity, because the objects you deal with are incredibly elementary

[tulip blade]

you should probably get the stuff that is necessary and move on

[manic fox]

you have to rip off the training wheels some point in time

There are only a few techniques you spam over and over

[marble solar]

Unironically my opinion. If you want to do diff geo just go for it

Pick up the other stuff along the way

[manic fox]

And the issue is how to approach the problem in a clever enough way.

this is specific to the problem/field at hand usually

[flint forge]

theres a similar adage when learning to program that like

the best way to learn is to get excited about a project

and backfill

its not the worst strat in math esp. if ur self learning

but dragging yourself through an intro to proofs book is probably unnecessary unless you struggle in which case ofc you can just go back

[manic fox]

Like even though i can write a proof, im horrible at doing it when it comes to analysis, though im much better wrt algebra. A proof book won't teach me good analysis proof skills or whatever, analysis will. So the point is if you want to get good at or learn a subject, actually do that subject. The prereqs are very minimum wrt "proof knowledge"

[marble solar]

I think this is the way to go for self-learning

University courses will make sure you get a rounded education

[warm glen]

for combinatorics im not sure but in general, i think artin is really good

ive liked the little ive read of halmos' linear algebra book too

[late plinth]

anyone got a good resource to learn octave or matlab for numerical analysis?
the class im teaching expect us to self teach the two languages lol

[flint forge]

you should also learn math via books so i dont see what you mean. wanting to understand some specific thing is probably not a terrible way to start learning a languGe

[tulip blade]

https://mitpress.mit.edu/books/series/mit-press-essential-knowledge-series

A lot of very cool books

Recently became obsessed with these

[hearty steppe]

@narrow talon would you recommend Stein and Sharkarchi after I get up to chapter 8 of Baby Rudin or should I go straight for Casella and Berger?

Or does it matter what order I go in with those books

I think I got a decent strategy to maybe get through half of what I need to get thru in baby Rudin by the end of the year, maybe

I am more than happy if I get to chapter 4 by December

[marble solar]

You could probably read stein and shakarchi after chapter 7 of Rudin. There's not a whole lot of pre-req

You should make time to read Spivak's Calculus on Manifolds in one form or another

[hearty steppe]

Is there any overlap between the stein and shakarchi measure theory focused text and Casella and Berger Math Stat text?

Or maybe I’m thinking of the wrong book if it’s not stein and shakarchi

I’m going to still do chapter 7 first if I end up needing to read S&S

[gray gazelle]

helpppppppppppppppppppp

[broken meadow]

@gray gazelle don't multipost

see #❓how-to-get-help

[hearty steppe]

Yea I will at some point

[gray gazelle]

just read all 5 volumes of spivak's differential geometry

xd

including the part with riemann's original paper

[sudden kindle]

Xd

[tulip blade]

That book is meh

[flint forge]

its very good for what it wants to do

i think its the ideal book for undergrad math majors who take calculus

[sudden kindle]

Spivak Calculus on manifolds =/= spivak calculus

If there was a misunderstanding

[flint forge]

oh lmfaooooooo

i didnt finish reading

thats on me

[gray gazelle]

Same

[sour venture]

Is there a sticky with all the mathematical knowledge with sections and stuff

Like compilation of books

[willow pecan]

No

There is too much mathematical knowledge

But you can take a look through #books-old for some recommended ones

As well as the pinned posts here

#books-old is kind of outdated

[sour venture]

Oh ok thank you

[tulip blade]

Prob should expand it

[willow pecan]

Also I disagree with some of the things in #books-old

[tulip blade]

Had combo, graph theory, diff geo etc

[willow pecan]

I would never recommend Rudin to anyone

[tulip blade]

Id add pugh to analysis i love that book

[static crest]

kekw

@ tterra

[willow pecan]

@gray gazelle

Coward

[static crest]

I didn't want to scar him

it was out of respect

not out of cowardice

[gray gazelle]

?

[viral hill]

is Rudin Analysis bad?

[static crest]

@gray gazelle .

[gray gazelle]

ok

[hearty steppe]

I feel like I’m starting to enjoy Rudin

[gray gazelle]

people are allowed to like the book

i personally dislike pugh

mostly due to that class i took

[willow pecan]

I'm not saying that people can't like Rudin

[static crest]

lol that class was something else

[willow pecan]

I'm saying that it is not good from a pedagogy perspective

[gray gazelle]

mat357

[hearty steppe]

Rudin is hard but it’s a book that forces you to interact with the thereoms and examples and use other analysis books to crack the reasoning behind them

It’s kinda woke

[gray gazelle]

why not just use another book at that point xd

[willow pecan]

Books should be self-contained

"I'm going to write a book but skip all the details so anyone who reads my book needs more books to understand anything"

What a disaster

[gray gazelle]

i'm going to be completely off-topic but i just managed to turn two pages of index pushing into a third of a page with no coordinates whatsoever :catglad:

i am proud of this

[willow pecan]

:catglad:

[hearty steppe]

How is it a disaster

[gray gazelle]

so nice

[hearty steppe]

What book did you use

[static crest]

2 pages of index pushing

[willow pecan]

It's the heat equation

I used Ross for undergrad analysis

Which is undesirable for other reasons

But at least it explains its examples and motivates things

[gray gazelle]

my index pushing was actually for the sake of proving the middle inequality

i just managed to tuck away the coordinates i guess

also oops one of my nablas is upside down

[static crest]

it's always very satisfying when you can ignore the coordinates

imagine having nablas

[gray gazelle]

all of these exercises are making geometric analysis seem very appealing

is this lee's way of selling his field

[sage python]

Somehow "geometric analysis" seems epsilon more appealing than "differential geometry" lol

[broken meadow]

"differential" strikes me as ... dissonant

maybe it's all this time seeing "differential" used for stuff that looks annoying

[gray gazelle]

Differential algebra

[sudden kindle]

These are all just feelings.

[gray gazelle]

[sage kelp]

What's your opinion on Stillwell Elements of Algebra?

[marble solar]

yeah all of Rudin's books suck

[prisma snow]

Rotman for Algebra

[whole rain]

are you actually speaking to a french without insulting him ?

I feel discriminated

😔

[prisma snow]

Rotman Propoganda is more important

If he ends up using DF, then no holds barred

[whole rain]

fair

the server doesn't support piracy

so I definitely won't send you a link in PM

[marble solar]

Terry Taos notes for complex

[narrow talon]

They’re more or less independent. The only thing that is really needed from Rudin to read casella Berger is the maturity, but lots of CB is just calculus

[gray gazelle]

please tell me the best book for algebra 1,2 and for trignometry

[gray gazelle]

hey anybody there

[manic fox]

society

we almost always end up reccing paul's online notes for this kinda stuff haha

i believe there is an algebra section for notes

[gray gazelle]

ok thanks

[sharp latch]

Paul’s online math notes are clutch

[gray gazelle]

OK

[gray gazelle]

where to learn modules from

[gray gazelle]

??? lol blocked

[slim peak]

I just received the first of the six books I ordered to MyCopy SpringerLink's program. It's dope.

[gray gazelle]

I want more than d&f

[karmic thorn]

[slim peak]

I recommend it to anyone who wants good books for low price

[hasty turret]

Get the DLC

[storm harness]

Commutative or more general theory?

For commutative alg atiyah macdonald, for non commutative Jacobson is really good

[gray gazelle]

ty I will check it out

[storm harness]

I helped why am I still blocked

[prisma snow]

Can we just ban ledog until he unblocks us all?

[gray gazelle]

because you react to my msgs with stupid emotes

you told me to block you lunasong

[prisma snow]

No I did not

Unblock me

If that's all it takes

You have my permission

[storm harness]

My emotes are not stupid they are genuine expressions of my feelings

[prisma snow]

same

[willow pecan]

#chill

[narrow echo]

ty

[quick hornet]

ty

[wispy pebble]

ty

[crimson vector]

ty

[hearty steppe]

ty

[gray gazelle]

ty

[karmic thorn]

ty

[hasty turret]

ty

[languid garnet]

ty

[oblique holly]

Can someone please suggest me book to learn wolfram mathematica?

[willow pecan]

Mathematica stack exchange

Online documentation

[oblique holly]

Its tough to read online, if you can suggest any book that will be very helpful.

[gray gazelle]

Anyone recommends a book for finitistic/formalist foundations?

[opal prawn]

I just finished Advanced Functions and doing vectors currently. I want to learn some calculus over the summer. Any suggestions for books or other resources suitable for self-study?

[marble solar]

Spivak's Calculus

[quick hornet]

note that spivaks calc spends more time on proofs and rigour than a typical calc textbook

it teaches you how to do that stuff, so that doesnt make it unapproachable or anything

[marble solar]

That's my go to recommendation if someone is serious about math

or physics

[quick hornet]

but if you just care about learning computational calculus

its a lot of extra work

(work that ostensibly pays off in the long run if you take higher mathematics than calc)

(but most calc students dont)

for a more... standard calc book, there are like 50 billion on the planet

but by far the most common is Stewarts Calculus

and its fine

really expensive and bloated

but fine

[opal prawn]

I just want to prepare myself for HL Math next year, so any introductory book to calculus is fine

ty ill check those options!

[quick hornet]

if you ask 50 intro calc professors what textbook they use

half will say stewart

the other half will have 25 different books

so... theres not really consensus

[broken meadow]

larson ...

Disgusting

[quick hornet]

honestly i dont think it makes much difference though

just do lots of exercises and youll be fine

no matter what text you pick

[hasty turret]

idk much about engineering math,but what purpose is a computational calc course supposed to serve?

A bunch of number bashing doesn't help anyone

[quick hornet]

lots of fields just need to number bash

any field that uses stats for example

[willow pecan]

What does computational calc refer to

[quick hornet]

which is most of science

[willow pecan]

Computing integrals?

Integration by parts?

[hasty turret]

Calc 1,calc 2 etc

[willow pecan]

Calculating derivatives?

[hasty turret]

The calc series

[willow pecan]

These are important in numerical methods

Which engineers definitely need to know

Finite element methods are fancy integration by parts

[hasty turret]

Can't they just learn those things while doing numerical methods

Why do they need a separate class

[quick hornet]

you have to learn them to read spivak anyway

spivak is literally just extra work on top of that

[willow pecan]

Because it is sufficient content for another class

There is already too much to cover in numerical analysis classes

[quick hornet]

also yea thats true too