book-recommendations

[queen rampart]

I see

well I don't, but I should

[narrow talon]

Which leads to a lot more flexibility in Bayesian setting, but on the flip side a lot stays theory because implementation is harder

[queen rampart]

I don't like stuff with numbers

[smoky surge]

What do u mean by constant?

[smoky surge]

Here

[narrow talon]

In frequentist setting theta is just a parameter controlling a family of distributions. But in the Bayesian setting you’re trying to find a distribution over the parameter space and then make point estimates with that distribution over parameters

[queen rampart]

ooooh

[narrow talon]

Often times the mean, but not always

[queen rampart]

frequentist: param -> distribution(s)
bayesian: distribution -> params -> distribution(s)

[narrow talon]

Mode is another common one, or you ever hear of MAP that’s all it is, the mode of your distribution over params

[narrow talon]

Exactly

[queen rampart]

moist-ass p-word?

uh, I'm guess MAP is akin to maximal likelihood estimations

[narrow talon]

So prior/posterior refer to the distribution over the parameters and the prior can be constructed based on domain knowledge

[narrow talon]

Exactly, WAP is similar

[queen rampart]

up to isomorphism

[narrow talon]

(Maximum A Posteriori Estimation)

[queen rampart]

I've heard all those words independently, yus

[narrow talon]

Basically, the maximally occurring value of the distribution on the parameters after updating that distribution based on data is the estimate that we take

[queen rampart]

yep

[narrow talon]

The updated distribution is the posterior distribution, hence MAP

[queen rampart]

ty

[narrow talon]

A ton of current research (at least at NYU) is on Bayesian ML since it's becoming computationally feasible

[queen rampart]

most of the stuff my friends did was applied

[narrow talon]

It's also got a ton of really weird people who get a bit too obsessed with the philosophy of Bayesian statistics

[queen rampart]

someone did matrix factorisation, a bunch on cascade learning, etc

[narrow talon]

Gross

One day I'll learn more about Bayesian nonparametrics, maybe this summer

Van der Vaart has a book on it, seems up my alley

[wooden sparrow]

Hey, Ted recommend me LA by friedberg. Do you have any more suggestions to study LA from?

[narrow talon]

Peter Lax, Linear Algebra

for a second course*

[queen rampart]

linear algebra done right is the go-to
heard a lot of people recommend hoffman and kunze for a harder one

[narrow talon]

I don't love Hoffman and Kunze, so dry

Says the person who will use Rudin till he dies

[wooden sparrow]

Why second course? Is it required? I don't know much about LA BTW

[narrow talon]

Probably don't use Lax then. It's definitely geared towards a second course at the sophomore/senior level depending on your school

[queen rampart]

oh, so is this a first attempt at LA?

[narrow talon]

Straang Introduction to Linear Algebra is what to go with for a first pass imo

It covers all the stuff you'll use all the time

[queen rampart]

I couldn't vibe with strang, it was very...numerical focused?

we will be solving systems of equations and we will be solving lots of them

[narrow talon]

I think a numerical focus is good for LA, at least for a first course. Gotta be able to deal with a shit ton of numbers in a matrix pretty often

And makes it really nice to work through problems concretely

But if your vibe is keeping things super abstract then maybe not, I just like working through explicit computations to get a feel for things

[restive raptor]

I foudn Hoffman and Kunze was a good supplement for (parts of) a second course in linalg, because I could get intuition and big ideas from lecture, and they present the nitty-gritty well. I do not recommend it for self study with no other resources

[narrow talon]

I just think it's boring haha! To each their own

[restive raptor]

I mean yeah that's why I don't recommend it for self study

but if you just want to see a specific proof of a specific theorem you saw in lecture and nothing else, the boring aspect doesn't matter if the proof is good

[narrow talon]

I'mma go through all the problems in big Rudin (both halves) this summer if anyone feels like joining

[restive raptor]

that sounds hellish

[wooden sparrow]

Yeah. I just started watching 3b1b video about it

[restive raptor]

gl

[queen rampart]

I would, but alas my analysis probably isn't up to snuff

[queen rampart]

gilbert strang has MIT OCW lectures on youtube

I love 3b1b's LA series but if you want something more meaty

[wooden sparrow]

Isn't that a bit engineering oriented?

[restive raptor]

my profs course notes for analysis already had a ton of fantastic problems so I don't feel the need to do that, but it'll probably be a fantastic exercise

[queen rampart]

depends why you're doing LA

[wooden sparrow]

More, UG pure maths oriented interest

[restive raptor]

also to provide a mildly alternate perspective to this, I Think starting abstract is a good idea for linalg, because you can always easily generate/find computational examples, and abstraction really helps with the underlying conceptual understanding imo. I think axler is great for a first course

[queen rampart]

so you're looking more at vector spaces over arbitrary fields

rather than systems of linear equations

[willow pecan]

Lol Axler is something

[restive raptor]

do you not like it?

[willow pecan]

It's fine if you don't care about either determinants or characteristic polynomials

And those are important

[queen rampart]

then just read linear algebra done wrong at the same time

[wooden sparrow]

Yeahh. Friedberg starts with vector spaces

[queen rampart]

LADR leaves determinants to the final? chapter

and the first 3 or 4 are just going through abstract bases and subspaces and whatnot

whereas LADW's first chapter is on determinants

[willow pecan]

Sure but because it has determinants at the end everything that depends on characteristic polynomials is also messed up

And it's like

I don't know

[restive raptor]

axler covers these at the end though?

[willow pecan]

I don't get the dislike for determinants

And they are useful throughout linear algebra

[broken meadow]

wait people dont like determinants?

why

[willow pecan]

Axler doesn't

[wooden sparrow]

There are two books where one is done right and other wrong?

[broken meadow]

they don't seem that bad... why is determinant bad

[willow pecan]

Determinants are wonderful

[narrow talon]

Yeah, I already know all the stuff from the real section, so it'll just be for doing a lot more exercises in real analysis and learning the measure theoretic complex

[queen rampart]

done wrong is sort of a response to done right

[broken meadow]

yeah i thought reading about them in friedberg was cool

[queen rampart]

because, as you can see, people got angry that axler didn't cover determinants much

[narrow talon]

I don't necessarily agree

[restive raptor]

copy pasted from LADR:

The audacious title of this book deserves an explanation. Almost
all linear algebra books use determinants to prove that every linear operator on a finite-dimensional complex vector space has an eigenvalue.
Determinants are difficult, nonintuitive, and often defined without motivation. To prove the theorem about existence of eigenvalues on complex vector spaces, most books must define determinants, prove that a
linear map is not invertible if and only if its determinant equals 0, and
then define the characteristic polynomial. This tortuous (torturous?)
path gives students little feeling for why eigenvalues must exist.
In contrast, the simple determinant-free proofs presented here offer more insight. Once determinants have been banished to the end
of the book, a new route opens to the main goal of linear algebra—
understanding the structure of linear operators.

[queen rampart]

maybe my linalg knowledge is showing its holes..but I've never found something that properly unified solving systems of equations and the whole abstract nonsense

[narrow talon]

I think abstraction and big idea is just generally a bit easier to understand. Being able to translate to concrete examples is surprisingly hard and worthwhile

[queen rampart]

everything did 1 or 2 but never 1->2 or 2->1

[willow pecan]

Oh please

Axler's breath takingly (melo?)dramatic exposition serves to help no one

[restive raptor]

Yeah, I think that when working with abstract stuff you should absolutely regularly do concrete examples

and good exercises will also encourage that

[sage python]

See I get what Axler doesn't like

[restive raptor]

I personally agree with the message, if not the presentation. I saw determinants in high school and they were frustratingly obtuse and unintuitive. My linalg course did determinants sooner than axler does but still relatively late in the class, and I think students really benefited from it

[sage python]

Because students think of determinants not with multilinearity

But as take a matrix crunch them numbers

And obviously proving big ideas using an object that sounds to you like pure number crunching is fully unenlightening

[willow pecan]

Determinant = product of the eigenvalues

[broken meadow]

as for invertability and stuff i always had rank nullity and stuff

[sage python]

But the problem is that there is an excellent conceptual description of the determinant

Multilinearity

[broken meadow]

but i guess i understand what axler is saying about the eigenvalues stuff

i don't really get eigenvalues and whatnot with the determinants so hmm

i guess i will have to take a closer look at determinants one day

[queen rampart]

I was always ever taught determinants as a number to calculate

never any theory behind them

[willow pecan]

Diagonalize a matrix with a unitary one

[sage python]

Metal Catto when it's time for you to learn determinants let me know and I'll teach you how to think about them properly

[willow pecan]

$A=U\Lambda U^*$

[hasty eagle]

星雄

[restive raptor]

and this is how they're almost always taught

[willow pecan]

And then determinant is multiplicative

And unitary matrices have determinant 1

[queen rampart]

and I am very sad that's how I got taught them

[willow pecan]

And lambda is the diagonal matrix of eigenvalues

[sage python]

But yeah so Axler looks at a problem, namely that determinants are taught as number crunching

[queen rampart]

because I did them at a-level, then nothing for 7, 8 years

[wooden sparrow]

Wow

[sage python]

And are then used to prove conceptual things

[queen rampart]

and then I needed to start trying to compute with determinants as measures of volumes of transformations in my phd, and I was just....completely lost

[broken meadow]

wait i already finished up my first course in linear algebra so i guess.... i can start now or am i supposed to wait for some more stuff to learn

[sage python]

His solution is to nix determinants altogether

Rather than... teach them correctly

He also I think is kind of a "pure functional analyst"

Which is where he gets the incredibly misguided idea that the only place in undergrad math where determinants are useful is change of variables in integration

metal alright so, this week I might be busy

[restive raptor]

I personally really enjoyed and (I think) benefited from his approach, but you're probably right, teaching determinants the right way is a good way to do it as well

[sage python]

But unironically pester me in about a week

[restive raptor]

there was an r/math thread about this recently

[broken meadow]

oh alright i will then

[restive raptor]

https://www.reddit.com/r/math/comments/mx1dz4/what_is_a_good_definition_of_determinant/

[broken meadow]

ty daminark

[sage python]

And I'll teach you multilinear algebra

[broken meadow]

niceee

[sage python]

Yeah so that's the correct answer Nicholas

You just teach students exterior products

[restive raptor]

I didn't see exterior products in either of my linalg courses. The second was supposed to teach it, but we fell behind schedule during the pandemic and so didn't get to it

[queen rampart]

is it weird that I've never seen multilinear algebra, exterior products, etc mentinoed in linalg

only in other fields

[sage python]

It's not weird but it's unfortunate

[restive raptor]

I came across them in diffgeo

[sage python]

I think linear algebra classes should just amp it up and teach multilinear stuff

[restive raptor]

and then again now in fulton and harris, so I've been learning more and more about them

[queen rampart]

yeah, I saw them in tu's introduction to manifolds

[sage python]

Rather than spending n weeks on Gaussian elimination

[queen rampart]

and in seemingly every not-basics abstract algebra text

and in penrose's road to reality, a book almost a decade later I've still not managed to understand past chapter 10

[restive raptor]

@sage python My intro to linalg course basically followed axler and I really liked it. I wish linalg 2 had done multilinear algebras though

[sage python]

So, I learned it a bit funny

I had a class summer after first year which did a mix of linear algebra and graph theory

And it covered a fair bit. It was 3 weeks of linear algebra but 2 and a half hours a day, 5 days a week

[restive raptor]

wow that is a lot

[sage python]

There we did cover determinants more computationally

Or not computationally but

Our definition of the determinant was in terms of rook formations and all that

Thing is we mostly focused on it being multiplicative, alternating, multilinear

And overall I don't remember getting the sense that a lot of stuff we did was especially unenlightening

[narrow talon]

Whole ass I’m grading linear algebra right now

And there are people who think that the column space

[sage python]

Now that fall I took analysis, and first quarter of that class exempts you from the linear algebra requirement

[narrow talon]

Of a rank 3 matrix

Is a number

So chill on multi linear

[sage python]

Students who think that way will fail lol

[narrow talon]

People are worried about other stuff

[sage python]

And so they should if they're not good at linear algebra

[restive raptor]

My school has 4 versions of linalg; one for engineers, one for science, one for math majors, and an advanced one for math majors

I feel like the advanced one could do multilinear algebra

[sage python]

Yeah I mean obviously engineering students don't need to worry about multilinear stuff

But I'm fine with requiring that if math students are gonna succeed they better know their shit

@gray gazelle yeah so the "irl work" kinda has to be done somewhere, it's a matter of packaging. The problem is more when you only do number bashing and start proving significant things

Like oh linear endomorphisms of C^n have eigenvalues because beep boop boop beep this is 0

[restive raptor]

and yeah oh my god some of the stuff you see in an intro linalg course - some of my friends graded the not advanced one and 💀 my god

[narrow talon]

Lol, are you French?

[sage python]

No but if that's how French people do it I respect it

America's way too chill about letting students be bitches

[queen rampart]

nah the french just surrender

[willow pecan]

[narrow talon]

Yeah pretty much

[queen rampart]

american mathematics education seems so far behind everywhere else

[narrow talon]

Older French profs at least complain about how everyone else knows jack shit

[queen rampart]

I was doing 2nd order diff eqs at 16 and americans are doing pre-calc in university???

[sage python]

I mean eh I'm fine with people being behind in a way

Thing is you have to separate different types of problems

One problem the US has is that funding for K-12 schools is largely based on property taxes

[narrow talon]

Bruh I hated math until 17

Err, 16

[sage python]

So like if you grow up in the wrong neighborhood your education is crap

[narrow talon]

^

[sage python]

I think the right angle for good college to get at is

[queen rampart]

that's the least of the problems with america

[sage python]

Honestly it's arguably the biggest

[queen rampart]

no I think america has bigger problems than how they teach determinants

[sage python]

If you fix the problem of funding being garbage most of the time

[narrow talon]

Literally my education would’ve been entirely different if I lived 20 miles south

[sage python]

Oh I thought you meant funding isn't the problem

And I'm like lol

But yeah so my overall take is that

College is kind of a separate beast from K-12 but it does get students who came from K-12

So you have a weird balancing act where it's like

[willow pecan]

Coordinates are underrated

And I don't get why people hate on them

[sage python]

You simultaneously don't wanna shit on students who went to underfunded schools

[restive raptor]

one of my favourites is there was a problem like
"Show if u and v are nonzero vectors so that u is not a scalar multiple v, then u is not in the span of (u + v, 2u + 2v)."

So many students wrote "span{(u + v), (2u + 2v)} is the set of all vectors in the form a(u + v) + 2b(u + v) = (a + 2b)(u + v), so the span is c_1(u + v) for all constants c_1 in R. If u were in this span, then for some scalar c_1, u = c_1(u + v), but you cannot get u from u + v so QED"

[sage python]

But if someone's being a bitch they're being a bitch

And you wanna have standards

[restive raptor]

like students in linalg 1 often struggle with basic proofs, multilinear algebra is not a great idea unless it's an honours stream imo

[sage python]

I think, definitely the good schools, should have an overall policy where...

We expect you to be able to think

[dapper root]

Nicholas I took an "advanced linear algebra" class

which was an utter joke

[sage python]

We don't expect you to have much background

[dapper root]

I think that's where you should cover it

[narrow talon]

Lol, there’s a reaaaly weird difference between poor students, rich lazy students, and international students

[restive raptor]

yeah mine was quite easy too, and I agree

[narrow talon]

At NYU at least

[dapper root]

but also I think you should be teaching eg the tensor product to do multi linear stuff

and imagining teaching the tensor product to the kids in my class is

...

D:

[sage python]

So idk maybe I'm off here

But I feel like the solution is

[dapper root]

I just think schools don't have an actual hard linear algebra class

which is a mistake

[sage python]

Teach it and make it clear that they're expected to know it

Their grade is on the line

They'll figure it out

[restive raptor]

I think you're vastly overestimating the capabilities of the average linalg 1 student

[dapper root]

linalg 1 is mainly like

engineers

and cs students

even my "advanced" one

was primarily non-math majors

[restive raptor]

ok this wasn't the case at my school

[dapper root]

yeah :/

[narrow talon]

So you have students who struggle because they come from places with less education, students who want a degree but don't really care, normal students, and students who took analysis 1 freshman year of high school and balancing that is fucked.

[restive raptor]

at my school as mentioend there are 4 linalg; eng, science, math, advanced for math

What did your advanced linalg cover chmonkey?

[dapper root]

pfffft

[narrow talon]

Nah, we covered lots of shit in honors linalg

[dapper root]

we did like "abstract" linear alg

which meant

we can't say field

[narrow talon]

All of Straang and like half of Lax

[dapper root]

but we define one and put it in that context

[sage python]

Yeah Jason it's hard. Honestly the correct answer in the abstract is fix equity in early education

[dapper root]

since I think the earlier Lin alg is basically just matrices and over R^n

[sage python]

So everyone gets a decent quality education early on

[dapper root]

then uhhh, we covered some crap, i don't really remember man

[sage python]

So by the time you're in college if you can't pull it off it's on you

[dapper root]

we did cover some canonical forms

and like eigenbases but

It was a waste of time, and I slept in it lol

[restive raptor]

yeah that sounds about like mine except we used the word field

[sage python]

UChicago's got an honestly decent strat for that

There's math for econ and math for physical sciences

They cover linear algebra whenever they cover it

And then if you're in the math track you learn proofs in calculus, before you touch linear algebra

So you either do abstract linear algebra, which tbf doesn't cover multilinear algebra either but it's only a 10 week course so I kinda forgive that

Or you do honors analysis which is basically "swim bitch"

[restive raptor]

yep! that's the same at my school. our calculus 1 has proofs, and we also have a course called "intro to algebra" which covers like basic proofs and number theory. Both of those also have advanced versions; advanced calculus 1 is basically analysis, advanced intro to algebra is either a deep dive into some algebraic number theory, a mix of abstract algebra and number theory, a mix of set theory, abstract algebra and number theory, or something else

linalg is taken in the second semester after you've done both of those

so you should know how to write a good proof

[narrow talon]

I'm really not so sure. I really disliked math courses even after coming to do mathematic but went for it because I knew independent of courses that I was passionate about it. But if I was on the fence and faced with sink or swim, especially through LinAl or analysis, I'd fucking dip and then there's even less people funding the math department

[restive raptor]

idk, my school kinda has "sink or swim" courses and our math faculty has like 8000 students

[sage python]

I guess in my mind funding for the math department shouldn't be tied to the enrollment in a way that losing one student influences your ability to do anything other than teach that one student

[restive raptor]

although granted, here you apply for specifically the math or CS program out of high school, you can't like start as a "general student" or anything then declare a math major

[narrow talon]

I still want to have a linear algebra course which teaches Lie groups

[restive raptor]

and u(t) definitely has sink or swim courses

[sage python]

Like that's the thing, obviously math department can offer courses to students in other majors

And in a service course you're teaching to their terms rather than your own

[narrow talon]

what's that quote? The amount of funding a math program has is directly dependent on the number of engineers taking it's introductory courses

[restive raptor]

this is just false, it might be the case at your uni but definitely isn't at mine

[sage python]

Canada works differently from the US overall, though US has a lot of variation

Well Jason in the thing I outlined above there were options for math for engineers

And that class sure you teach it to the demands of engineers

[narrow talon]

It's a quote from an MIT prof in the 90s or so? pretty famous mathematician

[sage python]

But what I think shouldn't be the case is that math feels the need not to teach its courses on its terms because of funding you know? Obviously if you turn everyone away that's sus

[restive raptor]

Sure but that just doesn't apply

like, here the math majors take 0 courses in common with engineering majors

[sage python]

But like, in principle what should be the case is

Yeah what Nicholas is talking about is what should be the case

[restive raptor]

unless the math student enrolls in a physics course as an elective or whatever

we have 5 different versions of calc 1

[sage python]

Nicholas is in Canada

[restive raptor]

sure but most of the courses taken in the math faculty are by math faculty students

[sage python]

But yeah let me clarify how I think it should be

[narrow talon]

I'm really not so sure if they should be so independent. I suppose I lean about as applied as any pure math person can, but I honestly wish I was required to take more engineering and physics courses to supplement my courses.

[sage python]

There's some set of "Math for not math people"

And it's taught to their needs

And then there's math for math people

[narrow talon]

I guess that I would lean towards the way MIT does it, having different tracks for different types of math people

[restive raptor]

no, math faculty offers calculus courses for eng students, but 'm saying that's not where the funding comes from

the funding comes from the 8000 students enrolled in the math faculty who take math faculty courses for all n years of their degree

[sage python]

And if you're in a math for math people class then I'm fine with saying

Yeah we've got standards if you don't like it you can walk right out

Nick are you mixing between the different campuses?

[restive raptor]

I'm at watelroo not u(t)

[sage python]

I think UT has 3 of them right?

[restive raptor]

waterloo has only one campus

[sage python]

Oh

How big is Waterloo overall?

[restive raptor]

38k students

[sage python]

I guess Waterloo is more specialized math/science right? And it's huge apparently lol

[restive raptor]

we have 8k math students, 10k eng students and 6k sci students

[sage python]

Yeah, UChicago is a weird special case because math is actually the second biggest major after economics lol

[restive raptor]

also it should be noted that here, CS is under the math faculty

about 2500 CS students in total - wait no this year there are suddenly 3000 lol

[sage python]

That's very few given Waterloo's CS rep

[restive raptor]

it's selective

[sage python]

Gotcha

[restive raptor]

there are 4648 undergraduate students in math but not CS right now

[narrow talon]

CS has taken over in the US it seems

God I hate “cs math”

Like, cs people approach math differently and it’s terrible

[restive raptor]

our CS students need to take the courses that the math majors take

[narrow talon]

I’m talking advanced course

[gray gazelle]

Oh?

[narrow talon]

Data science courses that I’m in are run primarily by cs faculty and their math can be so confusing

[gray gazelle]

UC Hicago

[narrow talon]

Not terrible in a legitimately bad sort of way, terrible in a I don’t understand the difference in notation and goals sort of way

[restive raptor]

@gray gazelle I realized I accidentally counted grad students too; the updated numbers are 7475 students in the math faculty, and 4648 undergraduate math students who are not CS students

[narrow talon]

My good DS prof uses completely different notation and focuses on aspects which I would find unimportant in a math class

My bad DS prof is incomprehensible

[sage python]

Yeah Waterloo seems actually quality unlike a lot of American schools

Speaking of data science I need to do a few hours of Python prep for a data science thing starting tomorrow

And I'm so lazy lol

[narrow talon]

What data science thing?

[restive raptor]

I mean I would hope so considering it's consistently ranked as one of the top 3 canadian undergrad math programs

[narrow talon]

I have to program a NN from scratch this week, it’s not that bad but OOP is weird to me still

[sage python]

Erdos Institute, they're doing a data science bootcamp

[narrow talon]

Oh cool, is it intro DS or ML stuff?

[sage python]

I think it's fairly introductory?

[gray gazelle]

I'm not sure if dami is talking about comparing waterloo to generic US schools or top american schools

[sage python]

Nah I was thinking relative to generic tbh

[restive raptor]

idk waterloo created a dedicated math faculty a while ago, like back in the 60's, so it's had a long time to grow

[sage python]

US is very top heavy

[narrow talon]

I can see myself doing research in ML, some potential theoretic deep learning like Grant Rotskoff or Eric Vanden rings Fien much

Lol autocorrect

[sage python]

Or I mean idk what I find in the US is this

You have the top schools and the top big public schools

[restive raptor]

also for buncho I counted our number of students at one point

30 profs and 2 lecturers in applied math
28 profs and 3 lecturers in pure math
54 profs and 9 lecturers in stats and actuarial science
33 profs/lecturers in combinatorics and optimization, breakdown is not listed, everyone is just called "faculty"
89 profs and 21 lecturers in computer science

[sage python]

And they're all quite good

[narrow talon]

Jesus, that’s insane

[sage python]

Oh stats also counts as math

[narrow talon]

NYU is ranked #1 in applied math and has like, a quarter of the profs in total

[sage python]

Okay yeah that makes the skew less surprising to me lol

[queen rampart]

and then you look at the UK and the current news is that a bunch of unis are completely removing their mathematics departments and making everyone redundant

[sage python]

I was still a bit surprised that math is so much higher than CS lol

A bunch? I only knew of one

[queen rampart]

leicester, uh

[sage python]

But yeah so what I was saying about the US is

[restive raptor]

@sage python if you remove stats and actuarial science, there are still 3807 math students, but lots of first years probably just haven't declared yet

[sage python]

You have all the really really good public schools

And obviously you have the top of the line places

[prisma snow]

Scary. Soon the UK will just remove its mathematicians.

Goodbye, you're french now

[sage python]

Those are all good. Like the good math students have great acceleration opportunities

[restive raptor]

in upper years, it looks like about 30% of students are in actuarial science/statistics

[queen rampart]

I wish I could go back 8 eyars and do pure maths

[sage python]

And overall there's a sentiment that within reason you gotta carry your weight and actually work

[queen rampart]

and do a phd in abstract bullshite

so abstract even nlab doesn't know what I'm talking about

[restive raptor]

I think the best Canadian schools are usually like your top public schools, at least from what I've seen - we don't really have things comparable to your top private schools

[queen rampart]

putting mochizuki to shame

[sage python]

I think it's less tough than people make it out to be, I remembered commenting to my calc students the other day that As are basically free at Harvard and they were quite surprised

[gray gazelle]

Is it too late to do math for you now?

[sage python]

Nicholas that sounds about right tbh

[queen rampart]

no, fortunately. that's why I'm here, actually.

[restive raptor]

like U(t) and Waterloo CS and math feel a lot like Berkeley from what I've seen and what I see about course material and graduate job placement

[sage python]

Like I vaguely have Toronto in mind as having similar quality to Michigan

[queen rampart]

but it's having to be a hobby thing.

[prisma snow]

How old are you Kitty and what's your math background? Just curious, you don't have to say

[gray gazelle]

What does it mean"quality"?

[queen rampart]

uh, is this predominantly US-ian?

[prisma snow]

And do you prefer Pretty, Princess or Kitty. I hope not Princess because I'm not calling you that lol.

[gray gazelle]

Probably like a 40 year old fuck

[queen rampart]

PPK, kitty, sloot, avery - any of the above work

[prisma snow]

Cool

[sage python]

My idea of quality is like, good training of students and good research being done

I say training instead of teaching because I don't wanna comment on pedagogical practices

[gray gazelle]

Oh, @queen rampart is it okay if I call you princess?

[queen rampart]

yeah if you want lmao

[sage python]

So more like, do they send out people who are vaguely competent?

[queen rampart]

so I was a 'gifted' kid, I finished GCSE maths (age 16) at 14 and a-level maths and further maths at 16/17; did CS undergrad, then straight from bachelors into a phd in computational biology
so my maths was basically all numerical in school, then obviously you get thrown in with basic linalg proofs and natural deduction and plenty of discrete-ness in university, bits and bobs of stats to get a solid hold on ML

always wanted to learn maths "properly", I think I took out copies of spivak's calculus and axler's LADR from the uni library 6 or 7 times through my undergrad but because I felt I KNEW half the stuff already I would jump ahead and skip exercises and therefore get completely lost

and for the past month, I've tried for what seems like the 10th? 11th? time to "properly" do maths; it's far too late to e,g. rigorously do differential geometry for my phd (which would've been great) but I'd still love to be able to, as a hobby, understand all the theoretical underpinnings of black holes or what nLab talks about, for instance

[restive raptor]

I'm pretty sure that people who graduate from u(t) math spec are more than vaguely competent on average

[queen rampart]

that's kind of a wall of text so enjoy

[sage python]

That wasn't commenting on these schools lol

[queen rampart]

for some reason, this time around my reading what should be fairly elementary textbooks has stuck

[sage python]

It was responding to 8da on how I'm measuring quality

I also think Michigan grads tend to be solid lol

[restive raptor]

Yeah, I was confirming by that measure u(t) should be relatively high quality

I know nothing about Michigan other than they have a great eng program

[sage python]

Michigan in my mind is firmly top 10 math

[restive raptor]

ah ok

[queen rampart]

(if you want me to move to one of the discussion channels I'm happy to)

[sage python]

Lol yeah this is a book recommendation channel lmao

Anyone want a book rec?

[ripe granite]

me

gib book

[sage python]

Lmao lurking

Automorphic Forms and Representations by Bump

http://wwwf.imperial.ac.uk/~buzzard/MSRI/Whitehouse_tf.pdf

Also "The Spectrum of Hyperbolic Surfaces" by Bergeron

Bergeron talks a bit about QUE

[prisma snow]

You've got this!

[glossy grove]

Is downloading this legal?

[ripe granite]

no

[sage python]

Lmao

These are public notes

[glossy grove]

I take that as a yes.

[ripe granite]

[glossy grove]

The EU

[ripe granite]

ewwwwww

[sage python]

Why would you unironically be European lmfaoooo

[south ferry]

lol, imagine piracy being illegal in your country

[glossy grove]

I know, what a weird concept.

[south ferry]

on that note, what book would you recommend for multivariable analysis?

[glossy grove]

posts another pdf

[queen rampart]

zorich

it's either right at the end of analysis I or the start of analysis II

but he has some 150 pages on it

[south ferry]

i opened it and i see physics

[queen rampart]

...zorich's mathematical analysis?

[gray gazelle]

I thought you've done multivariable analysis.

[south ferry]

probably just the motivation

[south ferry]

i've failed a couple of times

[gray gazelle]

Been there

[south ferry]

numbers hard

[glossy grove]

[queen rampart]

oh, zorich definitely does motivation

he does a lot about error approximation in vol 1

and errors of sequences as approximations

[glossy grove]

are you talking about this? https://www.amazon.com/Mathematical-Analysis-Universitext-V-Zorich/dp/3662569558

[queen rampart]

yes

but there's a vol 2

[gray gazelle]

What do you want to cover? Personally I liked Spivak's Calculus on Manifolds, which is what you might need.

[queen rampart]

is calc on manifolds different to multivariable?

I thought it was like, multi-multivariable

[south ferry]

i might need slightly more, but i will check it out, thanks

[queen rampart]

since we're talking book recs, here's what I'm currently thinking of plus topics I have no idea what to read for:
analysis - knapp
algebra - knapp, rotman
linear algebra - ??? I've read the first 4 chapters of axler like 5 times now please something else
model theory, computability, etc - ???
topology - lee and the category theory one too, maybe supplementing with willard? I cannot grok munkres
cat theory - riehl and the topology one
manifolds/diffgeom - lee again
please insert cool other areas that aren't stats or combinatorics - ???

[prisma snow]

Highly highly recommend Rotman for algebra and even more highly antirecommend D&F

[queen rampart]

haha, I think I said this earlier but I've drunk a lot of vodka

D&F was the first algebra text I properly stuck with

fraleigh, artin, aluffi never stuck

and then I reached the point that D&F completely lost me and was awful

and many literal hours of reading book reviews later I settled on knapp followed by solidifying it with rotman

[south ferry]

We have tried hard to reduce the number of ε–δ arguments
i'm sold

[prisma snow]

Rotman covers rings before groups and makes some reference to groups in the rings section already. But it's not essential that you know groups to read it. It's just in the remarks that he comments and compares to group.

[queen rampart]

(I legit don't get why people call D&F dry or bad; everything up until normal subgroups was phenomenal, then their treatment of normal subgroups/isomorphism theorems/composition series is awful)

[storm sleet]

Wait Rotman has a general algebra book?

[queen rampart]

oh, when I say rotman I mean advanced modern algebra, not the UG one

[prisma snow]

I mean that one too

[queen rampart]

he covers groups first in that one

[storm sleet]

I’ve only seen Rotmans group theory book which I really liked

[prisma snow]

He does not in AMA

[queen rampart]

he has groups I and rings I and most of the proofs are just very brief

[prisma snow]

I am looking at the book right now and it covers rings first lol.

[queen rampart]

advanced modern algebra
ch1, things past

ch2 groups I

ch3 commutative rings I

[prisma snow]

What edition?

[queen rampart]

2

the one before he splits it into 2 books

[prisma snow]

Aj

Ah

I have the split 3rd edition

[queen rampart]

I have <deleted under copyright law>

[prisma snow]

Wonder why he changed the order

Anyway, it's great

[queen rampart]

there was a blog post that went into huge detail about basically every algebra text

and it said rotman was the best they've ever read by a mile

[prisma snow]

I agree. Based reviewer.

[queen rampart]

but yeah that's why I chose rotman, and it seems like knapp goes into encyclopedic detail so if I read it first in knapp, really cement what I first read in D&F before I abandoned it

then read rotman's very brief proofs

I'll be an expert

[prisma snow]

You could read the two together instead of one by one.

[queen rampart]

yeah that's the intention

they don't quite overlap

knapp has 2 heavy LA chapters before groups

[prisma snow]

Ah

You can skip around though to see how they cover the same topics though

[queen rampart]

some of the stuff rotman does in groups I, knapp doesn't do til groups II, after multilinear algebra etc

yeah I'm definitely mathematically mature enough to get by and jump around and whatnot

[prisma snow]

okay, I sleep now. Please join the rotman faction here and overthrow DF

[queen rampart]

I should too

gnight!

[south ferry]

night

[queen rampart]

justkidding I'm sticking around to provide judgment on a billion books I've read 3 chapters of each

[sage python]

Idk how good Rotman is tbh

I like Rotman's group theory

Like not the group theory section of his book but the group theory book

[queen rampart]

have you read rotman's advanced modern algebra

[sage python]

Nope

[queen rampart]

then...

[prisma snow]

I will tell you dami, good!

[hearty steppe]

I’ll look into Rotman as well thanks for the rec

[sudden kindle]

@sage python do you have a personal/academic website

[queen rampart]

it is definitely not a first algebra course though

[sage python]

Not yet, I probably will soon though

[south ferry]

you're missing complex analysis btw

[queen rampart]

yeah I've got 0 clue about complex anal

[south ferry]

i liked Complex analysis by Eberhard Freitag and Rolf Busam, but this channel likes ahlfors more i think

[sudden kindle]

Have you though about how to make it?

Would you use google sites or wordpress?

[ionic wren]

Doesn’t Wordpress cost money

[sage python]

I had Google sites in mind

[south ferry]

not if you self-host

[ionic wren]

Forgot you can do that oof

[sage python]

Also check pinned messages where I gave my complex analysis book opinions lmao

[sudden kindle]

Oof I asked about websites in the wrong channel

[south ferry]

i like the Schlag description lol

[queen rampart]

since you clearly know your stuff, do I need real analysis before compelx analysis? I know they're very different but I guess...does anything else carry over except the concept of a sequence converging?

[sage python]

Depends on how you're treating the complex analysis

I feel with complex analysis the more real analysis you know going in the more you can do

While the opposite won't really hold

So better to do real analysis first

[queen rampart]

oh yeah, for sure

I've just heard that complex is kinda disjoint from real

since it's holomorphic this and whatnot

[gray gazelle]

complex analysis deals only with constant functions

[south ferry]

lol

[gray gazelle]

id say that's a pretty big difference

[ripe granite]

you probably want to be familiar with a lot of the stuff introduced in a first real analysis class before you take complex

stuff about metric spaces (compactness, connectedness, etc.)

and some stuff on sequences of functions/function spaces

[gray gazelle]

holomorphic arzela ascoli moment

function space stuff played a huge role in my complex analysis class

[ripe granite]

oh yeah and you'll want some of the real anal integration thms too

so that you don't have to be ing while switching integrals and limits

[gray gazelle]

"this is on a compact set and the convergence is uniform so it's ok"

[quick hornet]

tip for topology: whenever you cant justify a claim, just say "because f is continuous" or "because S is compact"

maybe "because S is hausdorff" if youre feeling spicy

works 99% of the time

[south ferry]

if i did topology exercises in latex "f from compact to hausdorff so f bar homeomorphism" would be a macro

[gray gazelle]

@glad prairie which analysis book do you recommend?

I saw so many.

for a cs student.

[glad prairie]

Personally I recommend Abbott's Understanding Analysis

[willow pecan]

@glad prairie which analysis book do you recommend?

I saw so many

[dapper root]

toxic

[willow pecan]

For a math student

[glad prairie]

What are you on about

[willow pecan]

It's fine we're friends

[glad prairie]

For you I recommend Rudin's functional analysis

[willow pecan]

[glad prairie]

Get to learning

How about Taylor's Noncommutative Harmonic Analysis

[storm sleet]

I second the rec for Abbot

Abbott is a nice, easy-going intro

[willow pecan]

[storm sleet]

I'm garbage at analysis and I still got an A in my course bc of it

[gray gazelle]

have problem with that?

[dapper root]

In my intro analysis class someone sent me a pdf of that

and I didn't open it once

😸

[glad prairie]

Classification of irreducible unitary representations... Come on, you already did the whole theory of that on your 202B homework ange.

[storm sleet]

Its a nice book, but I plan to go through Rudin at some point too, just to make sure I can actually do the stuff

[glad prairie]

This NC HA book should be easy

[willow pecan]

What

[storm sleet]

But I remember nothing of sequences at all tbqh

[willow pecan]

Rieffel stopped teaching at the end

Because of Covid

[glad prairie]

Hilbert space Peter Weyl

[gray gazelle]

is it cut out for self-studying?

[storm sleet]

I would say you should have some supplemental content, as some of the proofs/descriptions of things get weird at points (particularly in chapter 5 or 6 if I recall), but the exercises are nice and get the job done

I'd say its better suited than something like Rudin from what I've heard, but definitely have supplemental material you can access

[gray gazelle]

such as?

[storm sleet]

A lecturer Honestly I don't have any good references off-hand, I'm sure other people (like @glad prairie since they mentioned abbott) have some ideas

[glad prairie]

Maybe Pugh's Analysis book

Tterra will tell you it's irredeemable but I think as long as it's not your main source it's great for intuition and good exercises

[dapper root]

I've heard lots of ppl say Pugh was bad

[willow pecan]

[static crest]

it's very good for intuition, according to tterra pugh even does proofs by intuition

[broken meadow]

literally just

shows a picture

and the proof is obvious

AND THEN PROOF 2 is the normal one

[sage python]

I feel like it depends on you a bit

If you think you've got what it takes powering through Rudin is the strat

Kriz has nice contents but someone said it's bad wrt typos

Pugh is awkward

Sally is typo city

And tbh that's what I know for intro analysis books lol. I guess Kolmogorov-Fomin if you're okay with weird terminology and slightly strange coverage

[dapper root]

Do Folland

Advanced Calculus

[static crest]

[whole rain]

[karmic thorn]

Tao's Analysis gud 😌

[gray gazelle]

oman

based

[stray oyster]

Does anybody have B.S.Grewal book for engineers

[hasty turret]

It's probably on libgen

[remote ginkgo]

rudin is the only good analysis book besides hardy

[calm crane]

s&s tho

[narrow talon]

Folland

[remote ginkgo]

no

[narrow talon]

More advanced than Rudin

[remote ginkgo]

my little blue indian edition with single ply seethrough pages will never be displaced

[narrow talon]

Wait little Rudin?

[remote ginkgo]

witto tiny babeh woodin

ye

in response to the deleted post

[queen rampart]

[narrow talon]

Oh nvm then, Folland is not a good substitute for blue Rudin haha

[queen rampart]

bluedin

I'm looking forward to reading knapp because my god am I tired of analysis's neverending desire to do epsilon-delta sequence convergence

[marble karma]

Understanding analysis by abbott or principles of mathematical analysis which one is good for begginer?

[quick hornet]

rudin is famously difficult.

i dont have experience with abbott, but i'd wager it's more approachable than rudin

[marble karma]

What will you recommend for linear algebra?

[broken meadow]

friedberg linear algebra is chill and good

[smoky surge]

Axler

[karmic thorn]

Friedberg is certainly more accessible imo.

If anyone is using Friedberg for study, you can complement it with Tao's 115A lecture notes.

[queen hull]

anyone know of a good algebra textbook with either great examples/historical context behind the stuff?

[gray gazelle]

at what level

[marble solar]

Pinter?

[queen hull]

thanks I'll check it out

[karmic thorn]

Nothing gets close enough to you my brother. :todou:

[modest dirge]

Are there any good books to learn how to write and do proofs?

[karmic thorn]

Not a book and doesn't talk about how to construct proofs, but is a great article for learning how to present a proof:
https://kconrad.math.uconn.edu/blurbs/proofs/writingtips.pdf

[hasty turret]

I mean There's Velleman

[karmic thorn]

Some standard book recommendations for learning how to write proofs are Book of Proof(Hammack) and Velleman's book, don't remember what it is called. Although you could learn to write them in context.

[hasty turret]

But if you value your time, don't do it

.

Do this instead

[inner token]

Munkres or Mendelson for a first topology book?

[gray gazelle]

lee

[vale granite]

Topology without tears is what I prefer

Is Dummit Foote the best Abstract Alg book?

[marble solar]

no

[vale granite]

Is there any easier book? Like easier to read

[sage python]

No

[marble solar]

nO

[sage python]

Arguably Artin

[marble solar]

For easy to read

Pinter is hard to beat

[sage python]

But D&F is readable by anyone who's ready to be learning algebra tbh

[vale granite]

That was depressing to hear but thanks for your opinion

[wooden sparrow]

Does hard to read mean better book?

[marble solar]

No

[sage python]

I mean what's your background so far?

[vale granite]

Actually the G action part is where I get stuck the most

3rd year in Math

[vale granite]

I'll check it prob'ly

[sage python]

G actions take a minute to wrap your head around

[vale granite]

I fear that part...absolutely

[tribal gate]

Any handout on polynomial for olympiad???

[vale granite]

Isn't there Titu Andreescu's book on Poly ? Ig so

[tribal gate]

Pdf,,,

[vale granite]

Sorry no poly books by him...my bad

But wait...

This book has everything

[tribal gate]

Thanks

[quick hornet]

hey uh

please dont post pirated material

discord staff gets mad at us when you do

and i dont think the pdf is publicly freely available so

[inner token]

For a set A it that Mendelson book denotes the power set as 2^A. which irritates me slightly. so I think I'll pick up Munkres lol. Lee looks harder than what I need right now and I never studied cats yet. then again, no time like the present right?

[quick hornet]

advice: never read a formal set theory book

[crimson cipher]

Any difference between Multiplicative number theory by Davenport & Multiplicative Number Theory I : Classical Theory by Montgomery and Vaughan?

they both seem to be similar so idk which to pick

[molten wave]

why is that a problem

[inner token]

It's not, I was just being a goof. But I did end up going munkres just by recs combined with a gut feeling

[inner token]

Yeah it is more illuminating just old habits sorta thing

[still jay]

I’m trying to choose a text to study for Abstract Algebra, the two I’m thinking about are Herstein’s Topics in Algebra and Jacobson’s Basic Algebra 1. What do you guys think of these? I’m also open to alternatives.

[dapper root]

The former is easier, but

Apparently it uses (x)f for what you normally see as f(x), for me personally that would sorta break it for me

What’s ur background and how hard would you want it?

#book-recommendations message

Also read what’s here for an overview at a few texts

[prisma snow]

What an unbased list without Rotman

[dapper root]

It gets mentioned right below

Also people (like Lunasong here I think) will bitch at me for it, but I’m partial to Aluffi

Jacobson seems interesting, the amount of material it covers in vol 1 and 2 is more than any other of these general algebra books, Lang might beat it in some parts, but there’s also stuff on eg universal algebra, classification of rings (for central algebras or w/e)

that being said, I’ve heard the writing style can take some getting used to, and some people just don’t like it

At the end of the day tho, if you’re self-studying, I would find a book you enjoy. We can split hairs over what material is covered, things being too wordy, etc, but in my opinion the book that makes you want to read it is the best one

The material you’ll learn is gonna be similar enough for most of these, if you don’t need to know exactly these things because it’ll be on your final or w/e, find one you like IMO

[still jay]

Very true, thanks for the info. I suppose the one empirical factor would be background. I’ve done some real analysis, what I’m currently studying, and also have taken a computational LA course. Are there any texts I should stay away from with that said? Also I like to be challenged but that is second to the quality of the writing for me.

[dapper root]

What do you think constitutes quality writing?

Things that are terse, maybe leaves you to do a bit. Or things that are verbose, lots of examples

[still jay]

Clear motivation, well written exposition. Terse I would say, I don’t mind doing things myself, actually I prefer it.

[dapper root]

I guess the other thing is what do you want? Like one book you can just learn everything you’d have in say an avg graduate algebra class? Or like a nice introduction, without wanting it to be something you can have all your general algebra in?

In terms of writing, I’d steer away from D&F if you like terse things. I find it waaayyy too verbose. I like Aluffi’s writing, and a lot of people like it as well. I’d avoid Lang unless you already have a feel for algebra in like a linear algebra class that did it abstractly.

I haven’t personally seen a lot of the others, but Herstein seems like a good book potentially? Maybe Jacobson or Artin as well?

[still jay]

Yeah I’ll check those out, the best thing is probably to read some of each anyway and see what clicks. Thanks for the help.

[prisma snow]

Dw, I won't bitch about anything except DF

[gray gazelle]

If you shit on DF I will shit on you

[dapper root]

https://www.stumblingrobot.com/best-math-books/core-subjects/#abstractalgebra

[livid ermine]

[dapper root]

@still jay I spent a while trying to find this

I’m glad I found it again, check this link

[gray gazelle]

nice pfp

[livid ermine]

based

so

do we fight to the death now?

[gray gazelle]

lol

[livid ermine]

meow

[gray gazelle]

perhaps

[still jay]

Ooo thanks 🙏

[livid ermine]

@gray gazelle @hushed sequoia wain pfp gang. which one of these are the best for a pfp?

[gray gazelle]

hmmm

i'd say third

[queen rampart]

I did not like aluffi

herstein was good, but it does seem kinda short

I'm currently liking knapp, though it is quite heavy going. Not in a "prove this yourself" way, but it seems like he doesn't want to teach you half-assed

linear maps being over arbitrary bases

[gray gazelle]

lol

nice pfp godel

[gray gazelle]

Thanks.

[gray gazelle]

thank you yohan

[sly thistle]

Anyone here read diary of a wimpy kid hard luck

[static crest]

sully

[split epoch]

yupp

[quasi lintel]

Do you know of any good books to teach myself algebra? One that clearly explain the reasoning behind why I do the math

[karmic thorn]

Algebra at what level?

[static crest]

d&f is a good intro to algebra

they cover polynomials extensively

and well

they even do exponentials and sinusoids!

[quasi lintel]

8th grade

[static crest]

:^)

[karmic thorn]

Hmmm, something which explains reasoning at that level.

Have you tried books by AoPS?

[quasi lintel]

I've never heard of them

[karmic thorn]

Try out their algebra book. It goes into a bit more than what you might have covered, but it's written very cleanly, gives ample explanation/reasoning and has lots of problems.

[hearty steppe]

I might take a peek at D&F although I really like Pinter as well as Fraleigh

[gray gazelle]

allufi

[ripe granite]

I will buy the entire collection someday

just for the covers

[sage python]

@dapper root interesting site lol

[storm sleet]

I feel like Aluffi would be better served as a category theory book after you learn algebra

similar to the topology book

[queen rampart]

I mean, I read into aluffi as far as groupds

I think I have a solid grasp of groups

I still found his talking about groups confusing

[sage python]

I don't think Aluffi is really a "category theory book", most of the content is algebra

I feel like there's a case for throwing in more category theory in first year algebra but I don't know if Aluffi does it right

[queen rampart]

yeah, I've heard repeatedly that it's a terrible book to learn category theory from

[sage python]

If you start off on the categorical side you wanna be clear what's actual content and what's just words

[queen rampart]

more good as a mathematically mature algebra book with some category stuff as a fresh approach

[sage python]

Like e.g. emphasizing that specifying a linear map arbitrarily on a basis is an example of free and forgetful functors being adjoint, but that you're not proving anything categorically here

[queen rampart]

I actually thought D&F was good, up until normal subgroups and the applications of isomorphism theorems

at which point, it was clear they were just stating theorems and not explaining anything

yeah this is what I heard too

[static crest]

thonk

that's easily the stupidest thing I've ever heard

the main criticism of d&f is that it explains too much

and goes on and on forever

lol @ it's not explaining anything

[queen rampart]

it did explain a hell of a lot more than artin or herstein

but it was explaining a lot because it covered a lot of stuff

[static crest]

it covers normal undergrad algebra topics?

[queen rampart]

it did not provide intuition or explanation for anything

[static crest]

the only textbook that goes any slower than d&f is gallian

[queen rampart]

ahem, fraleigh

[static crest]

which treats you if you're 5 years old

maximum

[queen rampart]

fraleigh acts like you've never read a book before

10/10 to D&F for covering literally every facet of, say, lagrange's theorem

-50/10 for giving a single reason why we care about normalisers or whatever

[static crest]

but fraleigh covers like the same content, in like fewer pages?

[queen rampart]

no?

[sage python]

I think the point Kitty's making, which is kinda correct

[queen rampart]

maybe because I read fraleigh in paper like a year ago and D&F on a tablet

[sage python]

Is that if you're not predisposed to understanding what's interesting about algebra or why it's important

[queen rampart]

I swear fraleigh gets 9 or 10 chapters deep before lagrange's theorem

[static crest]

I can understand that as a criticism, d&f does assume you already want to learn algebra

[dapper root]

The fuck

What in the shit do you do without Lagrange

[sage python]

D&F will do no work whatsoever in making it interesting

[hearty steppe]

i like Fraleigh but Fraleigh is very short

[static crest]

but saying "d&f doesn't explain anything" is just not right unless you literally just didn't read it

[queen rampart]

not because they've covered so much, more that they act like you're a blind 3 year old

[sage python]

D&F is a list of facts

[static crest]

while awake

[queen rampart]

D&F did not explain why normalisers are important, or any reason we might want them

[sage python]

Wait hold on I just realized

[queen rampart]

literally, "blah is called the normaliser of G"

[static crest]

well it does at some point

[queen rampart]

that's it

[sage python]

D&F is literally the definition of ELI5 algebra

[static crest]

it doesn't explain about normalizers in 2.2, where they're first introduced

[queen rampart]

no reason why we might make it, or use it, or need it, or why we construct it that way

[static crest]

it just gives the definition there

really

and goes next

[sage python]

But yeah this is why I say that if you want D&F but more motivated you use Artin

[queen rampart]

it starts going on about stuff being subgroups of the normaliser to prove stuff but that doesn't help

[static crest]

gallian is like by definition eli5 of algebra

d&f is at least eli10

[queen rampart]

herstein did much more imo

artin was alright but it didn't grab me?

[sage python]

Herstein is good at group theory, it's where I learned it

But I hear it's straight up deficient for the later topics

[queen rampart]

herstein made me understand cosets

it's taken literally 5 different books for that

[sage python]

Idk Gallian but my overall policy with D&F is that if someone's having trouble with D&F they're not ready to learn algebra

[queen rampart]

yes it's gN but that doesn't shed light on why

[static crest]

I agree dami

[queen rampart]

idk herstein made it click

[static crest]

I don't think d&f can make it any easier without just veering into gallian territory

(which is not good)

[sage python]

Yeah normal subgroups should be explained in terms of group homomorphisms lol

[queen rampart]

D&F made everything before normal groups click

[static crest]

it's just really fucking boring

to read

if you aren't already wanting to learn algebra

a lot

[narrow echo]

read Gallian

[static crest]

if you want to lose braincells

completed the sentence for you no need to thank me

[wide meteor]

beachy and blair is decent

[queen rampart]

I have not read gallian, but having read fraleigh, herstein, artin...I feel like if you need to go more basic than herstein or artin you need to consider a different topic

[sage python]

Yeah that's just correct lol

[static crest]

gallian is the most easy algebra textbook in all of existence

[sage python]

Herstein I remember liking for group theory but I heard he barely covers shit afterwards

[static crest]

it's physically impossible to make algebra more easier than gallian

it's just gallian is somehow even slower than d&f

and covers barely anything

[sage python]

And having to unlearn and relearn his multiplicatoin convention was a pain in the ass

[queen rampart]

currently reading Knapp and it's a lot harder than I expected

for a book called "basic algebra"

[static crest]

ignore textbook names

[dapper root]

Lmao

[sage python]

Weil Basic Number Theory

[dapper root]

Basic some word

[wide meteor]

anyone tried rotmans algebra book'

[dapper root]

Means nothing

[sage python]

How to make undergrads look like stupid little shits lol

[dapper root]

Jacobson calls his book basic algebra

[queen rampart]

I've heard it's excellent (well, his graduate one) and I'm planning to use it as my advanced/supplement to knapp

[dapper root]

And it covers fucking universal algebra in vol 2

[wide meteor]

nice

[static crest]

jacobson is a grad algebra tb right?

[dapper root]

Yeah, look at the topics it covers. Literally insane

[wide meteor]

im gonna pickup rotman

[queen rampart]

advanced modern algebra

[wide meteor]

yes

[static crest]

maybe I'll look at jacobson

in the far future

[queen rampart]

wait

wrong blog post

[sage python]

Jacobson has two volumes

[queen rampart]

http://tableschairsandbeermugsmathemagician.blogspot.com/2015/08/normal-0-false-false-false-en-us-x-none.html

[sage python]

Volume 1 is fine as an intro if you know linear algebra going in

[queen rampart]

ever wanted like 3000 words on algebra textbooks, here you go

[sage python]

So it's a step up over Artin but it's not unreasonably hard

I already have a pinned post about algebra books

[wide meteor]

i dont like that artin has excersises at the end of chapters

[dapper root]

Wut

[queen rampart]

oh yeah I hate that

[dapper root]

Do you want them at the end of sections?

[wide meteor]

yes

[queen rampart]

doesn't cover knapp, rotman, fraleigh, or gallian 0/10

[static crest]

well gallian is not worth talking about

[dapper root]

Okay on a different note

[sage python]

I talk about KNapp lol

[static crest]

other than to shit on it

[dapper root]

Why does everyone split so many hairs and try like 4 textbooks

[sage python]

And Fraleigh/Gallian are "algebra for people who really aren't ready to be learning algebra"

[dapper root]

Just pick one and then use it

[gray gazelle]

I need a nap

[static crest]

true

[queen rampart]

I can't see a comment about knapp

[sage python]

See the very last one lol

[static crest]

I learned like 90% of my algebra from d&f

[queen rampart]

just some author called "challenger approaching"

[wide meteor]

lmao

[static crest]

I just skimmed through like 4 textbooks, and picked one (d&f)

and stuck with it

[sage python]

Yeah idk Knapp very well lol

Basically I was looking for another book of his

[queen rampart]

because it feels more rewarding to know that someone else, somewhere, also had problems

and therefore I am validated in switching books

[sage python]

On semisimple groups

[queen rampart]

source: have tried like 8 algebra books and about 30 analysis books

[wide meteor]

yikes

[sage python]

And stumbled across that one since I thought maybe it was a chapter in his "advanced algebra" book

[static crest]

on a related note, I hit 550 pages in my d&f solutions

[sage python]

But I saw the contents and I was like dayum

[static crest]

the end is in sight though

[sage python]

ANd then realized it was the wrong book

[queen rampart]

okay maybe a little exaggerating

[sage python]

But I still decided to append it to the list since it looks good and it's free

My algebra path was like

I started D&F

Got bored

Checked out Artin

Was better but still kinda got bored

Or not really got bored but like

I was like huh this is nifty but it's not very efficient

[gray gazelle]

D and F is not that boring, just speed read it

[sage python]

Then I tried Herstein and was like aight this is what I'm reading

Learned group theory out of that and Keith Conrad's notes

Then I took a D&F class

[queen rampart]

algebra books I've read more than 10 pages of: aluffi, herstein, knapp, rotman, artin, D&F, fraleigh
analysis same: zorich, tao, rudin, abbott, pugh, apostol, knapp, spivak, S&S

[sage python]

But I mostly worked out of lectures rather than the book

[queen rampart]

btw, anyone who goes "read X on analysis, it dumps all of that cauchy sequence bullshit in the first 5 pages and then does actually interesting stuff" I'll love you forever

[sage python]

And at some point I was like alright I gotta review for quals and chose Jacobson

Rudin chapter 1 isn't quite 5 pages but I think it's a decent/moderately condensed "everything you need to know"

[static crest]

exactly, I did all the d&f group theory in < 30 days

was plenty interesting

[ripe granite]

d&f is good

aluffi is good

but none of them are great

when youre learning it for the first time

d&f is excellent if youre willing to take on faith that a lot of the stuff learning right now will be useful later

[gray gazelle]

Anyone have a pdf of Riemannian geometry by do Carmo that's not scanned so you can copy paste the text?

[sage python]

Officially discord TOS isn't cool with distributing pirated materials

[willow pecan]

[gray gazelle]

Is anyone aware of the existence of such a book

Only want to know if one exists not looking to acquire

i would also like to know

[gray gazelle]

we fooled them

make your own

retype the entirety of do carmo rg, but fix his shit notation / errors

[sage python]

In other words: "Write a book that's not about Riemannian geometry"

[wide meteor]

riemmanian geometry sounds hard

[gray gazelle]

it's hard if you can't compute

[wide meteor]

i cant compute

[lavish lagoon]

What's D and F

[wide meteor]

names

of authors

[lavish lagoon]

Oh

[gray gazelle]

dummit, foote

[lavish lagoon]

Ok

Thank you

[sudden kindle]

D&F is kinda like S&M

[narrow talon]

Book discussion in a nutshell: how do I learn calc/linear algebra/algebra/cat theory??? Well use Larson/LADR/D&F/don’t? But what about Spivak/ew LADR is terrible/Jacobson or Lang/Riehl???

And then rinse and repeat

[wide meteor]

lol

[lavish lagoon]

What if I wanna learn complex analysis? I'm an undergrad and studied a CA grad school textbook, buuut it wasn't that helpful in understanding the material

[gray gazelle]

just intuit the material

[lavish lagoon]

4head

[marble solar]

If anyone is hung up on what analysis book they'd like to read

Might I suggest the upcoming fifth edition to the classic whittaker & watson

https://www.cambridge.org/core/books/course-of-modern-analysis/B2DDAE32B565419FA452C51FA03F6F3D#fndtn-metrics

I'm not affiliated with any of the authors or the publishers in anyway whatsoever, I just think this book is dank

[wide meteor]

sure

[hearty steppe]

how does this book compare to other books?

[hearty steppe]

@marble solar

[hearty steppe]

so I now have some interesting stuff, nice

moon feel free to throw as many RA recs my way

[marble solar]

Oh sorry

Uh whittaker & watson is the best I think

Rudin is ok, Pugh is good, Terry Tao's books are ok

Stein & Shakarchi Fourier (Volume 1) is excellent

[still jay]

Thoughts on Bloch?

That’s what I’m using

[marble solar]

I don't know bbloch

[karmic thorn]

@marble solar But Stein-Shakarchi doesn't go into intro real analysis, right?

[marble solar]

Eh, if you know spivak's calculus

You're good

[karmic thorn]

[storm sleet]

Can we get a megathread for intro to analysis books?

[hearty steppe]

Aye I’m down for that but I think I have all of the recs

[gray gazelle]

lmao

and also people recommending books they haven't read, and also people who can't just sit down and do it instead of searching for the perfect book

[karmic thorn]

[gray gazelle]

What's the best hentai manga?

[karmic thorn]

Pugh

Chmonkey probably saw this a few years back

[karmic thorn]

[remote ginkgo]

sending this to my algebra professor

[molten wave]

funny that the original book is porn

[gray gazelle]

lol

[hearty steppe]

Is this a good dynamical systems book?

I forget if someone recommended it previously

Any good self study ones

Cuz I’m on the self study train

I’ll give this a try I guess?

Hard is fine. No pain no gain lmao

[sage python]

Brin and Stuck was hard for me as a second year undergrad

But like doable in a way? Like if you focus hard enough you should be able to figure out what's up

@marble solar is this Whittaker-Watson book along similar lines to Rudin and all?

[marble solar]

it's very different

[sage python]

Yeah looking at the contents I feel like... idk WW has a lot of cutesy topics

But it's not a standard analysis course really

I guess I feel like overall those recommendations are for very different things lmao. S&S doesn't have the same audience as W&W doesn't have the same audience as Rudin/Pugh, Tao is its own thing kinda

[glacial stream]

I'm going to begin calculus can anyone suggest me some good books