book-recommendations

[wooden sparrow]

I'm doing apostol volume 1

It's great

[stray veldt]

i hope that in theory yes

for reference: thats about as much "intro proof" stuff i did but i wasnt self teaching

[gray gazelle]

I am trying to read How to Solve it - A New Aspect of Mathematical Method. Felt boring 😦

[karmic thorn]

Stick to reading Tao.

[gray gazelle]

@karmic thorn : Yes I am continuing that. Today I gave a rest to it. Tomorrow I will continue again. I have reached 'Definition 2.2.7'

[karmic thorn]

Good.

[gray gazelle]

Sounds like a pop math book

[cyan rapids]

I have a drive folder with like a 1000 books for math.

[gray gazelle]

do you ocd for collecting things ( books here)

its a thing

[cyan rapids]

[cyan rapids]

I have one for physics with like 5000 books, but that is already well ordered by the 'maker' pirate.

the maths one unfortunately isn't

[gray gazelle]

It's against ToC here to ask for sharing it.

[hasty turret]

Discord ToC?

[gray gazelle]

ToC

ToS

[cyan rapids]

hmmmmm, I wonder if math server is anti-pirate. I dunno how you guys spend real money buying things.

[hasty turret]

This is a marxist cat server,sir

[cyan rapids]

aaah perfect to my liking

[quick hornet]

discord's TOS requires us to prohibit the distribution of pirated material, and to recommend you avoid discussing it.

we don't exactly agree with discord's TOS

but c'est la vie

[gray gazelle]

post "this is not pirated" every time you post something

[hollow peak]

given that we literally just post entire pdfs in the server sometimes I would hope there are some loopholes

[narrow talon]

I’m not the person to ask, but maybe the first part of Fulton and Harris?

[tranquil ocean]

I've read through Serre and enjoyed it, but I also found http://sporadic.stanford.edu/bump/group/ super helpful

and there are a couple exercises there too

@split basin

[lone viper]

How is dummit and foote?

For this

[quick hornet]

dummit and foote doesnt really give a full treatment on rep theory, just an introduction

i dont think its treatment is bad though? at least its not one of the chapters people like to complain about

[static crest]

d&f does have a lot of exercises

and the exercises are great quality

outside some of the, uh, computational ones

[gray gazelle]

It's not one of the chapters people complain about.... Because nobody reads it? 🙃

[soft terrace]

anyone know any good books/pdfs available on digital manifolds?

[graceful bridge]

@soft terrace I haven't heard about that, is it a very niche topic? Have you tried any of the two references mentioned here: https://en.wikipedia.org/wiki/Digital_manifold ?

[soft terrace]

@graceful bridge Yes, they are rather hard to get a hold of. I was hoping for cheaper options. It seems to be a rare topic, I got interested in it when I was reading out geometric group theory and lie groups. It seemed like the topic would mesh well with those two subjects so I am investigating it.

[gray gazelle]

BTW interesting book I came across recently Jonathan M. Kane - Writing Proofs In Analysis

it's an introduction to proofs textbook but solely focuses on analysis

[hasty turret]

Like does it cover the same topics,as a normal analysis book?

[gray gazelle]

pretty much as an introductory course and the steps are super explicit in proofs:

also has proof templates for things like proving a limit doesnt exist and examples of incorrect proofs and why they are incorrect

[gray gazelle]

I have no knowledge in this subject. But this proof looks nice.

[quick hornet]

thats painfully wordy honestly

i'd understand it if they gave exposition on how they came up with each step, but it doesnt look like it? at least based off that image

its an interesting idea,, though, i can forgive being wordy when your target audience is students struggling with proofs

[karmic thorn]

Hmmm, presenting proofs in bullet points. That is indeed a good way of presenting proofs to the layperson.

[gray gazelle]

maybe more pictures could be good too

[karmic thorn]

Could have been made more useful by reducing the number of bullet points, and elaborating on the "core" idea of each proof.

[karmic thorn]

Yeah, that would be nice.

[cyan rapids]

the proof is painful I am lazy and will never use english

[gray gazelle]

How good are Dover books for maths? Amazon has good rating for them( mostly are 4+).

[karmic thorn]

Varies from book to book.

Dover mostly publishes classics which had been out of print for a long time.

[gray gazelle]

So, they are outdated as well?

[karmic thorn]

Some of them are extremely good, others are outdated for present purposes, while some others may be illuminating in their own ways due to non-standard coverage.

You can check with reviews on Goodreads before getting something, reviews on Amazon usually tend to be people complaining about paper quality so you don't get reviews about the contents itself.

[gray gazelle]

100 great problems of elementary mathematics: their history and solution --> This I liked. It seems difficult.

[gray gazelle]

I would say all exercises at the end of the chapter.

[quick hornet]

thats a bit much lmao

[gray gazelle]

So that you never miss any concept.

[quick hornet]

i mean, certainly do any of the exercises that seem important

dummit and foote first introduces the notion of kernel in exercises IIRC

but its usually fairly easy to tell which are like, super important

at least if youre experienced

[gray gazelle]

Ok.

[karmic thorn]

What I've been doing lately is this: for computational exercises, I would simply pick the most challenging ones. For proofs, I would try to formulate a proof-sketch inside my head. Most of the easy exercises can be dealt with in this way. If I think a certain result is not so easy to prove or seems more significant/general, I write down a complete proof in my notebook.

[gray gazelle]

But what if you feel like one is easy and once start solving it's tough?

[karmic thorn]

If in the formulate-a-proof-sketch-inside-my-head phase I realise that a result isn't very obvious, I write it down and work on it.

Checking answers, well, I usually rely on my instinct. I doubt my proofs if either they're too elegant, or too complicated. I often ask here to validate my ideas, and that works.

[real eagle]

So anyone ever worked through mathematical methods in the physical sciences by mary boas? I'm doing self-study but there's like 3000 questions with answers, anyone know how to efficiently go through them all. Doesn't help that the answer book is garbage and I can get stuck at everything

[karmic thorn]

Why learn from Boas?

Unless you're into physical sciences themselves and don't want to bother yourself with proofs, etc.

[real eagle]

Doin it as it's stated as a prerequisite for a master

Well more like the knowledge in it but still

And it's the technical side of a cognitive neuroscience master so I might need it

[hasty turret]

I don't think that's specific enough

[real eagle]

The book?

Admission requirements state something along the lines of this "calculus, linear algebra, vector analysis, fourier series and transforms, ordinary differential equations"

then states the book, I could only do those specific parts, and some of the rest if necessary

Oh and "Electromagnetism and calculus-based introductory physics "

[karmic thorn]

The latter can be covered well by a book like Halliday/Resnick

For the former, you can cover calculus from Khan Academy. For differential equations and linear algebra, MIT OCW has resources(lectures, notes, assignments). Maybe that should give you enough grounding to cover fourier series and transform from a book like Boas.

[real eagle]

Wait, so I should read those books/watch khan academy before attempting boas?

[karmic thorn]

Not really

How much of this stuff do you know already?

Have you done calculus/linear algebra before?

[real eagle]

Yes, I passed a course at uni for calculus

Although I'm not sure how much of it is left

[karmic thorn]

Maybe recap calculus from Khan Academy first

That would cover some ODEs as well

Try using Boas book on the sidelines for practising problems and reading up

[real eagle]

Oh it was from the book calculus: a complete course

[gray gazelle]

Revising it should be now pretty fast.

[real eagle]

Honestly I don't think calculus will be that much of a problem

[karmic thorn]

Hmm, then start with the linear algebra part?

[real eagle]

vectors and matrices could be a bit rough

Never really done them much

[karmic thorn]

It's worth revisiting, and I would put it in the basket of easier stuff.

How much time do you have at hand?

[quick hornet]

wait what the fuck

its me

[molten wave]

I was about to say

[real eagle]

Til september, though lots of time on my hands

[karmic thorn]

If you're comfortable enough, try reading it from a book devoted to linear algebra, probably one that is written for a first course in the subject.

Strang's Intro to LA/Lay's Linear Algebra and its Applications should be fine

You can study DEs concurrently

[gray gazelle]

What's DE?

[karmic thorn]

Differential Equations

[gray gazelle]

If it's neuroscience and is similar to neural network , you might be need matrices and light differential calculus and linear algebra. I don't think you need to go so much deep into it. Matrices is a must.

[real eagle]

Alright sounds like a plan, read up on linear algebra using strang, then look into halliday/resnick, further reading of boas perhaps

Thanks!

[karmic thorn]

No worries; goodluck!

[gray gazelle]

BTW Halliday Resnick is for highschool physics right?

[karmic thorn]

It covers more than typical HS does

And is generally used as a textbook for an introductory course in physics at the university level

[gray gazelle]

This is meant for an intro to proofs thing so making things wordy/explicit is important. Exposition explaining individual steps is typicaly in the main text.

[quick hornet]

yeah i think i was too negative on it initially

it's certainly interesting; teaching prpofs to students totally new to them is always tricky

i wonder whether an analysis course is really the best setting for it

since honestly the problems/proofs encountered in a more standard "intro to proofs" feel very... contrived? maybe thats the wrong word

but like

they dont require the "creativity" that actually proving things usually involves

whereas analysis problems frequently do, what with defining special functions or sequences or making actually relevant/novel observations or whatever

[narrow talon]

I’d argue it is, for exactly the reasons you’ve stated. Algebra can also take on a very “follow you nose” direction in a first course, and something like topology is only really motivated after a first course in analysis IMO

[gray gazelle]

as someone whos more on the rudimentary end for proofs (coming from physics/engineering) it's nice seeing the kind of explicit instruction around less obvious stuff like epsilon delta

[narrow talon]

At the level of like, spivak

[gray gazelle]

basically there's only so many times you can see the sort of introductory proofs stuff like "sqrt(2) is irrational, there are an infinitetude of primes, ..." "ok now you understand proofs" and then the text jumps to proofs that look nothing like that

[narrow talon]

Also, my prof said not to really worry about basic physics, maybe learn some Newtonian stuff but then just focus on dynamics and some other stuff directly

[narrow talon]

Yeah, I think there’s a basic set of proof tools that get you feeling comfortable enough with actually writing proofs to start encountering actual argument. I think most people are just at a loss as to wtf even constitutes a proof at first so showing them stuff like what exactly implies means, biimplication, proof by contrapositive, proof by contradiction, and proof by induction is really useful.

Then it’s pretty natural then to start trying to work on analysis. At which point we’re trying to build up ideas which should be easy to write up into a proof

Proofs of the BCT and Doob’s upcrossing inequality would be awesome introductions to proof if they weren’t maybe a bit too advanced (does everyone see BCT in a first course in analysis?)

Do people see discrete time martingales in a first course in probability/statistics? If so then maybe Doob’s upcrossing wouldn’t actually be a bad choice for a lot of people to look at. I think there’s some fudgy analysis in it though

[gray gazelle]

personally i think a useful approach to learning proofs would be taking a big proof and then breaking it down as to what it means in detail and doing that for a lot of different proofs

ie a reading centric approach vs writing centric that builds up to gradually longer and more complicated proofs

[narrow talon]

I disagree, reading proofs doesn’t build confidence in translating from idea to rigorous exposition imo

[gray gazelle]

two sides of the coin

you have to be able to read what your textbooks are saying when they do the proofs

to then write your own

and from more of a creative writing standpoint the best writers tend to also be the ones who read the most (for fiction/nonfiction)

[karmic thorn]

I think the first segment of any "intro to proofs" book or class should use simple proofs which highlight the logical flow and intuition of reasoning with simple arguments, and expose them to implications, etc. The next segment should show all this in context, where proofs have more to them-at such a place you could maybe use analysis/algebra to highlight how many proofs have a "core idea" supporting it, which may not have been obvious at first sight.

Highlighting core ideas, backtracking against known definitions/theorems would be fruitful for anyone learning how to prove things.

[narrow talon]

Anyone have an opinion on PDE books? I know Evan's is pretty standard, anything better?

(for a second look, may speedrun Strauss for a first look. Connections to SPDEs and/or including some ODE stuff would be especially nice)

[hollow peak]

strauss is not great

it's as basic as you can get imo

[gray gazelle]

What's a good topology book with very basics? Not directly jumping into theory and all.

[karmic thorn]

Uhhhhh what exactly are you looking for if not theory?

[gray gazelle]

do you mean like pop sci topology?

[karmic thorn]

Visuals?

[narrow talon]

Aight, anything better? Was basically planning to use it just to see the Laplace/heat/wave equations with some theory before looking at general eliptic/parabolic/hyperbolic pdes

[stray veldt]

i have heard that topology without tears is nice

@gray gazelle its probably the "easiest" topology book

[karmic thorn]

Yeah, but even TwT starts right off the bat with definitions and stuff.

[karmic thorn]

It's a good first read

[stray veldt]

i mean, otherwise you aren't doing topology

[hollow peak]

if that's all you need then it's probably fine

[narrow talon]

Probably this if you're avoiding theory

[hollow peak]

I think it's just a bit obtuse sometimes

[karmic thorn]

Yeah, prolly what Jason sent above makes more sense then

[hollow peak]

Evans is a genuinely fantastic book

[gray gazelle]

there's also Weeks - The Shape Of Space

for the pop sci

[narrow talon]

tbh the vector calc in Evan's scares me

[stray veldt]

if you just want to think about shapes, consider buying play dough

[narrow talon]

And the notation, while standard, is a bit frustrating

[hollow peak]

When I first opened it I felt the same way but you just kind of get used to it

especially the vector calc

pdes makes you into a vector calc god

[gray gazelle]

I can't find it in Amazon. Only nearest one available 'Statistics without Tears: An Introduction for Non-Mathematicians'

[hollow peak]

like, I never even took a class on multivariable calc and it just kind of comes together

[karmic thorn]

It's a free ebook

Available on the author's dedicated website for that book

It doesn't have a physical edition afaik

[narrow talon]

lol I thought that's what electrodynamics was for

Does having the background in undergrad (Strauss level) PDEs help a lot?

[hollow peak]

my class has been basically working out of evans while the class text is strauss

[gray gazelle]

I got the book TwT. And if it is called TwT then they failed on me 😦

[hollow peak]

you can jump in at either level depending on your analysis knowledge

[calm crane]

^^^

[narrow talon]

Gotcha, so it's not really worth dealing with Strauss

[hollow peak]

it's good for a supplement

[narrow talon]

I'll find some other book on SPDEs when I get to it

[karmic thorn]

Doesn't Arnold's book cover PDEs?

[narrow talon]

Where's your class stopping? You could kill someone with Evans so it's probably not a book to read cover-cover

[narrow talon]

Which Arnold book? ODEs or Classical Mechanics?

[hollow peak]

I guess there are some things that evans takes for granted now that I think about it (e.g. first order pdes) which is kind of annoying

[karmic thorn]

CM

[narrow talon]

Also I have a class using Brezis this semester so I'd skip a few chapters either way

[narrow talon]

Ah, tbh my ODE knowledge isn't great, didn't pay much attention in that class

[hollow peak]

It's currently unclear but I think the goal is to do stuff with greens functions, fourier analysis and sobolev spaces by the end of the semester

ODEs are basically irrelevant beyond "oh look we have characteristics so this pde is now an ode"

[narrow talon]

(don't worry, I didn't confuse first order PDE and ODE here, though that's not obvious from how I worded it)

[narrow talon]

Gotcha, not like "now that we have that characteristic, we have this very particular ODE which we can solve with this pretty useless technique from ODEs"

[hollow peak]

yeah things like that never show up

[gray gazelle]

The Art of Statistics: Learning from Data - This is nice for beginners. Rather than directly jumping to formulae.

[narrow talon]

Alright thanks! I'll probably just go back to Evan's and give it a more serious shot then, depending on what my advisor says (I asked him what to work on before PhD and am expecting him to say either harmonic analysis, PDEs, or nothing)

[narrow talon]

Sreeraj, where are you at mathematically?

[sudden kindle]

689uop[]\

[gray gazelle]

@narrow talon : 2/10 - Know basics of calculus, algebra, set, matrix, statistics, PDE

[narrow talon]

That'd be an insane amount if you consider how large math is

I mean, do you know calc?

[narrow talon]

Algebra as in "mx + b" or algebra as in "the polynomial ring of a UFD is a UFD?"

Also, are you in high school (or some equivalent) or undergrad?

[gray gazelle]

Undergrad

[narrow talon]

Eh, it's not too insane depending on level of PDEs, my uni offers a non-proof based class on PDE

[narrow talon]

First year?

[gray gazelle]

@narrow talon Was, 14 years back.

[narrow talon]

You were in your first year at uni 14 years ago?

Did you major outside of math?

[gray gazelle]

Yes

[narrow talon]

Gotcha!
Is there a particular area of math you find really interesting? You've asked about a lot of books and it's just left me a little confused as to where you're trying to get

[gray gazelle]

That what we all are pondering here

[narrow talon]

It's okay to just be interested in getting broad exposure right now

[gray gazelle]

I liked most of the subjects except Set theory. Now am I trying to relearn that as well. Doing Tao's analysis. Next chapter is Set theory. Excited. Now I feel Set theory needs most intuition(which I am lacking ). You can't cram it.

[narrow talon]

Set theory is very deep and useful to know so that's good. The sort of canonical trio is analysis, algebra, and topology. Usually in that order too

[karmic thorn]

Same, although I'm doing lin alg instead of AA.

And I also have some courses at uni, so that adds a bit more to my basket.

[narrow talon]

That's totally alright, I did it that way too

... that's a little sus

[karmic thorn]

I tried doing group theory without doing LA, and I was doing okay, but I think approaching it after linear algebra would make it very natural.

Like

I realised group homomorphisms are just a generalisation of linear transformations

I'm not sure if that's accurate

But there's some similar themes

Since vector spaces are Abelian groups under addition

[gray gazelle]

you're an abelian group under addition

[karmic thorn]

Yeah, abstract algebra is fun, I'll try to do it later this year.

For now, I'll be sticking to real anal and lin alg. Maybe follow up with differential equations and complex anal.

[gray gazelle]

approach group theory from the point of view of "we only care about these because they act on things" and you'll be 100% set

[karmic thorn]

That was my initial approach since I started group theory when I didn't even understand modular arithmetic, let alone vector spaces.

It didn't end well, but mostly because group theory was my first exposure to writing proofs.

[hasty turret]

Does the average cs student learn about proofs?

[narrow talon]

Sounds a little backwards to me

[quick hornet]

@hasty turret yeah, most often in a discrete math course

and then again in an algorithms course

(or vice versa)

[stray veldt]

and then they forget it

[narrow talon]

AA has pretty little in it. It's a lot of definitions and then understanding simple properties about those definitions. The only thing that makes it so tricky is the level of abstraction is higher than initially dealt with

[karmic thorn]

It's more appropriate to view linear transformations on vector spaces as group homomorphisms which also preserve scalar multiplication?

Yeah

[gray gazelle]

What's this channel name?

[narrow talon]

tbh I view linear spaces as linear spaces haha! They're sort of the atoms for a space I'd be working in most the time, as opposed to groups

[karmic thorn]

Fair

[gray gazelle]

linear algebra is important, mathematicians spend a lot of time multiplying really big matrices

[quick hornet]

continuous functions are just infty-by-infty matrices

prove me wrong

you cant

[karmic thorn]

I just thought vector spaces would make some good examples of groups, so you have something "concrete" to compare with when you study group theory.

[narrow talon]

However there is a lot of interplay, I believe Michael Artin's book very much takes the approach of linear algebra first

[gray gazelle]

@gray gazelle What's so big about 4x4.

[narrow talon]

Depends

[quick hornet]

well its very common to use linear algebraic arguments in a first group theory course

[stray veldt]

in first group theory course you mostly use some subset of matrices with matrix multiplication as a group though

[calm crane]

basically modules

[gray gazelle]

in lie group theory too

[karmic thorn]

Matrix stuff? People think math majors do arithmetic quickly

[calm crane]

me trying to understand finite group rep stuff: isnt this true

[stray veldt]

all lie groups are matrices to me

[calm crane]

hsisskajs

[gray gazelle]

lie groups that aren't matrix groups are a lie

[calm crane]

all math is secretly matrices

[karmic thorn]

All math is fancy logic

[gray gazelle]

Don't they 😦

[calm crane]

yea right

[quick hornet]

linear algebraic arguments are very powerful

in group theory

i remember a midterm problem that was like

[calm crane]

ikr i just learnt a bit of finite group rep today

[quick hornet]

suppose G is nontrivial abelian and each nonidentity element has order 5

[stray veldt]

i take a class on finite group rep next semester

or well "groups and their representations"

[karmic thorn]

I can't even pretend to know that I understand what a module is

[quick hornet]

show that the centre of Aut(G) is isomorphic to the cyclic group on 4 elements

[calm crane]

[quick hornet]

idk how you'd do this without linear algebra

but regarding it as a vector space makes it ez

[hasty turret]

A module is a vector space with a ring which is almost a field

[karmic thorn]

almost?

[calm crane]

huh that's interesting

[karmic thorn]

What's the missing bit?

[hasty turret]

There can be elements without multiplicative inverse

[gray gazelle]

field = commutative division ring]

[karmic thorn]

Aah

[gray gazelle]

field = quotient by maximal ideal

[stray veldt]

a module is like an ideal but more general

[karmic thorn]

I'll probably start with Jacobson this summer

[gray gazelle]

all of the theorems in algebra are true

[calm crane]

lmaooo i read nontrivial nonabelian

and was like

wait

am i really dumb

[gray gazelle]

Where will I use Bessel functions?

[calm crane]

wait wouldnt aut(G) be larger tho

[calm crane]

solving jacksons em problems

cuz like swopping 2 generators is still a aut

[worldly basalt]

Bessel function is solution to a type of ODEs called bessel differential equation which show up in a lot of natural phenomenon

[quick hornet]

@calm crane the centre of Aut(G)

[calm crane]

ahhh

lol i rlly cant read

yeye makes sense now

[quick hornet]

the idea is to view the group as a vector space over [REDACTED] and then your automorphisms are [REDACTED] which obviously linear algebra gives us a lot of tools to study

and [REDACTED] commute precisely when...

fill in the blanks

[gray gazelle]

[sudden kindle]

interesting perspective

[calm crane]

am kinda mentions it iirc?

vwey cute

[sudden kindle]

i hate it when people say a module is a vector space over a ring

[calm crane]

i mean it kinda is

[sudden kindle]

no

[valid moth]

@quick hornet oh that's nice

there's also like, i forget whose it was...

ah ernst witt

right so witt's proof of wedderburn's little thm

as seen in proofs from the book

yeah so just the initial idea is to treat R and C_s as vector spaces over Z (Z(R) that is)

(centralizer of some s)

im not sure if im allowed to post the link anymore as per the new rules lol but you can just find it easily by googling 'proofs from the book pdf'

@calm crane have you seen this btw

[calm crane]

just post

not yet

[valid moth]

yeah i mean it's like, it's literally a uni link so like i dont think it's against the rules lol

https://u.cs.biu.ac.il/~margolis/Sadna/Proofs rom the Book 3rd Ed..pdf

page 23

as in, proving finite division rings are fields

that's wedderburn's little thm

witt's proof goes into cyclotomic poly stuff

[calm crane]

oo

[valid moth]

yeah i mean this is a pretty nice book

if i ever had the occasion to try to get someone interested in math i'd definitely take inspiration from it

[calm crane]

ooo

i actually never read this book lol

[valid moth]

lol yeah I never read that much of it

but it's cool to just have as a reference as I use it

[narrow talon]

Okay, last book question for now, Tu vs Lee?

Leaning towards Tu

[gray gazelle]

Nice book

[stray veldt]

Tu is easier, Lee has significantly more detail

[gray gazelle]

they are equally well written

[narrow talon]

How about Shahshahani?

To be honest, I'm not sure my topology is up to snuff, just don't want to deal with a book like Munkres. So I lean towards Tu followed by Bott Tu

[gray gazelle]

lee's ITM

[narrow talon]

It's alright but bloaty

One day I'll have to be the one to write a "topology for analyst" book

[deft sedge]

any read infinite powers by that dude steve

?amazing

[narrow talon]

Ch4 of Folland might work actually

[gray gazelle]

folland's analysis book?

i guess i haven't read it

wait folland has a section on topological groups and haar measure

based

I feel Springer books are of good quality(content)

[narrow talon]

Yeah

Folland is a pretty damn good book, also has some nice sections leading very naturally into more advanced topics in analysis. Wish I would've had it as my real analysis text over Rudin (though I'm not a Rudin hater)

[primal mica]

When conducting independent study into mathematics (In my case as a tool for physics) is there a good way to judge what topics in text hold value for furthering studies, or should I cover all subjects in a text to some substance and just allow myself to naturally forget those that do not build upon themselves as much?
Additionally, what would be a good first semester PDE book? (Knowledge in ODEs/Basic Linear Algebra/Stats, should I have a broader base for this subject?)

An Engineering friend gave me "Applied Partial Differential Equations" by Paul DuChateau and David Zachman, but I thought I'd see if there are other recommendations.

[deft sedge]

i think knowing some stuff outside what your studying will help lead to original creativity by possibly finding a connection between two totally opposite subjects of each other

im trying to connect math with addiction and pyschology

using math skills like how you cant have a fact without evidence nor evidence without a fact can def be brought into addiction

[gray gazelle]

IMO you'd probably find some of the mathematical methods for physicists type of books provide you the best overview and then you can branch off into individual topics

So the main ones are Arfken&Weber, Boas, And Riley&Hobson&Bence

depending on how deep into math you want to go there are others

but they try to stick to stuff that will pay off for physicists

for self study all of those have solution manuals around

[tight crag]

There are many facts without evidence

[deft sedge]

youre going to have to give me an example... are you speaking of facts that are yet to be proven? or you have actual examples of facts without evidence?

[gray gazelle]

you've got your known knowns....

[tight crag]

Yeah lots of facts left to be proven, also there are theoretically some facts which cannot be proven at all

Eg the statement "this computer program will never halt"

[deft sedge]

thats a fact? thats a definitive known fact?

[tight crag]

Yeah this is the halting problem

Or alternatively Godel's incompleteness theorem

[gray gazelle]

continuum hypothesis

[tight crag]

Well that's a little different

[deft sedge]

i mean evolution is a theory vs gravitiy which is pretty much a law but i mean even those two are complete in different realms

[tight crag]

I'm not sure what that means

[deft sedge]

im saying event hough the differences are infinitesimal a theoretical fact is not a fact bc its a theoretical fact

[tight crag]

I'm not sure what a fact is then

[deft sedge]

fact is somehting thats proven with evidence

[gray gazelle]

I'm not sure what being sure even is

[deft sedge]

other wise its a hypotethis

no up without down and no down without up

[gray gazelle]

what about nonorientable spaces

[tight crag]

Are you saying you don't believe the evidence for evolution?

[deft sedge]

i know this stuff i lived with my mom for many years and she never has proof buit she calims its all facts

thats how im going to connect math and pyschology

i need to prove that without backing it up theirs a possibility its not fact

no gaps

[deft sedge]

whats an nonorientable space

wait

[strange mulch]

Evolution is obv a fact however the theory that man evolved from the ape isnt. It is a likely to explanation but its truthness is not something we can validate.

[deft sedge]

let me google first i wanna figure this out on my own

[strange mulch]

Is it a fact that the sun will rise tomorrow?

[deft sedge]

no

but it iwll

what if an astroid comes out of left field

small chance

but their is a chance

[deft sedge]

oh you just got me hyped on this one

i dont no poopie about that subject but this is why i joinied this math squad

these are the elite

im in recovery and the only thing that satisfies the same urge is trying to understand or figure out some truth

and math is th eonly way to discover that truth

[deft sedge]

are you asking if nonorientable spaces are real or not

am i even asking that question correctly

whats considered a mobius strip? time?

recording tape

i def want to start understanding some super symmetry and Shannon coding

i know theirs no program code in the foundations of life but theirs some sort of compression math at the bassis of life i thikn

[narrow talon]

This is circular, it’s impossible to give an example a fact without evidence if you consider evidence to be the thing needed for fact

But in fact this question sits firmly in the land of philosophy/logic. Say evidence is given, we need a certain amount of evidence to say that something is fact (if not I could provide a single example and give “god exists” as a fact). How do we come up with a notion of how much evidence is needed? Is the amount of evidence needed to prove something is a fact itself a fact? Ie. Is it a fact that having say, a p value less than 10^{-17}, guarantees that something is a fact?

[warm socket]

how are you going to prove that gravity will continue to exist in the future

if you get too hung up with your evidence requirements you can't do anything

[narrow talon]

You could of course define this, say a fact is something with xyz statistical properties, but how would that be well grounded

[narrow talon]

Yeah, exactly my point

[deft sedge]

theirs a limit to evidence for sure has to be

once you equal it

[narrow talon]

But how do you ground that? And what evidence do you consider significant?

[deft sedge]

but yes how to find that equation though

theirs got to be a way to be a spectrum

like heat

[narrow talon]

It doesn't necessarily have to be an equation I think, but it's hard to think of something that would make sense

[deft sedge]

or pH

[narrow talon]

What about them?

[deft sedge]

well the more evidence the more factual right so... wait now factual is like infinity

is fact unobtainable?

bc if it was then it would be law

[narrow talon]

Depends on what you mean I guess

[deft sedge]

well it freaked me out when i discovred all memory is subjective

[narrow talon]

The key word underlying this that you haven't mentioned yet is falsifiability of course. We need not evidence, but falsifiable evidence

[deft sedge]

word well thats wht i love wsa it einstein or who said

"everything is true until its proven false?

but then we record something

theres fact

now if our memory = the recording

is our memory fact?

[narrow talon]

But again, I think you'll run into some definition pushing no matter what, until you run into logic in which case you have to contend with incompleteness

[deft sedge]

video tape*

[narrow talon]

I'm not so sure math is the place to derive knowledge of what fact is either way. Math doesn't operate like the rest of the world, we can state the axioms we're assuming and definitions we're using. That's not exactly doable outside math or a similar construction

[deft sedge]

theirs gotta be a way to somehow capture old light and reflect it to show and older time and then some how find a way to access that old lighting

[deft sedge]

thats what im trying to prove is that we can connect math to everything somehow

bc if i can make addiction mathematical

i can prove an answer

I have ADD

[hearty steppe]

[deft sedge]

just hear me out

[narrow talon]

Of course you can connect math to whatever you want, the structure is abstracted, it's meant for you to be able to plug basically anything in. But getting an accurate representation, or somehow creating a mathematical structure which matches the underlying structure of what you're trying to model to prove anything about whatever you're modeling, extremely hard

[deft sedge]

it migtgh sound crazy but i got math behind it

[narrow talon]

Doing it for everything, not just extremely hard but completely unfeasible

And you would definitely not be proving anything about the underlying thing, just the mathematical abstraction you've plugged the thing into

[deft sedge]

if thats true than james gates jr is gonna be dissapointed bc if somehow we are in a simulation then it all has to be defined mathematically

[narrow talon]

Why? Where is evidence that it's mathematical?

[buoyant spire]

Right, say you want to model the velocity of an rc car being controlled by a person. What kind of model can you make that would reliably predict the kind of inputs they would make?

[narrow talon]

We've gotten lucky so far maybe, but have no way to know we will remain so lucky

[deft sedge]

physics is th ebackbone of eveyrhtighn

and math is the backbone of physics

[narrow talon]

Is it?

[deft sedge]

hmm

possibly

haha got me

but then math can prove that

[narrow talon]

Maybe see how much physics we just cannot describe mathematically yet and consider that we've built up a lot of math to handle problems in physics

[deft sedge]

well we havent proved it yet

but we def havent disporved it yet

[narrow talon]

Proven what?

[deft sedge]

that everythign can be explained mathematically

someday

[narrow talon]

You cannot prove that...

[buoyant spire]

It is honestly amazing the extent that physicists have been able to model our physical world through the use of mathematics, but like Jason said, there are certain things that are nigh impossible to describe using math as of right now

[deft sedge]

P vs NP

[tight crag]

What does that have to do with anything?

[deft sedge]

ive heard that question 20 times haha thats the point

[quick hornet]

how are we supposed to describe the universe with math when we cant even describe math with math

[deft sedge]

we can

we will

[tight crag]

Lol

[deft sedge]

thats what im trying to prover

[molten wave]

[deft sedge]

help

[tight crag]

Are you quoting hilbert?

[deft sedge]

help me disprove

[molten wave]

ok proover

[narrow talon]

[deft sedge]

hahahah

provith?

[broken meadow]

-Jaden Smith

[deft sedge]

mike tyson

[quick hornet]

really tempted to misapply incompleteness here

[deft sedge]

i have a lateral speech impetiment

[tight crag]

I already did

[quick hornet]

dang

[buoyant spire]

Maybe you would find it interesting to work with a local physicist or physics/mathematics professor?

[quick hornet]

i got owned

[molten wave]

an inconsistent formal system is complete 😌

[quick hornet]

the universe is inconsistent QED

oh god

so tempted to make

[tight crag]

I also applied the halting problem

[quick hornet]

a political joke

must resist

[deft sedge]

mom sweares i dont have a speech impediment... tell that to the people that need to put windshield wipers on their glasses whent they stand in front of me when i speak

[molten wave]

anyway what does this have to do with books

[narrow talon]

Are you an under-division undergrad?

[deft sedge]

Infinite powers opened my mind

by steven

[deft sedge]

i attended WPI for a year and then life obstacles swalloed me like black hole

i just read a lot and i like math

[tight crag]

I find it so funny that you semi quoted Hilbert while advocating for a program similar to the one he advocated for 100 years ago

[narrow talon]

Have you learned math past analysis?

[graceful bridge]

Im so confused. Where in Dummit & Foote is all of this?

[deft sedge]

but im in recovery from addcition and math actually help settles it

like poepl like watching bob ross

i enjoy math

[deft sedge]

who did me?

[tight crag]

Yeah

[deft sedge]

who isthat

im looking him up

[buoyant spire]

If you haven't checked out his channel, you might find Grant's channel 3blue1brown to be interesting

[narrow talon]

Then do more math m8! If you enjoy it surely none of us will stop you

[deft sedge]

i wanted to find a team of friends to like make a book club but do a math club

maybe tackle a textbook

[narrow talon]

Which textbook?

[deft sedge]

and then meet every week to go over it

idk something for bveginners preferbly

[buoyant spire]

Maybe you could make a discord server? You could also use it as an organizer for your ideas

[tight crag]

He said
"Wir müssen wissen, wir werden wissen!"
Which means roughly "we must know
we will know"

[deft sedge]

i wanan also prove college is striaght poopie caca

[narrow talon]

I'm pretty busy atm but there's one I'm reading outside classes if you're interested in probability theory

[deft sedge]

you dont need a rich capaltisist to sign a piece of a paper to deem us worthy

got math to prove t hat

[quick hornet]

if theres rich capitalists in charge of schools why are so many of them underfunded

[deft sedge]

thats hilarious i souded like that when braces bc i had a speech impediment and i speak english from new york but all i did was spit and make noises"

[buoyant spire]

Just wanted to say, I'm really liking Anton's Calculus

[deft sedge]

they take that money and buy cocaine and hookers

or in jeffery epsteins case rapes little kids

[quick hornet]

...

[deft sedge]

hey someone gotta stand up but move on quicly haha

poop those people in power too

o no cursing

damn sorry

can i delete that

[quick hornet]

i mean my point stands, most unis are nonprofit and barely manage to stay afloat

[gray gazelle]

hey, does anyone have recommendations for resources for learning statistics?

[quick hornet]

while the TOP officials (like, the president) do tend to make $500k-1 million a year, im not sure thats "rich capitalist" territory

though certainly very wealthy

the bigger problem isnt a single individual and more general administrative bloat

[deft sedge]

i just with evolution colleges are optional but should dicate someones career

like ive been watching trig and geo and logs and exponets on youtube

[quick hornet]

@gray gazelle stats is weird because it's kind of taught in 3 different ways depending on the students' mathematical background

[deft sedge]

now i gunateee bc i love math id outdo any kid that just went thru college barely putting in effort

[quick hornet]

do you want calculus-based? algebra-based? measure-theoretic?

[gray gazelle]

calculus-based

[deft sedge]

Mathematical Proofs: A Transition to Advanced Mathematics by Chartrand, Polimeni, and Zhang

i wanted to start with that maybe?

[gray gazelle]

my uni truncates statistics into a 3-week course, placed at the end of calc 2

[broken meadow]

that's an ok book yes seraph

[deft sedge]

my research tells me any beginner can start here

do you agree?

[broken meadow]

Yes

[quick hornet]

alright, admittedly im not too familiar with common textbooks there

[deft sedge]

https://tenor.com/view/yes-sweet-hell-yes-pump-it-gif-3532253

[broken meadow]

just spend like

idk

2 weeks

going thru the basic parts

[gray gazelle]

hm

[quick hornet]

i know the applied-stats people at my university love Field's Discovering Stats using R

[broken meadow]

and then when u want to just go pick up any linear algebra textbook to continue

[quick hornet]

as an intro text

but ive never read it/taken a course in the subject so idk how good it is

[deft sedge]

ok so dont dwell or spend to much time just get a jist for it and understand it and when i feel comfy then just moveon?

[gray gazelle]

i would use the textbook provided by my professor, but it’s unnecessarily convoluted and requires that we write his examples in it

[buoyant spire]

Gilbert Strang's linear algebra video lectures on mitOCW are very nice

[broken meadow]

yeah i mean it's not a whole lot of material imo but you can do whatever

don't dwell yes

[gray gazelle]

is there a yt channel that uploads/has uploaded good videos for statistics?

[deft sedge]

Elementary Linear Algebra by Howard Anton or Linear Algebra by Friedgber, Insel, and Spence

[broken meadow]

the latter is what im reading rn :3

idk how the other one is

i can vouch for the second one lol

[deft sedge]

the latter? can you send the full name and author

[broken meadow]

friedberg/insel/spence

that one

[quick hornet]

"the latter" means "the last in a list"

[deft sedge]

i just watched a few youtube channels of how to begin math and i made lists of all the texts books they suggested

[gray gazelle]

.

[quick hornet]

(usually the second in a list of two)

[deft sedge]

and then i made a tree of which ones were repeated in the videos bc clealry thoses are the better ones

[gray gazelle]

he was referring to the book that metal is reading

[deft sedge]

not gonna like my dopamine levels are off the charts im excited here fellow mathemticans... i want to make archmedes proud

thats my dude

[gray gazelle]

i unfortunately can’t relate

but go off, my man

[deft sedge]

oh... i was thinking clatter then thought santa landing on my roof"

thank you

[deft sedge]

haha what you mean math doesnt bring you that excitment?

[gray gazelle]

no, not at all lol

[buoyant spire]

Yes same here

[deft sedge]

ahh so read infinte powers by steve strogatz

[gray gazelle]

i need to finish calc 2 and take discrete mathematics and linear algebra for my major

[deft sedge]

prob change your mind

what you learning like the infinity series and stuff

'\

[gray gazelle]

?

[deft sedge]

calc 2 is the most difficult of the calcs right

[gray gazelle]

it’s a curve ball, yes

[deft sedge]

calc is so dope bc its like the language of gods

[gray gazelle]

i feel as if the later courses would be easier, given that they expand on the topics presented in calc 2

but i wouldn’t consider it particularly difficult if you study for it

[deft sedge]

word calc three is just the Z axis included

[gray gazelle]

not entirely

[deft sedge]

i found precalc and calc 2 to be most difficult

[gray gazelle]

you have to solve nth-degree integrals in calc 3 and beyond

those don’t seem fun, imho

pre-calc was undeniably more difficult than calc 1 is

but i also found it more useful than i do calc 1 and 2

navigation and logic were my 2 favorite topics

[narrow talon]

Cassella Berger is sort of the standard calc based math stats book

[deft sedge]

precalc is way more useful bc its a little of everything

[narrow talon]

But it’s also not really great, for me at least. Most people like it

[deft sedge]

calc 1 i loved bc it was like usiung a quality rollerball gel pen touching a piece of parchment

it was so smooth and easy to understand

then boom

all hopes and dreams sodomizing me when entering calc 2

like "oh you thought you new math take your seat little bitch"

[deft sedge]

ok in order to advance to understand symmetry and super symetry and string and super string... do you need to know stats?

[narrow talon]

Haha mayybeeeee? I’m not the person to ask. Probability, sure, stats idk

[deft sedge]

i wanna learn how to draw Adinkras

[deft sedge]

whats the quote he said? haha

[deft sedge]

i have not learned that never even heard of it

[deft sedge]

that would be awesome

im about to read all about david hilbert

wow Principles Of Mathematical Logic i downloaded

by hilbert looks awesome

[obsidian valley]

there are better mathematical logic books im sure

[narrow talon]

Very important topic, people here seem to like Tao’s book on analysis

[deft sedge]

im just gonna type Tao's book on analysis into google and it should pop up?

[graceful bridge]

@deft sedge Yes, google "tao analysis 1", it should come up. It's a great book, Im reading through it on a spare time basis. It doesnt assume anything, but some mathematical maturity will make the read easier (analysis is usually not taught in 1st semester). As title suggest, there is also a sequel

Also, the concepts will be better motivated after having learned calculus

[primal mica]

Very sorry for the late reply! I did take math methods. For some background I’m a medical student who did physics as an undergrad, but I’m still passionate about physics and would like to continue self study as far as I possibly can. An idealized ‘end goal’ would be the mathematics necessary to truly understand the edges of our modern physics, so quite far into the future. I hope that provides adequate background. I’m looking to essentially continue building on what I already know. I also have a pocket love for math as well, so widening my general base of knowledge feels rewarding ultimately.

[gray gazelle]

there are more advanced methods books as well Hassani - Mathematical Physics comes to mind

[primal mica]

I see, I will check into it. My math methods course went off of professor notes almost entirely, so I'm not really familiar with the books for it. I will look into it if they continue, in that case. 🙂

[gray gazelle]

Frankel - Geometry Of Physics is also pretty interesting

yeah my methods course in university was mostly off of the professors notes with boas for the problems

methods is pretty wide depending on what you are preparing people for

so what's actually covered is pretty individualized

[primal mica]

Yeah, I could see that. The graduate program where I did my undergrad was largely solid state based and was probably influenced by that. The Geometry of Physics is a book I have not heard of and seems very interesting, so thank you for the recommendation. I will look into it!

[fluid bay]

reccs for homological algebra?

[ripe granite]

weibel + errata list

[fluid bay]

thanks, bro

[sudden kindle]

[quiet rose]

good morning everyone, is it possible to get some recommendations?
i really need to get better at the "maths" language (not sure what it's actually called if it even got a name)
but the kind that looks like this or similar Z={na | n∈Z}
i never had any focus on this kind of writing systems in my classes until i hit abstract algebra... So if anyone knows any good books, articles or something for practice i would greatly appreciate it

[stray veldt]

maybe look at the first few chapters of velleman's how to prove it

or the sets chapter of #book-recommendations message

[quiet rose]

thank you mate!

[narrow talon]

Halmos’ “Naive Set Theory” is another popular choice, but give Velleman a look first for sure

[deft sedge]

Can someone recommend a book about David himbert preferably one that is about logic/exponents and then one about a different topic of math that involves some form of Algebra or calc or trig or after calc

[pulsar geode]

anyone have good books on stochastic calculus?

[gray gazelle]

@pulsar geode : Is it for finance?

[deft sedge]

david Hilbert*

[pulsar geode]

honestly, just wanted to learn more math, but possibly finance applications later on

so id prioritize quality of book over applications

[narrow talon]

I have a few, what level? Ie. stochastic calculus or analysis

Shreve Stochastic Calculus for Finance is very popular for the stoch calc side of things, I’m using Le Gall right now for the analysis side

[gray gazelle]

What about 'Stochastic Calculus and Financial Applications by J. Michael Steele'

[narrow talon]

Pretty great, you’ll see it referenced all the time too so it wouldn’t be a bad thing to get familiar with the layout

For some reason I equate it with William’s book on probability, another great book at the level of Durrett (ie. use it before Steele)

[pale linden]

Is there an introductory number theory book that is good on intuition? I have no intuition for number theory

[gray gazelle]

@pale linden Copied - intuition in any subject of mathematics is a skill which can only acquired only though thorough exposure to that particular subject, by familiarising oneself with common proof techniques (to that subject/field) and by working through many toy problems (exercises, if you wish). As such, nothing is "intuitively clear" to novices, and this holds for experienced mathematicians approaching an entirely new subject for the first time, too.

[narrow talon]

Stillwell has a book, haven’t read it but he’s an amazing ug author so check it out

[pale linden]

Alright! That's a fair point! But some authors are better at conveying the intuition of what you're doing rather than just presenting formalism

Thanks for the rec

[onyx garden]

Things to make and do in the fourth dimension by Matt Parker.

Best. Book. Ever.

[deft sedge]

im about to begin Mathematical Proofs: A Transition to Advanced Mathematics (4th Edition) (Chartrand, Polimeni, Zhang)

anyone have any suggestions or advice or want to join

[gray gazelle]

@pale linden http://illustratedtheoryofnumbers.com/ might be the kind of thing if you are a visual thinker

[deft sedge]

if i wanted to learn super string theroy and super symmetry what are the text books starting with calc 3...i would use to self teach myself?

like what order to reach that destination

[gray gazelle]

imo that's more something you'd get help with on a physics server

https://math.ucr.edu/home/baez/books.html#physics

baez has some textbooks up to string theory

[sudden kindle]

@gray gazelle nt book look sick

[gray gazelle]

its like the number theory version of visual complex analysis/visual group theory

[sudden kindle]

This book looks really good!

Teach python along side elementary nt

[gray gazelle]

the python is more an add on later

the book doesnt have python from what i recall

but he added it on his site

speaking of visual complex analysis though

look whats coming out this year: https://press.princeton.edu/books/paperback/9780691203706/visual-differential-geometry-and-forms

[sudden kindle]

Ooh

I should try out his complex analysis book

I read ahlfors but I still dont know any CA

[deft sedge]

i just read chap 0 in mathematical proofs a transition to advance math by zhang and two others

wow

like mathewmaticans know how to write

shit just got me hyped

[velvet briar]

I feel like I know some basic diff geo but don't know how to use it well. This book looks interesting

[gray gazelle]

he offers the first undergraduate introduction to differential forms that treats advanced topics in an intuitive and geometrical manner.
"the first" :sully:

looks neat

thanks for sharing

have you read his Visual Complex Analysis book?

[sudden kindle]

nah

[gray gazelle]

really gave a bunch of insight into the branch cuts and stuff that my complex variables course never did

[sudden kindle]

I'm gonna read that book, just need to rememebr when I have time

[pale linden]

I am a very visual thinker

I have trouble thinking of things without some kind of visual

[pale linden]

So there are visual CA and visual group theory books too??

[gray gazelle]

yes

[pale linden]

I'm in an abstract algebra course rn and the visual group theory book might be really useful!

[gray gazelle]

Tristan Needham - Visual Complex Analysis, Nathan Carter - Visual Group Theory

there's a set of lecture notes that has a lot of the visualizations too

lemme find the llink

http://www.math.clemson.edu/~macaule/classes/m19_math4120/

goes along with the visual group theory book

[pale linden]

:D thanks!!

[gray gazelle]

Oh there's a second complex analysis book with more colour: Wegert - Visual Complex Functions

[pale linden]

sidenote, but what exactly is the difference between an introductory group theory course and an introductory abstract algebra course? I get the impression the latter deal so much with groups its essentially the same thing

the group theory book looks neat

[gray gazelle]

i don't know what the difference is between them having never taken a course on that

sometimes there's a group theory for physicists course at some schools that focuses in on the stuff physicists needs and is probably less rigorous

[velvet briar]

They are commonly the same thing? Haha

As always refer to the syllabus for these tiny differences between courses

[pale linden]

Okay, you confirmed my suspicion though

[gray gazelle]

ie the physicists approach: https://courses.physics.ucsd.edu/2016/Spring/physics220/LECTURES/GROUP_THEORY.pdf

"1.1 Disclaimer
This is a course on applications of group theory to physics, with a strong bias toward condensed matter
physics, which, after all, is the very best kind of physics. Abstract group theory is a province of mathematics, and math books on the subject are filled with formal proofs, often rendered opaque due to the
efficient use of mathematical notation, replete with symbols such as ∩, ⋊, ∃, ⊕, ⊳, ♭,
c , ♠, ♥, ✸, ♣, etc. In
this course I will keep the formal proofs to a minimum, invoking them only when they are particularly
simple or instructive. I will try to make up for it by including some good jokes. If you want to see the
formal proofs, check out some of the texts listed in Chapter 0."

[pale linden]

typical physicist

[supple loom]

not really

[sudden kindle]

This dude literally just wanted to name a section ,"crystal math"

Hehe crystal meth

[hidden herald]

haha lattices

[gray gazelle]

he's got jokes all the way through

"This is possible only when k ∈ ∂Ωˆ lies on the boundary of the first Brillouin zone, for otherwise the vectors Kg and Kh are too short to be reciprocal lattice vectors[32]"
"32 My childhood dreams of becoming a reciprocal lattice vector were dashed for the same reason"

[pale linden]

What are your top math books?

[gray gazelle]

"question closed as too broad"

I don't really keep a list of favorites if that's what you're asking

[gray gazelle]

This has become another stackmathexchange

[hasty turret]

This has become another stackexchangemath.

[gray gazelle]

This has become another mathstackexchange.

[gray gazelle]

Another stackmathexchange this has become.

[gray gazelle]

Basic Maths For Dummies by Colin Beveridge is my favourite. I haven't yet understood all the topics bcz of complexity.

Become another stackexchangemath this has.

What Yodha says?

[pale linden]

Is this sarcasm?

[gray gazelle]

btw fun fact: you can jumble up the words in english sentences and usually still figure out what they mean

you do that with math writing and it's gibberish

Isn't it same for all language? At least for my mother tongue it's true.

most languages yes

there's a lot of redundancy built into natural languages

[wise vine]

What's the best probability book that is measure-theoretic? I plan to go into some Machine learning stuff in the future and I am building up my maths foundation.

On another note, should I also get a book about Manifolds? I'm still ignorant about ML tbh. I want to do applications but I'm not confident in my maths yet.

[gray gazelle]

@wise vine Machine Learning: A Probabilistic Perspective, by Kevin Murphy?

[pseudo forge]

book for real analysis?

[marble solar]

Pugh real mathematical analysis

Next

[gray gazelle]

Terrence Tao's Analysis Volume I and II

[hasty turret]

Pugh doesn't spend like 7 million years on peano axioms

[gray gazelle]

Understanding Analysis by Stephen Abbot

Can we add a free book(legal) sub channel with this channel? So that we can point them to the ppl?

[pale linden]

Ross, Elementary Analysis

[gray gazelle]

I am starting to like Springer books 🙂

if you have no proofs background Lay - Analysis With An Introduction To Proof is gentle

[calm crane]

not rlly one can usually decipher errors

[gray gazelle]

You won't need anything beyond early undergrad math if you are only concerned with the implementations

[wise vine]

I'm interested in the theory as well. And also I like the rigor in maths textbooks.

[narrow talon]

You definitely don’t need measure theoretic prob for ml, though something like “the elements of distribution theory” by Severini would be quite good for book like Murphy (or Bishop, which is my preference). Severini isn’t measure theoretic, but rather focuses on those elements of probability that are used often in statistics and machine learning (it’s about masters level, so not super introductory)

[wise vine]

I already know some measure theory from Tao and Stein though. That's why I asked what's a good measure-theoretic probability book.

[narrow talon]

Gotcha, in this case my rec actually wouldn’t change, Severini has little overlap with traditional measure theoretic prob books, so it’s kind of its own unique beast rather than something you read to avoid measure theory.

[gray gazelle]

You do need measure theory for ML,

If you are looking to go into research

Check out the book "Foundations of Machine Learning"

[narrow talon]

That book is really rough, the lines of thought are algorithmic more than mathematic imo which makes it tricky with a math background

[narrow talon]

For measure theoretic Durrett is standard and it’s pretty well written, Billingsley is a bit more thorough but I have not used it. For the PhD class we used Dembo and that was very rough, big jump from big Rudin to Dembo in difficulty

[gray gazelle]

Well what do you think about the one recommended in #book?

It's more introductory, probably suited for undergrad

[narrow talon]

Severini would also be more useful for FML, and the author expects a background in convex optimization and info theory. I’d say read it after an ISL or even ESL

[narrow talon]

Which one?

[gray gazelle]

"Measures, integrals and martingles"

[narrow talon]

Williams?

[gray gazelle]

R L Schilling

[narrow talon]

I’ve heard it’s basically the best book at this level but I have only checked out some chapters so I can’t say

[narrow talon]

Williams that is

[gray gazelle]

Hmm, I am asking about more books than I could read 😦

Is it good to spend 12 hours straight in Tao on the weekend(If I am not bored)?
Or should I split it across multiple days?

[gray gazelle]

If you can, then why not?

I am asking about others experience who spend huge amount of time on such texts at a go. Will it make me less efficient in absorbing?

I have hard copy of 'Euclid's Window: The Story of Geometry from Parallel Lines to Hyperspace' . Slow for me.

[narrow talon]

Multiple days! There’s lots of research showing that spreading study time over days is better than all at once

[narrow talon]

Don’t know much if anything about schilling

[narrow talon]

Also active recall, I’ve set up pages in each class where I’ve asked questions about all the important results so I can go back through them later and try and answer them. Below the questions are the answers so I can study them again if I really forgot

[narrow talon]

Looking at the table of contents it seems a little all over the place to me. Maybe that's not a bad thing, but it's definitely nonstandard

[gray gazelle]

My book. But why is it 'trim'?

Hmm, I hope that doesnt mean some trimming. Number of pages are same as pdf.

[marble solar]

I think that's one of the publishers or something

[gray gazelle]

Page quality is extremely good. 'Springer' word missing in the entire book.

Trim looks like an abbreviation

Yea, got it -- trim = 'Text and Reading In Mathematics' 😄

[prisma snow]

Lol

[karmic thorn]

TRIM is a collaboration book series by HBA and Springer. The distribution in (atleast) the east is handled by HBA, and afaik (atleast) in the US by Springer.

[gray gazelle]

Could anyone tell me by looking at https://www.ias.ac.in/article/fulltext/reso/024/01/0029-0050, is the journal good to follow. The journal has mixture of physics + maths + biology

[gray gazelle]

it's unlikely you can tell the quality of a journal from a single article

unless it's really really really bad

But you could say about the publisher by looking at how good are they in choosing?

particular things I'd look for: is the publisher good/respected? what is the impact factor of this journal? are they on a list of predatory journals? etc.

[subtle siren]

Maybe we can judge Ann Math with this article
https://annals.math.princeton.edu/2003/158-3/p04

[gray gazelle]

It's very complex. Ofcourse to me.

[flint forge]

im gonna say based off that one article

its not a real journal and it has terrible formatting standards, ignoring even the most basic of normal academic formatting

i.e. it looks like it was made in Word

[gray gazelle]

based

[flint forge]

I mean that paper looks intersting @subtle siren

[gray gazelle]

That's from most rated uni of India

[flint forge]

idk what to tell you its like

pop math with crank formatting

i didnt bother to evaluate correctness, im sure its fine, but its not good

Why is that lol

I only said objective stuff about it.

[sudden kindle]

The journal article @gray gazelle linked is from a journal called Resonance - Journal of Science Education and its published by the Indian Academy of Sciences and co-published by Springer. "The journal’s objective therefore is targeted primarily at science education for undergraduate students and teachers and focuses on enriching the processes of teaching and learning science thereby stimulating science education in the country."
The topics are not limited to mathematics; "The journal invites articles in various branches of science -- physics, chemistry, biology, mathematics, computer science and engineering and emphasizes on a lucid style that will attract readers from diverse backgrounds."
https://www.ias.ac.in/Journals/Resonance_–_Journal_of_Science_Education/

From what I can tell it's not a journal in the research sense, its more like a magazine for undergrads.

[subtle siren]

^That's a good look at things.

[karmic thorn]

The standard arxiv preprint format is the best.

[narrow talon]

Really weird request, but is there a short paper on like visual functional analysis? Trying to think of how to represent an operator visually effectively

Obviously the natural way is to just view how it acts on the space of continuous functions, similar-ish to how we visualize GPs when dealing with regression. Just curious to see if there was an exposition taking this route somewhere

[marble rock]

are there any textbooks on algebraic topology that

are easier on the point-set topology side?

i just finished point-set but idk i dont feel so confident yet

and i want to try learinng at

i also learned some on banach spaces and hilbert spaces if that helps

[pine igloo]

if you understand french, there is this book
idk how you will feel about though
but strengthening yourself in point-set topology isn't a better option for now?

check this one out too

[marble rock]

i dont

i mean idk how should i strengthen my self in point-set

and i ugessed if i learnt some AT it would strengthen by force

ig

@pine igloo

this doesnt have as much problems tho

the jp may

[gray gazelle]

my best guess is see if something written by a physicist has a bunch of diagrams

i don't know if this book is any good:

Shima - Functional Analysis For Physics And Engineering

does have diagrams though

[hearty steppe]

Shima seems to have a book for mathematical methods for physics and engineering. Might be the same level and depth of concepts covered in a more popular math methods for physics and engineering which I believe is Riley et al.

@gray gazelle

[narrow talon]

Thanks, I’ll check it out!

[fluid bay]

@marble rock i read a little bit of rotman's intro to AT and liked it. Maybe you could give that a try

[marble rock]

ty

[gray gazelle]

My New book 😄

[calm crane]

not rlly lol point set is like just set theory at kinda jus assume sufficiently nice spaces half the time

there isnt too too much in point set to really care about tbh

[marble rock]

yea i figured

i only like used sets when learning point-set

and talked about properties of sets ,

connected/compact

etc

but i still dont know how like people actually did AT b4 general topology

what were they talking about

[calm crane]

all you really need tbh is like compactness continuity and appropriate notions of connectness tbh

[marble rock]

say i know about those topics with some seperation axioms and weirestrass approximation theorem

can i read hatcher

( with algebra )

[calm crane]

i gave up on hatcher too much intuiting

rotman was a pretty chill intro

[marble rock]

can i read rotman with what i said

i am not that into pictures honestly

and polyhedra and shit gross

XD

@calm crane

[calm crane]

iirc rotman is pretty simple

tbh

my advice is dont be scared

just read

if you realize it's too hard

then figure what prereq you're missing

theres no harm in seeing what a area has to offer

cuz nowadays books are free

[marble rock]

its not about scared as much

i dont know when im supposed to know if im good enough at this topic to move on

cuz sometimes i struggle with problems etc

some level

is good

i like pictures but im not INTO them

like i dont want ot prove shit with pictures

or having pictures instead of things im used to with math

how can u be

not rigorousu

uh oh

like for example saying a homotopy exists

by a picture?

but not explcitily stating the homotopy

[gray gazelle]

Dieck - Algebraic Topology has no pictures unless you count diagrams

commutative diagrams that is

[narrow talon]

Btw, maybe look at Folland’s (the analysis text) chapter on topology and do al the problems? It’s basically a crash course on point set topology

Also, @gray gazelle Fomenko and Fuchs? Really? I thought that book was really advanced looking at the ToC, could you actually learn the content from it? (Genuinely asking btw, I will inevitably have to learn AT for real rather than at the level of the bs class I took and am curious)

[steel viper]

no he has square homotopy diagrams

like bottom right side is the first map and left top side is the second map and the square is a htpy between them

[gray gazelle]

ah misremembering

certainly more spartan than hatcher

[steel viper]

yea

i think the only example i can recall off the top of my head is him showing that smth is a natural transformation

htpys between maps yield a natural transformation between the functors under the fundamental groupoid or smth

[graceful bridge]

Why not just read Lee's Topological manifolds? The first chapters covers the necesseary topology in a pretty compact way, and the second part of the book will cover the fundamental topics of AT. It was enough for my intro course in AT (even though Hatcher was formally the course book).

It's also a great book which prepares you for another well-regarded book - smooth manifolds by the same author.

[steel viper]

that seems fine for a preliminary pass through but id be pretty wary of it if your goal is just to learn AT

tho if your goal is to learn point set in some depth with some AT as a bonus that seems nice

[graceful bridge]

What I don't like about Hatcher is that I feel like I'm supposed to understand the concepts by reading all the examples. But I don't.

[steel viper]

it is definitely a very geometrical book ¯_(ツ)_/¯

but there are other options

bredon does AT as well with a more geometric slant

[graceful bridge]

Most of the examples I can hardly understand.

[steel viper]

geometric as in like

it does some geometry too lol, its less visual than hatcher

yeah idk i feel like working out the examples and drawing diagrams is how you develop ur visual intuition

[hollow peak]

doing topology for the geometric aspects

no I am here for the categories 😎

[steel viper]

do bredon then

[hollow peak]

I read the first like 4-ish sections of hatcher before I lost my motivation

one day I will

but not soon 😎

[steel viper]

galois correspondance for coverings? oh u mean an equivalence between the category of covers of B and the transport category of B?

[graceful bridge]

Even the last chapters of Munkres covers fundamental AT topics. It's probably better to start learning AT in such a book, as a natural successor after basic topology. And only then move on to dedicated AT book.

I have tried several AT books, I never found one that I like

[steel viper]

idk if i agree with that tbh

for one thing thats a lot of time learning point set that i dont think is necessary for AT if u just want to learn AT

or if uve already taken a point set course

[hollow peak]

to be fair point set and at are very different beasts

like, I wouldn't really call point set required reading to do AT

as long as you understand the basics

[steel viper]

AT is like a hard boss in a video game point set is like a boss in a video game with too much health and a sleep spell

actually the putting you to sleep is literal

[hollow peak]

I like point set topology

it's good for the soul, like LA

[graceful bridge]

Yes, you can probably skip many chapters. Personally I just learned AT concepts much better from Lee and Munkres than any AT book I tried

[steel viper]

idk i think there are a lot of good AT books with a lot of different approaches

you can probably find something

spanier, tom dieck, hatcher, bredon, uhh

topology and groupoids

[hollow peak]

why read AT when you could just reinvent the field yourself independently of literature

just figure it out lol

[steel viper]

[hollow peak]

SO TRUE!!!!!

[broken meadow]

:sotrue:

come on

please add

😭

[steel viper]

tbf there is a very natural progression from htpy to algebra if u are category brained

[hollow peak]

did you... study algebra moth

[steel viper]

yes

[hollow peak]

based

[steel viper]

im better at algebra than i am at AT

[hollow peak]

I just assumed you did AT and picked everything up lol

[static crest]

I read "category braindead" first

[steel viper]

lol

fomenko and fuchs seems based af

i will probably try the latter half of the book once i finish bredon

idk how much overlap there will be but bredon doesnt really do spectral sequences

wait no why did i say i did AT first i did algebra first

jacobson

sry my brain died

[hollow peak]

homo-logical algebra

man I just need to get algebra pilled

[graceful bridge]

Im probably not going any deeper into AT than the intro course anyways... Homology was just a pain

[steel viper]

@gray gazelle tbf F&F seems like it does shit fast

also no groupoids sadge

i do like the diagrams tho