book-recommendations

[steel viper]

is it a blessing or a curse

[karmic thorn]

I don't like Linear Algebra for some weird reason

I wish I never have to study it lmao

[steel viper]

define "linear algebra" here

because there are lots of approaches to teaching it

[karmic thorn]

Matrices, vector spaces and stuff

[steel viper]

some of which are much less interesting than others

[karmic thorn]

I like the approach starting off with vector space axioms though; I might pursue it once I finish introductory abstract algebra

[steel viper]

you should learn linear algebra before starting abstract

do artin

it combines them

[karmic thorn]

Artin's too terse

[steel viper]

but most abstract alg textbooks will assume some familiarity w/ linear

[hasty turret]

define "linear algebra" here
@steel viper abelian groups with field action

[steel viper]

monkaS

[karmic thorn]

I have Gallian's text, it doesn't assume any background in Linear Algebra

[steel viper]

gallian is uh

[karmic thorn]

What? It's good! XD

[quartz pawn]

Yea Artin assumes some familiarity with LA i feel

[steel viper]

artin assumes less familiarity than D&F and jacobson

and uhh

aluffi

[karmic thorn]

Lol I'll just stick with Terry and Gallian for now; I'll come back to Topology latersss

[valid moth]

they should make one that assumes a bit too much familiarity and call it the step-book

[serene crater]

I like the approach starting off with vector space axioms though; I might pursue it once I finish introductory abstract algebra
@karmic thorn I recommend you Halmos 'finite-dimensional vector spaces'

[karmic thorn]

Cool, I'll check it out!

[gray gazelle]

Does anyone have "Elementary Linear Algebra, Applications Version" the 12th Edition? I tried to look on libgen but I didn't find the 12th edition

[broken meadow]

did you try searching by isbn

[gray gazelle]

I tried

And I still can't find the book

[broken meadow]

F

[gray gazelle]

author?

by Howard Anton

[trim narwhal]

Is Thomas better than Stewart for starting Calculus?

[golden bear]

Almost every college uses Stewart. @trim narwhal

But choose whichever is cheaper for you to purchase

[hearty steppe]

I think most colleges use Stewart and some use Larson. They’re similar in the amount of problem sets you get. Maybe a bit more with Stewart.

Use Professor Leonard Youtube Channel to learn while doing problems out of the book

[pulsar aurora]

My college uses neither

[tulip pawn]

We used Spivak's Calculus, but I don't think that's really for learning Calculus, more for proofs. I've heard of Stewart being standard though

[gray gazelle]

If it isn't, it's close to being one

Overall, a pretty good text for teaching yourself from

[reef talon]

any great precalculus textbooks?

[wooden sparrow]

AOPS seems to be a good option

[reef talon]

I looked up Math stack exchange and found Precalculus Mathematics in a Nutshell

[reef talon]

I think AOPS is too hard for me @wooden sparrow 😅

[wooden sparrow]

Ohh

I like their way of teaching though

[reef talon]

yeah me too, I checked out the first few pages

[wooden sparrow]

Okayy

[reef talon]

I think the textbook from open stax is a great resource to start

[wooden sparrow]

Yeah they're not bad

[remote bobcat]

What's the best measure theory textbook?

My measure theory course doesn't have a specific textbook but I want to make sure I use a good one for reference

[gray gazelle]

can someone recommend a book for Functions and Graphs, for aptitude.

[limpid gazelle]

I'm currently reading "Real Analysis for Graduate Students Measure and Integration Theory" by Bass, and I think that book is pretty good. Also heard that Stein, Tao, Folland, and Bogachev are good

@remote bobcat

[remote bobcat]

Awesome thanks!

[marble solar]

Stein gang all the way

[reef heron]

https://www.cnn.com/2020/09/02/politics/joe-biden-nobel-laureates-endorsement/index.html?utm_source=twCNN&utm_medium=social&utm_content=2020-09-02T07%3A40%3A06&utm_term=link

[gray gazelle]

this we need ^

For right now

[crystal spade]

Hi I'm doing GCSE higher edexcel paper for 2021 and I haven't worked in around 6 months due to the lock down and I have forgot 90% of the topics I learnt before even tho I hadn't covered all the topics

Is this book good and does it cover all the topics?

[hidden abyss]

you should try and understand the topics, not memorize, so that you dont forget that much

however, the way schools teach maths isnt great

[hearty steppe]

Most people in US are screwed in public education honestly. Unless your parents have money

[gray gazelle]

that is why I teach myself maths

Much better education

[wooden sparrow]

Yup same here

Private schools here are horrible too

[marble solar]

I think US public education is actually pretty good

But this is book discussion

[gray gazelle]

I think lots of people say education in their own country is bad and worse than others

[marble solar]

Well it's easy to criticize what's going wrong than see what's going right/has been improved

[hearty steppe]

Everything pretty much goes right when your born with a silver spoon in your mouth.

[long bear]

It's called investing all your skill points into luck

I'm pretty sure the original statement

Most people in US are screwed in public education honestly. Unless your parents have money

[karmic thorn]

Does anyone know of good references for Euclidean Geometry(not analytic, the polygons and circle stuff with their theorems/proofs)? I'm out of high school but I never really got a grip over Euclidean geometry, and want to brush up to get some idea with proof writing.

[marble rock]

if you want an idea with proof writing

you should get a proofs textbook

instead of learning euclidean geometry for its sake

if you want euclidiean geometry you can try the olympiad stuff

by evan chen

[karmic thorn]

I looked at Chen, I'm not exactly looking for olympiad stuff

Mostly the basics, working from basic postulates to the way up.

[marble rock]

try euclidean geometry: a first course

[karmic thorn]

Aight, I'll look at that. Thanks!

[hearty steppe]

Some people just get proof writing I guess and don't have to go through a whole proofs book. I don't understand those people personally. I'm thinking they all have comp math experience.

[gray gazelle]

I don’t think anyone gets it overnight

[hasty turret]

Olympiad experience, prob

[hearty steppe]

thats what comp math is

[slender sphinx]

what no

[hasty turret]

I don't get why you need an entire book to learn "how to prove things"

Can't you just learn it by looking at some math proofs?

[hearty steppe]

no

its not that easy

kids in grade school spent years doing olympiad and their own extracurricular spare time learning this stuff before majoring in math when they got into college. I'm talking about the kids that score on the top of the curve and immediately go to grad school.

[slender sphinx]

what

[hearty steppe]

those are the ones that "get it" when they freshmen in college lol

[slender sphinx]

In my opinion, proofs are a lot less scary than one might expect

Intuitively, they are just a logical extension of how we think

People may find difficulty with the "rigor" and formalness of proofs, but that comes with practice

[hearty steppe]

yea but it gets more complicated than that when you do proof problems. I'm speaking from personal experience

[slender sphinx]

Yeah, and I speak from mine

[hearty steppe]

definitely but that doesn't happen overnight

[slender sphinx]

I never claimed it happens instantly

[hasty turret]

Neither did I

[long bear]

I don't get why you need an entire book to learn "how to prove things"

Can't you just learn it by looking at some math proofs?
@hasty turret

regarding that

From my minimal experience with proofs, I'd imagine just looking at proofs and trying to learn it just from their structure would be analogous to looking at a game of chess and figuring out the rules

It would be a longer process than being explained the rules up front

but again

really

[hasty turret]

Ok,That came off in a bad way

I meant,You would learn proofs eventually if you are exposed to proofs enough

[long bear]

I'd now like to try it lol

What do you mean by exposed to proofs enough? As in being exposed to several "conjectures" and proving them? Or do you mean analyzing proofs and studying their structure and building an intuition from that analysis

[hasty turret]

Yea,The latter

Ask yourself what the author does or what motivates the said set of steps

[long bear]

Interesting

[hasty turret]

For example,Take a look at the Contradiction proof of irrationality of √2. A natural approach would be to ask if √2 is rational and ask what would that fact imply

[long bear]

Well, I'm not quite through the meat of Vellemans book, but that actually sounds like a really fun approach

[hearty steppe]

The point is you have to practice to really get it. Maybe there are some people that can just get it.

Like actually work through a proofs book

[hasty turret]

Any math textbook would force you to get good at proofs

[shadow nebula]

what about height

and uh other genetic things

I'm saying "you have to practice to really get it" is not true for genetic things

[long bear]

Danny Andrews the lad @shadow nebula

[shadow nebula]

what did the lad do this time

[long bear]

Well uh, there's going to be a multi-billion dollar class action by all the businesses that have been shut down for such extended periods of time because of Danny

[hearty steppe]

What exactly is your point

I'm just speaking to regard of spending time studying something to understand it

I like to be very explicit about it honestly cause people like myself can miss between the lines of what other people say

Maybe some people don't need to use a proofs book to understand proofs, but it has been my strategy so far to use a proofs book and it has helped immensely. That is all I'm really getting at here.

[vernal compass]

@karmic thorn A Course in Geometry: Plane and Solid by Weeks and Adkins, published 1982 by Bates Pub. Co., is a very proof-centric intro-to-Euclidean-geometry textbook which starts at the most basic postulates

[karmic thorn]

Thanks!! I'll check it out for sure.

[vernal compass]

You're welcome 😄

[sweet anchor]

Can someone recommend some good sources from where I can learn abstract algebra?

[long bear]

Dummit and Foote: the default, nice coverage but wordy in a bad way. This is where I learned most of my ring and field/Galois theory (though I mostly went off lectures). In principle could be done without serious LA but the jury is out on whether that's a good idea.

Artin: The objectively correct entry point for most people. Does a good job at showing you algebra is cool, and doesn't assume any linear algebra background (like I'm pretty sure he defines a matrix lol).

Jacobson: Extremely clean writing, my personal favorite. Covers an interesting set of topics. For this you want some LA

Herstein: Clean writing, good for group theory in particular but kinda deficient elsewhere. Uses x(f) instead of f(x), so you'll have to unlearn it which is a pain in the ass (though I get the point). This is where I learned GT.

Hungerford: I've seen it described as a "watered down rewrite" (presumably of Lang?). Seems clean. Probably a book for which you want LA going in

Lang: The king, good writing but probably a bit too efficient to be a viable first pass

Aluffi: Category memes (which can be good or bad), kinda slow, bad exercises

Challenger Approaching - Knapp: seems like Artin but with a lot more coverage, very promising
@sage python

(sorry for tag)

I took a look at this list and chose lang lol

but ya, choose your poison according to this lol @sweet anchor

[sweet anchor]

Alright, thank you @long bear

[long bear]

thank daminark

he curated the list

I merely saw this one day and decided to take note of this for when I go down the algebra rabbit hole

oh it's in pins

smh

all this time i've been searching "Lang the king" lol

[sweet anchor]

lol

good to know

[idle blade]

@sweet anchor Hungerford is really a nice and tight one as a standard graduate textbook

[sweet anchor]

@idle blade I will try it then.

[crystal spade]

Is the Collins edexcel higher maths book good?

[gray gazelle]

Is the Collins edexcel higher maths book good?
@crystal spade the bible is

[crystal spade]

nah i wouldnt say so

to many false statements in there

i need something 100%

[gray gazelle]

god is always 100%

[hearty steppe]

I would go with Pinter and Fraleigh if your starting to learn Abstract Algebra. They’re working out great for me so far

[serene crater]

To those who read it, how long do you think does it take to finish Halmos 'finite-dimonesional vector spaces'? Doing about 3/4 of the exercises?

[gray gazelle]

Ima guess dolva is a troll

Or am I wrong?

[radiant basalt]

Hey guys, I'd like to know how y'all consume math books ? Like do you solve it from cover to cover and read everything, or make notes ? Just wanna have some different perspectives on this.

[slender sphinx]

I do take notes, but rarely review them

The act of taking them help me

I do latex solutions to textbook problems I solve

I won't say I solve every problem in every book though

Granted my current learning is just out of self interest, not for any class or something

[marble solar]

The only ppl that go through a book cover to cover solving almost every problem are i) PhD students preparing for Quals/Orals or ii) ppl getting paid to write solutions

I made a rule to try 2/3rds of problems, actually solve 1/3rd to 1/2 of the problems

I think that rule has served me well

[radiant basalt]

Granted my current learning is just out of self interest, not for any class or something
@slender sphinx I'm pretty much in the same direction

[hearty steppe]

Yea I follow same strategy myself. The only time I work out more problems is if I’m struggling a bit with the concept and I need to work through a little more to understand different scenarios of problem sets

Velleman has probably been the only case where I go through almost 90% of the problems but there’s a perfect number of problems per section

[radiant basalt]

I made a rule to try 2/3rds of problems, actually solve 1/3rd to 1/2 of the problems
@marble solar That's interesting...was that rule like something that you realized should work, after solving a lot of problems ?

[marble solar]

I asked myself the question "How can I get the gist of what the text is saying, while getting some exercises done without wasting a lot of time trying to get every last one"

and I just decided to do about that

[hearty steppe]

Just skip the problems that seem too easy to you

[radiant basalt]

and I just decided to do about that
@marble solar that does make sense.

How about proofs, how do you deal with them ? do them yourself or just read them and then apply them lemma to the problem, without deriving yourself ?

[marble solar]

Some ppl say that reading the theorem and trying to figure out the proof is a good way to learn

I tried to do this with Rudin, but he was much too slick for me

I don't think I've ever been really able to do this unless I've been pretty familiar with the concepts already

e.g. I'm reading a PDE book now and I've been able to prove some of the theorems without looking at anything

[hearty steppe]

Do you feel like going back to Rudin after spending time with other analysis books works?

[marble solar]

No I just hate Rudin

[hearty steppe]

I think it’s important to have a good analysis foundation if your going to dig into graduate level texts anyway. Personally working on that lol

[marble solar]

Yeah, that's definitely true. But every time I try a text by Rudin

It just ends up feeling alien to me

[hearty steppe]

I might look for more accessible Linear Algebra texts tbh

I started reading Intro to LA by Lang, so far so good. I like something with examples of concepts and not too much formalism for now

[weak fossil]

Hello. I'm from Sweden and for certain reasons I'm studying from English textbooks. Swedish math syllabus in all HS math classes is really all over the place and it's always really difficult to find an equivalent resource. I'm currently in a class which I pretty much have all the necessary material for (which took some time to figure out) and I'm almost done with it too, thanks to prof. Leonard's work. I must now go into Pre-calc with Trigonometry by prof. Leonard's course order, but in to prepare for the math class that I'm going to start in Januray it seems like I need something else. The class is going to include the subjects listed bellow (forgive the AI translation, but not knowing the names of the concepts in English unfortunately deems this to be my best attempt).

Someone told me this is a mix of high school Trigonometry, calc 1 and calc 2. Should I just find 3 textbooks and learn them respectively one after another? Selecting the correct resource is the absolute most important thing for my self-studying. If I have a text which I can follow I really study amazingly. Otherwise I'm really lost. Please aid me in this task and help me select a textbook that would not only help me ace the upcoming class but also be the right step on the path towards understanding all of calc, linear algebra, probability and stats.

The cosine theorem
Area theorem
Sinus theorem
Trigonometric relationships
The Unity Circle
Basic trigonometric concepts
Problem solving with integrals
The fundamental theorem of the integral calculus
integral calculation
integral calculation with primitive function
area under the graph
integrals
Primitive functions
second derivative
optimization problem
asymptote
maximum and minimum value
suburban derivative
growing or declining
extreme points and extreme values
the equation of the tangent
derivatives of polynomials
limit
change ratio

[quasi remnant]

is anyone familiar with the book "The Art of Mathematics: Coffee Time in Memphis" ? what base knowledge do you need to do the questions in the book?

[karmic thorn]

@weak fossil I've used Thomas' Calculus, 14th ed. and it seems to cover everything you're looking for, and beyond. I found the book to be nice; the exposition is clear and there are lots of practice problems, as well as decent coverage of the underlying theory.

[weak fossil]

Thanks Manan!

[hollow current]

@weak fossil Thomas calc is not bad, but I would suggest read some analysis book

[weak fossil]

analysis_

[hollow current]

i mean many analysis book do what calc does, but more solidly

[weak fossil]

?*

im still in high school

im looking for a precalc book mostly

[hollow current]

well, i mean thomas calculus is not bad in the sense that it will provide you computational instruments

ah ok

for precalc i guess it would be fine

[weak fossil]

great

[hollow current]

https://www.amazon.com/Calculus-Analytic-Geometry-George-Thomas/dp/0201163209

i used that one

[weak fossil]

would this book you linked explain the aforementioned topics?

[hasty turret]

Is there a difference between a calculus book and a analysis book?

[hollow current]

calculus is lighter

much lighter

@weak fossil optimization problem - what exactly you mean here? what is also suburban derivative?

and i do not remember thomas covering trig a lot

he covers, but not so much

[weak fossil]

sorry bro but this is as much as i can tell u myself

i dont know the names of the topics in english to begin with

so its all i can give u from translating the swedish syllabus

[hollow current]

maybe you will give name in swedish?

[weak fossil]

maybe they meant first derivative

https://www.youtube.com/watch?v=63cQ6OZVeIY&list=PLvQzFdt9swYoKSVVm7TmLRqRbMtmRHSfN

If you're really interested here is a playlist with the entirety of the syllabus of that class

@karmic thorn Thanks for the recommendation dude. My absolute favorite teacher prof. Leonard has full courses on calc 1 2 and 3 and he uses 13th ed of the book! I'm stooooked

Now to find pre-calc resource to bridge the gap..

[karmic thorn]

Great :)

[stable bloom]

can anyone recommend a game theory book? especially for single player games

[flint forge]

Do you mean game theory like

The formal math subject

Or game theory like advice on how to play games

Single player games arent huge in the former normally

[quick hornet]

i havent beat myself in tic tac toe in the past decade

😦

[hearty steppe]

Wdym Ultra

[slender sphinx]

@quick hornet I'm 1-1 chessboxing myself

[hearty steppe]

It sounded kinda deep lol

[stable bloom]

i guess single player games is basically decision theory

[shadow nebula]

there's a part of me I can beat tho :)

[valid moth]

your feet

[shadow nebula]

yep, want pics?

[valid moth]

you can send them to gabe for quality control first

[faint charm]

what do you all think of early transcendentals?

[gray gazelle]

Stewart's calculus?

https://www.amazon.com/review/R2IADID8E966E8

this review sums it up

[obsidian valley]

is Stewarts the red one?

no thats Taalman/Kohn my bad

[vapid dagger]

Which book should I read for proofs given I don't have any experience with them and my end goal is to study Abstract Algebra (Thomas W. Judson).

I have narrowed it down to either Sets, Logic, Computation of Open Logic Project or either How To Prove It by Velleman but can't decide any further because I really don't know what should learn in proofs as a pre-requisite for Abstract Algebra
Thank You

[hasty turret]

Just Start studying the abstract algebra book?

The book seems Pretty approachable

[vapid dagger]

Yes, just completed the first chapter. While doing the back exercises I realised that I know the theory used in solution but I don't know how to start or formulate the proof.

Once I read the solutions, I be like "how come I didn't thought of that"

[stray veldt]

then read a bit of velleman, but generally you pick up proofs by doing proofs

and proofs in abstract algebra have a different "flavor" than proofs in say elementary set theory

[karmic thorn]

Once I read the solutions, I be like "how come I didn't thought of that"
That's me 90% of the time.

[gray gazelle]

Is there a good linear algebra book? (except Axler)

[stray veldt]

linear algebra done wrong is also decent for a first class

[marble rock]

hoffman kunze

[stray veldt]

and ofc hoffman kunze

[marble rock]

and you can also try paul halmos

it was cute for me

[gray gazelle]

finite dimensional vector spaces? Isn't it too advanced for an intro?

[marble rock]

nah

its cool

[wooden sparrow]

Any suggestions for introduction to number theory?

[gray gazelle]

@marble rock k thanks

[marble rock]

@wooden sparrow try a friendly introduction to number theory

by silverman

[wooden sparrow]

Thanks I'll check it :)

[karmic thorn]

Any suggestions for introduction to number theory?
I guess Burton's Elementary Number Theory is neat.

[gray gazelle]

Also +1 for burton from me but I’m sure Silverman is good too

[fathom monolith]

Favorite pop math books? I’m looking for biographies but I’ll take any suggestion

[marble solar]

Love & Math - Ed Frenkel

[flint forge]

higher topos theory

[hearty steppe]

Janich was fine for me for 2 chapters then I switched to Lang

[quick hornet]

is road to reality just pop math for actual math students

[hearty steppe]

Kunze and Treil a bit too formal for me right now

[gray gazelle]

are you still reading rudin?

[hearty steppe]

No rudin too dense

I switched to Abbott, Schroder, and Apostol

[stray veldt]

i enjoyed both the erdos and perelman biography, even though they are regarded as bad

[serene crater]

finite dimensional vector spaces? Isn't it too advanced for an intro?
@gray gazelle I'm reading it as first literature (i had some exposure to numerical linear algebra) and in my opinion it's a really good read and extremely well structured. Of course, some sections are harder than others, but overall doable.

[radiant basalt]

Favorite pop math books? I’m looking for biographies but I’ll take any suggestion
@fathom monolith

I want to be a Mathematician - An Automathography

~ Paul Halmos

[marble rock]

mathematicain apology

[hollow scaffold]

Hey, I'm a 11th grade student and I'm self learning maths. What book would you recommend I use to self learn? I'm looking at something which will cover trig, inverse trig, logarithms, limits and derivatives

[limpid gazelle]

Stewart’s calculus probably

[gray gazelle]

rudin

(don't)

[marble rock]

yea stewarts

no rudin plz

[quick hornet]

does stewart not assume knowledge of trigonometry?

[hearty steppe]

There is a whole precalc Section but I never looked at it

[marble rock]

no

he begins with it

or not begins with it but

is gentle when introducing calculus on trig functions

[deft owl]

does anyone know how is 42points math academy

[hollow scaffold]

I'll check it out. Thanks

Has anyone used elementary linear algebra by Howard Anton?

[hearty steppe]

No I haven’t. I’m using Into to LA by Lang atm. I switched from LA by Janich and Linear Algebra Done Wrong by Treil

My formal understanding of math rigor is not on par yet for Janich or Treil tbh

[hollow scaffold]

I'm trying to find a good book to self learn linear algebra. But there are so many recommendations. Dk which one to use

[hearty steppe]

I’ll go back to Janich and Treil tho but not atm

Try Lang, I just started it but so far I like its approach

I got up to Chapter 3 in Janich and then it just went over my head

[long bear]

i like intro to la by lang as well

[hearty steppe]

And Treil is substantially a bit harder than Janich

Just so you know

Just a bit tho

I think Linear Algebra is traditionally approached assuming the students have some knowledge with proofs. Least old school texts tend to be that way? Idk why.

[hollow scaffold]

I'll try Lang. Thanks

[long bear]

i think it goes

[hasty turret]

Well, Because they didn't have these proof books

[hearty steppe]

Linear Algebra is still relatively elementary at intro level anyway but I think a lot of old school authors treat it like a bridge like with analysis

[long bear]

intro to la => la => aa

for langs books

[hasty turret]

They assumed it is natural,ig

[hearty steppe]

I can see Linear Algebra being part of the bridge of transition to higher math

Eventually it gets high level

[hasty turret]

Depends on the book you are using

Some books might be "higher" math, while others might be "lower" math

[hearty steppe]

The problem I have with some books like Hoffman-Kunze especially is just the amount and level of rigor involved.

I am new to reading math rigor like this coming from a CS background

[buoyant spire]

I haven't read this textbook in its entirety, but you may find it useful
The online version includes a couple of nifty visuals and tools

https://textbooks.math.gatech.edu/ila/index.html

[devout crow]

Hey, can someone suggest me a good book on constructing proofs.

I want to learn the basic proving techniques

[marble rock]

check out how to prove it by velleman

or book of proof

[devout crow]

ah thx

I will check them out

[tropic lion]

What do you guys think is the best book for learning real analysis (both single variable and multivariable)?

[marble rock]

rudin

but rudin not best for multivariable

[tropic lion]

I don't think I'll need to learn multivariable that much though

but I'll check it out

[marble rock]

then yea go ahead read ruddin

its the gold standard

it was a bit tough for me

but if u power through u will benefit significantly

[tropic lion]

oh jeez it's expensive

is it that good

[marble rock]

yea its the go-to book to learn real analysis cold

[hasty turret]

Libgen

[tropic lion]

I could try to become a pirate

eh I think about getting it. I'm not planning on learning analysis until december but when I do start I want to have good study material

[marble solar]

Multivariable is best done by Spivak Calculus on Manifolds

[gray gazelle]

agree

[marble solar]

Single variable has a lot of good options, Rudin, Apostol, Pugh, Tao, etc.

It's simply a matter of taste at that point

I'm partial to Pugh

[wooden sparrow]

Terry made a book on single variable calculus?

[acoustic pelican]

I think its about analysis

[hasty turret]

Ofc

[wooden sparrow]

Ohh

[marble solar]

Terry doesn't even teach undergrad anymore

Unless there's an absolute emergency

[wooden sparrow]

Bruh

Priorities

Well it's good if his lectures are recorded

[tropic lion]

Looking through that book I think I understand now why analysis is so difficult

[marble solar]

It's very easy to ask very difficult questions

Does there exist a function that is continuous everywhere but differentiable nowhere?

[heavy barn]

Can all even numbers greater than 3 be written as the sum of two primes?

[marble solar]

4 = 2 + 2

6 = 3+3

8 = 5+3

[hidden abyss]

[marble solar]

10 = 7 + 3

Looking good so far

How many more to check?

[gray gazelle]

a few

[past yew]

I think we can just do a proof by exhaustion

[marble solar]

12 = 7 + 5

[past yew]

yeah just keep going, you’re almost there

[marble solar]

14 = 7 + 7

16 = 13 + 3

[past yew]

18=11+7

20=13+7

22=11+11

[marble solar]

Woahhh

[dense pewter]

I'm convinced

[gray gazelle]

[past yew]

monkaS

I want Advanced role

[marble solar]

Type it in then

[past yew]

Where at?

[marble solar]

Anywhere

[heavy barn]

24=12+12

(since 12 is prime)

[past yew]

.iam advanced

[marble solar]

,

[past yew]

,iam advanced

[hasty eagle]

Your roles have been updated!

[past yew]

Nice

Ok now that I’m advanced I can prove this conjecture by exhaustion

it will be quite a long paper though

24=13+11
26=13+13
...

😆

[limpid gazelle]

why are you guys in #book-recommendations tho

[past yew]

y not

we’re discussing a topic which a book no one will read will be published about xd

Goldspock conjecture

[brittle latch]

https://www.perse.co.uk/wp-content/uploads/2016/05/Cambridge-reading-list.pdf

interesting list of books to read from cambridge

[tropic lion]

proof by "It's true every time we check"

[unreal copper]

Proof by intimidation is the best way to prove something

[civic carbon]

the nice thing about proof by intimidation is that unlike other, lesser proof methods, it even works on things that aren't true.

[sage python]

It's even more powerful!

[quick hornet]

proof by just adding an axiom

as a side bonus: if you use this proof technique enough, eventually you dont need to use it anymore

!!!

thats some good bang-for-your-buck right there

the contradiction is what i was implying, yes

although "just start working in true arithmetic" is also tempting

and a valid interpretation of "enough"

not necessarily

i work exclusively in inconsistent logics

not paraconsistent ofc, inconsistent

i dont tell this to the journals i'm submitting to though

see if they figure it out

[sage python]

Gotta make sure the editors are on their toes

[valid moth]

yep, I know that's why sometimes there are mistakes in your work dami

you're just trying to see if your profs are alert

[shadow nebula]

was namington testing us in math discussion by applying integration by parts on a composition?

[quick hornet]

wdym

multiplication by x/x is an application of id (at least as far as integration goes)

and similar for other common "integration tricks"

addition of 0, etc.

[shadow nebula]

sorry I don't see how this is multiplication by x/x :(

[gray gazelle]

maybe he meant \cdot instead of \circ

or uses \circ to mean multiplication

[quiet remnant]

Hello, I'm a professional programmer with 10 years of experience. However I do not have any education. I dropped out of high school. (My programming knowledge is self thought.) I want to learn math on a master's degree level. I know I can get up to the high school level with https://khanacademy.org/ but I don't know what should I read after that? I like to read the "classics" I mean books that everyone knows and are really fundamental.

[wooden sparrow]

@quiet remnant Khan academy goes a little more than highschool right?

You have lessons till differential equations

[long bear]

diff equations are hs

in aus

[stray veldt]

it depends how you do diffeqs

[wooden sparrow]

Bruh

Differential equations and linear algebra is taught in our second semester of college. High school peaks at single variable calculus and intro to probability

[green kelp]

im in middle school and im starting differential :)

[steel viper]

nice i guess lol

[green kelp]

u r in immense pain

that's not good

[steel viper]

[hasty turret]

[quiet remnant]

@wooden sparrow yeah khan academy goes up to basic college level but it's aimed at elementary to high school level.

[wooden sparrow]

Okayy

[quiet remnant]

so any suggestions?

[stray veldt]

just learn up to high school level, then read an analysis and a linear algebra book

[long bear]

@wooden sparrow specialist mathematics in year 12 covers differential equations

obviously not to the depth of a course of a college student

[wooden sparrow]

Ohh okayy

My bad

[long bear]

similar to how our vector calculus isn't quite as rigorous as the vector calc a college student does

[wooden sparrow]

I didn't know that

[long bear]

but that's spesh lol

[prisma snow]

im in middle school and im starting differential :)
And we can only hope he means differetial equations and not differential geometry

[long bear]

could mean very basic differential calculus

didn't wolfram learn topology at 12 lol

[prisma snow]

They could mean that, but don't underestimate them

No clue

[wooden sparrow]

didn't wolfram learn topology at 12 lol
Bruh

[long bear]

As a young child, Wolfram had difficulties learning arithmetic. At the age of 12, he wrote a directory of physics. By age 14, he had written three books on particle physics.

Thats all it says on his wikipedia

[steel viper]

if you're in middle school and doing diff geo i feel genuinely bad for you

no child deserves to be corrupted that young

[long bear]

but i'm pretty sure i heard him say he learned topo at year 12 lol

corrupted

[stray veldt]

why does the internet hate diffgeo so much

[steel viper]

ugly

[long bear]

🦵

[stray veldt]

thats a matter of opinion

[long bear]

do you like it?

[steel viper]

ugly.

[stray veldt]

im not familiar enough

to have a strong opinion

[steel viper]

hello g*be

i am failing at topology

🙂

[wooden sparrow]

Two are different things?

[long bear]

what

[wooden sparrow]

I didn't know

[sudden kindle]

Yo

[long bear]

two of what things

[wooden sparrow]

Topology and geometry

[sudden kindle]

What would happen if I murdered someone

[wooden sparrow]

I thought one is a subtopic

[long bear]

Very different.

@sudden kindle you get deleted

[deep dirge]

@sudden kindle depends if you get caught

[long bear]

kekw

[sudden kindle]

I feel like everyone gets caught

[long bear]

why are you asking?

[sudden kindle]

I had a dream I murdered someone

[long bear]

Do you know this someone?

or is it a completely made up person

[sudden kindle]

And in the dream I got an email asking me to turn myself in

Made up

[gray gazelle]

Hi I'm looking for something to read in my free time, when I'm not doing my university math

I'm starting 2nd year of undergrad from october

I will be doing multivar analysis (analysis 2) and group theory and a bit of classical and differential geometry

https://www.amazon.com/Thinking-Mathematically-J-Mason/dp/0273728911

this one is a nice book

Thanks, I'll give it a try

https://www.amazon.com/Riemanns-Zeta-Function-Harold-Edwards/dp/0486417409

Did anyone read this?

Nah don't read any of that

Any book that claims to teach you how to think is nonsense

Find a hobby or something

I want that hobby to be mathy

Do you know how to program

Yeah I did competitive programming

But idk

I don't like computers too much

Reading math books won't teach you anything

You need to do mathematics

I know that ofc

I'm looking for a side thing to work on

You could learn every known proof of quadratic reciprocity

[hasty turret]

Or every proof of fermat's little theorem

[gray gazelle]

But quadratic reciprocity is actually beautiful, and I'm someone who doesn't experience the feeling of beauty often

Hm so doing random proofs

Seems like a good idea

[hasty turret]

Beauty as in aesthetic beauty?

[gray gazelle]

Yes

Learn the proof in class field theory

That should keep you occupied

[hasty turret]

Or work on unsolved problems

You might even solve them

If not,You would still learn something new

[gray gazelle]

Unsolved problems are unsolved for a reason

Or two

[lost fjord]

@gray gazelle would you like one now?

[gray gazelle]

Either no one cares about them or they're effectively impossible

With the current theory

[hasty turret]

Well,People do solve "unsolved" problems almost every year

[gray gazelle]

@gray gazelle would you like one now?
@lost fjord from october

[lost fjord]

?

[hasty turret]

Not talking about big ones like rh or collatz

Smaller ones

[gray gazelle]

@gray gazelle do you know the statement of quadratic reciprocity at least?

So many people graduate a math degree and don't it's crazy

Nop

[lost fjord]

actually scrolling up this will be a little too trivial for you and I regret interrupting your convo. sorry

[gray gazelle]

You should rectify that @gray gazelle

Seriously learn the proof with Gauss sums

It's elementary number theory and you should know it

Alright

Also you should learn as much linear algebra as possible

Every waking moment of your life

Can you explain to me what the determinant of a linear transformation is?

What about an eigenvalue or eigenvectors?

These are some more fundamental things that people graduate without a real understand of

Also useful in analysis and differentiatial geometry

Especially for multivariate analysis

A lot of undergrads think they know linear algebra but they in fact do not

[quartz pawn]

It's funny cause I'm reading a graduate textbook called "The Linear Algebra and that Beginning Graduate student should know" lol. It's made specifically for this.

[deft owl]

what is 3x-90y=x^y

[gray gazelle]

That's not an answerable question

[quartz pawn]

^

[gray gazelle]

It's an equation

[quartz pawn]

I wouldn't know how to answer that in an explicit formula in of one variables in terms of the other

You would just be the set of ordered pairs that satisfy that relationship. You may want to check out an online graphing calcultor or something and start plotting values.

like fix y and then allow x to vary or something .

if you fix it then it's a polynomial in x.

[flint forge]

I genuinely have no idea what quadratic reciprocity is

[sudden kindle]

It takes two numbers and tells you if the first is a square mod the second

[flint forge]

Why does it have such a silly name

[sudden kindle]

Because it says the first number being a square mod the second is equivalent to knowing if the second is a square mod the first

Hence quadratic (square) reciprocity (switching roles of the first and second number)

[flint forge]

I see

[sullen field]

quadratic reciprocity is based

[stray veldt]

quadratic reciprocity tells you more though, you can figure out for which primes a given number a is a square in Z/(p)

and the real interesting stuff starts when you study it's connection to cyclotomic fields

which is the "motivation" for class field theory

which is ofc one of the biggest research endeavours in modern mathematics

(langlands)

[sullen field]

Can you elaborate a bit on cyclotomic fields? I've done galois theory but i don't know what you're meaning

[stray veldt]

basically https://en.wikipedia.org/wiki/Proofs_of_quadratic_reciprocity#Cyclotomic_field_setup

[flint forge]

Ok that seems kinda based

Not sure if I care

But kinda based

[stray veldt]

actually langlands himself thought quadratic reciprocity is just some curiosity

especially since the elementary proofs are

well

bad

[dapper root]

Isn’t quadratic reciprocity some special case of some big boy thing?

[stray veldt]

there are higher / more general reciprocity laws

[lost fjord]

I've heard of this before

aren't there like ~200 different proofs

[sudden kindle]

@stray veldt explain Artin reciprocity pls

[stray veldt]

i can't

mostly because i don't understand myself

[gray gazelle]

Does anyone know the best high school geometry textbook to master high school geometry?

[wooden sparrow]

AOPS has a book on high school geometry, but I don't know if it's for everyone

[civic carbon]

@sudden kindle The paper "What is a reciprocity law?" is highly recommended if you want an intuitive understanding of the higher math at play here.

[gray gazelle]

Can you guys help me plz, I’m a cs major and I enjoy theoretical math but I have a hard time with understanding applications, specifically in statistics and combinatorics. Do you guys know any good books that are easy to understand for stats and combinatorics( preferably computations related)

[smoky surge]

this might not be the right place for this but for anyone with experience in ML i am trying to decide between two books: Mathematics for Machine Learning or Linear Algebra and Learning from Data which in yalls opinion?

[long bear]

aight

so in pins

the list dami curated

with all the algebra books

says lang is too efficient for a first pass

Is this the case with his introductory linear algebra book?

[smoky surge]

this is a different LA i think

[long bear]

as well as the linear algebra that comes after that one

[hearty steppe]

Lang has two books

[smoky surge]

and this isnt my first past

[quick hornet]

lang has like 40 books

[long bear]

lol

[hearty steppe]

One is Intro to LA and the other LA

But he has grad text for LA too I think

But he has grad text for LA too I think

[long bear]

I was asking for myself but i realized you were asking about LA

[smoky surge]

ohhh

sorry

[hearty steppe]

I’m actually reading Lang’s Intro to LA rn and recommend it

Not to be confused with his other undergrad LA book which is titled Linear Algebra

[long bear]

yeah

so from my understanding

there are three books in that series

but then there is also the massive Algebra book he wrote

I assume dami was talking about the one part of the series

since apparently the other one is massive

like 900 words lol

[sage python]

Wait huh

When I said Lang was king or what?

I was talking huge Lang, the one that's just titled "Algebra"

That's the king of algebra books but it's too much for a beginner

Idk Lang's linear algebra books tbh

[long bear]

I was wrong

The huge one is part of that series lol

[dapper root]

900 words?

Sweet I can learn all of algebra in a few pages

[long bear]

900 pages I meant lol

[quick hornet]

but it's german, so each word is as long as a page.

[white pebble]

[steel viper]

an algebra book where every word is just aufheben stylized a different way

[long bear]

every character takes up one page.

[weak fossil]

Can you recommend a really good pre-calculus book?

[karmic thorn]

Lmao you still haven't decided on one?

I'd say grab any book you can, and make sure you understand its contents

You can fill in the gaps on the move

[weak fossil]

im doing other things before I start doing precalc its quite annoying

im losing my mind actually but its fine 😄

[trim narwhal]

@weak fossil I used Blitzer, it's very good

However it's a bit long

[weak fossil]

I have it too, and the fact that it's so long got me to reconsider

I'm also a bit discouraged that the chapters I thought I've learned in previous courses of intermediate alg, like u know, just the basics, blitzer teaches in a way that exposes things I didn't know before

terminology etc

[wooden sparrow]

Someone here once said that you can't go that wrong with books till high school standard

[weak fossil]

should I just work all the chapters from A to Z regardless of what I studied before?

[wooden sparrow]

Just skim through what you know

Once

[flint forge]

My normal strategy is this

Read a chapter

Do 3-5 exercises

If yoy can do them all move on

If you cant, keep doing them until you can get 3-5 right in a row

[wooden sparrow]

Also if you can re-derive something after going through it, that's a good sign

[weak fossil]

Good advice I'll try that. I always do too many lol

[flint forge]

Make sure to do hard ones

A few hard exercises is worth more than 20 easy ones

[weak fossil]

Yeah I'll pick the last ones

[trim narwhal]

I would suggest you to do that. It could happen that there is something you don't know hidden in a long chapter. I know it's boring, but if you do the good exercises you'll be fine

[weak fossil]

Can you also recommend something to learn this:

Geometry

The concept of curve, the equation of a straight line and a parabola and how analytical geometry connects geometric and algebraic concepts.
Use of basic classical theorems in geometry about similarity, congruence and angles.
Relationships and change

I suppose Khan Academy is the answer here?

I dunno if I can trust that site, some say its amazing some say its their worst mistake ever learning from there

[flint forge]

Its pretty good

Idk what people would disliek

[weak fossil]

Thanks, and since you guys are so helpful, stepping outside of the resources topic, Im wondering about something

Ive been studying several hours a day every day since May, its the first time I study like this so maybe im just inexperienced

What the fk is up with this frustration when something makes no sense like fr

its so draining

hm, well, i guess thats just something one has to figure out on their own

[flint forge]

Thats a pretty natural part of studying

[weak fossil]

i didnt know that lol

[karmic thorn]

A few hard exercises is worth more than 20 easy ones
I guess 20 easy exercises are also worth the effort; part of the reason why I didn't find calculus daunting at school is because I had practised loads of easy algebra/trigonometry problems. Then somehow simplification techniques were just ingrained in my brain, and I didn't struggle with them in calculus.

[hasty turret]

Hopefully,not all 20 such questions are the same with different numbers

[karmic thorn]

Certainly not. That'll be a waste of time.

But 20 questions, maybe disguised in different forms are a lot better.

[weak fossil]

Honestly I agree with both Ted and max. I used to do 150 problems per section, like just all of the problems

And the reps made me just do them automatically

Though now I might just do a few of the hardest ones when im revising the old chapters

[flint forge]

Be wary of diminishing returns

At some point doing an extra problem probably just isnt worth it

[karmic thorn]

I'd say solve some of the easier ones first; if you're getting them right without issues, jump to the tougher ones.

[prisma snow]

Who has time for this?

[marble solar]

You do this over several years Luna

There are math books I used 6 years ago with problems I still can't solve

Every now and then I'll pull it out and try to make progress

[smoky surge]

So i am trying to decide between two books: Mathematics for Machine Learning or Linear Algebra and Learning from Data which in yalls opinion?

not sure if anyone here is familar with either

[limpid gazelle]

Both

[smoky surge]

hahahah ok im also taking classes which would you recommended first?

[hearty steppe]

Who are the authors?

[warm glen]

ayo has anyone taken a look at grillet's abstract algebra?

grad level math book?

[dapper root]

never heard of it

[gray gazelle]

Does anyone have suggestions for textbooks on (a) real analysis and (b) differential equations (ordinary and/or partial) that have a "modern" style to them (with colorful illustrations, lots of practice problems, solutions at the back of the textbook, etc.)?

I'm looking for books that are in the "style" of Larson Calculus 10e and Stewart Calculus 8e - those sorts of books.

Please ping me if you have any really good suggestions.

[solemn mantle]

Anyone know whether I should buy Schneier’s applied cryptography

[quartz pawn]

Don't buy it

use libegn.is

[solemn mantle]

don’t buy it?

Oh is that like a pdf version or something

[quartz pawn]

Yea

[limpid gazelle]

👀

[solemn mantle]

It’s 30 bucks though, you sure lol

[limpid gazelle]

after discovering libgen you will never be the same

[quartz pawn]

if you like physical copies, sure.

http://gen.lib.rus.ec/book/index.php?md5=DA2EA2B346FE3D22F060A0DC07E721F9

if that's what you're looking for.

[solemn mantle]

Yeah

I’m not sure which edition/volume I should read

Any ideas

Wow that’s kinda op

[gray gazelle]

Does anyone know of any modern style real analysis or differential equations texts?

Books in the style of high school / undergrad calculus textbooks like Larson and Stewart

[limpid gazelle]

I think Stephen Abbott's "Understanding Analysis" fits your description. It's a basic intro analysis book

[gray gazelle]

does it have colorful pictures?

[sage python]

I feel like analysis books are far more likely to have pictures than colorful pictures

Since the point would be less wao fancyyy and more, this helps you visualize what's up

[limpid gazelle]

I mean it does have pictures

Like most analysis books

Well except for Rudin lol

But those pictures are not colorful

[gray gazelle]

well as long as they're high quality

[limpid gazelle]

I think they are of high quality

Also as you move farther you should produce these kind of pictures yourself

Either mentally, on a piece of paper, or using some sort of program

[sage python]

Yeah, the pictures mainly serve a purpose of trying to give you an idea of what the formal stuff you're saying "means" in a... squishy way for lack of a better term?

[lost fjord]

If that doesn't work out, the alternative would be to simply buy a pack of crayons and color those textbook diagrams yourself

[limpid gazelle]

@ Category theory

[hasty turret]

Pretty sure, graphing them on a program would be better

You would be able to change and experiment,as much as you want

[limpid gazelle]

Being able to mentally visualize it is important as well

[gray gazelle]

i mean im pretty bad at visualizing functions in 3d tho

[hasty turret]

Before that, you need to play around a bit

[gray gazelle]

things like <3, t, t^2> are easy

but idk how to even DRAW <tt, tttt, tttttt>

[limpid gazelle]

That's just basically <t,t^2,t^3> where t≥0

[gray gazelle]

😳

but still how'd u draw that tho

like, that makes more sense to visualize

but drawing in 3D is so HARD 😡

[limpid gazelle]

well you see looking at it from the xy plane it will be a porabola

looking it from the xz plane will be the y=x^3 curve

[gray gazelle]

yea i was considering just drawing traces LOL but the book wanted an actual 3D drawing 😭

also, do u have any good ODEs or PDEs book suggestions?

I have Morris and Tenenbaum's ODEs, but it's not illustrated much

[long bear]

hello

[gray gazelle]

henlo

[lost fjord]

there is a download for a book on diffeqs pinned in #multivariable-calculus

[gray gazelle]

is it colorful and "modern-style" tho

[lost fjord]

Yes actually

[gray gazelle]

OWO

OMG

OMG

IT'S ACTUALLY EPIC

THANK YOU

[limpid gazelle]

Actually

If you want pictures

You can check out Schaum's outline

It's a collection of many math textbooks

All of them are in the style of hs textbooks

With many illustrations

They have most of the undergrad material I think

[gray gazelle]

❤️

are they on libgen

[limpid gazelle]

Yes

[lost fjord]

yw ig

[limpid gazelle]

Tbh I wouldn't say they are great textbooks tho, but they are good for problems and illustrations I guess

[lost fjord]

I want to learn ode's in more depth the future since I liked playing around with the simpler versions of them

also it seems to have a lot of cool applications

[gray gazelle]

whoever with helper role?

[long bear]

heresy

[gray gazelle]

welp ive downloaded too many things from libgen at once

and its not letting me download more books ;-p;

gotta wait 25 mins ;-;

[sage python]

Just do what I do and don't draw things in 3D 🙃

[lost fjord]

mfw desmos 3d graphing calc

[gray gazelle]

honestly desmos needs to get 3d into it

[lost fjord]

https://www.geogebra.org/3d?lang=en

[gray gazelle]

yea but that's not as good

the desmos "interface" is nicer

geogebra ugly

[hearty steppe]

I second Abbott. Abbott is great and very visual

[lost fjord]

I used to hold the hot take that geogebra was better than desmos

which it kinda still is for plotting geo on cartesian plane

but for everything else ig desmos takes the cake

it seems more versatile

and kinda has a community built around it

[granite ferry]

anyone read "A Concrete Approach to Abstract Algebra" by W. W. Sawyer ?

[solemn mantle]

@granite ferry I haven’t, but I was considering reading it. It looks like it’s a pretty casual-type style

[smoky surge]

So i am trying to decide between two books: Mathematics for Machine Learning or Linear Algebra and Learning from Data has anyone here gone through them? Which would you recommended?

[granite ferry]

@solemn mantle I've just been reading the sample ebook, I like the goals behind the book, appears laid out reasonably well

[long bear]

just

libgen it

libgen.is

download it for free

[granite ferry]

interesting examples so far and it has a unique way of laying out concepts that I was not seeing at all in "Abstract Algebra" by Dummit and Foote

idk

I don't condone downloading books for free. The effort is valuable enough to deserve payment. @long bear

[long bear]

alright

[flint forge]

Thats a bad argument

[granite ferry]

However ever, if an author chooses to give his wirtings away for free, then fine

[long bear]

why not download it, give it a try, and then delete it immediately after

[flint forge]

The authors dont get any money

Only the publishers so

Do*

[long bear]

yeah

[flint forge]

Downloading books doesnt hurt the mathematicians

[granite ferry]

royalties

[flint forge]

They dont get them

[long bear]

[flint forge]

The standard in math lit is that you only get paid to write it

[hasty turret]

Do you get paid well?

[granite ferry]

Interesting and I'm certain that is always the case.

[flint forge]

Ive never heard of an exception

And i think the pay is okay

[granite ferry]

I'm not sure I agree that downloading books doesn't hurt the mathematician. Perhaps not directly, but if the publishers are not making as much they may not pay as much in the way you suggest?

[long bear]

Alright

So, let's assume

you don't download the book

[granite ferry]

technically I am downloaded it after I pay for it

[long bear]

what's the effect on the author?

[granite ferry]

ok so, it may not directly effect the author who wrote the book, however ever if over time a large number of us only use free copies, is it not possible that the revenue from book sales for the publishers would effect future book deals?

[long bear]

Has this movement started?

[granite ferry]

thus, less revenue for the mathematicians trying to sell the books

has it started? movement? people have been pirating books since scanners were invented

even before that haha

[long bear]

Precisely.

[gray gazelle]

Lol people been pirating since the printing press was invented

[long bear]

I mean, I get the idea, grains of sands make pile

[granite ferry]

assuming the continuation of book deals, does not discount the possibility of the overall decrease in mathematicians payment over time

[long bear]

But we're talking about a dessert worth of grains of sand.

[granite ferry]

So the number of math books is so great that the number of books pirated is so low that the effect on revenue is negligable?

[gray gazelle]

One thing to also factor in, people who would have never payed for it may now cite it or recommend it to others

[granite ferry]

I like to keep things simple. Book are good, read more of them.

Yes this is clearly an over generalization and assuming many factors.

[long bear]

the number of people pirating books is so great that one person not pirating a book wouldn't make such a huge difference on the "revenue" of authors

[granite ferry]

yea I mean the logic appears associative

[molten wave]

In a lot of publications in science, the author doesn't get shit from the publisher

[gray gazelle]

in fact often the author has to pay to publish

[molten wave]

Books are kind of special but not many people write what are technically published as "books"

Unless we're talking baby maths

[granite ferry]

Very interesting. Actually no, it's sad. It's really sad.

Science is lacking the glory it deserves.

[molten wave]

If youve ever been asked to pay to see an article in some science journal... 0% of that goes to the author

[granite ferry]

Yes I did actually know that.

Instead of downloading them, we should make a group book share where we loan them out to each other for free. Then limit the amount of loaned books based on the actual number of physical copies owned.

or perhaps some sort of book sharing where you only pay shipping

[molten wave]

you mean physical books

[granite ferry]

anonymity would be preferred

[molten wave]

ehh you can't have anonymous shipping

that's just not a thing in post-9/11 world

[granite ferry]

I don't mean annonmous shipping per se

[smoky surge]

wait so when i pirate white papers

i shouldnt feel bad at all

[granite ferry]

everyone would post a book they want to share to the site .... the end user looks through the "library" ... picks a book or books ... puts in their address and pays the shipping cost ... then the owner of the books sends it off with the end users address

the annonmyity would just be protection from having a bunch of public addresses on the "library page" to be scrapped

member only access

idk, more details need to be worked out obviously

[long bear]

libgen gang

[marble solar]

That is wildly illegal

In many countries

[granite ferry]

illegal to share books? wtf is a library for?

[marble solar]

They have licenses to do so

[granite ferry]

ok how about we "rent" them out

[marble solar]

If you have anything that's centralized with a sort of vertical organization then you can pin it exactly on the organizers

Usually these things have horizontal organizations so if one goes down more pop up

[smoky surge]

is anyone here familiar with Mathematics for Machine Learning or Linear Algebra and Learning from Data? I want to go through one but i cant decide which

[granite ferry]

my job is analyst/data scientist so yes

[smoky surge]

which would you recommend?

[gray gazelle]

https://tenor.com/view/hail-hydra-cut-head-red-skull-villain-gif-17278080

[granite ferry]

hail Hydra

oh those are acual book titles? lol

[smoky surge]

yea lol

[granite ferry]

I have not read those so unfortunately I do not feel right giving advice.

[smoky surge]

ah

no worries i might just pick one and go nuts

[granite ferry]

I personally find ML much more interesting

[smoky surge]

I think Linear Algebra and Learning from Data is suppose to provide the LA side of deep learning

[gray gazelle]

oh LA and learning from data is strang

nice

i havent read that one but his other textbooks were usually pretty good

[smoky surge]

yea i went through his first one

and really enjoyed it

[gray gazelle]

yeah if you like an author's style, probably worth trying another

what aspect of deep learning are you wanting though

[smoky surge]

thats the problem i dont know

i kinda want to start with a high level overview then move from there

[gray gazelle]

do you have exposure to ML or anything AI?

[smoky surge]

basic stuff

[hearty steppe]

Be very good at linear algebra and you should be ok for the most part

[smoky surge]

i.e. basic neural nets

and @hearty steppe i went through strangs first and 70% of axler

i would say i feel pretty solid about my LA

[gray gazelle]

that was the standard reference people were giving for DL a year or two ago: https://www.deeplearningbook.org/

[hearty steppe]

I’m going thru Lang’s intro to LA atm

[smoky surge]

I just want somethign that was a bit more applied

Ive heard great things about lang

[gray gazelle]

i mean like how applied? like you just want to implement a project with it or just less theoretical?

[smoky surge]

less theorectical

or more focused on the applications

especially the practice problems i would like to be more trying to solve a problem than proving something

[gray gazelle]

ah, not too sure which book to go for then

there's a lot at either end

[smoky surge]

yea i think looking at strangs practice problems it looks like that

but the other book is a good resource because my prob theory is needs some strengthign tbh

and that can give me some stuff to focus on

[gray gazelle]

https://xkcd.com/1838/

xkcd: Machine Learning

The pile gets soaked with data and starts to get mushy over time, so it's technically recurrent.

[smoky surge]

hahahahah

i love those comics

[hearty steppe]

I feel like if you spent enough time working with tensors, you’ll be ok

Did you try the 100 page machine learning book?

[smoky surge]

@hearty steppe no whats the name?

is that it?

yep googled it hahahah

that kinda of stuff always makes me a bit wary tho

[graceful glen]

There is a book on group theory, by American Mathematical Society, has rubik's cubes drawn near its title.. not too long.. around 100 pages.. I can't remeber its name .. it was for basics.. i liked its approach.. but can't find now. Please help !!!!🙏 🙏

[quick hornet]

perhaps An Elementary Introduction to Group Theory by Charkani?

[graceful glen]

No.. it's pdf was available online

like directly in google search

Got it. Visual Group Theory by Nathan Carter. Thanks anyway ,@quick hornet 🙂

[gray gazelle]

Yeah it’s got a lot of nice pictures

I’ve got the similar book for number theory

[graceful glen]

which one ?

perhaps An Elementary Introduction to Group Theory by Charkani?
This is good too 🙂

[gray gazelle]

An Illustrated Theory Of Numbers

[steel viper]

the rubiks cube group is disappointingly ugly

[gray gazelle]

http://illustratedtheoryofnumbers.com/

[granite ferry]

@solemn mantle I paid the $10 for the kindle version last night when I was done with the sample (worth it for darkmode alone lol). That looks like a scanned copy of the original text from 1959 though which is crazy.

[long bear]

[granite ferry]

@smoky surge If you are looking to solve practical "real world" machine learning problems there is always kaggle.com competitions and such. Even if you just want to play around with some real world data, kaggle has enough massive data sets where you will be entertained for years. If you are looking to solve problems at the cutting edge of model design and manual creation of models that is a whole other area. There is a lot of research conducted around model design/layout/types of layers/activation functions/numbers of "neurons" used/gradient decent and other such optimizations all used to solve various types of problems and explore how some designs are more effective than other for different reasons.

[remote jewel]

Beginner in math as well. I read several chapters from "Visual Group Theory" and while its aimed at high schoolers to give an intuitive overview of group theory, I found its lack of rigor really confusing, so I ditched it and started studying from a rigorous book in abstract algebra and it cleared the confusion up.

[granite ferry]

Gotcha. Yea so currently i'm reading: " A Concrete Approach to Linear Algebra" - W. W. Sayer; For more of a "light" reading before I go to sleep. "Abstract Algebra: Theory and Applications" - Thomas W. Judson; as my primary read during the day, and source of exercises to do. Then I also have the lecture notes from here: https://ocw.mit.edu/courses/mathematics/18-703-modern-algebra-spring-2013/ which I find very useful so far.

I also have "Abstract Algebra, 3rd Edition" - Dummit and Foote ... which is apparently the classic goto book but it was a little deep for me personally. For now at least. I'm still trying to catch back up where I left off years ago.

[granite ferry]

No problem.

There is also the homework and practice exams

[smoky surge]

@smoky surge If you are looking to solve practical "real world" machine learning problems there is always kaggle.com competitions and such. Even if you just want to play around with some real world data, kaggle has enough massive data sets where you will be entertained for years. If you are looking to solve problems at the cutting edge of model design and manual creation of models that is a whole other area. There is a lot of research conducted around model design/layout/types of layers/activation functions/numbers of "neurons" used/gradient decent and other such optimizations all used to solve various types of problems and explore how some designs are more effective than other for different reasons.
@granite ferry So im actually interested in using "ML" to help with diagnosing mental health disorders but I hate treating models as black boxes so while I dont necessarily want to be creating new models I want to have the capability if need be

not sure if that makes sense

[granite ferry]

Yea that makes sense. You are looking to have some more transparency into the models themselves? is that what you mean?

So that you may design them yourself.

[wooden sparrow]

But won't involving neural networks in machine learning make it virtually impossible to understand?

[granite ferry]

I would not say "impossible" at all.

There has been a lot of work in the area of understanding what the models, specifically each layer of a model is actually doing.

[wooden sparrow]

Ohh that's nice

[granite ferry]

And a lot of work in the area of design such as this LSTM (long short term memory) model which has applications in time series analysis

[smoky surge]

Yea exactly

[granite ferry]

The tools used to design these such as Keras/Tensorflow have abstracted away most of the actually maths needed to design/experiment with these types of designs.

[smoky surge]

i dont necessarily want to be just designing models but if I need to I want to be able to understand when and how

does that make sense?

[granite ferry]

Yes I agree. First principals thinking can be beneficial in most areas.

[smoky surge]

yea exactly

[granite ferry]

There are certainly limits though. I personally find myself in "analysis paralysis" to often. Where i'm researching/reading much more than just doing/making something.

[smoky surge]

yea i guess id just have to be cognizant of that Im not at that point yep but i could see that happening

[hearty steppe]

Part of the "analysis paralysis" is simply just learning more until you have developed concept fluency to navigate the waters.

[limpid gazelle]

@sage python is the second half of Bass's Real analysis for graduate students just functional analysis?

[granite ferry]

@hearty steppe yes that is absolutely true, however you can also easily branch out down tangents that are far enough away from the original scope of the problem where they eventually become irrelevant

thus, time is spent wastefully analyzing instead of applying topics already learned

If everyone spent all of their time researching and reading only, problems would not ever get solved in a lifetime. It's not like you can just instantly transfer knowledge gained in a lifetime to another person (not yet anyway, #neuralink #elonmusk) lol

Does anyone else struggle with balancing between having loose associations and concrete connections between ideas?

lol

[trim narwhal]

So I'm reading Spivak, and I'm enjoying it very much. The only problem is the exercises: many of them are quite difficult, and it takes a long time to solve them, however I would really like to go on with Calculus. Can I go on and go back to the exercises later or should I do the exercises before moving on to the next chapter?

[hearty steppe]

Try doing calculus problems out of a book like Stewart

[gray gazelle]

you dont have to do them all, especially in a book like spivak

some books put results essential for later chapters in the exercises with the expectation that you'll do them

but spivak does not iirc

[hearty steppe]

Also Paul’s online notes

[sage python]

@limpid gazelle Yeah I think starting chapter 15 or 16 it starts moving away from straight measure theory

[narrow dragon]

is anyone here familiar with davenport's multiplicative number theory?

[limpid gazelle]

Alright

[sage python]

Not personally but I know that the class here on analytic NT used that as its textbook

[narrow dragon]

I'm around 60 pages in, it is well on its way to becoming the best NT book I've read

[sage python]

Nice, given that my area is shaping up to be analytic number theory I should prob look at it lmao

[narrow dragon]

so I'd recommend that to anyone interested in analytic nt

haha go for it

i had to re learn some complex analysis though, was a bit rusty

[sage python]

Makes sense lol. What kinda stuff are you learning in there now?

[quick hornet]

oh no

is dami turning to the dark arts

of analysis

[sage python]

Wait have you guys not known about this? I'm like n% a harmonic analyst now

[narrow dragon]

dirichlet's class number formula and stuff currently

[quick hornet]

i vaguely knew that but i figured

you would see the light

but it seems youve fallen deeper into the darkness

analysis is a cult

[marble solar]

Analysis > Other Fields

[sage python]

I mean I started off as an analyst, like for most of my 4 undergrad I was very much into algebra but way better at analysis than at most other subjects

[narrow dragon]

the main purpose in algebra is to prove theorems about number theory