book-recommendations

[quick hornet]

if principia uses some notation, it's safe to assume that notation is terrible

[golden halo]

I'm looking for an intro abstract algebra book that's good for self-study. I'm familiar with a lot of the basic concepts but haven't covered algebra formally.
Vinberg, Knapp, and Artin all look good - what do you guys think is best?

[hasty turret]

As a anti anti recommendation,I suggest dummit and foote

[prisma snow]

As an anti recommendation, I do not

[hasty turret]

Probably artin

[haughty dove]

https://youtu.be/UXTz-eFDmjc

My reading plans for the new times

[golden halo]

tyty I'll go for it

[drifting elm]

bourbaki books in english yes or no

[gray gazelle]

I want a book on combinatorics .I am confused between chenchuang chon and richard brualdi

[karmic thorn]

Let me add to your confusion by suggesting Miklos Bona's A Walk Through Combinatorics.

I suggest you skim through all the three books first, see what suits you, and go with that book(although there's nothing wrong about consulting multiple books, it could be time consuming I guess).

[onyx crown]

anyone know a good book to look at alongside strang's intro to linear algebra in order to get a more rigorous understanding of what's being discussed

[civic python]

Perhaps axler langleys book?

[onyx crown]

thanks, i'll take a look

[smoky surge]

Don’t do axler

First time around

The determinate treatment is odd

Loved the book but

[gray gazelle]

determinants bad

-axler

[marble solar]

Unironically not wrong

[gray gazelle]

@onyx crown the book by K jänich

[onyx crown]

thanks 👍

[storm sleet]

Isn't Pinter a decent starting point for algebra?

[flint forge]

yeah i think so

[hearty steppe]

Pinter is such a cool book. Although I barely have gotten through it besides the first two chapters cause I’m jumping around a bit between math books and shit

[marble solar]

I find that I'll be on one or two books for a about 8 weeks

Before I move on

Jumping aroun

[red oasis]

I'm studying algebra with a book from kaufmann

Do u guys know?

"Algebra for college students 9ed."

[static crest]

lol I thought it would be an abstract algebra textbook

[red oasis]

well idk whats abstract algebra

[dapper root]

If it says 9th Ed. I don’t think it’ll be abstract algebra

[quick hornet]

maybe its just a really cutting edge algebra book

so they have to update it every year as new papers are published

i'll confess that "algebra for college students" is a weird name for such a text, but hey, look at weil's basic number theory

the point of mathematics textbook names is to talk down to perspective readers so they think "man i'm such an idiot i should pick up this text so im not an idiot anymore"

it's academic negging

[hearty steppe]

I feel like that sometimes

[quick hornet]

are you really gonna say "I am not cut out for Basic Number Theory"

imagine saying that to your mother

how disappointed she'll be

[hearty steppe]

Damn

[valid moth]

lol

[karmic thorn]

Gallian is in its 9th edition rn.

[sage python]

@quick hornet well you see my mom doesn't know what number theory is so it's perfect

[sudden kindle]

how hard is basic number theroy

[static crest]

ya but it's gallian, so is it even real algebra

it has like colors and pictures

gallian is to abstract algebra as stewart is to calculus

[karmic thorn]

I'm liking it as a first book for AA. Has loads of exercises, and they seem to be as good as D&F. ¯_(ツ)_/¯

[static crest]

it's joke

[calm crane]

meanwhile jacobson basic algebra volume 2

[gray gazelle]

Hi

#❓how-to-get-help

[fossil island]

in general, is the international edition similar enough to the us edition of a textbook?

[quick hornet]

typically yes

but problem numbers might be different

[fossil island]

goddamnit

its like 5 times cheaper

[quick hornet]

and it may be a different edition or w/e

[flint forge]

whats the book title

you can probably get it illegally if a pdf is okay

nami tell me to do my grad apps

i just need to like

reread them

and hit submit

[fossil island]

i was thinking about that, but i found out that i'd rather dish out the 20-50 bucks and save my eyes from staring at my screen even longer

[flint forge]

ah, fair enough i guess

ive long since accepted that i will spend most of the day Staring At Screen

[static crest]

imagine if the int'l edition just ctrl-F swaps imperial units for metric units

[fossil island]

maybe they swapped the decimal points for commas, too

[static crest]

ah that annoys me so much

if they use SI notation anyways, with decimals as commas

then it's fine

but if someone writes
123.456.789,123.456.789

my eyes cannot accept it

[hidden robin]

ok...i guess ill ask for the 3rd time here lol. anyone know a good place to find calculus 2 life science resources? Just trying to find example questions that show step by step what's going on.

[static crest]

what do you mean "calculus 2 life science"

[gray gazelle]

tai's method

[static crest]

lmfao

[valid moth]

i believe tai is currently working on rediscovering lebesgue integration

[static crest]

I cannot wait for the conclusion of the tai's character arc

he will prove hodge

at the end

[hidden robin]

there's calculus for enginnering and calculus for life science i dunno how else to explain it

[gray gazelle]

[static crest]

I'm not sure what you mean by that

[gray gazelle]

you could like

you know

include topics?

say what the courses cover?

[static crest]

calc is either like rigorously taught, or it's not

I don't know any other divisions of calc

[hidden robin]

no idea the school isn't open yet and i want to get ahead im guessing its just everything I learned in calc 1 just more advanced but yeah I honestly have the same questions

well my school is retarded

[gray gazelle]

isn't there like

a website

[hidden robin]

...thats what im asking lol

[gray gazelle]

[static crest]

I mean idk any specific lifesci tailored calc resources

[gray gazelle]

for your school, i mean

wait is this highschool or college/uni

[static crest]

stewart is probably the easiest "comprehensive" calc tb you can find

[hidden robin]

ok so if i just go thru lets say 100 derivative equations and a 7 hour course on calc 2 on youtube that should cover everything right?

[static crest]

no

not even close

[flint forge]

Don't use this as an insult.

[static crest]

unless you're a galaxy brain or the calc course is covering like 1/4 of the content of a normal calc course

7 hours is not enough

to even read the calc content

let alone learn it

[hidden robin]

ok...so where can i find resources for calc 2? or do i have to go chapter by chapter to find resources? i just don't understand how this is so complicated

[static crest]

khan academy for video sources

stewart tb

for a textbook

[gray gazelle]

rudin

[static crest]

lmfao

[gray gazelle]

(/s)

[static crest]

forcing a lifesci student to read rudin would be considered a warcrime I think

[hidden robin]

ok yeah i got the stewart tb book honestly i don't understand what im reading

[static crest]

khan academy is a good source

for videos

that explain calc concepts

[gray gazelle]

well i am being forced to take mat347 with repka so i'm just trying to share the war crime victim experience

[hidden robin]

i need to figure out the gaps in my understanding. alot of resources are either too simple or only give you answers with no explination how they got it.

[static crest]

I mean doing exercises is the only real way to get through it

all of stewart has been solved on slader

so if you're really not being able to solve a question in stewart, slader will have a solved version of it

[static crest]

no one's forcing you to only learn the algebra in 347 though

[gray gazelle]

[static crest]

you're free to learn stuff properly if you want

[gray gazelle]

such as

lie groups

[static crest]

I was reading the last chapter of d&f for groups

and they mentioned things called Sylow p-complements and Sylow groups for infinite groups

I didn't want to know these things existed

day ruined tbh

[gray gazelle]

[hidden robin]

ah yup I was using mathway to help breakdown where I went wrong it seemed to be the best way good to know thanks i forgot how useful it is basically like having a automated tutor.

[static crest]

as you get ahead in math, you'll have to get used to more and more independent learning

just a sad fact of life

calc still has a ton of resources however

past calc is when you'd really have to be good at independent learning (if you want to go past calc, that is)

[hidden robin]

luckily I'm done after this one.

[crimson wolf]

Anybody gone through Calculus (3rd or 4th editions) by Spivak? Trying to figure out if it's worth it for me to go through it. I've got a B.S. in physics so I've gone through typical calculus, diff eq, lin alg. I'm trying to get a better understanding of how to think like a math person or even more so like a theoretical physicist. I do plan on going through Velleman's proofs book and Tarski's mathematical logic book. I might go through Kleene's book as well. Physics grad students don't have mathematical logic or like real analysis courses in their curriculum though so idk. I just find it hard to believe solving problem after problem in regular calculus textbooks for years can result in some hot new physics theory. I figure they must have a better understanding of math than that?

Also considering Analytics on Manifolds by Munkres. From reading reviews it seems like it's at the same level of Spivak's book, but multivariable calculus/analysis.

[flint forge]

Don't spam this in multiple channels lol

[hearty steppe]

Yea I have a problem with that too slim because isn’t the goal to bridge math and physics together consistently for all phenomena?

[marble solar]

That's why their theories are bunk

[gray gazelle]

just forget the proofs

you could get through a lot of math curriculum by just telling students you don't actually need to prove anything, just do some calculation that seems to make sense

[crimson wolf]

yeah we just calculate, but I seriously don't feel my critical thinking skills grew much because all i did was calculate, and never learn to understand why we do anything or how we do it.

And this is annoying. I'd really like to better understand the reasoning, not just the calculation.

Urs?

Yeah I went there first

Not much.

We love Quantum Mechanics by Griffiths. That is like nothing but hand-wavy math. We love it I guess. But it doesn't help build intuition for how math works.

Community in general.

Nah haha I didn't quote that from there lol

I don't even remember the discussion, so yeah I don't know if it was very fruitful lmao

hmm ok ok

I wonder if just a proofs book will quench my thirst, if you will. I do have one math logic book so I'll probably go through that too.

But yeah I'll ask that hehe

[gray gazelle]

but, to go back on topic, i would guess spivak calculus is too simple (although i personally haven't read it), maybe pugh or rudin is more interesting

[crimson wolf]

I've read good things about these...

https://www.amazon.com/dp/1493927116/?coliid=I1DLVMJNXMFEJH&colid=DXNSK4CUHFXV&psc=1&ref_=lv_ov_lig_dp_it

https://www.amazon.com/dp/1441973990/?coliid=I38KBHI2MGJV3M&colid=DXNSK4CUHFXV&psc=1&ref_=lv_ov_lig_dp_it

Well it's like 3D real analysis or something?

like uhh... multivariable real analysis?

hmm and those are very different?

[gray gazelle]

No, it relies on knowledge of that

[crimson wolf]

ok ok

gotcha

is "real analysis" strictly like the proofs version of differential and integral calc?

[quick hornet]

calculus on manifolds is the bridge between multivariable calculus and differential geometry

if that makes sense

sometimes "real analysis" is used a bit more broadly

it can include measure theory and stuff

at my undergraduate measure theory and funtional analysis was called "real analysis"

[crimson wolf]

oh wow even topology?

[quick hornet]

whereas the rudin type stuff was "honors calculus"

[crimson wolf]

hmm interesting... thats a bit annoying honestly

Rudin is hard as fuck isn't it?

[quick hornet]

basic topology makes analysis a lot easier

[crimson wolf]

I'm autodidacting this math so I'm scared of going for something really difficult. 🙂

[quick hornet]

unfortunately it means the topology becomes the hardest part

[gray gazelle]

i think rudin is good if you already know calculus very well

[crimson wolf]

@gray gazelle what real analysis book do you like?

Any of you guys read Terrence Tao's books? I'm so buying into the hype haha

This book yeah?

https://www.amazon.com/Principles-Mathematical-Analysis-Rudin/dp/1259064786/ref=sr_1_2?crid=3OSKLIF9OMT0L&dchild=1&keywords=rudin+analysis&qid=1609550298&sprefix=rudin%2Caps%2C170&sr=8-2

He also has Real & Complex Analysis?

Looks like it.

kk

I feel like we don't know, or respect, math though.

I'm just being honest.

[flint forge]

how so

i meant like in what sense

idk i think most of its in jest

i feel like most math people are aware that the entire field is kinda a meme

i mean 'i hate applications' reworded as 'i don't care about stuff w applications' is a fair personal opinion imo

[storm sleet]

What about “math in its pure form is more beautiful than applied”

[flint forge]

idk 'i hate applications' doesnt make any sense to me as a sentence lol

[flint forge]

i think this is true

i think this is silly

[storm sleet]

That’s how I characterize my dislike of applied math

[flint forge]

hot take it makes sense to disrespect pure math

[storm sleet]

Without applications some things are much harder to conceptualize

Math is pain

[flint forge]

its a very selfish pursuit imo

i could be doing any number of more beneficial things w my time

i'd probably major in like

phil/related

if i didnt do math

[storm sleet]

I wouldn't say selfish, its like devoting yourself to any number of things that may not make an appreciable differences to the world

[flint forge]

which would be more productive imo

[hasty eagle]

Send me catgirl pics

[storm sleet]

For many things, its a matter of time until they find applications

Sometimes, its a very very long time

[valid moth]

wtf infty cats are gonna cure covid ok

[storm sleet]

Unless you do computational

[valid moth]

just give them 100 years

[storm sleet]

Its funny because the stuff (from what I know) thats the most CS-adjacent is simultaniously the most concrete and most abstract parts of math

But the middle stuff is less relevant

Theoretical Comp sci

[flint forge]

TCS is the common term

literally everyone uses TCS

[storm sleet]

I'm a big programming language enthusiast and intend to study it in grad school, so the abstract math is applicable in some areas, but I also realize I'm an intern at a big company and they don't care about TCS

TCS is common yes

[flint forge]

because youre like 15

arent you

high or low

[valid moth]

nah yohan is a boomer

[storm sleet]

I haven't heard people refer to it as "pure" cs very often

[flint forge]

look, how the fuck can Morava K Theory be a thing

ive never heard of it

[valid moth]

hence it is not a thing

[storm sleet]

How can you claim calculus exists when I've never seen epsilon positive irl

We live in a simulation written in FORTRAN in 1998

Back to the last point, its always interesting to try to find applications of the pure math I'm studying to CS

Like trying to find a connection between topology and CS is quite hard, and makes grounded examples in many fields difficult

[quick hornet]

morava k-theory isnt a thing

thats what they dont want you to know

[flint forge]

thats not hard

google TDA

[storm sleet]

Telephone and data systems?

[flint forge]

Topological Data Analysis

[quick hornet]

topological data analysis

[storm sleet]

oh thats the second result

I'm not incorrect

I don't do data related things so explains a lot about my lack of knowledge

Side note: don't invest in TDA their stock is dropping/hovering below consistently in case the graph didn't say it clearly /s

[flint forge]

yes

[storm sleet]

TDA is a meme

Examples of topology in CS

Hmm

Diff Geo is useful - at times

[flint forge]

something something neuroscience

[storm sleet]

Physics finds a use for it

Something something pure math bad

Wait

Doesn't General relativity is manifolds?

excuse my dumbness lol

Stop bullying the poor undergrads

Category theory is great tf

[gray gazelle]

Is it

[quick hornet]

"category theory is a meme" is a meme

its like millhouse

[storm sleet]

I mean

Haskell is what got me into pure math sooo

[flint forge]

1. category theory in CS is a meme

[storm sleet]

It gives a good framework for developing more pure or more provable code

Monads are a plus

[flint forge]

2. category theory in pure math is basically the bread and butter of a ton of fields

[storm sleet]

crys in cs

[flint forge]

like you simply couldn't do modern AG/AT/Htpy without CT

[storm sleet]

It is pretty superficial though

Like in research (mostly PL/"applied" type theory) it has more of a place

The deepest I can imagine any programmer would go is about halfway through the Bartosz Milewski blog

i.e. functors, monads, algebras

maybe even some free constructions if you're feeling adventurous

[uncut zealot]

Can anyone recommend any books on number theory interesting and accessible to an undergrad who's already taken a first number theory course? Most books that I can find are either written for a graduate audience and require a whole slew of prerequisites that I don't have yet or are a rehash of the same standard undergrad number theory that I've already learned (modular arithmetic, the prime number theorem, chinese remainder theorem, quadratic reciprocity, linear diophantine equations, etc.)

[warped cedar]

A classical introduction to modern number theory by Ireland and Rosen

[uncut zealot]

Thanks.

[quick hornet]

note that ireland-rosen does expect you know some ring theory

just basic stuff though

nothing fancy

[gray gazelle]

Was just about to say

Very basic stuff about rings

[quick hornet]

yeah like

honestly if youre not already familiar

you could probably learn the necessary ring theory in

a week?

or just learn-as-you-go

[gray gazelle]

Yeah

[quick hornet]

its not too intense

[gray gazelle]

Ring theory is a very deep subject though so it's kind of like calling "learning about sets a bit" "set theory"

[quick hornet]

meh

you get what i mean

[gray gazelle]

Yeah

[silver herald]

I agree. In fact - I have seen dynamical systems theory making using use of CT quite a lot as well

[sudden kindle]

I <<learned>> ring theory

[gray gazelle]

Hi

[red stream]

anyone have any good books on chaos

specifically of the readable form, not necessarily looking for a textbook

[hollow peak]

chaos by james gleick

[red stream]

@hollow peak would you say there's any major prerequisites for that?

[hollow peak]

it's a fun piece of nonfiction reading so you're good

[red stream]

nice thank you

[hearty steppe]

I mean that’s like a history book, not really an academic book on chaos theory

[red stream]

im interested in both

so if you have more please recommend

[hearty steppe]

Oof, I’m not quite ready to read a whole book on chaos theory yet that is actually academically packed with content so I can’t quite help you there.

Maybe start with trying to get into stochastic calculus

Not sure how mature your understanding of calculus or probability theory is

But I think that will be very important for learning dynamic systems because that’s basically what chaos theory revolves around?

Tbh I’m open to book recommendations on dynamic systems myself. Would like to know what people prefer

But more or less this idea of “chaos” is essentially that the system under question is highly unstable and seems unpredictable to some extent due to its unstableness?

[hollow peak]

the standard text I believe is chaos by steven strogatz

I think the only real prerequisite is calculus

[red stream]

stochastic calculus seems interesting

im doing a research term this semester on stochastic processes and optimization

[hearty steppe]

I am pretty sure some basic enough understanding of Bayes Theorem from Probability is required at the very least too

Cuz the stability of a system has probabilistic implications

[red stream]

yea i take probability this term as well, however i had a introductory class on discrete math that covered bayesian stuff just a tad bit

[hearty steppe]

Right and because unstable implies degree of unpredictability, this implies patterns of randomness via stochastic variation

[sage python]

Brin and Stuck is nice

Hard but nice

[hearty steppe]

Hmmm interesting thanks for the info

[late plinth]

Anyone has good book rec for intro combinatorics?

[muted hearth]

anyone familiar with Smirnov's Course in Higher Mathematics volumes?

i snuck a look at a pdf and it seemed quite nice

but it's borderline non-existent across any storefront

[gray gazelle]

Yo peps

I needed help

[marble solar]

#❓how-to-get-help

[karmic thorn]

Miklos Bona, A Walk Through Combinatorics.

[gray gazelle]

you recommend that book a lot

one second

i'll dm

👍

basically

every section was thrown together after a lecture

and then i put them all together

😎

[ripe granite]

too bad it's on differential geometry

[gray gazelle]

I would like to see it too if you don‘t mind

i will dm

though

at some point

i was just doing them for the sake of having a complete set of notes

i could have stopped and like, spent the time doing problems or something

the good part is i don't use these

i just open lee whenever i need to look up something lmao

i used them during the class tho

but now, after the class? nah

i think if i actually went back through them i would want to change everything

[gray gazelle]

.

also for the first class those notes are from, the other students were using them, so i would have felt bad if i had stopped

[karmic thorn]

Ultra recommended it to me. This book is just too good, I was moved enough to pay for a physical copy. You should take a look sometime.

[gray gazelle]

at some point

maybe if i can't figure out this lie groups exercise i will download it and skim

[karmic thorn]

Definitely.

[karmic thorn]

Relatable. The perfectionism is often counterproductive though.

[gray gazelle]

yup, those notes were a good lesson in that

[karmic thorn]

I just skim through books for later reference.

[gray gazelle]

if i had done exercises from lee in the time i spent typing those notes i probably could have done better in the class

not like i did poorly, just i choked on the exams

[karmic thorn]

If I would bother reading and studying ahead instead of TeXing the same stuff I've already studied for the sake of completeness, I could have gone a bit ahead. :p

[karmic thorn]

[gray gazelle]

okay im gonna look at a copy of the book

[karmic thorn]

Goodluck for your future exams. TeX bad, retvrn to chalkboard.

[gray gazelle]

return to drawing in the dirt

[karmic thorn]

Based.

[gray gazelle]

make commutative diagrams with sticks

and rocks

[static crest]

I had to make my first commutative diagram today

was a bad day

pretty sure the diagram is wrong too

[gray gazelle]

alright ted i have acquired the book through legal means

[karmic thorn]

I acquired through legal means first, then paid for illegal means.

[static crest]

d&f making me draw commutative diagrams without teaching how to draw them

[gray gazelle]

explain this diagram to me

why are we quotienting out by the uh

[static crest]

I would love to if I could

[gray gazelle]

frat boy subgroup

[static crest]

P/frat P is the largest elementary abelian quotient

so if P/N is also an abelian quotient

[gray gazelle]

ah yes

7 > 6

[static crest]

you can make a surjective homomorphism from frat quotient to P/N

[hasty turret]

Well,d and f also introduces p adics

[karmic thorn]

Look at the problem set.

[hasty turret]

And direct and Indirect Limits

[gray gazelle]

are you frat boys

[hasty turret]

That's false if I define a>b iff a<b

[hollow current]

ttera i also want your notes

[karmic thorn]

Rn I'm thinking about problem #39

[gray gazelle]

what page

[ripe granite]

it doesnt work like that

you need to simp for a bit first

[gray gazelle]

vimes already has

[karmic thorn]

Pg.14

[ripe granite]

oh

my bad

[gray gazelle]

ted we migth have different copies

pdf numbering is a bit off i think

on page 14 it has exercise solutions

[karmic thorn]

Ohh

You have the fourth edition, right?

[gray gazelle]

oops

Wait it has exercises?

[hollow current]

ttera is my edate tho

[gray gazelle]

i did not

i got second

[karmic thorn]

Lmaooo

[gray gazelle]

just picked the one that was highest up on the list, and in pdf format

[karmic thorn]

The fourth edition has a neat PDF as well

[hasty turret]

This is clearly cat theory

[karmic thorn]

Use Z-Lib instead of Libgen

[gray gazelle]

🏴‍☠️

Well at least it has abstract nonsense

[static crest]

rip, I went from 192 pages to 190 pages

because I changed my font to the STIX2 fonts

because I need to surpass ttera's 215 pages

[gray gazelle]

poros they aren't 215 pages anymore

[ripe granite]

just write down the proof of feit thompson

[gray gazelle]

i cut down the page size a lot when i messed with the margins

[ripe granite]

you will surpass 400

[static crest]

oh I see

[gray gazelle]

182

you win

[static crest]

pog

[gray gazelle]

well i never typed the last lecture since i didn't understand more than 50% of it

but

i don't think it'd go over 190

so yeah you win 👍

[static crest]

poggers, I didn't even have to do rings

that's half my motivation gone smh

add some pages to it

[gray gazelle]

Inb4 700 pages

how about i add on the page length of my optimization notes as well

73 + 182

get working buddy

i expect you to be at the representation theory part of d&f by next friday

Add exercises and proofs

[static crest]

ten

[gray gazelle]

uh oh

i did some of those in my notes

[static crest]

exercises and notes are separate

examples from class are fine

[karmic thorn]

[gray gazelle]

the prof for the manifolds course would say "i'm leaving this as an exercise for you" and then i'd type a proof in that lecture's notes, but then he'd put it on the homework

let me find an example

[karmic thorn]

My notes so far have been taking out contents from the book almost verbatim, with all examples and exercises with solutions.

[gray gazelle]

prop 2.4.3 was literally on the homework i wonder if the other students copied my solution

Not proofs for the exercises, proofs for the theorems

[karmic thorn]

It would be nice if video lectures could be embedded in a text-file format.

[gray gazelle]

Just put a link to yt

[karmic thorn]

Hmmm, interesting.

[karmic thorn]

That is reasonable, but I'd like to have something internal to the file itself.

[gray gazelle]

That file's gonna be 10gb

[karmic thorn]

Maybe a spoiler element in PDFs would be neat.

[karmic thorn]

Well, just create seperate file with each lecture and the corresponding notes+exercises.

Hmmm, fair enough.

PDFs could be made more dynamic than they are.

That would be neat.

Your opinions are based Yohan.

[static crest]

oh I got the word count to work

had to install a perl script

[karmic thorn]

@gray gazelle Did you find the 4th ed or should I DM you the legal copy?

[gray gazelle]

i went back to doing my lie groups exericse lol

[static crest]

nice

[karmic thorn]

Lol, alright.

[gray gazelle]

you can dm if you would like

[dapper root]

Lie groups hahahaha

You should ditch those

and learn algebraic groups

[gray gazelle]

that's a lie

[dapper root]

It's like a Lie group but you replace smooth manfiold

with something more based

[gray gazelle]

inb4 variety or some crap idk

[dapper root]

yeah

Dude... come on

like... GL_n is an algebraic group

[gray gazelle]

yeah but it's also a lie group

[dapper root]

afaik the basic theory is like mianly just for the matrix groups

[gray gazelle]

well for F = R or C

[dapper root]

which are also all lie groups

haha

[gray gazelle]

my body recognizes the AG pill as a threat

dont worry

one day

[marble solar]

I think geometers/topologiraffes and algebraic geometers think in very different ways

[hasty turret]

Example?

[marble solar]

Manifolds don't really deal with singularities whereas varieties do

Ok, that might be a bit of an over simplification

but usually from what I've seen algebraic geometers are more interested in taking some geometry into the land of algebra - commutative rings, numbers, polynomials, etc.

And leveraging those tools to say something about the geometry

Topologiraffes tend to think about the actual manifolds/structures from what I've seen

Again, I'm no expert in either

[gray gazelle]

[warped cedar]

talk to jacob lurie

he is cracked at geometry and topology

[drifting elm]

in the forward to this it says the prerequisite would be predicate calculus https://www.amazon.com/Lambda-Calculus-Combinators-Introduction-Roger-Hindley/dp/0521898854/

but the book I got for predicate calculus is really hard even though it says no prerequisite

I see sup() without explanation

had to google it finally found it was suprenum

this is the other book https://www.amazon.com/Mathematical-Logic-exercises-Propositional-Completeness/dp/0198500483/

is there something I should read before this or is there an easier book on predicate calc?

[gray gazelle]

Halmos, naive set theory would probably be sufficient.

To get your elementary mathematical notions

On sets at least

and it needs no previous knowledge in the domain, but only basic notions of mathematical logic
if you are referencing this, then is sounds like you don't need to know the in-and-outs of first order logic, or even as referenced in the book you linked about it, the completeness theorem

@drifting elm

[drifting elm]

@gray gazelle on the contrary, I would like to know the ins and outs of first order logic but I don't understand why this book would say the prerequisite is HS math but then sup() is in the book without explanation

[gray gazelle]

If you would like to know those then I'd recommend something like ebbinghaus, very well written book

[gray gazelle]

I don't know, but you could probably google what sup means if it is just that

Least upper bound of a set is sup

[drifting elm]

there is something else but I need to write in latex so stand by

$\mathcal{F}=\cup_{n\in\mathbb{N}}\mathcal{F}_n$

[hasty eagle]

0000000000

[drifting elm]

a bit much for HS math

don't ya think?

[gray gazelle]

[drifting elm]

I understand set theory though

I started reading axiomatic set theory

just never seen this notation

[gray gazelle]

Yeah maybe start with halmos naive set theory. You could probably get some pdf and see if it is elementary enough for you.

[drifting elm]

what ebbinghaus book were you thinking of?

[gray gazelle]

Mathematical logic.

It would require naive notions of logic and set theory however.

That is getting to the ins and outs of first order logic usually requires that.

It's not a topic one would do the first time one looks at math.

[drifting elm]

maybe this is offtopic but why do they define sets with nothing prefixing $\cup$

[hasty eagle]

0000000000

[drifting elm]

like as if it was unary

[gray gazelle]

It's like $\sum_{n\in\bN} \frac 1{n^2}$

[hasty eagle]

ℋ/𝔄

[gray gazelle]

One might also write this as $1+\frac 1 {2^2} + \frac 1{3^2}+...$

[hasty eagle]

ℋ/𝔄

[gray gazelle]

But the prefix is easier to write down

So like $\bigcup_{n\in\bN}\mathcal F_n=\mathcal F_1 \cup \mathcal F_2\cup\mathcal F_3\cup ...$

[hasty eagle]

ℋ/𝔄

[gray gazelle]

@drifting elm

[drifting elm]

ok I get it now

they use it like sigma

[gray gazelle]

Yeah

[drifting elm]

I read a lot of NT books

so sigma is easy but never seen this use of cup

or you prefer union

latex calls it cup

[calm crane]

$$\subset!!!\bigcup$$

[hasty eagle]

a cute cat ٩(˃̶͈̀௰˂̶͈́)و

[calm crane]

clearly a cup!

[gray gazelle]

now turn this into donut

[drifting elm]

$$\subset!!!\bigcup \cong \circ $$

[hasty eagle]

0000000000

[drifting elm]

it broke

[gray gazelle]

what were you trying to do

[drifting elm]

tried to make coffee cup homeomorphic to donut

[prisma snow]

Is $\subset!!! \bigcup$ supposed to make it bigger?

Or why the !?

[gray gazelle]

Spacing

Make it stick to the U

[prisma snow]

Ah

[gray gazelle]

You'd have to write it as \! however

[hasty eagle]

Lunasong

[prisma snow]

Cool

[drifting elm]

ok last one then I stop spamming

$\subset!!!\bigcup \cong \raisebox{0.05 em}{\Huge \circ}$

[hasty eagle]

0000000000
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[waxen elbow]

any review on Smirnov's collection "higher mathematics" ?

[gray gazelle]

This is great

[hearty steppe]

I’m curious about that too adri. You peaked my curiosity

[waxen elbow]

can you please tell more about it ? was it better than some other textbooks you read ?

[gray gazelle]

Oh lmao I was talking about the mug=doughnut

[waxen elbow]

i don't have time to read everything, it looks like a pretty intuitive approach to analysis and algebra. It looks like it's geared towards engineers/physicists and not mathematicians (which is a pity, since I've just changed to a math major... lol)

sorry then : (

[hearty steppe]

Not a good mentality to have “I don’t have time to read everything”

I mean like sure you don’t have to read everything but I wouldn’t go into learning or self-study with that mindset.

Better to be in the mindset of... “how do I map out what I’m learning for what I want to do or how do I map it with what I’m doing”

[waxen elbow]

i mean.. today i didn’t have the time 😭

[hearty steppe]

Cuz you may need to learn shit you never thought you’d have to learn

So it’s important to be open minded

[waxen elbow]

but yes i was planning to read a bunch of paragraphs to see, i just wanted some reviews because i’m not that familiar with english textbooks in general

[muted hearth]

where'd you find smirnov?

[waxen elbow]

online pdf

i’m a poor student : (

[muted hearth]

oh fair enough, lol

I asked about it the other day, I'm trying to snag a physical copy

since it seems cool

[waxen elbow]

isn’t it like super expensive ?

[muted hearth]

will be free if it comes to fruition

[waxen elbow]

did you read a bit on pdf ?

[muted hearth]

yeah, I downloaded volume 1 to have a look

[waxen elbow]

whats your impression about it ?

[muted hearth]

that particular volume seems like a fairly rigorous and not awfully written intro to calc & analysis, and I'm just assuming thst continues through the rest of them

although you can tell it's an oldddd book

especially in the graphical presentations of stuff

[waxen elbow]

ill give it another look, i thought it lacked of rigour, but i might be wrong

[muted hearth]

i mean it's not a real anal book but it seemed like a fairly high level for a physicist catered calc book

[waxen elbow]

i mean i got french textbooks which are suuuuuper rigorous, and i took a look at calc2/3 ans it seems like it’s good for intuition / computations

then it could be good, paired with a real analysis book

[muted hearth]

i mean I'm not in a position to really want a super proof focused book, spivak is a lovely presentation but heck those exercises

also i think you'd be hard-pressed to find calc through func analysis in any other single set

that seems nice

[waxen elbow]

yea spivak’s exercices are quite familiar with those i got in class, some are tough

[muted hearth]

but I'm thoroughly unqualified to judge any of this

[waxen elbow]

i’m trying to find the balance but it seems like it’s impossible

long story short

[muted hearth]

i was only focused on it because it's free

physical copy

[waxen elbow]

i was on a french forum and some guy said « i want a book to do some more maths in my prepa » which is like intensive college courses, and someone mentioned smirnov’s, the guy wrote that it was super great to get a deep understanding etc

and since i’m struggling to find a good book..... i tried

can you give me the name ?

thank you 😋

btw

since i’m in math major now, i wanted to complete my eng calc courses but i’m not satisfied with the book i have

it’s stewart calc, i feel like it doesn’t go deep enough. any recommendations ?

spivak is for real analysis right ?

oooo

[muted hearth]

eng calc would need more than just spivak tho yeah

since it probably goes up to calc 3?

[waxen elbow]

i was in 2nd year, we did calc3

i mean if calc3 is multiples integrals and stuff yes we did

[muted hearth]

wait I'm an idiot

but that still stands I thinn

so you'd want to do calc 3 again, spivak won't cover it

[waxen elbow]

oh ):

[hasty eagle]

Yohan Wittgenstein

[waxen elbow]

yup

gradient etc, a bit but mostly in physics

[muted hearth]

isn't this more of a summary than a textbook?

[waxen elbow]

ooo written by komolgorov !

it must be nice

[gray gazelle]

Any good books on differential algebra?

[muted hearth]

nvm I read an epub of something similar that was exercise free and kinda weird

[sturdy sail]

Wtf is even that?

[muted hearth]

💍

[gray gazelle]

Ah no sorry

https://en.m.wikipedia.org/wiki/Differential_algebra

Was the right link

I thought for a sec it was the wrong one

[hearty steppe]

OH that math book series

[sturdy sail]

Oh yeah

I've heard once in a differential geometry lecture that ''A linear map that satisfies the leibniz rule is pretty much all the differential of a smooth function is about''

So it kind of makes this notion clear

[waxen elbow]

hahaha i’ll give it a look

like my courses are more like rudin’s but with many many applications too

[muted hearth]

i think they're very similar

[gray gazelle]

No sure what you mean. I was referring to this

Differential algebra refers also to the area of mathematics consisting in the study of these algebraic objects and their use for an algebraic study of the differential equations. Differential algebra was introduced by Joseph Ritt in 1950.

[waxen elbow]

but it’s too dense, i need a textbook to help me a bit

[sturdy sail]

I mean

This is just like a generalization of what I said

instead of studying differentiation on smooth manifolds

[muted hearth]

i can see why you probably didn't think smirnov was very in-depth if your courses are rudin esque lol

[waxen elbow]

gonna sleep, may i DM you tomorrow to ask your more about it ?

[sturdy sail]

you just think about differentiation as an abstract linear map

[waxen elbow]

yes that’s why 💀

[sturdy sail]

and depending on which algebraic structure you are working with

[muted hearth]

whereas point of reference was basically high school textbooks

[sturdy sail]

You can study what different properties of this differential operator you can get.

[gray gazelle]

I'm not sure if we are talking about the same differential algebra.

[sturdy sail]

I'm not trying to describe it lmao

Just saying that the notion of a derivative being only a linear map that satisfies the leibniz rule is a thing I've already encountered before.

The definition of a derivation on a smooth manifold is pretty much this one

[gray gazelle]

Okay

I see thanks

[drifting elm]

I noticed there are a lot of books by chaitin. all pretty heavy material. how does he do it.

also, does anyone have a fav book by him?

[hearty pollen]

man does anybody have any good book recommendation

[flint forge]

any like

particular book

requirements?

subjects?

[hearty pollen]

like sci fi

[soft terrace]

the horus heresy series

siege of terra

[hearty pollen]

oh ok

[silk quartz]

I just finished reading Harrow the Ninth, book two of the Locked Tomb trilogy (bk 3 forthcoming).

It's quite a trip.

For other sci-fi (and this should probably go in #discussion), it might be useful to hear what you've read and enjoyed in the past.

[drifting elm]

https://en.wikipedia.org/wiki/Foundation_series

[hearty pollen]

thanks!

hopefully I can find a free pdf

😆

[drifting elm]

https://www.amazon.com/Big-Book-Science-Fiction/dp/1101910097

this because it contains a short story "repent harlequin!"

but the audio book from the radio show was really better than that with all the sci fi music and fx

[hearty pollen]

oh thanks

[drifting elm]

https://en.wikipedia.org/wiki/The_Maze_Runner_(book_series)

this is pretty good because it builds up a world that makes you reflect on your own world as possibly being an illusion constructed by someone playing a game or building a prison

[silk quartz]

If you liked Foundation, you might enjoy Dune.

[drifting elm]

my avatar is dune

so yeah

the mentats were a special breed of human that could do math better than people without mentat genetics

[languid galleon]

Hey!

I would like to retake all math prerequisites. Like Pre-Algebra etc. Could anyone recommend smth?

I am at university studying CS and already passed all math subjects, like linear algebra, Analysis etc. but I would like to retake the fundamentals because I new my foundation isn't the best.

Could you recommend eventually some books?

[drifting elm]

@languid galleon https://www.amazon.com/Mathematics-Electricity-Electronics-Arthur-Kramer/dp/1111545073/

this goes over everything from addition and subtraction all the way up to complex numbers around the unit circle

you can get it super cheap on ebay

https://www.amazon.com/Precalculus-Ron-Larson/dp/1337271071/

this would be my other suggestion

I tried using this but it was kinda really big book designed for lower grades so don't get this https://www.amazon.com/Southwestern-Advantage-Math-Moore-2011-08-02/dp/B01K3QDD2C/

vol 2 might be ok I have vol 1

here is a nice free online interactive lesson in pre-algebra https://spot.pcc.edu/math/orcca/ed2/html/orcca.html

[languid galleon]

I already bought Understanding analysis by abott and linear algebra by axler to g through them again

thanks mate!

I used this as guide:

https://www.youtube.com/watch?v=fo-alw2q-BU&list=FLBFVLV0tT1s1oDsT2ENY1fw&index=2

[fossil island]

his pacing is a little interesting

[drifting elm]

if you went through analysis and calc 1 but you still feel like you don't understand it then you should probably do more differential equations. you will need ordinary differential equations for fourier series and fourier transform.

https://www.amazon.com/Fourier-Dover-Mathematics-Georgi-Tolstov/dp/0486633179/

if this is hard to understand then you need a book on ODE

[static crest]

I don't think you need ODEs for fourier

a very basic knowledge at best

[drifting elm]

my books have it listed as a prerequisite. ODE with constant coefficients

very basic ODE

[static crest]

kinda weird, you don't really use much ODEs knowledge to fourier, past the most basic 2nd order diff eq of all time

[drifting elm]

I can agree with that

[static crest]

which doesn't need ODE knowledge at all really

it only needs basic calc

a proper prereq to fourier would be complex analysis

[drifting elm]

well the books are covering DFT DTFT in one book

[static crest]

if you want to work with fourier properly

[drifting elm]

both of my text books

[static crest]

well signals is a whole different beast than fourier, signals does require ODEs

[drifting elm]

yes these are signals and systems

what would be the point of learning the fourier transform if you don't actually use it for signals?

[fossil island]

books for differential geometry? i was thinking about spivak's but are there any other's worth a try?

[karmic thorn]

TTerra moment

[fossil island]

@gray gazelle

i require dire help

[marble solar]

Spivak is the best

Some people like Jack Lee's books

[fossil island]

he has books on three kinds of manifolds

i don't really know anything about any

riemannian, smooth, and topological

[karmic thorn]

I guess the sequence is Topological->Smooth->Riemannian

From what I recall from the preface of Smooth

[fossil island]

"this text is used for the first third of a year-long course on the geometry and topology of manifolds"

makes sense

[gray gazelle]

Ted got the sequence right

[fossil island]

i assume that a study in dynamical systems would be good with a study of topological manifolds first?

[gray gazelle]

there's spivak's calculus on manifolds, which is like a calc 3 + intro to differential geometry book (great book!). then there's spivak's monstrous 5 volume set, meant to be read after CoM, which covers roughly the same content as lee's intro to smooth manifolds (at least for the first volume)

then you have lee's trilogy

the first book, intro to topological manifolds, is more of a intro to topology book with a focus on manifolds (topological manifolds) as a rich source of examples of topological spaces

the second book, intro to smooth manifolds, is exactly what the name suggests. this book is thicc and good, covers the important content and a lot more

third, intro to riemannian manifolds, continues the study of smooth manifolds by introducing ways to measure area, length, angle, etc. on abstract smooth manifolds (kind of like generalizing classic curve and surface theory)

that's the rough outline

[gray gazelle]

idk anything about dynamical systems so i can't comment on this, sorry

[fossil island]

damn, but thanks for that outline

[flint forge]

dynamical systems has a sub-field called smooth dynamics

which is normally done on smooth manifolds

[gray gazelle]

oh there's also tu's introduction to manifolds, which is like an easier version of lee's ISM

[flint forge]

however dynamical systems in general is not restricted to the context of manifolds

and you can take an intro course in dynamics w/o knowing the word manifold

the real prereqs for a good first course are measure theory and point set topology

[fossil island]

would it be worth to take such a class?

ah ok

[flint forge]

here point set topology is more than a meme requirement

you really want to be comfy w some of the more annoying parts

its a fantastic subject

i recommend everyone take it

[fossil island]

is the book that is given in #books-old good?

for dynamical systems

[flint forge]

brin and stuck is good

but very terse

i've heard people like Katok Hasselblatt or whatever

but never read it

brin and stuck is alike a multi-hour per page type book at times lol

and the exercises are quite hard

[fossil island]

how far do you think one could get without measure theory in brin and stuck

[flint forge]

like

not that far?

both of those are hard pre-reqs

i don't suggest trying before that

[fossil island]

ok thanks

[sage python]

Ah Brin and Stuck

I should give that another shot now that I'm less of a scrub

[marble solar]

Dami you scrub

[sage python]

no u

[silk quartz]

Hey Dami. Max was pining after you earlier.

[flint forge]

this is true

[timber mesa]

I think it's kind of terse and leaves out a ton of details, I'd recommend Clark Robinson's Dynamical Systems Stability, Symbolic Dynamics, and Chaos instead, plus references on ergodic theory (Brin-Stuck's chapter 4 and Yakov Sinai's Introduction to Ergodic Theory) if you care about that.

[timber mesa]

all chapters but the one on ergodic theory (edit: and the final one on measure-theoretic entropy. Also the chapter on complex dynamics requires complex analysis of course)

if measure theory is a problem for you don't worry, just follow Robinson and see if you want to study ergodic theory later

Robinson even introduces the basics of manifolds right when you need them

which is actually really late on the book, chapter 8

(before that it's simple one-dimensional dynamics, some ODEs and bifurcation theory. Chapters 8-12 are essentially the dynamics of diffeomorphisms on manifolds)

[flint forge]

side note

Brin and Stuck has like very little reference to ODE/PDE/Bifurcation

and if you're interested in dynamics through the lens of group actions rather than diffeq

brin and stuck does that well (if a little terse)

also Lan Wen Smooth Dynamics

is a great follow up to brin and stuck

but you should learn what a (smooth) manifold is in between

[fossil island]

I'm doing topology and numerical methods in ODEs this spring so maybe I'll look into dynamical systems after that

[fluid shard]

Does this look like a joke or is this reasonable for someone looking to restart mathematical knowledge? (I'm just a Electrical Engineering student)

[timber mesa]

lmao these guides are 100% meme

[fossil island]

Idk why they need you to do like 2 or 3 books in proofs/logic

[timber mesa]

exactly

[flint forge]

the next iteration of that guide will just have like HTT on it

[timber mesa]

do you just want to review or are you planning to, say, study maths full-time in the future?

[fluid shard]

Get the basics for a full time transition

[timber mesa]

out of all /sci/ guides I've saved this is the most decent one I'd say

[fossil island]

What math classes have you taken, Kolios?

[timber mesa]

are you accustomed to proofs already? if not perhaps I'd skim through Hammack's Book of Proof and a "rigorous" Calc and LinAlg pair, I'm thinking Spivak and Hoffman-Kunze

maybe Hefferon or Linear Algebra Done Wrong instead of the latter

[fossil island]

Linear algebra was my intro to proofs and it was fairly good

[fluid shard]

The typical classes for Electrical engineering, so no proof of anything, just applying theorems. Covered Calculus (up to basic Vector Calculus), application using Linear Algebra (matrices and so on), ODE and PDE class to solve oscillator problems (no non linear stuff), numerical methods (more about MATLAB), applied math for signals (Fourier """ analysis """)

[timber mesa]

you should be good on intuition and computations then, I'd focus on getting the hand of proofs first (which could mean either reading a book on them or going through a "proof-based" Calc or LinAlg, it seems to be a matter of personal preference)

[timber mesa]

Hammack's book is good and it's free, from that meme guide Transition to Advanced Mathematics is also pretty good from the bits I've read

[fluid shard]

Not yet. I will get that book then

[fluid shard]

Thanks for the recommandation

[timber mesa]

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

had it on bookmarks lmao

[fluid shard]

Yeah I have a lot of bookmarked papers and sites for my projects, it's a pain lol

[timber mesa]

these two are also freely available in their respective authors' webpages

[fluid shard]

Now that I remember, I think the mathematician teaching did proof even if the class was just for Engineering students. For other classes, they didn't bother.

[fossil island]

That's good, just getting the ideas of linear dependence is a huge leap

[timber mesa]

before changing to math major I somehow passed linalg without understanding the difference between a matrix and a linear map

[gray gazelle]

there is no difference

modulo basis

[flint forge]

i feel like R-linear counts as linear

do people say module homomorphism?

[obsidian valley]

theres a difference?

[flint forge]

i know some textbooks do

[fossil island]

${e_1,\ldots, e_n} \mod \mathbb{R}$?

[hasty eagle]

Trichloromethane

[flint forge]

For finite dimensional vector space a matrix is the data of a linear map and a specified basis

[sage python]

Lmao

[gray gazelle]

hey jesse

[obsidian valley]

hi

[fossil island]

Breaking bad reference?

[obsidian valley]

it feels like a party everyday

hey jesse

hey jesse

[gray gazelle]

still haven't done this problem

[obsidian valley]

https://www.youtube.com/watch?v=lfjjJwXDR4U

wtf why not tterra

[gray gazelle]

it's just frustrating at this point

[sage python]

This is veering off book discussion lmao

[gray gazelle]

okay let me make it relevant

[obsidian valley]

just go to the next problem

[sage python]

What's your favorite book on insert topic here?

[fossil island]

#❓how-to-get-help

[obsidian valley]

come back when you're more mathematically mature

[gray gazelle]

i am going to read lee's introduction to smooth manifolds textbook in order to review so that i may do the problem

i mentioned book

it is now on topic

[dapper root]

I remember someone brought one to us and there were like legit 7 proof books and you did like 12 books before touching calculus hahaha

We all said "this is really fucking stupid" and they went "hmmmm, okay. I'm gonna do this tho"

[valid moth]

what do you mean you can do calculus without googology

[quartz pawn]

Anyone have logic book recommendations. I know the standard text is Enderton but I'm just curious if anyone here has some personal favorites you think are good for learning math logic.

[gray gazelle]

https://www.amazon.com/Ninja-Good-Ultimate-Guide-Gaming/dp/1984826751

[obsidian valley]

The other one that I see recommended is Ebbinghaus I think

I haven't really touched it though

[drifting elm]

I tried mathematical logic by cori and lascar but I really didn't like the part about languages and alphabets before it was properly introduced

so you would need another book to talk about languages

but I also think that propositional calculus and predicate calculus is as basic as you can get.

unless you want to learn languages from here for free as a primer for mathematical logic by cori and lascar

https://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-001-structure-and-interpretation-of-computer-programs-spring-2005/

[obsidian valley]

[drifting elm]

logic could mean many things, it could be first order logic, boolean algebra, philosophy books about formal logic, prepositional and predicate calculus

[obsidian valley]

Does this introduce models and stuff?

Cori and Lascar I mean

yeah it must

[drifting elm]

yeah all models

[obsidian valley]

nice

If he's referencing enderton he just means a basic overview of mathematical logic I'm sure lol

[drifting elm]

this goofy book is for noobs https://www.amazon.com/Discrete-Mathematics-DeMYSTiFied-Steven-Krantz/dp/007154948X/

the book has some questionable themes

[obsidian valley]

[drifting elm]

the author uses an example as a woman who only marries a rich man

and the fat girl who never gets married

using discrete math to prove it

[calm crane]

nice

[dreamy perch]

does anyone have advice for how to effectively self study from a book?

notes and whatnot?

[static crest]

take notes if it helps you retain information, it does for me.

most important thing is to do exercises

however

[dreamy perch]

Im mainly thinking about format of notes

Im wondering if it makes more sense to do paragraphs or bullets

(or both ig)

[gray gazelle]

just do a shit ton of exercises

[hollow peak]

I forgot to ask this yesterday

is there is a good resource for a really basic and quick introduction to the fundamentals of category theory?

I started reading https://arxiv.org/pdf/1612.09375.pdf but I'm not liking it so far

[ripe granite]

The first few chapters of Emily Riehl's Category theory in context

[drifting elm]

I write down all the theorems, definitions or the methods for solving a problem. that way my notes replace that entire book.

the stuff that is not short I don't write down.

[opal pumice]

guys what's random processes ?

[hearty steppe]

https://en.m.wikipedia.org/wiki/Random_walk

[devout vault]

For a very basic introduction, I would highly recommend Conceptual Mathematics by Stephen Schanuel and William Lawvere

[timber mesa]

a stochastic process is basically a bunch of random variables parametrized by time, there's tons of examples such as Markov chains and random walks

[opal pumice]

ohh i get it

[wind aspen]

Is there any book the good people of this server would recommend that could probably help make Maths click
as in the idea of Maths as a whole, I guess

[flint forge]

do more problems

and different kinds of problems

[wind aspen]

alright, thanks for the answers!

[hearty steppe]

Not sure how relevant category theory will be for me but that book seems like a promising first course

[scarlet pumice]

Does anyone have any book recommendation for High school mathematics concepts?

[gray gazelle]

lang's basic mathematics

is apparently alright

you may have to don an eyepatch to get it

[scarlet pumice]

thanks, I'll have a look at that book

[sudden granite]

its good

i am reading it rn

lang is bae

[wise vine]

What's a good textbook for mathematical logic with a specific focus on CS?

[hearty steppe]

Maybe Rosen

[wise vine]

His discrete math book? It's not that rigorous for me

[gray gazelle]

The Bible is pretty good.

[wooden sparrow]

Harry Potter is better it seems

[gray gazelle]

One can atleast understand harry potter

[gray gazelle]

Have you checked the Open logic text?

It's in #books-old

[frail horizon]

Any good books to prepare for the IMO?

[gray gazelle]

Are you complete beginner or have experience with comp math?

[frail horizon]

Beginner.

@gray gazelle

I've got experience with analysis though. I'm just a beginner to comp math.

[gray gazelle]

You can check out Paul Zeitz 'Art and craft of problem solving'. And then follow up with the recommendations at the back.

[drifting elm]

https://artofproblemsolving.com/store

volume 1 and 2 are competition math books

I think competition math has a lot of number theory in it and a lot of proofs for geometry and algebra

there are also the mind your decision books

[warped cedar]

It has a lot of number theory, geometry, algebra, and combinatorics mainly

If you are doing something like the IMO

[drifting elm]

the art of problem solving books are great practice for word problems. you don't realize how much harder these things are as word problems till you actually do it.

I messed up on a basic probability problem because it said balls and urns

so I thought it was a binomial coefficient problem but it was just a basic algebra

[warped cedar]

If you are doing something like Putnam there is more you need to know

Calculus, linalg, complex, diffeq, probability

[wise vine]

Oof I've been browsing this discord for a year and I haven't seen that one. It looks pretty good, thanks! Though I guess it's pretty long haha.

[stiff sandal]

agreed.

[stiff sandal]

how to fix that?

[inner sentinel]

Strang or Axler?

[fossil island]

Thoughts on "An Introduction to Abstract Algebra" by Robinson? (https://books.google.com/books/about/An_Introduction_to_Abstract_Algebra.html?id=F9ZkUcWX3WoC). I don't know why profs can't just use d&f

We go all the way up to vector spaces

[marble solar]

some professors don't like d&f

If you don't like it, you can use d&f, it has everything lol

[static crest]

d&f is very long and very dry

some people like their texts to be more flavorful I guess?

[marble solar]

They might want to cover different topics in a different way

e.g. maybe less time on finite group theory

[static crest]

that book seems extremely brief

I guess d&f might be considered too involved

or that it has too much extra information

I am a bit skeptical about how short that textbook is

[marble solar]

Short books are the best

[static crest]

but books only shows a preview, so I can only go off of the table of contents

[marble solar]

They're too the point

[static crest]

d&f is also pretty to the point

it's just there's a limit to how much content you can cover

with such few pages

[marble solar]

If you're learning a subject for the first time, you don't want gobs and gobs of additional topics, long lists of exercises

It's better to introduce it in small batches

and then in grad drop the vehemoths

The monsters

[static crest]

like all of rings in 30 pages? seems sus

but again, depends on the course

[fossil island]

i guess the book characterizes itself as a "high level overview"

[gray gazelle]

i mean spivak does multilinear algebra and stokes' theorem in 30 pages

so...

[fossil island]

galois theory in 19 pages

but i dont know squat about algebra

except group = symmetry

[quick hornet]

my calculus course did stokes' theorem in 1 page smh

[fossil island]

proof: trivial

[marble solar]

You don't need everything in super hyper detail to get a good education

[static crest]

from a brief skim through the groups content, it does seem like more of a review book than a book I'd use to actually learn from

[marble solar]

Sometimes giving students a taste