book-recommendations

[vital bane]

But another fun option is the bible

[mortal ore]

Yeah I'm using this for grad algebra lol

[vital bane]

you can use it right now tbh

[mortal ore]

Well its more that the class I'm taking uses it as a textbook

[vital bane]

it's perfectly fine for UG algebra, it transitions nicely into grad algebra as you go through the book

[molten gulch]

We haven't like the sections nor formatting of gallian very much tbh

Colour should not be in textbooks unless absolutely neccessary

[vital bane]

Color should be in more textbooks

[tame tree]

bizarre opinion

[vital bane]

it makes it so much more fun to read

[molten gulch]

Axler handles it fine, for example, but still genuinely hard to focus for us

[mortal ore]

https://tenor.com/view/captain-underpants-gif-13886158771766943429

[vital bane]

I like the visualizations Gallian has

[molten gulch]

Our opinion is definitely a unpopular one..or at-least uncommon one, we acknowledge that

[vital bane]

I see, I guess it depends on the person, I don't find Axler's colors distracting at all

[molten gulch]

Visualizations and diagrams are awesome, colour is...frankly colour just ends up distracting us

[vital bane]

"we", "us" bro is talking like the sin archbishop of gluttony 💀

[molten gulch]

😭

[vital bane]

I just realized, it's because you're "the cat collective"

[molten gulch]

LMAO WE THOUGHT YOU KNEW 😭

[vital bane]

Lmao I thought you used "I" and "me"

I guess I remembered wrong

[molten gulch]

Depends on if it's specific to a single alter or to our whole system

[vital bane]

bro is a hive mind fr fr

[molten gulch]

Welcome to DID/OSDD my friend

[vital bane]

just a system of cats spread throughout the globe

[vital bane]

oh I see this is a specific disorder

[vestal niche]

Good and bad for me just depend on how clear and understandable the mathematical exposition is

[vital bane]

I didn't know

[molten gulch]

Lmaoo nah rather centralized entirely in front of a specific cola machine in [REDACTED] building at [REDACTED] university

[molten gulch]

Yep

[mortal ore]

How do you like lang

[vital bane]

SCP 7689 - Ryan "The Cat Collective"

[vestal niche]

Cause Lang's clear

[mortal ore]

I feel like it'd be even clearer had he given reasons to even define what a group is before doing so

[vital bane]

isn't Lang supposed to be a grad algebra book?

so it just assumes you've seen UG algebra once

[vestal niche]

Exactly

[mortal ore]

It's literally called undergraduate algebra

[vestal niche]

If you want undergrad and everything up read Artin

[hard dust]

any good books to start real analysis

[vital bane]

oh I suppose you guys are talking about different algebra books

Lang has two algebra books iirc

[molten gulch]

I mean if you're mad enough you could read lang on a first pass I guess

[molten gulch]

Abbott

[vital bane]

"Algebra" and "Undergraduate Algebra"

[vital bane]

Abbott

[vestal niche]

Abbott or Tao

Do not touch Rudin if you haven't had at least 2 years of undergrad-level proof writing

[hard dust]

whats tao?

[vital bane]

I think Abbott as a main text + Rudin PMA as a reference (for more exercises) is a goated combination

[vestal niche]

Terence Tao's Analysis I and II

[hard dust]

ohh

[hard dust]

hmm thxx

[vestal niche]

Man's not only an absolute genius of a mathematician but also a master expositor

[molten gulch]

One of my irl friends was visiting the uni the other day

He is currently taking college algebra at the local community college

Now uh

Imagine what happened when picked up lang

[vestal niche]

Hope he writes more expository books after turning 50

[vital bane]

damn Tao is gonna turn 50

[molten gulch]

Thinking "algebra" meant college algebra

[vital bane]

we are all becoming so old

[molten gulch]

We just turned 20 a few months ago

[vital bane]

same

[vestal niche]

Yea he's turning 50 in July

[molten gulch]

He just went "what the fuck? Do you actually comprehend any of this stuff????"

[vestal niche]

I still vividly remember how famous he was in the late 2000s

Cause that was after the 2006 Fields Medal

Dude was writing like 30 papers a year or something

[cursive orbit]

I think Pugh is a pretty good book

for undergrad analysis

[vestal niche]

Apostol is very good too

Literally Rudin with a better exposition

[foggy relic]

i like browder the best

[tame tree]

I recommend a more "standard" analysis text alongside Tao

[mortal ore]

I didnt know tao wrote an analysis book

[dim pendant]

It's definitely one of the biggest modern analysis books out there

So I suppose you wouldn't know unless you needed to self study real analysis to some extent and didn't know what book to use

[graceful moon]

He has 2, they’re very good

[mortal ore]

yeah im not quite in the analysis scene yet

getting there

[graceful moon]

Well technically he has more than 2, he’s got two mainline RA books

[dim pendant]

Have fun when you get there

If you struggle, I suggest learning some topology in your free time even if it's just like 20 minutes a day it will help you escape epsilon delta hell and still understand analysis.

[mortal ore]

i mean ill likely be fine

im doing topo in the fall

im just using abbott for an introductory

[dim pendant]

Oh I see you're self studying

[mortal ore]

nah im in uni

[dim pendant]

Oh

[mortal ore]

but i self study so i get As lol

im not letting a single class trip me up

[normal crystal]

you're a tough grader gg

[mortal ore]

i work hard what can i say

[molten gulch]

he also has an MT book

[mortal ore]

whats MT

[molten gulch]

measure theory

[mortal ore]

i see

[normal crystal]

damn
I was excited for the Terence Tao travelogue of Montana
not meant to be

[graceful moon]

#book-recommendations message

[molten gulch]

oop missed that sorry >.<

[royal scaffold]

ngl his lecture notes on his blog are higher quality than most textbooks

[molten gulch]

his blog is awesome, though we don't understand a lot of the maths there (yet :3)

[gray gazelle]

I'm looking for a book that teaches linear algebra in an abstract way (I have experience with real analysis) and uses mathematical symbols. I don't care at all about computation.

[valid narwhal]

Friedberg

[gray gazelle]

thanks

[rough nymph]

Very praised book around here, more than Axler and H&K?

[valid narwhal]

Certainly

[grim ore]

Hot take, learning Abstract Algebra first and then going back to Linear Algebra esp with a book like friedberg was enlightening

Ofc I had a weird book as I learned rings and fields first before groups (Baby Hungerford (ug))

[molten gulch]

For me they've just blended together and like...all algebra is so fucking comfy

[grim ore]

Interesting

[hearty steppe]

I guess nobody has any recs for me this time around >.>

[kindred viper]

Hi guys I am an electrical engineering undergraduate and was wondering what would be the best book to learn about numerical methods

[pine tundra]

In Italy we typically use Quarteroni "numerical mathematics", even though I still have to read it I've heard it is pretty good

But here there's plenty of people who can suggest you much better references

[grim ore]

People dont usually like mcgraw hill texts, Numerical Methods for Engineers by Steven Chapra is what we use in my uni

[vital bane]

you should care about computation tbh it's important of course computation isn't everything but it's an integral part

[gray gazelle]

im learning mathematics for fun though

[vital bane]

still, don't neglect computations

[vital bane]

perhaps you will have better luck in #dynamical-systems ?

[tropic nacelle]

pensavo che tu eri spagnolo, hahaha

[ivory shore]

I totally agree, Chapra is an excellent introductory book to learn Numerial Methods. Numerical Methods by Richard Burden & Douglas Faires is also good

[grim ore]

Yep

[hearty steppe]

I’ll try that out

[kindred viper]

Thanks 🙏🏾

[kindred viper]

Thanks 🙏🏾

[pine tundra]

No no italiano, anche tu?

[tender cobalt]

What's "perturbation theory" about?

[willow merlin]

which book explains

the concepts of hamel basis vs schauder basis

[slate pilot]

What about it makes u comfy?

[grim delta]

Hey there! after finishing precalc which book you recommend me on linear algebra? Thanks in advance :))

[rigid trail]

What do you want to use linear algebra for

[grim delta]

Just for knowledge

[rigid trail]

from a pure math perspective?

[grim delta]

Well, I think so, but my math level is very low, literally im finishing a precalc book

[rigid trail]

You can watch 3blue1browns essence of linalg series on YouTube

An actual linear algebra book would probably be a little too advanced

[worn monolith]

What is a good introductory textbook on linear programming and integer programming? A clear exposition of the foundations would be sufficient as I only need this insofar as to understand a section in another book I am reading. To be clear, I am not looking for a rigorous reference, just something quick and dirty to get up to speed with, ideally with a lot of examples.

[grim delta]

integer programming?

[grim delta]

So what do you recommend, just watching those videos?

[rigid trail]

Yeah it's a pretty good series to build some intuition

It doesn't go over the actual calculation processes you'd learn in a linear algebra course or book

It teaches the concepts

[grim delta]

And then, should I just start with calculus? I mean, i just finished a long precalc book and I don't know what follows

[rigid trail]

You can do calculus now

Linear algebra doesn't help with single variable calculus

It helps for multivariable but even then, a lot of students take multivariable before linear algebra

Also note that there's a difference between "engineer's" linear algebra and general theoretical linear algebra that you'd learn slightly later in a math undergrad program

[grim delta]

Okay, I see

Thank you very much for your knowledge🫶

Thanks for your time

[ionic zephyr]

.

[remote sparrow]

https://www.amazon.com/Introduction-Probability-Theory-Applications-Vol/dp/0471257087

this is nice too

also you should consider applying for the postgraduate math role

[willow merlin]

which book explains schauder and hamel basis

[vital bane]

wouldn't any intro functional analysis book explain this?

since every basis that's used in LA is a Hamel basis, only in FA Schauder basis is employed right?

I'm not sure I'm just guessing I've not FA yet

I think it's just
Hamel basis = finite linear combinations of the elements in your basis
Schauder basis = countable (maybe even uncountable?) linear combinations of the elements in your basis

[tropic nacelle]

desafortunadamente, non sono italiano (perdonáme, ho estudiato spagnolo ma non italiano)

[ivory shore]

Do you know spanish?

[cursive orbit]

no such thing as an uncountable linear combination

unless only countably many coefficients are nonzero

[vital bane]

that makes sense

but couldn't an integral be interpreted as an uncountable linear combination?

[willow merlin]

im looking for resources that speaks about this topics

[tropic nacelle]

yes

[willow merlin]

what would be "any fun anal" book for that matter?

[vital bane]

maybe people in #advanced-analysis might know of resources that speak of this topic

[vital bane]

I cannot say for sure as I haven't gone through any functional analysis book I was just guessing

[ivory shore]

Aprendiste por tu cuenta o tomaste cursos?

[tropic nacelle]

lo he estudiado en mi colegio (secundario)

[ivory shore]

Pero después de eso no seguiste estudiándolo?

[tropic nacelle]

no

estoy tan contento con mi nivel ahora

[ivory shore]

Tenes buen español. Ojalá decir lo mismo sobre mi inglés

[slate pilot]

What’s the difference?

[wide dragon]

Any intro measure theory books? Preferably with a focus on probability, stochastic processes, control? The more applied the better but I still want rigour

It’s literally been popping up everywhere in my classes. We spent last week in my reinforcement learning class going over MDP theorems and they were all fked up measure theoretic proofs that no one really understood. Same thing in my probability class, machine learning class and data science class. I feel like I’d enjoy seeing all of these tied together

I understood one of the MDP proofs, in that one he ended up with an optimizing policy by finding the fixed point of the Bellman operator and then bounding it. That was very cool and I’d like to know how to use those measure theory tools for myself

[wide dragon]

Uhh Bertsimas for linear programming? I believe the later chapters cover integer programming. I’ve only taken a single class on it

There’s like, a million lectures on the web too, I can privately share with you my prof’s notes they’re great if you’d like

[stable flicker]

I have an OR background, I suggest instead of looking at measure you just learn measure-theoretic probability.
I don't think bounding arguments come from measure theory, measure theory only tells you what are legal moves in your argumentation and/or permissible modellable space

[wide dragon]

Ya, that’s it, the bounding part was the first and last step in the proof, but in between it’s as you described

What’s OR?

[stable flicker]

operations research

You generally don't need anything more generalisable than a Polish space

[wide dragon]

Okay, sure, measure-theoretic probability, any recommend3 texts that you know of?

[stable flicker]

• too terse for me: https://link.springer.com/book/10.1007/978-3-030-61871-1
• readable for me: https://link.springer.com/book/10.1007/978-3-031-14205-5
• probability bible: https://link.springer.com/book/10.1007/978-0-387-72206-1 https://link.springer.com/book/10.1007/978-0-387-72208-5
• 'just' measure theory: https://measure.axler.net/

[wide dragon]

Ya, that’s perfect, thank you for your recommendations

I’ll check all of them

[cursive orbit]

check out: https://www.cambridge.org/core/books/measures-integrals-and-martingales/7BEE19069C88A1376AEB988487D4131C

seems like a good fit for what you are looking for

[stable flicker]

Schilling's too hard for me too

[fresh skiff]

https://www.amazon.com/Advanced-Linear-Algebra-Textbooks-Mathematics/dp/1466559012
any feedback about this linear algebra book

[wide dragon]

I’m looking through it and I’m just thinking how much I appreciate my probability prof because he translates all that weird notation and vocab into plain English lol

But ya, this book definitely has what I’m looking for

[stable flicker]

as you long as you resign yourself to accept that you might not completely comprehend what Talagrand is writing, I think it's fine

(that's what I tell myself)

(a more contemporary figure for that might be Duminil-Copin or Hairer)

Actually Talagrand's like really key tbh

[wide dragon]

No idea who any of those people are

I’m a beginner

[stable flicker]

The latest and greatest data science relies on Talagrand's work. i.e. this stuff is applied
The other two are phase transitions and rough path people, fields medal probability theory, which thankfully are not anywhere near applied math in most cases

[remote sparrow]

https://www.amazon.com/Measures-Integrals-Martingales-René-Schilling/dp/1316620247

FYI you linked to the first edition

@wide dragon

[fresh skiff]

Sour Drop did you ever check this

[remote sparrow]

a bit

seems interesting

[fresh skiff]

how did you find it

[remote sparrow]

idk

[fresh skiff]

thats okay, thank you

[vital bane]

FIS

that's quite a strange order

I don't think so

still strange order

maybe it does

check it out

[daring wolf]

wow such a strange order????wtf

[vital bane]

FIS

[mossy flume]

is it that different?

seems pretty similar to me, just different names of things

Hm I guess inner product spaces in FIS come much later

[vital bane]

inner product spaces and linear transformations are covered in different and might I add strange orders

[merry sphinx]

inner products before lin transforms is weird yeah

[wide dragon]

Ahh ic. Thanks for mentioning his name

[wide dragon]

Thx, AA had the second edition which I saw

[wide dragon]

I’ve seen linalg II taught in this order at my uni by some postdoc, and that class was full of complaints and had an exceedingly low average

[sleek python]

Somethig similar to Neamesis' book is more standard I think though

Quite rare to see something significantly different

[thin frigate]

Best college algebra books?!

[torn blade]

false……..

[unborn jackal]

serge lang

[quiet wave]

boys, i'm in a required non-major ODE class using the boyce book which seems to not even contain any proofs... not feeling good about this one 😭
i am fairly comfortable with analysis / topology proofs, and i am much better at understanding things than memorizing things, is there a better book i can follow along to not rely on memorizing a bag of tricks for the class?

[willow pecan]

Arnold ODEs

[quiet wave]

ah, i've heard people praise this one

[ionic zephyr]

yknow guys

[quiet wave]

but it's also pretty difficult no?

[vestal niche]

I'd suggest Hirsch et al

[vestal niche]

I'm reading Arnold rn and it's not difficult at all

[quiet wave]

oh word?

i'll check it out

how come u suggest hirsch tho?

[vestal niche]

I did read Hirsch before

And it fits your description (of the writing style you're looking for)

I prefer books that build their theories up as well

[rigid trail]

it's good

[rigid trail]

no it's intuitive

[mortal ore]

https://tenor.com/view/spongebob-patrick-boo-gif-1281926785517906930

[young fern]

Does anyone have a good list of books for self studying maths that go from arithmetic all the way to calculus

[earnest wolf]

khan academy; I don't think books are beneficial at that level

[normal crystal]

I don't agree with that
but you can use both
Openstax is free

[young fern]

Why Wouldn’t they be ?

[heavy vault]

If ur learning addition idk how ur able to work through textbooks

I would say AOPS covers the like high school math topics well

[earnest wolf]

might take much more time to cover the same thing

textbooks are really great for learning proofs and such, but there are much more efficient ways to learn computational tricks

u don't really need a textbook to learn how to add two fractions

[young fern]

Sorry I was being stupid I didn’t mean to put arithmetic I’ve already covered all the arithmetic content

[earnest wolf]

to learn calculus I'd argue one doesn't need books either

it's just a bag of tricks after all

real analysis on the other hand... probably impossible without a few good textbooks

[wide dragon]

…unless you’re Ramanujan.

[spark elbow]

i started using books for abstract algebra, but tbh they also wouldve been helpful for diffeqs

[warm cave]

Do you guys happen to know of a good book that has a chapter that talks about combinatory, permutations and variations with and without repetition?

[daring pier]

Can anyone please suggest me youtube channels or playlists to learn the basics of calculus?

[remote knoll]

3b1b has a good primer.

[remote knoll]

Most discrete mathematics books should cover this material.

https://discrete.openmathbooks.org/dmoi4/ch_counting.html

[compact eagle]

if its like actual computation practice, blackpenredpen has good calculus vids

[vast jackal]

calculus made easy by thompson and gardner

probably the best one

well for the basics ofc

or Stewart's

or khan

[daring pier]

Thank you

[gray gazelle]

Hi evry one

Does anyone have good books for complex analysis

[flat marten]

Grillet

[fresh skiff]

Have you read it?

How's it? Like prerequisites and material

[flat marten]

Ive read up to chapter 5

Working on making that higher

But the material is very good IMO, nice and curt but not without explanation

But not much messing around

The exercises are generally quite good too

I prefer them over dnf

[fresh skiff]

Are both at same level of difficulty

[flat marten]

Grillet is harder but more rewarding imo

For example he has material on group extensions and on separability in the sense of maclane,

Although they're non-required

[fresh skiff]

I see

[flat marten]

I dislike some of his exercises for groups but past that its top quality

[fresh skiff]

I would consider this books maybe with or after D&F
Meanwhile, i will start D&F soon

[flat marten]

I'd say, if its ur first time do dnf for groups and then do grillet for rings fields etc

Also he does cover cat theory but weirdly its at the end

After everything else

Including after ext and tor, which feels out of order to me

But it was 2007 where cat theory was still more fringe

Awww I can't upload images 😔

[fresh skiff]

Oh. I am kinda a new baby in Algebra
Like i will start ch6 of Fridberg linear algebra soon

[fresh skiff]

Why?

[fresh skiff]

Then i will start D&F

[flat marten]

Was gonna post th3 content's

[fresh skiff]

I am really excited to start AA

[fresh skiff]

Grillet?

[flat marten]

Functors.
Propositions 1.1, 1.2, and 1.3 can be expressed more compactly using a language that will be defined less informally in Section XVI.2.

A functor from bidules to doohickeys is a construction that assigns to every bidule B a doohickey F(B), and to every homomorphism ϕ : B − → C of bidules a homomorphism F(ϕ): F(B) − → F(C) of doohickeys, so that F(1B) = 1F(B), and F(ψ ◦ ϕ) = F(ψ) ◦ F(ϕ) whenever ψ ◦ ϕ is defined.

He defines functors out of order like this lol its funny but also kinda weird

[flat marten]

Ye

[flat marten]

Its very peak

[fresh skiff]

Oh lol
For basic cat theory for algebra i would use Aluffi

I believe he has done a good job

[fresh skiff]

I think i have a pdf lemme check

[tender cobalt]

wanna do Aluffi notes from underground

[fresh skiff]

i will, once i do enough Lin Alg

[flat marten]

I'll be real grillet was the first maths book I ever sat down and properly tried to read

[fresh skiff]

wow
I hope i will enjoy it as well

[marsh ingot]

Conway

[fresh skiff]

for first course?

i will start CA somewhere soon

[marsh ingot]

Barely read it but looks fine

Has 2 volumes for single complex variable

[fresh skiff]

oh 2

interesting i will check

[vital bane]

#book-recommendations message

[marsh ingot]

2nd is more advanced for a 1st course

[vital bane]

2nd is supposed to be read after you read volume 1

so no one would read it as a first course

[fresh skiff]

i see

[marsh ingot]

I mean yeah lol

Just I wouldnt rush and read 2nd volume after finish the first one

To be more familiar with the topic

[novel hound]

I think everyone can post images in "chill" and you can reference it from here...

[gray gazelle]

Thank you guys

[flat marten]

Thx

[dim pendant]

Another great book is Jacobson's "Basic Algebra II". It covers a lot of really good stuff for graduate students and uses category theory

[fresh skiff]

true, its classic. I have pdf of this book and its looks amazing

[dim pendant]

I've got it on my shelf and it will remain there until my passing

[gray gazelle]

Any book recs for learning the calculus of functors?

[floral lantern]

Any recommendations for an introduction to Algebraic Geometry assuming just a semester of algebra (groups, rings, fields, no modules) and linear algebra that is not Cox (no offense to fans, but I'm not interested in that kind of stuff)?

My current idea is Fulton, but I don't know if there's a better option.

[vital bane]

Isn't commutative algebra a prerequisite to Algebraic Geometry?

why would you want to rush in?

take your time🗿

[floral lantern]

the commutative algebra can be taught with the alg geo

the goal for this is to get an independent study with other students at my school

and I don't want them to get bored by super unmotivated comm alg

and drop

which some of them might bc it's senior year and all

[vital bane]

Then maybe you would like "commutative algebra with a view toward algebraic geometry" by eisenbud

i've never gone through this book neither have I learned comm alg

I just know that book is a thing

[vital bane]

AG might not be the best choice DG might be

Andrew Pressley's DG book "Elementary Differential Geometry" is easily accesible by motivated high school students

[floral lantern]

everyone is taking analysis in the fall and topology in the spring, so the idea was not to touch something analytical and do something more algebraic (we've all taken absalg)

[gray gazelle]

If we’re changing one word from AG, I’d just suggest AT..

[floral lantern]

but I shall take a look at this

[vital bane]

ehh it's more geometry than analysis

sure it's analysis flavored but still...

[rigid trail]

yay differential forms yay I can finally formalize standalone dy and standalone dx

[floral lantern]

I shall take a look at this book :3

[gray gazelle]

AG, CT(unless y’all have already learned much of it?) DG and HDA would all seemingly fit, fwiw

[floral lantern]

the only time my knowledge of diff forms has ever come up was in differential equations when I saw exact equation 💀

actusally

physics

and the little bit of de rham cohomology that I know but that's all scuffed

[floral lantern]

CT and HDA?

idk those acronyms lol

[vital bane]

Computed Tomography

[floral lantern]

😨

[vital bane]

and High Dimensional Anti-commutative algebras

[gray gazelle]

Well close, I just meant Higher Dimensional Algebra(might be the same thing..? As far as I know they’re “supposed” to be non-Abelian)

[floral lantern]

like multilinear algebra?

[gray gazelle]

Category Theory and Higher Dimensional Algebra

[gray gazelle]

Nah, it’s about higher dimensional analogues of groups, groupoids, etc.

[floral lantern]

oh

maybe

[vital bane]

yea marlin karp even category theory might be a better idea than AG for people with a 1 semseter algebra background

[gray gazelle]

groups have “horizontal” composition

Higher dimensional groups would also have “vertical” composition

[vital bane]

maybe even calculus of functors

[floral lantern]

category theory is fried I have to learn some for my research project and it's terrible

braided monodial categories 😔

[gray gazelle]

[floral lantern]

ty guys for the recommendations tho

[vital bane]

Lmfao

[gray gazelle]

Np

[floral lantern]

I shall think deeply

[tender river]

that has rattus' fingerprints all over it

[dusk hemlock]

https://cdn.discordapp.com/attachments/268882317391429632/1304485174326722601/99popx.gif

[trail hemlock]

wtf based

[graceful moon]

Undergraduate algebraic geometry by Reid

[floral lantern]

no it was in a 2 week minicourse and I basically know some minor applications to physics

lol

basically nothign

[floral lantern]

doesn't this have commalg as a prereq

[graceful moon]

Not in any real sense

Its like the most basic of basic commalg

If you know any ring theory you can for sure fill in the gaps as you go, but a lot of it is just LA

[floral lantern]

ok lol

I will take a look

ty

[foggy relic]

shafarevich

it's a nice book

[ivory shore]

Any opinion about "Complex Analysis" by Stein & Shakarchi?'

[rigid trail]

A gonad is a gonoid in the category of endofunctors

[floral lantern]

hmm the prereqs look just about right

ty for the rec

[foggy relic]

its def the best book for what ur looking for

it's light on the prereqs but takes you very far

[tawdry agate]

Hi does anyone have good suggestions for books to learn synthetic and analytic geometry

[floral lantern]

looks very cool yes and part 1 looks reasonable to do in a year

[worn monolith]

Apologies for the late reply, thanks for the suggestion. Part of the reason I ask is that there are so many resources on the web I don't know where to start. I imagine any one would be fine for my purpose but I thought it doesn't hurt to ask.

[worn monolith]

I rarely see this book mentioned, but I think Elementary Algebraic Geometry by Klaus Hulek is decent. It was recommended by my professor.

[remote sparrow]

#book-recommendations message

[rough nymph]

Anyone wants to start a reading / study group for Spivak's Calculus or FIS Linear Algebra? (for motivation and accountability mostly)

Preferably someone with less experience in math so we can suffer together.

[tawdry agate]

Hi does anyone have good suggestions for books to learn synthetic and analytic geometry

I want to prepare for a math competition(IKMC) so please i would like some help with the books for it

[slow roost]

you might like Miles Reid - Undergraduate Algebraic Geometry. Fair warning though, while it says Undergraduate in the title, it's for pretty strong undergrads, and the writing style is somewhat unusual. I think it requires pretty good 'math maturity'

it's one of the bunch of books on AG I'm trying to read

the best thing about that book is it's really short - just 125 pages not counting the index

and it covers a lot in those

[grim ore]

I personally didnt like this text due to the unusual writing style

Like a really strong opinion that I have is that "I wouldnt wish my worst enemy to read this text" but thats an exaggeration ofc lol

[grim ore]

If anything Royal Road to AG by Audrey Holmes

[slow roost]

I remembered seeing someone here say they hate that text, guess it was you

I can kind of understand, it's a weird mix of high level and casual loosey-goosey

[grim ore]

Yeah im definitely a hater of that text

I also felt like the exposition didnt prepare you for the question bank, but I read that text front and back and worked through the problems, but did it really early in my math maturity. Idk if it would be any better now

I also did the reading with a prof which helped a lot

If you have atleast done Abstract Algebra and want something more complicated than Royal Road, then Id prefer BAG I by Shafarovich as its more stricter to Hartshorne (each book is one chapter of hartshorne) and goes into nice detail with good examples

[mortal ore]

https://tenor.com/view/mad-angry-crowd-waiting-the-simpsons-gif-14161923

[limber fern]

Any good finance-centric stochastic calc books for self learning?

[thorn cloak]

Shreve stochastic calc for finance

[limber fern]

Shreve it is then. Thankies 🙂

[frosty wing]

Probability book for self teaching, at high-school level

[gray gazelle]

Topology - James Munkres

[grim ore]

crazy name lmao

[gray gazelle]

Huh

Why would you recommend topology for probability

[gray gazelle]

general recommendation not recommending for above my comment

[loud cradle]

assuming you know calculus, try ross "a first course in probability theory"

[frosty wing]

yea, Ik calculus
i'll check this out
thanks

[remote sparrow]

https://stat110.net

[frosty wing]

Thanks, I'll check this out if Ross doesn't work.

[astral temple]

Anybody know a good website or book to learn differential equation

[vital bane]

https://tutorial.math.lamar.edu/classes/de/de.aspx

[astral temple]

Thank you I will check it out

[tawdry agate]

Hi does anyone have good suggestions for books to learn synthetic and analytic geometry

[gray gazelle]

Danke!

[hollow kiln]

chat i need some information about Fibonacci sequence and proof of it properties and identitys

mostly the proof, i pretty much have enough info

[vast jackal]

YouTube

Wikipedia

[hollow kiln]

there are identitys and properties but not the proofs of them

cant even find good proofs in sources of wikipedia

[vast jackal]

math stack exchange

[hollow kiln]

ill try it thanks chat

[tidal cairn]

#help-5 i want to know about a good book of geostatistics. It will be very helpful. thanks!

please it is quite urgent.

[willow merlin]

books that define general linear groups?

A ∈ GL(n, R)

all A^nxn matrices such that det is nonzero

[wet wren]

what is FIS?

[molten gulch]

friedberg, insel, and spense, Linear Algebra

[remote sparrow]

well, do you know what a group is?

[novel shoal]

advanced based proof linear algebra

[keen orbit]

what are the prerequisites of measure theory and what are some good books about this topic

[keen orbit]

isnt FIS more on the computational side

[loud cradle]

elementary analysis and topology

[keen orbit]

point set toplogy ?

[loud cradle]

yea, or at minimum, metric spaces

[keen orbit]

and is it only bits like the ones introduced in an analysis course

or does it need more

so for example if someone studied from baby rudin

[loud cradle]

yea like what's covered in baby rudin is sufficient for measure and integration

both in terms of analysis and topology prerequisites

[keen orbit]

also for the analysis prerequisite does it require only single variable analysis or also multivariable

[loud cradle]

depends on what's covered but you don't need much multivariable stuff even to do fubini's theorem (which is the theorem about double integrals)

[novel shoal]

not as much as Gilbert Strang, Anton or David Lay

[keen orbit]

ohh ok , if you have any recommendations on the topic can you please tell me the names of the books

[keen orbit]

ohh i see

[remote sparrow]

varies between books

[loud cradle]

on measure theory and lebesgue integration? the newish book by axler is supposed to be good but i haven't read it
for other books there are a couple of different approaches, some do R^n first and others start directly with general measure spaces, so it depends on which you prefer

[keen orbit]

it would be better if the book starts from general measure spaces but both options are fine

[loud cradle]

my preference also, i quite like "measure theory" by cohn

(2nd edition)

[keen orbit]

idk i didnt like his linear algebra book so i would avoid him in other topics too xD

[loud cradle]

fair enough!

folland's "real analysis" is also very good and covers more than cohn, but it's more terse and demands more of the reader (lots of gaps in proofs) and also has annoyingly many typos

[keen orbit]

alright i will keep these 2 books in mind

[remote sparrow]

https://www.amazon.com/REAL-ANALYSIS-THEORY-MEASURE-INTEGRATION/dp/9814578541

https://www.amazon.com/Problems-Proofs-Real-Analysis-Integration/dp/9814578509

[loud cradle]

^ the opposite end of the terseness spectrum 😆

[remote sparrow]

this book spells out things in sometimes painstaking detail, and there's a solutions manual to accompany it

[keen orbit]

but how does an analysis book cover measure theory more than a book on measure theory

[remote sparrow]

?

[loud cradle]

well, cohn's "measure theory" is an analysis book, it's just called "measure theory" haha

[keen orbit]

i am talking about folland's analysis

[remote sparrow]

rather confusingly, there isn't a standard term for a measure theory textbook

[keen orbit]

oh hahahahahha

[remote sparrow]

i don't ever see a measure theory book being called "advanced calculus" though

[keen orbit]

ohhh

[loud cradle]

the point of measure theory is to provide an environment in which you can define a better integral (and also develop probability rigorously), a book only on measure theory without doing either of these things would be a very boring book

but hey, people study set theory for its own sake so who am i to judge?

[keen orbit]

tysm

[keen orbit]

oh i see , then it is reasonable to have less pure measure theory books

[remote sparrow]

the lebesgue integral has better theoretical properties, to be sure, but i believe the riemann integral is the only one used for numerical integration

[loud cradle]

oh sure, riemann is sufficient for many purposes, by "better" i really meant "better for real analysis and probability" i guess

one with better limit theorems, basically

[remote sparrow]

usually there is some basic treatment of functional analysis included

[keen orbit]

ohhh it seems that things are getting more exciting : )

anyway it will take some more time to reach this

but it doesnt matter since its a nice journey hahaha

tysm both of you

have a great day

[remote sparrow]

https://r-bass.scholar.uconn.edu/

@keen orbit this book is free online

just scroll down a bit

[keen orbit]

tysm

i will check this one too

[merry sphinx]

folland covers more extra topics, i think, like some functional analysis and some topology in c4, cohn feels like it is more pure measure theory (and i think theres more probability theory but i could be wrong)

might throw in stein shakarchi as another rec, although i havent gone through it much

it does spend some time on the jordan measure stuff and R^n to develop intuition

[lapis kiln]

can i get a few book recommendations for olympiad mathematics?

i'm a third of my way done into being selected for imo from my country and i need a bit of help

thanks in advance ❤️

[vast jackal]

pls go to the mods server

they can help you more

https://discord.gg/mods

[lapis kiln]

okay thanks

[limber basin]

anyone got some resources for locus points for complex numbers? stuff like equations describing lines, rays, and inequalities and converting into cartesian form. my textbook doesn't use it

[vital bane]

also throw in Rudin RCA for exercise

[teal prairie]

Can someone suggest a modern text for information theory

something that covers asymptotic equipartition theorem

[broken pecan]

guys. is there a standard textbook (preferably a relatively popular one) covers foundimental solutions of helmholtz equation? deviation and all that. physics books also welcome

[tawdry agate]

can anyone suggest a book for geometry

[vital bane]

this is too epic

[heady grove]

hi can someone recommend a book that is like an intro or a explanation of calculus?

i have a good idea of calculus, i have done calc 3 but now i want to know more about how we arrive at this and sort of the way mathematicians found these out

or just any fun math books that isnt too textbook-ey

[vital bane]

I would recommend 3blue1brown's essence of calculus series for that

[heady grove]

i see, thank you!

[cold elbow]

<@&268886789983436800>

[fresh skiff]

damn i was about to write "wait for your gift from mods"

but the man is gone already

[cold elbow]

lmfao

[orchid canyon]

My friend is really into physics

and I'm thinking bout giving theese Fundamentals of Physics

from Haliday and Resnik

but I can find only 1 to 4

mechanics, thermodynamics, electromagnetism and optics

will he be able to enjoy it without the complete set?

[dim pendant]

No, it's impossible to enjoy the initiation and interior of a series without its finality.

I mean can you imagine if I only purchased Baby Rudin and Papa Rudin and not Grandpa Rudin, or Silverman & Tate + Arithmetic, but without Advanced Topics?

I'd lose my mind...

On a serious note, I might recommend books from the Feynman lectures, if they don't have them all. I dont know.. I prefer to buy the typical books myself, and to be gifted the more fun books while they're cheap.

[vital bane]

I wouldn't recommend them to a beginner, you would already have to have seen some undergrad physics to enjoy them

same goes for Lifschitz

[ivory sigil]

Lifshitz mentioned

[ivory sigil]

We talking about Landau-Lifschitz?

[vital bane]

ye ye

[ivory sigil]

I enjoyed it quite a lot

I picked up field theory for my 16th birthday

Enjoy it to this day

[vital bane]

I'm just saying you need some prior exposure to physics to enjoy it

[ivory sigil]

But truth be told, we have a cult around landau in our region, and generally the whole physics spirit is based around landau’s practices

[dim pendant]

My 16th birthday was great I got Hartshone Alg Geo and Bredon Top and Geo

didnt read em forever but thats when I got em

[vital bane]

My 16th birthday was not great, I was sitting around wasting time, and not even doing calculus properly

[dim pendant]

relatable lol I think I was forcing myself through calc 2 and odes and general top none of which I had an actual interest in

Much wasted time

[sharp goblet]

how is that even possible lol?

[sharp goblet]

oh lol

[dim pendant]

I put it on my amazon wishlist and my mom said bet

yeah lol I was def not prepared for em

I just have too many math books for my own good

[ivory sigil]

Read all of them?

[dim pendant]

yes and no

[ivory sigil]

Homie its either yes or no, it aint a qubit

[dim pendant]

I finally went through and figured out what I don't want so I'm straight up givig those to my pal when he visits

and I'm slowly making my way through the rest as I need the info

I regret buying these undergrad books because most of it is unspecific to me and you shouldn't fully read books that are unspecific to you

borrow until you find your heart 🙏

[ivory sigil]

I love every part of mathematics apart from abstract algebra

[dim pendant]

you might love it all but there'll be a few areas of problems that get your full attention

[molten gulch]

Abs alg is awesome

[ivory sigil]

Can’t, too preoccupied with physics to give myself up to math

[molten gulch]

Wishing real analysis was kinder

[dim pendant]

I like all things to do with algebra, topology, and geometry, except geometric topology, but where math really stands out to me is motivic cohomology, Langlands program, and class field theory

those are my babies for sure

[ivory sigil]

Oh a langlands fella

Heard you had a pretty big discovery recently

Breakthrough

[dim pendant]

the proof of the geometric correspondence?

[ivory sigil]

I believe so i don’t remember exactly what

Its a very long paper, scrolled through it in summer i believe

[dim pendant]

Yep, a long time expert in the field worked with a number of folks to release 5 papers proving it

over 1.1k pages

[molten gulch]

Yeah a proof of the categorical unramified geometric langlands conjecture

[dim pendant]

also kinda real

you're right i apologize 🙏

[ivory sigil]

Single most nerdy joke ive ever heard

But i guess there will be more of that to come

[dim pendant]

says the physics guy

[ivory sigil]

Mathematics is to physics what masturbation is to sex

[long niche]

Hi everyone 👋
May someone please explain to me how to work out Q1 b) please

[ivory sigil]

🗣️

[dim pendant]

😡

[torn blade]

other way around

[dim pendant]

fr

[ivory sigil]

🤫

Can’t prove 1+1=2 🤡

[torn blade]

trueeee

[dim pendant]

physicist; yeah our theory says theres a quantum field there but you cant touch it only make predictions and conduct exeriments
mathemtician: haha field go brrr

[ivory sigil]

Without physics, you’d have no kepler’s equation which means no cauchy contour integrals and residue theorem

True

Symbiotic relationship

[dim pendant]

math without physics: 80% of math but we'd have the other 20% soon enough
physics without math: yeah if I exact my will on this thing via the instrument of my modality, then its spatial relation is inflected in some unquantifiable way
random guy: like i didnt already know this

[ivory sigil]

You do not speak his name in this household

(Copenhagen interpretation and generally Dirac-Neumann axiomatized QM)

Physics is the study of the creations of god

Mathematics is the study of his mind

Lmao, accurate

[dim pendant]

1000s of years of philosophy when i say "just live and let live"

[ivory sigil]

That’s real philosophy should sound

Not whatever the sophisticated aneurism modern physicists try to force upon others

[ivory sigil]

Meta conscious subdimensional relativistic spontaneity of an objective collapse through subjective experience of a material illusion

And quantum tubular induced wavefunction collapse

[dim pendant]

For real!

To make sure we remain relevant to the topic of this channel

can someone recommend a textbook on contemporary metaphysics from a mathematical perspective

[ivory sigil]

Just read Hegel or Decartes

[dim pendant]

Nonsense dreamt up by the utterly deranged

[ivory sigil]

Mathematical truths don’t change

[dim pendant]

🙏

[molten gulch]

absolutely disgusting comparison <@&268886789983436800>

[dim pendant]

Perhaps Hoffman & Kunze or Greub

[molten gulch]

check section 4.5 of chapter 4

[vital bane]

it's a quote from Richard Feyman, but yes I agree

[ivory sigil]

😢

[vast jackal]

that's like a proof bro

it's like math

nothing + something = something

idk why you're hating physics

[willow merlin]

which book covers gershgorin circle theorem

[remote sparrow]

axler, friedberg, garcia and horn

https://linear.axler.net/LADR4e.pdf

https://www.amazon.com/Linear-Algebra-5th-Stephen-Friedberg/dp/0134860241

https://www.amazon.com/Matrix-Mathematics-Cambridge-Mathematical-Textbooks/dp/1108837107

[dim pendant]

We're just trolling none of us hate physics dw c:

[zealous sapphire]

Does anyone know if there exist recorded follow-up video (!) lectures on more advanced topics of Sipser than here? https://youtube.com/playlist?list=PLUl4u3cNGP60_JNv2MmK3wkOt9syvfQWY&si=Uf8pzZhk_JzJf-KR

[modest kite]

Read berserk

[molten gulch]

There is no context to this

[cursive rivet]

here's a whole book on it https://link.springer.com/book/10.1007/978-3-642-17798-9 lol

[willow merlin]

thanks

[willow merlin]

thank you

[normal crystal]

#book-recommendations

[vital bane]

Read Re:Zero

[rigid trail]

remremremremremrem

[vast jackal]

read Steins gate

[earnest wolf]

I agree; it should've been the converse

it was said by a physicist, so he was biased

[chilly crypt]

fr

read shadow slave

[vital bane]

I have watched it

it's peak

[remote sparrow]

https://www.amazon.com/Actions-Groups-John-McCleary/dp/1009158112

leaving this here for recording purposes

[deep moat]

Hi!
Any stats and prob problem books that I can get my hands on? Im self studying stats and prob for fun, thats why im asking if there is a problem book with tons of excercise and other stuff

thanks :D

[remote sparrow]

https://www.amazon.com/Mathematical-Statistics-Applications-Dennis-Wackerly/dp/0495110817

i know there's a full solutions manual out there for this book

https://stat110.net

some exercises have solutions

https://www.amazon.com/Introduction-Probability-Theory-Applications-Vol/dp/0471257087

there are hints to select exercises

all of these books have calculus as a prerequisite

https://www.amazon.com/Basic-Probability-Theory-Dover-Mathematics/dp/0486466280

oh almost forgot about this

there are full solutions to select exercises

[deep moat]

Thansk!

[fading stratus]

good books for getting into real analysis/measure theory?

[remote sparrow]

https://measure.axler.net

[fading stratus]

:D

[torn blade]

there’s a pinned message for this

hmm it doesn’t have Axler on there, maybe it should be added. ive never read it tho so idk

[fading stratus]

my bad i didnt look to check

[tawdry agate]

hi any good geometry books

[torn blade]

if anyone can give a quick review of this id be interested, i dont know much measure theory atm

[vital bane]

Also check out "A User Friendly Introduction to The Lebesgue Measure and Integration"

[torn blade]

it has the sour drop vouch tho 💯

[vast jackal]

what topic in math is usually the most fun after finishing spivak?

[marsh ingot]

Real analysis

Depends on what you mean by "fun"

[vast jackal]

fun = interesting

[marsh ingot]

Real analysis then

[slow roost]

I mean there's really no consensus answer to that, it depends on what you like

and what you're prepared to study

[vast jackal]

physics

but I do like manifolds tho

[slow roost]

how about differential geometry without manifolds?

curves and surfaces in R^3

fantastic stuff and a natural progression from calculus

[marsh ingot]

Do you have the prerequisites?

[vital bane]

MANIFOLDS MENTIONED!

manifolds are insanely cool

[vast jackal]

ohh sure sure

[vital bane]

and diff geo of curves and surfaces will be a natural progression into smooth manifolds

[vast jackal]

still not I'm still doing lang's basic mathematics

and probably spivak

they're pretty fun

[marsh ingot]

I see, take your time then

[vast jackal]

differential geometry looks fun too

[earnest wolf]

click open in browser for better res

no idea where I've got this from, so can't credit the author

oh, here it is: github.com/TalalAlrawajfeh

[vital bane]

okay this is actually pretty cool, I don't necessarily agree with all the progression, but it is pretty cool

lol the latter book is not algebraic number theory I mean yes there is some basic algebra in it, but it's an introduction to number theory (as the title suggests) but for advanced readers, someone who already knows some undergraduate mathematics like analysis and algebra

[earnest wolf]

open a PR ig

[vital bane]

okay the book "Precalculus - Mathematics for Calculus" by Stewart, actually looks pretty cool, but the only thing I take issue with is that it introduces matrix multiplication, calculating determinants, and inverse matricies as just a bunch of calculations with arbitrary rules the worst way to introduce basic linear algebra

geometric intuition where?

a few words about basis and linear transformations and a few pictures would make all those calculations seem so obvious!

[jaunty vault]

they ought to make a reliable crowd-sourced progression, because how can I trust this 😭

[rain wren]

ugh, I hate such graphs

they're lowk stupid

this is literally so stupid

calculus then real analysis then real analysis then functional analysis then real analysis

also, artin, then linear algebra then algebra

????

[vital bane]

Lol they can be quite fun, but this specific one is stupid I agree

how's algebraic topology and convex analysis going darQ?

[rain wren]

I haven't done any of those in a year lmfao

i'm doing CoV and evans rn

[vital bane]

damn PDEs! nice!

[rain wren]

and I also wanna do lee riemann stuff this semester

[vital bane]

DarQ turning into RYC

[vital bane]

IRM!

Nice!

[vital bane]

CoV? calculus of variations?

[rain wren]

ye

it's quite fun

shit ton of applications to geometry and PDEs

[vital bane]

CoV from Func anal POV?

[rain wren]

hm, not that yet, no

[vital bane]

ah so like Gelfand and Formin then?

[rain wren]

maybe soon I onno

[rain wren]

no, I'm following giaquinta

gelfand is lowk so slow 😭

[vital bane]

chiquitita...

[rain wren]

and also, it's old as shit

[vital bane]

you know what they say, old is gold

[rain wren]

meh

[vital bane]

https://link.springer.com/book/10.1007/978-3-662-03278-7

this one?

[rain wren]

yeb

it develops things from a modern POV

[vital bane]

darQ's physics arc

[rain wren]

which is super smooth

[rain wren]

you chose the worst of those actors

[vital bane]

too little*

[vital bane]

interesting

I shall check it out then

[winged herald]

So, yesterday I bought a copy of Anderson and Fulton's “Equivariant Cohomology in Algebraic Geometry”. I had been waiting for this book to be published for a while, and only yesterday did I learn it had been published last year.

Is there a way to get a notification when books on a specific math topic are published?

[loud cradle]

go up, thou bald head

[molten gulch]

<@&268886789983436800>

[modest saffron]

Any good geometry books for beginners?

[remote sparrow]

https://www.sumizdat.org/pl_ebook.shtml

[trail hemlock]

the abba song ?!

@drowsy nacelle

[dim tapir]

guys any good books for jee preparation co-ordinate geometry?

[rough umbra]

alg geo before abstract alg being an option seems ill-advised

[vast jackal]

SL TONEY?

[ebon heath]

Advanced illustration in mathematics by vikas gupta
If you do this nothing more is needed

[livid drift]

hello

[vital bane]

[stable axle]

So I've started work on my bachelor's thesis and I need to read up on nets/net compactness which to my understanding is basically a generalization of compactness? Any recommendations on where to start?

[tender river]

nets are a generalization of sequences from metric spaces to general topological spaces

[tender river]

what kind of math background do you have at the minute?

[stable axle]

Basic topology, working through real and complex analysis right now

And completed algebra sequence

My real analysis class ends next month and for complex I'll be studying that for the rest of the semester

Other than that I've done all the other basic math classes you'd expect an undergrad to have studied

And I've also taken a course on Fourier analysis and algebraic geometry (though it was pretty basic)

[vital bane]

so instead of considering a sequence which is a function from N --> X you consider a function from a directed set to X? it's basically a change in the domain right?

why are directed sets more desirable than natural numbers when you want to define sequences in some space? more flexible?

[vital bane]

Nice

I can't wait to be able to say that

[stable axle]

It was by the skin of my teeth but I did do it lol

[tender river]

the older topology books like dugundji, engelking, kelley all cover them and so do some measure theory (folland covers them) and functional analysis books (pederson uses them heavily for all the theory). dugundji was the most readable book to me and engelking is probably the most research level as in it is written very much just as a reference so maybe it has stuff that might be helpful for you. i must say im no expert on any of this so you should wait until someone who knows what theyre really talking about sees this

[stable axle]

Alright fair enough

[vital bane]

I think Munkres also covers nets

[stable axle]

Interesting that you mention functional analysis I'm actually signed up for a functional analysis class starting in a couple months but I wasn't sure if I'd actually do it

They use kreyszig though

Also I have munkres but I don't see any sections on nets

[vital bane]

strange

oh it's given as exercises

[stable axle]

Ah that makes sense

I guess I'll give it a quick look since I have the book but ideally I'd like to learn about it from a more "pedagogically sound" place

[vital bane]

Munkres slanderists shall be executed

[stable axle]

That eigenchris topology video spoke directly to my soul and I now have no shame in saying I have a personal hatred for munkres

Like seriously I think Rudin is more understandable than Munkres

[pallid quail]

[remote sparrow]

think willard has some discussion on nets and filters

[pallid quail]

pretty much all book/lecture notes i have seen has it as "Supplementary"

Idk if people love big list or not!

[summer lagoon]

Hallo, do you guys

know some books on teichmuller space for beginners (have a background in riemann geometry)

and possibly with dynamic systems in mind

[trail hemlock]

valid take

[blazing rune]

Probably one of the better ones (despite being an old version): https://www.amazon.com/Introduction-Teichmüller-Spaces-Yoichi-Imayoshi/dp/4431681760

[tender river]

halmos

[gray gazelle]

Yeah. A topology is completely characterized by the way nets work on it. You could define any topological property purely in terms of nets.

For example, a space is Hausdorff iff every convergent net has one limit point

A space where every convergent sequence has one limit point may not be Hausdorff.

[vital bane]

What the hailll???!?! thats crazy!!

damn nets are so cool!

[gray gazelle]

You can do the same with filters too

[vital bane]

so it's because "every convergent net" not only changes the function f : D --> X but it also changes the underlying set D? like you're considering all possible functions f from all possible directed sets D?

[gray gazelle]

Yeah from arbitrary directed sets. The collection of all of those functions is a proper class though, so it’s easier to use Filters sometimes, since they’re equivalent but there’s a set of filters.

[vital bane]

Broooo wtf nets are awesome!

Friendship ended with sequences, nets is my best friend🗿

[tawny copper]

Hubbard maybe?

Milnor has a book on complex dynamics too

[tender river]

thanks

[wet wren]

steamuconmunity

ban

[gray gazelle]

<@&268886789983436800>

[wet wren]

hey u still up for this? i have strang's linear algebra book tho

[gray gazelle]

Not sure why there are sullies, this is entirely subjective and I can definitely see Munkres being less understandable for others than Rudin

Just how Lee is more understandable for me than Rudin

Though i think that's just due to my interest in geometry being strictly greater than my interest in analysis

[stable axle]

I seriously don't get peoples' obsession with the first textbook they used to learn a subject

Just because it worked doesn't mean it was optimal

[merry sphinx]

tbh its more the first comment lol

[wet wren]

has anyone heard of "calculus made easy" by silvanus p thompson? that book got me into calc

[gray gazelle]

I learned Calculus from Khan and my AP Calculus class

[merry sphinx]

yeah looking at actual calc books i dont think id have a lot of fun doing calc from calc books ngl

feels like a slog

khan, paul's notes, and some channels on yt (bprp, leonard, etc) are enough imo

[versed stirrup]

obligatory "is there a categorial interpretation of this"

[wet wren]

do you have some similar resources for linear algebra? i am absolutely hooked on linear algebra after 3b1b, but reading textbooks seem boring (mostly because i have to read them on my own). i have strang's book, but i want other resources...
also is that mob psycho opening in ur about me

[gray gazelle]

I need to learn Measure Theory and Functional Analysis this summer, it's holding me back from doing some nice things, plus it will help me get an easy A when i take them formally in Fall

[wet wren]

shidou becoming isagi with all that math

[dim pendant]

Real and Functional Analysis, by Serge Lang

[merry sphinx]

anton is a nice first time book, imo, if you want smth more pure there is friedberg insel spence

[wet wren]

thank you!!
https://www.youtube.com/playlist?list=PL6AU1UrGh9PUHmIeKdDFro9WCE2ktR2h-
i found this goldmine too

[modest saffron]

ok, thanks!

[rigid trail]

ladr

[remote sparrow]

https://www.sumizdat.org/geom2.html

there's a follow-up book too

[tender river]

you dont have to read them all on your own exactly, as in you can just be active in #linear-algebra and get help whenever you need it, you can even start a book reading group with other people - make friends or document your journey as you work through the book like other people are doing in the threads in that channel

[gray gazelle]

Honestly I got no clue! I guess you could define a topology in terms of filters on some set satisfying some coherence condition(so that they do actually define a topology), and then take the category of these with the limit(as a filter) preserving functions, and then prove this is equivalent to Top.

For nets specifically it might be harder

the collection of nets in a space X is a proper class

[remote sparrow]

what does NAT stand for

[slow roost]

something algebraic topology.. I forget what the N is for

[tribal crow]

Non-abelian Algebraic Topology, so I’ve been told

[modest kite]

Soda

Boku ga kira da na

[remote sparrow]

https://www.ocf.berkeley.edu/~abhishek/chicphys.htm

Townsend, J.S., A Modern Approach to Quantum Mechanics

I can't point to any particular reasons that I like this book, but I do indeed like it. It's a well thought-out coherent study of the structure and essential techniques of quantum mechanics...very nice for a second reading on quantum theory. It's reads like a kind of undergraduate Sakurai, but it's got strengths that Sakurai doesn't. (For one thing, Townsend did not die midway through writing his book.) It's a little less cavalier in its derivations, and a little more careful in its expositions. I guess that's because it was intended as an undergraduate text.

@vital bane

are there references for quantum computing for math students with no physics background beyond the introductory calculus based physics sequence? the only one i know is https://a.co/d/20WsNiy

@rain hound

[earnest wolf]

can anyone please recommend some resources for a probability course, going by these topics?

Probability
Infinite probability spaces
Discrete random variables
Generating functions
2D discrete distributions
Continuous random variables
γ- and ß-distributions
2D continuous distributions
Inequalities
Moivre–Laplace theorems
Central limit theorem
Law of large numbers
Transformations
Markov Chains
---
Descriptive Statistics
Random sampling
Normal sampling
Point estimation
Hypothesis testing
Confidence intervals
Linear regression

This is a rigorous, first intro to probability and math stats course. And measure theory is introduced along the way

could be more than one book, and/or video lectures / lecture notes

[rain hound]

I don't really think the usual quantum computing books require a physics background. It's just supplement and by no means necessary. Nielsen and Chuang is fine. In the absence of that I really like Scott Aaronson's lecture notes (he is a complexity theorist who specializes in quantum computing).

[remote sparrow]

thanks

[remote sparrow]

along the way? that sounds roughly grimmett and stirzaker level

@subtle violet

i don't see anyone use shao or keener for their very first intro to stats

casella and berger is a standard math stats reference

[merry sphinx]

(For one thing, Townsend did not die midway through writing his book.)

[remote sparrow]

wackerly is more elementary but goes well with c&b

also it has more topics

[earnest wolf]

thank you!

[rigid trail]

yo why do you have the same nickname as nagisa now 😭

[merry sphinx]

idk, never talk to him

[remote sparrow]

https://bookstore.ams.org/gsm-243

@rain hound i found this

copyright 2024

[rain hound]

oh my god Landsberg wrote a quantum computing book?

please for your own sake do not read that

he is an algebraic geometer who writes incredibly terse very difficult to read books. He does have things to say, but you will not understand his writings unless you're already an expert in my experience.

[subtle violet]

yeah the first 6 chapters of grimmett and stirzaker cover all the probability topics here. as for the measure theory, they sprinkle bits of it in until chapter 7 where it starts to get a bit involved, but it's by no means a proper treatment

they introduce enough of it for the material that follows it, more or less

[earnest wolf]

by any chance, could you suggest something for (mathematical) stats as well?

Sour Drop mostly mentioned a reference, an elementary book, and a book I shouldn't use

mb there is something else as well

[subtle violet]

only stats book I have is “All of Statistics” by Wasserman which I never really opened so maybe take a peek at that

[foggy quest]

For probability theory, Durrett's book is good: https://services.math.duke.edu/~rtd/PTE/pte.html. For point estimation, https://link.springer.com/book/10.1007/978-1-4899-0027-2 is a classic that is advanced but very detailed.

[remote sparrow]

who said casella and berger was bad?

also shao and keener are measure theoretic

by reference i mean it's an actual textbook

[earnest wolf]

I mean, not bad
u just implied I probably shouldn't use it, since it's going to be my first intro to probability

[earnest wolf]

oh, ok

I thought u meant something like Rudin, but in the world of probability

[remote sparrow]

casella and berger is math stats

so are shao and keener

not probability

wackerly is half probability half math stats

[bright epoch]

casella and berger was great. Wackerly is way less advanced, they're not even close.

[full cairn]

This is such a beautifully bound book I think the binding is sewn and not glued (?)

[remote sparrow]

it may be glued signatures

but AMS hardcovers are nice

[full cairn]

ah yeah, I think it's glued signatures

[remote sparrow]

i agree, it's just that wackerly does have some topics not in c&b

[gray gazelle]

As they said, Non-abelian algebraic topology!

[vital bane]

thanks

[vital bane]

this is actually insane wtf

[remote sparrow]

oh not a serious book rec, just thought it was funny

[vital bane]

so the group of homotopy loops on your space or something is non-abelian?

[vital bane]

Oh I havent clicked the link and read it yet

[vital bane]

Lmfao the Sakurai shade is insane

i see now Sour drop

[remote sparrow]

no i pasted the relevant block quote

all good

[slow roost]

in general yes, the fundamental group can be non-abelian (but it is abelian sometimes)

a basic example is the fundamental group of a figure 8 shape, based at the point in the middle where the two loops join up

if you call going once around one of the loops in a chosen direction “a”, and going once around the other loop “b”, then its fundamental group can be represented as all “words” made up of a, a^-1, b, and b^-1

where a^-1 and b^-1 are the opposite direction versions of a and b

a typical word looks something like a * b^3 * a^-2 * b * a^5

and the product for this group is concatenating words and then reducing them (I.e. a * a^-1 cancels out, and similar)

in particular, in this group a * b does not equal b * a

it’s called the free group on two generators

and it has a cool fractal-like visualization:

(going left is a^-1 and going down is b^-1. Going right twice is a^2, and etc.)

[remote sparrow]

@pure parcel which zwiebach book are you talking about? if it's his QM book, i'd be happy to know if it is a sewn-bound book

https://www.amazon.com/Mastering-Quantum-Mechanics-Essentials-Applications/dp/026204613X

i do see a review which prominently features a crappy gluebound

[remote sparrow]

https://www.youtube.com/@markweitzman

nice book review channel i found from his amazon review on zwiebach's book posted above

@vital bane

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

currently watching this

[vital bane]

Nicee

thanks

[remote sparrow]

https://www.amazon.com/Modern-Classical-Mechanics-T-Helliwell/dp/1108834973

[remote sparrow]

is your copy of nielsen and chuang the 10th anniversary edition?

[remote sparrow]

What are some nice physics books or resources with problems that are (relatively) simple to solve by appealing to physical principles and intuition but are tedious or difficult to work out mathematically? Are there books or resources which have problems that meet the opposite conditions (relatively simple to work out mathematically but difficult to explain physically)?

[vital bane]

Are we getting a Sour Drop physics arc

[daring lake]

mine is

[remote sparrow]

yeah i was wondering about which edition she has

since she says her copy is sewn-bound

[daring lake]

https://markwilde.com/qit-notes.pdf i think this is also a nice source

[daring lake]

Oh I see, mine is just paperback

[remote sparrow]

it's not like a (new) hardcover would be much of an improvement

like most publishers, they make mostly print-on-demand slop now

[rain hound]

It is

[rain hound]

Unfortunately this has been my experience with publishers today. Springer and Cambridge used to do purely sewn binding hardcovers. And now, yeah lots of pod books exist 😭

[gray gazelle]

NAT is specifically about finding more generally non-Abelian homotopy invariants(not just the fundamental group)

Homology groups and higher homotopy groups are always Abelian, so NAT uses other methods, and has higher homotopy theorem’s like Seifert-van Kampen

E.g. relative homotopy groups, they’re Abelian for n>=3, but can be non-Abelian for n=2

[rain hound]

This question is a bit difficult to answer because as you get further along with physics, I think both of these (the physical intuition difficulty and the mathematical difficulty) quickly increase and spiral out of control together.

So instead for the first question I will answer a topic I think the physical intuition is significantly simpler relative to the mathematical requirements.

And for the second question, a topic which mathematically is much simpler than the physical intuition required.

• Classical mechanics (especially hamiltonian/lagrangian) answers your first question. The physical intuition required is quite modest, it is the physics of the large and every day experience. So systems where quantum decoherence dominates, where gravity is weak, where particles travel significantly slower than the speed of light. Nonetheless, the math can get quite sophisticated. Lots of differential geometry (symplectic really) and functional analysis (calculus of variations one might call it) and ODEs can get more cracked than you might imagine, you’ll quickly run into stuff where you need numerical analysis or asymptotic analysis.

• Electrodynamics answers your second question. Relatively simple math for the most part. It’s just vector calculus + PDEs. Ok PDEs are difficult but they’re PDEs which are linear and separable, we know the green’s function, we know the kernel. But the physical intuition is insane. You think you know how electromagnetic fields behave and what they are? No you don’t. They’re fucking magic. It gets even (better?) worse once you get to dynamics and relativity.

Quantum physics cannot be included in response to your question. It requires cracked physical intuition and cracked calculation ability. Both in quantum mechanics and especially in QFT and later. Anyone who says otherwise is totally fucking lying.

[stable flicker]

I don't think QM, considering just statics and the most basic of cases, needs 'cracked physical intuition' or 'cracked calculation'

[hollow shore]

Looking for a lightweight Differential Geometry book aimed at non-math/engineering croud

Lecture Notes would do as well, as long as they have exercises

[vital bane]

maybe you can check out "Visual Differential Geometry" by Tristan Needham

I was once recommended "Applied Differential Geometry" by William L. Burke by a physicist, I haven't yet gone through it, but it might suit your more applied needs

[vital bane]

perhaps you can check out MIT OCW to see if they have such Differential Geometry courses

[tender cobalt]

@vital bane i starting loomis steinberg

[vital bane]

Have you finished Shifrin??

[tender cobalt]

only until differentiation :P

[vital bane]

finish Shifrin first

lock in bro...

[tender cobalt]

na bro loomis steinberg contents making me drool, they alluring

they do calculus on normed vector spaces

also builds good amount of linear algebra 🙏

its like shifrin but on steroids

[vital bane]

persist.

you have to finish one book before moving onto another one

switching wildly between books is inefficient

also the content of a book says nothing about the quality of exposition of said content

[tender cobalt]

can i skip chapter 4, 5 and 6 and go learn integration chapter 7? (visit 4,5,6 later?)

[barren vortex]

Does anyone know of a book concerning differential and geometric topology from a categorical viewpoint?
My professor likes to teach the classes approaching the subject from a perspective that I can't find in any book. For example, his definition of a smooth manifold made no use of charts but instead defined smooth functions as a certain subalgebra of the continuous functions satisfying a diagram for local conditions. Similarly, his construction of many other objects are done through categorical means and then instantiating them in some appropriate category

[vital bane]

why would you do that

chapters 5 and 6 are extremely based

[vital bane]

instead defined smooth functions as a certain subalgebra of the continuous functions satisfying a diagram for local conditions

wow

algebrization of analysis

[tender cobalt]

oh wait yeah, can i skip 4 then

[vital bane]

4 is very useful

you can knock out ch 4 in like a week