book-recommendations

[naive lava]

you need to know the normal proof to find the proof for supermanifolds??

idk

physics mf's when it comes to slapping "super" to anything related to supersymmetry

[vital bane]

Lmao yeah

[native cradle]

Would ross be a bad idea

[remote sparrow]

no

[native cradle]

what about A. N. Kolmogorov

[remote sparrow]

dunno

[native cradle]

okay , so would you suggest ross or Blitzstein?

[remote sparrow]

blitzstein

[molten gulch]

I believe that is measure theoretic

[native cradle]

I see

Also, Hi ryan, how are you doing?

[merry sphinx]

i love 100 pages of hw

[vital bane]

QFT my beloved 😍

[molten gulch]

Blegh but alive

[gray gazelle]

Hi, I am new to this server...can someone recommend a book that improves my trigonometry from the basic level?or maybe a website

[native cradle]

SL loney's trignometry

[gray gazelle]

Thank you

[molten gulch]

SL Loney

oh wait wai already said that

[fathom kindle]

Hallo. Can someone recommend books that can improves my calculus from the basic level?

[molten gulch]

Thomas or Stewart Calculus

[wraith cave]

khan academy can help you all the way up to surface integrals and some basic laplace transforms

[proper rose]

hi, i want to start learning multivariable calculus, can someone suggest me a really good book(preferably with both theory and tough problems)

[vital bane]

Shiffrin or Hubbard

[dim pendant]

Shiffrin is a really good shout

I tried my darnedest to acquire a "free PDF copy" and ended up caving in and buying it only to realize I didn't care

[molten gulch]

hubbard is nice, shifrin too

[grim ore]

Which book?

The Multivar and Algebra ones are free on our UGA website iirc?

I think Diff Geo is on his personal site

Theres no way, he switched over to the publishers site now

https://jasoncantarella.com/downloads/ShifrinDiffGeoLatest.pdf

This is the diff geo one though

If you are looking for multivariable calculus, Dr. Shifrin gave reigns to Dr. Cantarella at our uni and hence teaches it every semester practically. Has his entire course notes online. Still uses shifrins text though, and problems arent posted.

https://jasoncantarella.com/wordpress/courses/math-35003510/

These notes are a little old compared to how he teaches it now though, but still good nonetheless

Also Dr. Shifrins lectures, are kinda low res, but still good

[torn aspen]

@opaque hull

[graceful moon]

Ted Shifrin is a legend, that man's answers SE answers are phenomenal

I think Ted Shifrin and Martin Brandenburg should be entiled some credit in my degree with the amount of help those two have indirectly given me

[dim sierra]

Lol he is so rude sometimes

[dim pendant]

My parents know of my interests, but have no idea what they're actually about

[golden salmon]

I had that problem back in my early undergrad. When talking about what you're learning, it helps to frame it in terms of a concrete problem. For example, I would never talk about quantum mechanics as the non-relativistic physics of matter at extremely short distances, I would say something like 'it's the starting point to learn how industrial lasers and MRI work', or relating to chemistry in some way. It's much less precise this way, but they're not looking for precision (or even accuracy!) - they're just interested in being able to engage with the stuff you're doing.

If your maths is on the more 'pure' end of town it can be harder, but every pure maths concept has some root in the 'material world'. :)

[proper rose]

I looked for Hubbard, i found this one: "Vector Calculus, Linear Algebra,
And Differential Forms
A Unified Approach"

Is this it?

[proper rose]

i found it, the "free pdf copy" 💀

[vital bane]

Lmao ikr he's savage

[vital bane]

Yes, by Barbara Burke Hubbard and John H. Hubbard

Wife and husband

[proper rose]

Oh damn ❤️ then they really put their heart in the book

[open steeple]

Books

[dim pendant]

Hacks

[proper rose]

https://tenor.com/view/hacker-test-gif-26409572

can't even upload gifs 😭

[stuck zephyr]

you need to get active or booster

[remote sparrow]

you need to be active in # discussion

or one of the math channels maybe

you don't have to be perma active

once you get active, the role will fall off after a period of inactivity, but you'll get emeritus like me

https://tenor.com/view/reimu-fumo-bounce-skill-issue-skill-gif-27514402

[vital bane]

https://tenor.com/view/fail-riscord-discord-eminem-rap-gif-22846615

https://tenor.com/view/no-gif-no-gif-perms-gif-27679658

Okay that's enough gifs for one day

[quasi umbra]

What’s the most efficient way to get a working knowledge of mirror symmetry? Is the Clay Mathematics Monographs still considered the best resource for this, or are there more recent or comprehensive alternatives?

[dim pendant]

Might be a great question for the physics server

[vital bane]

@median fossil

[gray gazelle]

Thank you

[median fossil]

Idk mirror symmetry

[remote sparrow]

?

you can learn analysis without any mention of metric spaces

there's a few good books covering metric spaces i'd recommend tho

#book-recommendations message

no

no

https://www.amazon.com/Variables-Basic-Metric-Topology-Mathematics/dp/0486472205

oh i should probably add this to my list

there's solutions to all exercises in the back

not many exercises though

and the exercises are on the simpler side

you mean the one i just linked to?

i already have the book

no

[graceful moon]

Not before just kinda together, in many ways metric spaces is the correct language to do analysis in. But if all you’re interested in is R (not R^n) you don’t really need to know about metric spaces

I also support the recommendation of Magnus Metric spaces book though, great book

I would say probably learn standard analysis over R from like Tao or Abbot or whatever then read Magnus or read something like Rudin which just does it via metric spaces basically from the start

It is, but it does assume familiarity with analysis, off the top of my head I don’t remember how approachable it would be if you hadn’t done analysis before and I my copy is at home so I can’t check

[vital bane]

You can play around with metric spaces as you are learning analysis, try generalizing the definitions of sequences, convergence of sequences, limit of functions, continuity, compactness, connectedness to metric spaces

see what holds, what fails

imo you can do it via metric spaces from the start, it's not hard to generalize everything before differentiation to metric spaces just by yourself, most of the time it's quite literally just replacing |x - y| with d(x, y)

though you have to play around with different metrics to realize that certain metrics can be quite counter-intuitive and some properties break down in general metric spaces when they hold in R

[remote sparrow]

not me

[normal crystal]

I post a 24 hour freeform stream of consciousness reaction video to each book
then add the video to my Books I Read playlist
to track my reading
couldn't be simpler

[atomic flume]

any book reccommendations for self studying calculus? righ now im using https://calculusmadeeasy.org

[native elk]

@atomic flume that website is sufficient i think, for multivariable ones maybe check out dr trefor bazett on youtube

anyways, who has measure theory recommendations

except for the halmos one

i hate his style

[remote sparrow]

https://measure.axler.net

royden seems pretty good too

[heady ember]

I liked Rudin's metric space topology chapters

[vital bane]

I like the exercises

[heady ember]

James recs
Dietmar A. Salamon Measure and Integration

[dim pendant]

I advocate for stronger low undergraduate training so that students can do analysis with metric topology right off the bat

I understand that people call topology "the study of continuous functions of topological spaces" but I like to think of it as "what makes analysis tick", thanks Chen.

What a dense course but I mean the single variable does fall out of the many so I guess it works

Is it an honors level course

Guess not

There we go

[graceful moon]

I don’t think it seems all that dense or crazy

My analysis course covered all that plus lebesque integration and a brief introduction to Fourier analysis

My point is more so that it doesn’t seem too dense in my opinion

[dim pendant]

Y'all gotta remember I'm an American so analysis in R^n is sometimes a graduate course here

[fresh skiff]

is it enough for one to read the Book of proof by Hammack for discreet maths?

[remote vortex]

Yes so long as you keep quiet about it

[vital bane]

By discrete math do you mean combinatorics and graph theory?

if so I was recommended "A Walk Through Combinatorics" by Miklos Bona

that book looks really good

[quiet lantern]

If you are doing olympiad stuff do as many problems as well
I personally recommend Pranav A Sriram, Arthur Engel for problem solving
And for theory Douglas West graph theory, he also has a combinatorics book which is new

Need a good RIGOROUS THEORETICAL book on ordinary differential equations that does all the proofs
And followed by a theoretical PDE book
I prefer if it uses differential forms approach ie it frames differential equations as functional equations between differential forms interpreting all the dx dy rigorously as differential forms

Personally I want something
MOST books don't even properly tell what a differential equations is rigorously compared to our known real analysis
Just the initial value problem that's all
I want something to interprete something like xdy-ydx=0
As a functional equations where the x ,y are functions
The dx dy are first order differential forms
And relations between them
We need to solve for x and y
With a given initial condition

[glad prairie]

the best differential equations book for this is Arnold's book

[glad prairie]

this is not really a thing people do outside of differential geometry. one can do it, but it is not a useful thing to do in R^n, because in R^n differential forms are defined directly to be the things such that d(x(t)) = dx/dt dt. so it is adding an extra step for no benefit at first

the benefits come when you want to study things that differential equations are useful for, but are not directly part of the theory of differential equations (complex analysis, algebraic topology, hodge theory)

[foggy quest]

See Introduction to Differential Equations here https://mtaylor.web.unc.edu/notes/math-524-second-semester-ode/ and https://link.springer.com/book/10.1007/978-3-031-33859-5, depending on your background

[glad prairie]

so if you would like to learn this perspective you will want to learn about those things

but people who study ODEs and PDEs and dynamics do not use differential forms in this way to do their work, and if you were ever told "separating variables in dy/dx = f(x)/g(y) is possible due to differential forms", that was a lie and has absolutely nothing to do with why that's possible

manipulations we can prove we can do with differential forms are a consequence of the validity of this, not a cause of the validity

[quiet lantern]

Bruh that book is unreadable

[glad prairie]

it's univerally considered the best

i really like hirsch smale devaney which is the dynamical systems perspective

but that's not really what you're looking for

the book Barreira Valls is what i used for the Honors ODEs class I TAd for this semester. that book doesnt use differential forms but it's crazy rigorous and very very hard

Viana Espinar is also good, similar content (all theory and no focus on how2solve) but a little less hard

Viana Espinar has better exercises imo

[astral meadow]

I stumbled upon Hirzebruch's Topological Methods in Algebraic Geometry the other day. I gave it a quick look, and it seems like it's become quite old. The title is sligthly misleading to my taste, but I still like the contents. Does anyone have a better and more "up-to-date" reference that covers more or less the same things? More specifically: Hirzebruch's signature formula, Cobordism rings and genus functions of complex projective varieties

[dim pendant]

Lmao this book looks awesome

[quasi umbra]

bumping this

[velvet cove]

Kindly Recommend me different books (textbooks) for calculus 1 , 2 , 3 and beyond to master the subject starting from basic to advance

[astral meadow]

Kindly don't ping-reply my question about a specific book on a specific topic by asking me entry-level references that you can learn about in the pinned messages.

[inland lagoon]

Kindly suggest me some textbooks on representation theory

[remote knoll]

To answer your question, if you just want an elementary treatment of Calc 1-3, then Stewart's Calculus is a good book with many problems.

[remote knoll]

Harris and Fulton has a book that is generally well regarded as a good introduction. Lorenz has a good book as well.

[vital bane]

Khan academy is also great

for calc 1-3

[remote knoll]

Especially calc 3, which was done by 3b1b

[dim pendant]

Kindly recommend to me some books on non-commutative Iwasawa theory

I imagine Professor Leonard is a good shout for Calc 3

[inland lagoon]

thank you

[cunning elk]

kindly recommend me books on how to achieve omniscience 😁😁😁

[dim pendant]

Serre also has a book on linear representations of finite groups , and any Serre book is a must read if it is relevant

[inland lagoon]

Yea that's linear representation

[dim pendant]

That's totally linear, man

[cunning elk]

if you’re just trying to pass calc 3 I think it’s fine

though yeah that’s why I’m turned off by live video lectures

too much dead air

[celest cedar]

guys, what do you think of spivak's calclulus

[dim pendant]

Most people watching the video lectures probably need to be watching them, so it's understandable that the runtime is so great

But you can also watch the video at, for example, 1.5x speed, or even skip around to get on to the next point.

Given that you'll just be doing it again in the analysis of Functions of multiple variables, I'd rather do the easy problems just to get calculus over with

[normal crystal]

Chipper would like it if it was the transcript
converted to epub
with screenshots as oddly spaced graphics, like epubs will do

[dim sierra]

Anyone know a book that talks about estimating eigenvalues of finite matrices? I’m totally clueless about this stuff lmao

[loud cradle]

do you mean like algorithms to compute eigenvalues numerically?

[dim sierra]

Not algorithms but just methods of estimating them, like I don’t really care about computational time I’m just trying to establish some bounds on the eigenvalues of a certain matrix

[loud cradle]

i see, i assume you already know about simple ones like gershgorin's theorem?

[dim sierra]

Yeah

There’s this project I’m working on and I need to bound the eigenvalues of a certain magic matrix so if there is something particularly geared in that direction it would be helpful

[loud cradle]

ah got it, i can't suggest a book but will be interested to see what responses you get

[remote sparrow]

@loud cradle i received my copy of algebra in action yesterday

idk if u can see it, but in the last pic u can see the pages are sewn

yeah

how'd u know?

[dim sierra]

@remote sparrow do you go to Pomona?

[remote sparrow]

no

i'm aware garcia and shahriari both work there

[dim sierra]

yeah haha

[full cairn]

I've almost finished Naive Lie Theory, and I'm ready for the next step, maybe something relying on more maturity in algebra and diff top. Any suggestions? Can I get far by just reading the Lie groups chapter in Lee's ISM? And is there a big difference between algebra-focused Lie theory and geometry-focused Lie theory?

[loud cradle]

ah nice, was this a new copy or used?

[remote sparrow]

used

[loud cradle]

looks almost brand new, nice copy

[remote sparrow]

yeah was $39.95 before other fees

actually i think shipping was free

[storm sapphire]

does anyone have any book recommendations for self-studying time series? Preferably a more gentle one (i graduated 5 years ago with a math degree and took real analysis abt 6 years ago - did very meh in it). I also took a time series class in college & used Introduction to Time Series and Forecasting by Brockwell & Davis (3rd ed) but honestly I find it very hard to follow (still have the book downloaded)

[remote sparrow]

https://discord.gg/ZNsDTKk

you can also ask here in case you don't get an answer

[storm sapphire]

Thank you

[ivory lance]

does anyone have a good book recommendations for studying geometry i still a high schooler i prefer e-book

[gray gazelle]

What do you guys think about The Structure of Fields by David Winter?

[fresh skiff]

yes, oh i will check this book (iirc sour drop once suggested this book)

[fresh skiff]

oh no, i wanna just learn combinatorics and graph theory (for UG level)

[cunning elk]

prefer ebook

KA probably does a decent job covering the basics

I wouldn’t recommend it for anything beyond the basics tho

[willow merlin]

what books explain the concept of euclidean space and affine spaces?

idk

[mortal ore]

Physics is okay I guess

[broken otter]

unless it's quantum

[mortal ore]

Even quantum is just whatever

[broken otter]

there is a book named quntum theory for mathematicians or smth

[cunning elk]

introductory physics is kinda bleh

computation spam

[broken otter]

i hope that would do better job than most quantum books out there

[cunning elk]

you need a sufficiently advanced mathematical background to actually do anything substantial

[broken otter]

i did not enjoy any quantum physics book

[cunning elk]

but when most intro physics classes don't require calculus beyond a superficial level if at all...

[broken otter]

ideally one need to know ALL maths to do physics

even the uknown

[heady ember]

Ideally one needs to know ALL tex-related source code available in CTAN and beyond to do math.

[broken otter]

writing a book on tikzcd

[heady ember]

Just use something local, then.

L take

A is better than B in every way other than the features it provides

🗿

Tex itself it also one of the most bug free programs in the world, I think? I don't think Typst can match that, now can it?

Plus, if I need to find a solution to a (La)TeX problem, it likely is relatively easy to find, with its longer history and larger userbase.

[heady ember]

Perhaps, I only know a tad about Typst.

But with how feature-lacking it is, it is inadequate for many people's needs. Also, even if Typst seriously rivals (La)TeX i capabilities, people like me are too lazy to switch unless Typst can do significantly better.

My tcolorboxes

If Typst has true 3d vector graphics, that'll be tempting. But I can just write a TikZ True 3d package by myself ez (no I can't)

LaTeX takes getting used to. But if you're doing stuff you're used to, then it's pretty fast.

Yes, practice makes perfect.

If you're trying to do custom stuff to get your document to perfectly fit your aesthetic desires, then it may occasionally be tougher.

or if you're trying to write TikZ

[naive lava]

there's one by hall, i heard good things about it

there's also my fav, qm from a functional integral point ov view

there's also popular book by folland on qft for mathematicians

[broken otter]

i would make sure that knuth sees this

[broken otter]

too much functional analysis

[naive lava]

welcome to physics

[broken otter]

brah i just found a book that shocked me

i thought i would never took up QM again

https://www.math.columbia.edu/~woit/QM/qmbook.pdf

what did i just see

[naive lava]

this much group theory for qm might be an overkill

but certainly lie groups play the most fundamental role while constructing quantum fields

[broken otter]

group might be the only thing i strive for as of now

just started rep theory 1 day ago

im learning lie theory as well

physics is gonna be cool, finally

[naive lava]

hell yeah

how about hilbert spaces?

[broken otter]

late 2023 i crashed out and took an oath of never doing physics again

[naive lava]

I did the same for math after hs

look where i ended up

almost the full circle lol

[broken otter]

not too familiar, touoched a lil bit in metric space, but thats about it

what do i need to learn

[naive lava]

well most physics books will actually tell you about them without specifically mentioning it's name

depends on what you want honestly

If you just wanna see what Qm is about and whatnot, you don't need groups nor hilbert

[broken otter]

I wanna learn more algebra, if I see applications it feels nice to the things being used(hopefully in a grand and meaningful way)

[tame ruin]

Sorry for late response OpenStax books might be a good place to look

[vital bane]

ya all you need is like MVC and lots of linear algebra and some knowledge about fourier transforms

[dim pendant]

No more taking about learning math. It's time to just learn it

[heady ember]

Knuth

[broken otter]

thanks for the input but essentially i wasn't asking for books as of now, just contributing to the jest

[floral lantern]

Woit’s book is great

[vital bane]

@slim nacelle

[slim nacelle]

the Clay monograph is still probably the best source

everyone I know who seriously studies mirror symmetry read that book like the bible at some point

depending on what parts of mirror symmetry you're trying to study there are certainly some papers that will get you there faster than this sort of book, but the book is a very good overall survey of the area

[vital bane]

This one?

[molten gulch]

yes

[vital bane]

🔥

Don't ask me why I have a PDF of this (One day I will read it...one day...)

[molten gulch]

lmao same

[indigo thistle]

My friends, do any of you have a book that contains an introduction to basic mathematics?

[cunning elk]

idk do we

the market is incredibly oversaturated with resources for basically the entire precollege curriculum, if you actually cared to google around for 5 seconds you would’ve seen this

and you’re nowhere near specific enough, what do you mean by “basic math”? arithmetic? algebra?

ask an ill-formed question, get an ill-formed answer

[dim pendant]

What is "basic mathematics"?

Arithmetic, variables, solving equations, Euclidean geometry?

Or perhaps you mean advanced mathematics? Proofs, sets, functions, sets with structure?

[cunning elk]

they only have the pre university role

[indigo thistle]

algebra or history of mathematics is also fine

[indigo thistle]

i want algebra

[cunning elk]

^^^

[indigo thistle]

oh i'm sorry bro 🙏

[cunning elk]

khan academy is supposed to be the usual recommendation for k-12 math, I have my reservations about it (too easy and has progressively enshittified over the years) but try it out and see if it’s useful

[indigo thistle]

okay thank you very much 🙏

[willow merlin]

.

?

[vital bane]

any LA book no?

Euclidean space is just R^n

every LA book does that

but affine spaces specifically I don't think are that common in LA books

at least I only saw it once in Axler 3rd ed. it was during the quotient spaces section

[willow merlin]

is 3rd edition latest?

[vital bane]

nope

4th edition is the latest

[willow merlin]

did he removed?

[molten gulch]

https://linear.axler.net

4th ed

[vital bane]

I don't know

[molten gulch]

searching the pdf for "affine" returns no results

[willow merlin]

what about codimension? which books cover that?

[willow merlin]

quotient spaces?

[vital bane]

4th ed?

[molten gulch]

yes

[vital bane]

well it's probably not explicitly mentioned

[molten gulch]

yeah

[vital bane]

ye ye it's like you take a subspace and divide out the vector space by that subspace, in the sense that you collapse that subspace (and its translates) to a point

so quotienting R^2 by the y-axis would be isomorphic to R

so you just get the x-axis

[vital bane]

these "translates" of your subspace are what affine spaces are

[willow merlin]

ok, I dont exactly get it tho will it read on axler aswell, is codimension covered in that book aswell?

[vital bane]

so quite literally, it's just a subspace but translated

[vital bane]

In how much detail?

iirc codimension of a subspace W is just dim V - dim W

[willow merlin]

U disnt defined what V is related to W?

a complementary subspace?

[gray gazelle]

what are some good books to start proof writing?

(for beginners)

[molten gulch]

hammack's book of proof

[vital bane]

V is a vector space, W is a subspace of V

[molten gulch]

https://richardhammack.github.io/BookOfProof/Main.pdf

[gray gazelle]

Ah alr thx James!

[molten gulch]

It's no problem, enjoy

[lavish thistle]

Guys i need recommendation on optimization

[rich sun]

And i need optimization on recommendation

[dim pendant]

I've already got the answers

[quasi umbra]

thank you! im curious if anyone has compiled a bunch of resources in one place, something like the cluster algebras portal or khovanov’s representation theory references page.

i want to eventually get into enumerative geometry, and programs like Gross-Siebert seem really interesting (though they might be a few years down the road for me, given where I’m at with prerequisites).

also does anyone have any thoughts about john lee's introduction to complex manifolds that was published last year? im curious how it compares to voisin's 2 volume hodge theory, huybrechts complex geometry, and griffifths and harris.

im trying to propose a reading course for next semester and i want to learn some more complex/kahler stuff - does anyone have any other suggestions?

[normal zenith]

any recs for calc? pdf if possible. thanks!

[dim pendant]

There are some recommendations if you search calculus for messages in this channel

[warped kayak]

If I wanted to learn from Allen Hatcher's Algebraic Topology, what would the algebra prerequisites be? If I have a good handle on group theory, but not rings and fields, is that sufficient?

[graceful moon]

You should understand rings and modules first really. I think just group theory is enough for chapter 1 though

But when you start dealing with homology you’ll want to understand R-modules

[warped kayak]

@graceful moon thanks!!

[cunning elk]

most precalculus texts are isomorphically bad

so pick your poison ig

[rigid trail]

do you really need books for anything before calculus

or even (non proof centric) calculus books

[wispy bay]

Could someone please recommend fa good book to study for IOQM (India’s IMO first stage) for algebra and number theory

[dim pendant]

I think some people just really don't like videos. My personal issue with videos is that they're super slowly paced or the speaker is miserable to listen to (not really a complaint for math since you should be doing lots of exercises, hence long videos)

And I think some folks who are new to math get all caught up in the book stuff and forget that there's video lectures for most of an undergraduate degree

[rigid trail]

I agree with ochem

Khan is good though

[dim pendant]

Books are nice because they tend to be complete, and you can pace yourself. But you can skip around videos and play them at a faster rate so I think it comes down to what you end up with, and personal preferences.

But I imagine that all mathematicians eventually tend to prefer books, as there aren't good video lectures out for everything you'll want to know

Fair

I'm glad I realized something like this early on cuz trying to take dense notes and process things during a lecture is just annoying

I like to just sit there and listen and redo the lecture as I need to later on

[cunning elk]

no not really

there’s a huge wealth of online resources for those anyway

[rigid trail]

Yeah

[cunning elk]

TRUE AND REAL

😭

ochem tutor is way too shallow in his coverage of the material

KA is its own whole bag of worms with how much it’s enshittified over the years

[rigid trail]

Small lectures >>>

my analysis class had ~10 students

I think that's the ideal way to learn, alongside books ofc

[manic cairn]

how so?

[cunning elk]

the ai slop they've been pushing

[manic cairn]

oh, i see

[cunning elk]

and how they nuked missions entirely a while ago

[manic cairn]

never paid attention to it

[manic cairn]

forget what that was

what was that?

[cunning elk]

i think they've repurposed it in recent years

basically there'd be a whole list of topics that each had a mastery level assigned to it

[manic cairn]

i used it in middle school and am picking it back up to go through all their ap course content over the summer

[cunning elk]

you could do practice tasks for topics of your choice

and then "mastery challenges" would draw questions from topics you've practiced and give you opportunities to raise your mastery level

[manic cairn]

don’t they still have this

i used khan academy just this week

[cunning elk]

they've reskinned it from what i understand

but i think with how they kept changing the topics list

[manic cairn]

also is that a max0r reference?

[cunning elk]

a lot of exercises got lost in the transitions, now i remember some AP calc topics having like maybe 10 total exercises before you started seeing repeats

[manic cairn]

that’s true, but the tests seem to have more

i’m just annoyed that some require a calculator

i know you need it irl

[cunning elk]

dont they have a built in calculator now

[manic cairn]

but i don’t like decimals

[cunning elk]

exact answer enjoyer 🤝

[manic cairn]

yeah, but it’s evil

gonna convince the local high school to let me take ap exams, so i get out of half my college

i know khan academy isn’t enough, but it’s kind of satisfying to do anyway

ugh, this is book recs

whoops

[cunning elk]

lmao

[dim pendant]

That's because they don't talk about math over there

But if you don't have access, definitely grab #advanced-lounge

You wouldn't believe how much the discussion in there can vary

If you can get access and are here for the community, it's worth getting access

[remote sparrow]

no

[dim pendant]

I don't have the grad role so definitely not

[remote sparrow]

that's what graduate-lounge is for

[primal token]

Any book recommendation fro general/algebreic topology that has solutions manual or at least solutions to selected problems?
For fast learning I usually find reading some exercises useful. Then I start a new book from scratch and try all of the exercises myself. (I am self learning with a book so I literally see no solved examples)

[dim pendant]

Could you elaborate? How do you do the exercises if you don't read anything else from the book

When I look at the solution to a problem I just download that method into my head and I become incapable of solving it on my own

[normal crystal]

I think he wants two books
one with solutions and the one he already has
idk

[primal token]

yes exactly

[woven spade]

What do you guys think about the book Multivariable Calculus with Linear Algebra by Trench

[normal crystal]

maybe take a look at Clark Bray et al - Algebraic Topology
I had it in mind for myself later, and might suit your needs

[naive lava]

where's that guy with 200 AT books when you need it?

[broken bramble]

old looking

[opal hull]

Hey guys, I'm looking for book(s) to review all the math I've missed through the years. I've passed the calc 1-3 sequence and differential equations with good grades, but its been a bit since and I feel like I'm not so great with more basic math I probably missed from being a poor student in high school. I've also just begun my physics degree on top of my current major requiring PDE's and an upper level multivariable calc course in the coming semesters, so i want to get a good grasp on everything before that. I was wondering if starting from the basics of the art of problem solving series? Or will I just be wasting my time?

[gray gazelle]

you will be just wasting time

yeah

just pick up a calculus book like stewart or thomas calculus

def not do AOPS

[normal crystal]

GARY YOU LET ME DOWN
it was your time to shine
and suggest Lang Basic Mathematics

[gray gazelle]

i would have if they didn't mention they passed calc 1 - 3 and different equations

lol

[normal crystal]

no that's why
they want to review the HS material before that
they're the perfect candidate

[gray gazelle]

its def an eye opener book any math proofs stuff i know is because of it

if thats smth u wanna do and learn doing proofs def yeah

[gray gazelle]

highly highly highly

recommended

thats all u need

[opal hull]

nah not really looking into proof writing or anything, just that sometimes i feel like i missed out on some really simple stuff i should've learned in my precalc class (wasnt as good of a student back then). i'm just not the best at algebraic manipulation and other stuff like that

[gray gazelle]

are u gonna be taking calc again?

i thought u gonna take advanced stuff now

huh

[opal hull]

yeah i need to take a course on PDE's and then some advanced version of calc 3 it looks like. i also just want a refresh before i get into my upper level physics courses

[opal hull]

i just picked up a copy of stewarts calculus which we used in my calculus sequence

[gray gazelle]

alright so u do have a calculus book

u need pre calculus stuff

if possible get the stewart pre calculus book

[opal hull]

i was looking at this a bit ago, it looked pretty good tbh

[gray gazelle]

its goated book

contains everything u need to succeed in calculus

👍🏻

yeah i would suggest going through that book and then start with james stewart

or just do both with more focus on pre calculus first

which works great

[opal hull]

how so?

i'm also sure i'll blow through it since i have a lot of experience in both of the subjects so far

[gray gazelle]

💯

sure

u def can do that

complete the pre calculus then i say

then just all in calculus

[opal hull]

thats true, i could also skip the limits section since i'm gonna just use his actual calculus book. also the matrices stuff as well as i plan to self study linear algebra separately

[opal hull]

i do have one question though, what do you mean by "complete"

[gray gazelle]

read through the book and do enough problems or all is considered complete to me

[opal hull]

i have a bad mentality of "i feel like i should complete every problem" when it comes to textbooks and i drain myself out and it's 100% not an efficient way of studying

[gray gazelle]

i do that too actually but lately what i started doing is when im doing very new topic i do all the problems otherwise i would do even or odd or occasionally do every hard problem other than those numbers

if i don't do a problem i just look at the problem and think about how i will solve it

and just move on

[opal hull]

i understand, thats how i tackle my school subjects. for my circuits class last semester i would attempt every problem in the book (of relevant chapters) because it was all new to me. but obviously i'm not going to sit here and do every problem about functions in a precalculus book

[gray gazelle]

EXACTLY

u got the idea

[opal hull]

i think stewarts book also has different sections of problems? like applied ones if i recall correctly? maybe i should just do those?

[gray gazelle]

just do the hard ones and just do the easy ones in the head or just

in a very rough way

but making sure u know them very well

[gray gazelle]

yeah

i suggest like each section is in sub sections do odd or even ones then also making sure

u don't miss any hard ones

[opal hull]

true. sometimes it's just exhausting because there could be 100-200 problems per chapter 😭

[gray gazelle]

and most of them just repeat we don't wanna do that

u wanna be smart about it

[opal hull]

right

what was the reason against aops btw?

[gray gazelle]

u need to do unique and hard problems

[gray gazelle]

its for kids

olympiads

[normal crystal]

if you don't do them all
the Problem Gremlin will sneak in while you sleep

[gray gazelle]

literally no depth for an engineer

[opal hull]

fair

stewarts goes into decent depth?

[gray gazelle]

decent? it goes as much there is

which is covered in college

atleast looking from engineering perspective

it has everything u need to know

[opal hull]

awesome

thanks so much

[gray gazelle]

👍🏻

[gray gazelle]

💀

[vital bane]

https://www.damtp.cam.ac.uk/user/tong/vc.html

for vector calc

[gray gazelle]

Good Galois theory books that covers both finite and infinite Galois theory?

[karmic thorn]

I really liked Patrick Morandi's Fields and Galois Theory

[gray gazelle]

Cheers 🙂

[vital bane]

perhaps try cleaning the charging ports

Maybe something is clogging it

[gray gazelle]

def yeah

make sure don't break it tho

because that will be permanent

[vital bane]

yea you have to use soap and water to clean it or else it will break

(this is a joke, don't actually use soap and water)

[gray gazelle]

make sure no dust or smth in the chargoing port

becuase it can't be battery as the charger can run the laptop directly

so thats def smth has to do with port

if its not ugh well its smth deeper

[rose hinge]

dungeon crawler carl

[fresh skiff]

For physicists?

[vital bane]

For anyone, but yes it's aimed at physics undergrads

[vital bane]

idk what giving up is

Hell yeahh!! 🗣️🔥🔥🔥

I don't know what it is either🗿

[fresh skiff]

I see

[white parrot]

hey, have some math background (math B.S.). i was required to take an intro to programming class in python, but don't have any experience with programming otherwise. i'd like to read CLRS, but according to the preface, the authors say,

You need some programming experience. In particular, you should understand recursive procedures and simple data structures, such as arrays and linked lists (although Section 10.2 covers linked lists and a variant that you may find new).

in your opinion, would i need to read a basic data structures book beforehand (just to gain some familiarity with them by using and implementing them) before reading this book, or is it pretty self-contained? as a side note, i'm moreso interested in the theoretical aspects of computer science than the practical side atm, so if i can read clrs relatively smoothly without needing to do all that programming beforehand, i'd be happy to know.

[vital bane]

intense emoji

[fresh skiff]

Yeah i got nitro from discord idk how
My friend told me discord sometimes gift for 1 − 2 week nitro

[whole jasper]

recommend set theory book

[late ruin]

Suggest Real analysis for Complete beginners with little to zero knowledge about real analysis please.

[heavy vault]

jay cummings

[heady ember]

What level are you looking to learn set theory at?

[white parrot]

@rain hound @tulip blade @foggy quest i saw you three while using discord search to find people discussing clrs and searching through some of your msgs, i thought you all would be qualified to say more

[late ruin]

Is Bartle and Sherbert good

Jay Cummings is a little expensive tbh

[remote sparrow]

???

sorry but his book is one of the lowest-priced ones out on the market by far; mid-priced textbooks are at least $60-100

is there a parent/guardian/parental figure/someone who's close to you in your life you could ask to buy you the book? i'm sure they would understand

[vital bane]

Understanding Analysis by Stephen Abbott

[remote sparrow]

try some that look easy first. then, pick a few that you don't feel are immediate but feel you could solve with some applications of known properties. then try a couple that you feel you have no idea how to solve, at least initially.

[vital bane]

as many as possible in the time that I have available

[remote sparrow]

if you have a ton of free time, sure

however, you should note that neam and grass have been doing intro real analysis for a long time this way

like a few years

[remote vortex]

I will admit that it's not always easy to determine which problems are worth doing, that's where experienced advice can be helpful; if the problem list is long you can always post it in the appropriate channel and ask which ones they think are the most essential.

[remote sparrow]

however, learning new things that build on old material can help reinforce or teach things about old material

[remote vortex]

Doing literally all of them is in a sense ideal, but not always practical

Neamesis has been reading it for like 3 years, although to be fair he does it in between lots of other things

It's entirely doable in a summer if you focus mostly on that

[remote sparrow]

try not to sweat it too much if by the end of the summer, you aren't anywhere close to reading the whole thing

[graceful moon]

The book is like 250 pages, it will not take you years lol

[remote sparrow]

just trying and succeeding at just part of your reading goal will put your further ahead than most of your peers

[remote vortex]

There are counterexamples to this claim

[graceful moon]

But also yes how long it takes doesnt matter so much, maths isnt a sprint, its a marathon

[graceful moon]

I mean not if youre actually trying

Ive been reading crime and punishment for about 3 years and I imagine theres similar reasons behind it

[heady ember]

[heady ember]

Oi oi oi I feel personally attacked

https://tenor.com/view/steven-he-emotional-damage-steven-he-emotional-damage-gif-23428142

[remote sparrow]

until the third book comes out
so never?

[remote vortex]

That was the intention, yes (but also as stated, it should go reasonably fast if you focus mostly on that, like several hours most times per week)

[heady ember]

[heady ember]

That was the intention, yes

it should go reasonably fast if you focus mostly on that, like several hours most times per week
When I do real analysis, I do it a number of hours per week.

One exercise can take hours in of itself

[graceful moon]

By trying I more mean intentionally dedicating time to it. If youre doing an hour here or there when you have time thats obviously different

But like if you make it a priority it should only take a few months

[remote sparrow]

feel free to look up solutions, too.

[remote vortex]

When I was a student, my real analysis course (comparable in scope to Abbott) was 5 hours of lectures and 4 hours of problem-solving sessions weekly, over 15 weeks, so it would be 75 hours of lectuers and 60 hours of exercises; 135 hours in total.

Not counting own work of course, just the class hours themselves

[graceful moon]

Mine was 2 hours of lectures, 1 hour of problem solving and 10 weeks

I feel like ive been scammed by being born in the UK

[heady ember]

How do you consistently dedicate a huge amount of times to it everyday though? Sometimes after spending a lot of time on the same question(s) you just feel quite tired for the day.

[graceful moon]

I mean I do this all day most every day for my degree, this person was talking about doing it over summer so im presuming theyll have some free time

[median fossil]

@vital bane

[remote sparrow]

since i went to a community college and a "commuting" school, recitation hours didn't really exist for me

[heady ember]

Not even necessarily on the same questions, but thinking hard for prolonged periods can be exhausting.

[graceful moon]

But yes youre not wrong, this is just kinda how degrees go though

[remote sparrow]

they suck if you don't live close (i do live close in both cases)

[heady ember]

Wdym? Yout just power through it?

[remote sparrow]

tuition isn't as expensive too

generally speaking

probs cuz not as many students live on campus

[graceful moon]

I mean yeah, if youve got 5 classes a semester and a dissertation to write, youve just kinda got to get on with it

[heady ember]

True

[graceful moon]

But also this is essentially my full time job (aside from my part time job), so this is how I spend my days

[vital bane]

[vital bane]

[heady ember]

Fair enough ig. But I don't wanna burn myself either

[graceful moon]

Im not saying you should

[remote sparrow]

also a good number of students have jobs/are nontraditional students

[vital bane]

this

[graceful moon]

I work an unhealthy amount, my course load is objectively too much lol

[vital bane]

burn out, and burn bright while going out, that's my philosophy

[graceful moon]

In any case my only point here is that if youre actually dedicating consistent time to it, introductory analysis is very doable in 2-4 months

[vital bane]

100%

any undergrad subject actually

[heady ember]

There's so many math things I wanna learn before the start of uni, but it would require such dedication and great ability to avoid burnout.

[vital bane]

LA, Algebra, point set topology

measure theory

[graceful moon]

And I know because I did that while taking 3 other classes and having plenty of free time

[vital bane]

Grass: There's so many math things I wanna learn before the start of uni
Also Grass: TikZ!

[heady ember]

Wasting time on TeX & Friends aside, one or two analysis questions can already that me a day or two already. How do you achieve that speed?

[vital bane]

I see

[heady ember]

Heh we share the same mind: I was typing about TeX at the start of my sentence.

[vital bane]

Simply be better

[heady ember]

Very helpful mate.

I'm gonna read the TeXbook :3

One day I'll implement true 3d vector graphics in TeX

[vital bane]

is TeX open source?

[heady ember]

Of course

[graceful moon]

Necessity is a hell of a drug

[heady ember]

so is LaTeX and most relavant packages

[vital bane]

Nice

hell yeah

Change the compiler, implement 3D vector graphics

[graceful moon]

But also just experience, for the last 4 years this is all ive really got up to

[heady ember]

TeX is one of the most bug free programmes in the world

[vital bane]

you keep repeating that but I'm not sure if that's true

[heady ember]

Meh. That's boring. Implementing it in (La)TeX is where the fun lies.

[heady ember]

Me looking at my last four years: ...

[vital bane]

me on my way to spread misinformation on the internet

Trauma...

Ever since Covid lock downs, it hasn't been the same

[heady ember]

I've completed Enderton's Elements of Set Theory and am still progressing through

1. FIS
2. Analysis

[vital bane]

btw I've actually completed Axler

[heady ember]

To be fair, if I didn't read Rudin, I would been done with intro analysis already. But, Schroder's exercises for differentiation and integration are not as strong as Rudin's.

[vital bane]

well the book has 10 chapters, I did 7.2

and I got sick of it

so

I would count that

[median fossil]

Deadlines push you to be more efficient, and also sometimes make you give up and ask classmates for hints

[remote sparrow]

you should probably look at the 4th edition of axler

[vital bane]

No

I am FIS and HK pilled now

I have looked at the 4th ed btw, I don't wanna go through it

[heady ember]

I sometimes get pissed off when I need to ask for hints lol

It makes me feel that I haven't learnt the material well enough

[graceful moon]

Ok but youre not at uni though

[heady ember]

Fair

[remote vortex]

nah

[heady ember]

Well, I'll just try my best; that's what I can do.

[vital bane]

Me when asking for hints isn't an option while working on an unsolved problem

[graceful moon]

During highschool I just played CSGO for 6 years, youre in a far better place than I was before I got to uni

[vital bane]

The Bomb has been planted

Terrorists win,

[vital bane]

I didn't play for 6, but I did for like 1 or 2, it was so fun

[graceful moon]

I didnt even really know what maths "was"

[vital bane]

CS is such a great game

[graceful moon]

Long story short, dont stress about it, youre incredibly fine

[vital bane]

I only have like 500 hours, and nowadays I don't have time for CS

or any game

[remote sparrow]

https://tenor.com/view/lol-defeat-game-defeat-gif-16680812

i still try to play games whenever i can

[heady ember]

You guys should form a TeX reading group with me

We shall cook up the most esoteric TeX known to men

[vital bane]

Grass making TeXbook solution manual when?

[heady ember]

https://tenor.com/view/the-darth-side-of-the-force-is-a-pathway-to-many-abilities-gif-21623328

[vital bane]

Surely there are some mean exercises?

Like Algebraic Football?

Or Topological Cricket?

[heady ember]

https://tenor.com/view/cody-ko-noel-miller-thats-cringe-eww-what-the-fuck-gif-14490952

[vital bane]

Engineering is insane

I want to learn it some time

possibly after PhD

[naive lava]

no, don't.

[heady ember]

Of course you do you filthy Phy*icist.

[median fossil]

TeX is esoteric in itself

[heady ember]

Real men becomes TeXnicians

[remote sparrow]

there's plenty of interesting mathematics adjacent to some fields of engineering (e.g. control theory)

[heady ember]

True

[vital bane]

or algebraic geometry

[remote sparrow]

yeah in robotics

[vital bane]

I think even algebraic topology

in robotics

[naive lava]

yeah but that's the research level

no textbook discusses manifold version of control theory afaik

[vital bane]

really?

[heady ember]

Company: So, you have familiarity with programming? Do you mean Python or Javascript?
You: TeX, LaTeX and TikZ.
Company: ...

[vital bane]

Are you talking about engineering textbooks or control theory textbooks?

@silver herald surely there are textbooks like that?

[naive lava]

Engineering textbooks

[vital bane]

Also hello Doom 👋

[naive lava]

i haven't read any specific, that type textbook

[remote vortex]

fortunately I'm an owl

[heady ember]

Owls can alsobecome TeXnicians

[vital bane]

Owlnicians

[median fossil]

You, while being dragged away by security: TeX is Turing complete!!!

[heady ember]

I mean, its true.

[remote sparrow]

league of legends

goated game

[remote vortex]

yes, but it shouldn't be!

I'm so glad I was born too late for gacha and other live service games.

I did spend quite a bit on WoW subscription over the years, but it seems to pale in comparison to something like Fortninte or Roblox

[heavy vault]

Outlandish take 😭

[late ruin]

Im from India

Thanks

[gray gazelle]

LMFAOO

[remote sparrow]

there are usually international editions of some more commonly sold textbooks

you can also have a print shop print and bind a pdf for you

[whole jasper]

im interested in other math but for any math i need some background knowledge

i want to learn homotopy theory/algebraic topology

but i need something before i think

[heady ember]

You don't need anything much beyond naive set theory, then.

[heady ember]

You need to learn algebra and some point set topology first

[whole jasper]

thanks for recommendations

[fluid violet]

I'd join that

[heady ember]

Smurf moment

[fluid violet]

Smurp

I also have other recommendations for reading material

[heady ember]

Preach your words, O' Soup Slurpin.

https://tenor.com/view/ramen-slurp-slurping-dive-in-dig-in-gif-5072099429053351263

What are you gonna recommend me? The manual for expl3?

[fluid violet]

Well obviously

1. The TeXbook (which you already said)
2. The Advanced TeXbook (for OTRs)
3. My article on pdfTeX primitives
4. I intend on writing an article on programming in plain TeX as well
5. Parts of different documentations for various packages (eg pgf, maybe expl3)

[fluid violet]

Well that's less my area of expertise

I do plain TeX, not LaTeX, and certainly not LaTeX3

[heady ember]

What does OTR stand for, btw?

[fluid violet]

Output routine

[heady ember]

Yeah I know

[heady ember]

I see

One day we can cook TikZ wizardry together 💪

[fluid violet]

TikZ is for newbs

One day we create our own graphics package together maybe

[heady ember]

Real 3d vector graphics for PDFLaTeX

[fluid violet]

[dim pendant]

Why did he squat down like that 😭😭

[silver herald]

You are not looking at the correct place then. The manifold version of control theory is well established within many books on "Geometric Control". Examples include -

Bullo & Lewis, "Geometric Control of Mechanical Systems"
Agrachev & Sachkov, "Control theory from the geometric viewpoint"

[silver herald]

Well, geometric control is kinda weird there because geometric control theory has accessbility and implementation problems when looked at broader engineering POV

Incoming Wall Of Text, readers be warned:

A bit of culture and history first -

Geometric Control was actually developed by pure control theorists back in the 70s-80s to have a theory for (smooth) nonlinear systems that we do have for linear systems for aerospace applications (this was the field that actually gave rise to a lot of deterministic optimal control theory) by replacing the underlying vector spaces we were working with to smooth manifolds and using lie algebra to have a similar algebraic framework that we do for linear systems. (Brockett has a nice paper on detailing the early history and applications - https://d-biswa.github.io/Teaching/RM12_Brockett--Early_Geom_NL_Control.pdf)

Prior to this, a lot of the nonlinear systems tools were local stability ideas based on linearization -> lyapunov arguments (called as perturbation theory).

So, what changed?

1. For starters, geometric control does not really describe controllers that will have newer guarantees compared to things we already had like LQR or using Pontryagin/DP to solve for an optimal control problem but it allowed for a stronger theoretical framework to do your optimal control for smooth nonlinear systems. The problem is that you should be able to describe your state space well. This is not always possible for systems like electric circuits, networked systems like power and telecommunication grids as your network topology affects your state space manifold (and things get even worse....as we will see in point 3). The only other big geometric control domain Doom can think of where the manifold description is similar to robotic/mechanical systems would be quantum systems and QFT (The underlying lie group structure is some product group given by SU(2), which has interesting double cover stuff with SO(3), so a lot of the tools in robotic systems are applicable there).

2. Remember the perturbation/analytical tools Doom was talking about? Yea, so around the 80s, Control had a seminal paper on Dissipativity (see - https://link.springer.com/article/10.1007/BF00276493) by J.C Wilems that described Lyapunov-like analysis using storage functions. This was weaker than the lyapunov analysis and extensions to this (alongside the other dominant theory, Integral Quadratic Constraints (IQC)) applied quite nicely to nonlinear systems. It also turns out that, these frameworks required less assumptions than geometric control (which, from a theory sense we always like) and they were easier to use to synthesize controllers from. More yet, these frameworks in conjunction with uncertainty quantification of the dynamics models can yield controllers with more guarantees (Robust Control)! Which is one the big reasons why Geometric Control isn't usually adopted much - Geometric Control has no robustness guarantees. The big section of control synthesis in Geometric Control is based on Optimal Control, which has the assumption that you know your system dynamics precisely - so there's no way to add any sort of "uncertainty margin" to the synthesis methods.

3. Geometric Control only really works for smooth dynamics....non-smooth dynamics that we see in, say - Robot Manipulation (and a lot of Robot Locomotion as well TBH. Stiction is a big thing) are not amenable to geometric control (you lose differentiability!). Recall the applications in point 1? Yea, so in networked systems, motors and electric circuits - the dominant nonlinear behavior is switching, for which - the classical approximation in the domain is to see them as discontinuous (non-smooth) dynamics rather than approximations we do in mechanical systems for like friction by saying that the friction interactions happen in a different timescale and when working with controller synthesis In locomotion cases, we combat coulomb friction by using conic constraints/pyramidal constraints in the traj.opt/MPC we write. This sort of naive treatment becomes quite difficult to do when non-smoothness in manipulation, electric and networked systems become a dominant thing. The approach that has been successful so far have been from the POV of "Hybrid Systems", which take the POV from Dissipativity/IQC land to talk about Semidefinite Programs/Mixed Integer Programs based on the "operating modes" you are working with (In manipulation, you would have heard of these as contact modes). In fact, because of the connection with Robust Control, one can add robustness guarantees alongside the hybrid system control synthesis methods, so the techniques are quite extensible.

4. Due to the rich history of Geometric Control, the hype on it from (pure) control theory researchers have started dying down (think circa late 2000s) as the theory is relatively complete and the stuff that's not have remained unsolved for decades now. For instance - "The connection between nonlinear reachability and stabilization synthesis" are not fully explored yet (particularly, with the stabilization synthesis not being feedback invariant, so there's a non-trivial relationship between the two). Besides that, the extensions of geometric control theory to tackle similar concepts as non-smoothness, robustness and stochastics have it's very unique challenges with the mathematics prerequisites being too vast for people usually from an engineering background to cover (for instance, a popular way to talk about non-smoothness and stochasticity in geometric control is using what's called Geometric Measure Theory, so besides some background in Diff.Geo and Lie Theory, you need upper level Measure Theory and Analysis. There's also a fact that the mathematics are still being worked upon by Pure Maths people for things beyond Euclidean Spaces in this setting). That has caused the number of geometric control researchers to dwindle.

5. More as a side effect, Stability results in MPC as done in late 90s and early 2000s by Mayne and his group (see this - https://www.sciencedirect.com/science/article/abs/pii/S0005109899002149) offered simple extensions using the same Dissipativity framework with Control Lyapunov Functions that can be for Nonlinear MPC in case of regulation, which often doesn't need much geometric insights. This led to MPC/NMPC to succeed as the de facto "traj.opt" method in non robotics/aerospace domains like power electronics and networked systems. There's also a fact that robustness to known dynamics uncertainty can be added to the MPC framework (see Tube MPC and similar) which are much harder to do with other Traj.Opt. methods.

[foggy quest]

You will be able to read CLRS. CLRS is about introducing algorithms and proving their correctness. It does not give real code implementations, only pseudocode. You need programming experience to understand how the pseudocode would be implemented and that it is realistic.

[compact eagle]

I need a basic ordinary diff eq book just to get introduced to the topic. Do yall have any suggestions?

[coral narwhal]

Coddington

[rain hound]

It’s pretty self contained but it can be a bit of a shock to start, it is suitable for an advanced undergraduate or a graduate student even.

I strongly recommend even if you’re only interested in theory, implementing a significant portion (perhaps even all) of the algorithms and data structures you work through in a language of your choice. Implementations are similar to formalizing a proof vs a rigorous proof, it’s a much more exacting requirement than just working with pseudocode and will ensure you fully understand the thing.

Dynamic arrays/tables are already implemented for you in python, so I’d suggest looking up or even figuring out an implementation in another language. C++ say. But if not it’s not a big deal, it’s a simple data structure (memory safety and some other caveats aside). The rest you can probably happily implement in python using classes.

[foggy quest]

https://mtaylor.web.unc.edu/wp-content/uploads/sites/16915/2020/10/diffeq.pdf

[compact eagle]

Is that one better than the other one

[foggy quest]

I haven't read the one by Coddington

[compact eagle]

This one's a bit long and idk the average content of a diff eq course so idk if id be wasting my time on anything

[vital bane]

applying control theory to QFT is insane, also hello! How's it going?

[vital bane]

Geometric measure theory mentioned! sick! it makes sense though, why you'd need GMT for extending geometric control to non-smooth stuff

[foggy quest]

the one by Taylor is short and terse at times. None is a waste.

[compact eagle]

Ill try getting through chapter 1 then thanks

[spare osprey]

Anyone suggest book
For real analysis, algebra.?

[molten gulch]

Check pinned

[silver herald]

Yes! Application of Control to QFT is kinda the idea with modern pushes to Quantum Control (especially in terms of applications beyond Quantum State Preparation in Quantum Computing like Optical Tweezers - https://en.wikipedia.org/wiki/Optical_tweezers , and Control of Ultrafast Chemical Dynamics stuff -https://www.sciencedirect.com/science/article/abs/pii/S000926141730218X))

This sort of thing is also nice for perspectives in information limits to control (a traditional control theory field) like Information Field Theory IMO - https://en.wikipedia.org/wiki/Information_field_theory because a lot of the success in Quantum Information related domains are in information quantification and interaction effects in quantum many-body systems and they yield some very interesting insights

[silver herald]

So, GMT angles are more for stochasticity and uncertainty representations in geometric control (because, again - these things are important when working with safety critical systems) than non-smoothness but there are some works done in the sense pure GMT theory for non-smooth geometry like so -

https://www.ias.edu/video/geometric-measure-theory-non-smooth-spaces-lower-ricci-curvature-bounds

Doom usually sees more Hybrid Automata/Piecewise Affine/Linear Parameter Varying representation based work being the more popular paradigm within control theory groups for non-smoothness. (Which, has the problem combinatorial mode explosion stuff in practice because increasing the number of hybrid nodes/edges increases compute drastically.....so the problem then becomes learning/reparameterizations suited for "performance shaping").

[silver herald]

As for how it is going - Mostly recovered from the knee injury Doom sustained in February. Had the first quarter exams done after returning back to Uni. (after opening up an exception case for yours truly) - aced 2 courses, failed one by a small margin.

So on the whole - an eventful few months and Doom is finally getting back to more research.

[sharp latch]

Good recs for 3 and/or 4 manifold theory? I’ve seen a couple of different ones floating around but wasn’t sure which ones would be “good”. Mainly interested in the stuff having to do with pseudo anosov maps, handlebodies, and algebraic topology aspects, but would be perfectly fine with a big introductory survey of the different viewpoints as well

[dim pendant]

What's your background? A lot of commonly known books on the subject are firmly rooted in graduate level ideas

[sharp latch]

I’m a grad student lol. this is just stuff adjacent to my work that I think is really interesting and I’d like to learn

[dim pendant]

no solid just wanted to make sure you weren't some guy who just did a litttle bit of topology in an analysis class and wanted to study real low-dimensional topology

fine by me in those cases but RIP 💀

I'm not familiar with this area of math but I know that a couple of common shouts are

• Topology of 4-Manifolds (Michael Freedman and Frank Quinn)
  And uh.. I seem to have lost track of the other on so I guess I'll go a-searching

ah I guess it's slightly lower but Geometric Topology in Dimensions 2 and 3, that was the other one I had in mind

anyway hopefully someone more knowledgeable can get you some more options

[sharp latch]

🔥 thanks

[opal hull]

@gray gazelle still thinking about those books from last night. i know stewarts precalc is good because it has a ton of info, but would Langs basic math book be good if i was just looking for a little more intuition and catching up on some things i might've missed rather than blowing through a ton of problems?

[gray gazelle]

Nah well tbh it won’t really benefit u very much

Just do pre calc

One

[gray gazelle]

It can but I mean not really worth it for now

You wanna start doing calc first

[opal hull]

wym

[gray gazelle]

Doing calc will open up many subjects

[opal hull]

tbh i might just jump straight back into stewarts calculus book and pickup anything i missed along the way, that might be more beneficial

i just wanted to see if that book would be good just to read for intuition

[gray gazelle]

It has no calculus but a lot of proofs

But u said u don’t want that

So

[dim pendant]

What is your goal Dazed

Dased

Oh my heavens

[opal hull]

@dim pendant heres the context

[dim pendant]

I see

My honest opinion is to go back through calculus. I don't think much of the stuff you've forgotten will show back up. And if it does, you'll probably see some examples worked out so you'll be re-familiarized with the content

Like when I think of the stuff I've forgotten from high school I think basic series, factoring cubic polynomials, Euclidean geometry, etc.

Useless for me but I'm also not a physicist

[cursive rivet]

very much not on the topological end, but if you're interested as well in the gauge theoretic angle to 4-manifolds, I liked "Gauge Theory and the Topology of Four-Manifolds" edited by Friedman and Morgan

here's the table of contents: https://www.ams.org/bookstore/pspdf/pcms-4-toc.pdf

[opal hull]

thats a good point as well, its probably best i just have a deep understanding of calculus more than anything before moving on. i'm mostly concerned about forgetting some random precalc things and lacking some intuition but i guess that can all be regained by going back through stewarts calculus and facing it there when it comes up

[dim pendant]

For sure

[cunning elk]

there's a reason most calc 1 classes in US universities are just remedial algebra classes in disguise

[dim pendant]

You'll be doing lots of that in the more advanced stages of your degree, realizing you don't know something and opening up a book to read 15 pages out of it

[opal hull]

so is this normal? because sometimes i feel guilty for forgetting how to do things i should already know. for example last fall i was taking differential equations, and something came up where i had to do synthetic division and i had completely forgot what that even was. luckily i never had to experience that again

[dim pendant]

It depends on what exactly. I don't remember polynomial division either so each time I need it I have to go back and learn it and then I've got it for the next couple weeks

[cunning elk]

if you've seen it before generally it's easier and faster to pick it back up than if you had never seen it before

[dim pendant]

But I more so meant that later on you'll need new tools that you won't have seen in any class so you'll crack open some random book you didn't expect to need

[opal hull]

ohh i misinterpreted

i understand though

well thank you guys

[dim pendant]

Same

[normal crystal]

probably won't change your species, sorry

[dim pendant]

Haha nerd

[normal crystal]

no
they both evolved from a common ancestor

[dim pendant]

Yeah we're super epic apes but we're bros

[dapper root]

The chmonkey….

[normal crystal]

ancestor, I will light some incense and leave a slice of pizza at your altar🙇‍♂️

[dapper root]

Mmmm pizza….

[dim pendant]

Yeah..

[gray gazelle]

bro

[elfin scarab]

Turn into a monkey then

[foggy gorge]

I have noticed that a great deal of precalculus books follow a similar structure, sometimes even the same didactic. For example, you can find some pattern in the way the topics are structured and in the didactic in "mathematics for the international student (Robert Haese)", Precalculus (James stewart), the Algebra and Trigonometry by Openstax,Precalculus by richard rusczyk, precalculus concepts through functions by sullivan, etc

I've tried to read all of them to see how they explain things, sure there are some differences here and there but they are so similar

Maybe it is due to the fact that it is a textbook. I wonder if there is some book that tries to flee from that way, with a more unique didactic

What books are in the "few" set?

[dim pendant]

In other words, those books take a rigorous, qualitative approach, rather than a naive, quantitative approach.

[dim pendant]

Relatable

me whenever I do math

[ancient creek]

Thanks for sharing this. I totally neglected this approach with geometric control, I shared it with my classmates, everyone is very interested 😀

[thorny badger]

you can give 'Basic Mathematics' by Serge Lang a try.

[naive lava]

It's not a lang book if it doesn't have proof of inverse function theorem

[past girder]

any good vids to accompany abbott?

[vital bane]

[mortal ore]

i mean its a lang textbook

[past girder]

heheheha

[tender river]

https://youtube.com/playlist?list=PLysi2xmniDSzz6xT7IzOifpoexeKccThh&si=xJa5IsOh6m1g6PLm theres this yt series

And theres an mit ocw course on real analysis that you can look into

[past girder]

i see thx

[past girder]

i tried it, professor is a lil boring to listen to for long periods

[vital bane]

Honestly with Abbott you can just read the book on it's own

it's just that well written

reading that book is like listening to a really really good lecture

[heady ember]

You can read any book on its own

[vital bane]

Rudin RCA moment

[heady ember]

Real men come up with the intuition themselves

[vital bane]

Real men don't use books

[heady ember]

Real men write TeX research

[past girder]

indeed

i wish i had abbotts phone number

so that i could talk to him

[manic cairn]

(for banach spaces)

[median fossil]

Neam solving D&F exercises, 2025 colorised

[naive lava]

that book should come with antidepressants

and a carton of cigs

[dim pendant]

Most professors are this way.

[past girder]

unfortunately

[vital bane]

https://www.middlebury.edu/college/people/stephen-abbott

You can find his office phone number

sotrue

[vital bane]

[vital bane]

Like me🗿

[past girder]

i know a guy at mid im going to ask him for an autograph

[vital bane]

I wish I could get one

[past girder]

i wanna too

does he still teach

[vital bane]

Same

[vital bane]

Yup

[past girder]

hehehehhehehe

i want to see him teach calc 1

[vital bane]

It would be insane

[past girder]

looks like he teaches the main courses

[vital bane]

Honestly this looks a lot like the courses you teach @remote vortex

Analysis, LA, measure theoretic probability

Outsider is Abbott?!?! Conspiracy....

[heady ember]

He is Outsider.

[vital bane]

Sniped

[remote vortex]

Coincidence?! ||Yes||

[past girder]

🙂‍↔️

[remote vortex]

or, well, not a coincidence since there are literally thousands of academics with a similar list of taught courses

[vital bane]

That's true

[remote vortex]

I.e. general analysis

[vital bane]

Do you teach calculus? I think you mentioned you sometimes teach the calculus courses for engineering and other non-math undergrads

[remote vortex]

I do

[vital bane]

True anyone with analysis adjacent research would teach that

[vital bane]

What do you start with?

like on Day 1

[remote vortex]

for mechanical engineering students this semester, in fact

[vital bane]

Nice

[remote vortex]

general concepts related to subsets of reals and real-valued functions, then sequences and their limits, then function limits, then derivatives, then integrals. As for the second lecture...

series and functions of multiple variables are second semester here

[vital bane]

Interesting, that's actually pretty good that you start with real numbers and real functions and sequnces before limits of functions

I think way too many calculus courses just drop the students straight into limits of functions and then derivates and say "well real numbers and sequences will be taught in analysis, engineers dont need that"

perhaps there is truth to that but still

[heady ember]

Since I have been drawing 3d diagrams lately, I wonder which books have an abundance of such (colored) diagrams?

[vital bane]

Gallian

Algebra

[heady ember]

It has 3d diagrams?

Show me some

[remote vortex]

I'm not going to specify my circumstances any more than I already have

[remote vortex]

Just for clarity, we don't do the axioms or reals or Dedekind cuts or anything like that, we just discuss the number line, sets and basic operations on them, and basic properties of functions: the concept of domain, codomain and range, composition of functions, elementary functions (including the basic properties of exponentials, logs, trigonometric functions and their inverses) and graphs of functions.

[heady ember]

Bro is trying to dox an Owl

[remote vortex]

Many such cases.

[remote vortex]

I mean, fortunately not.

I have few enemies, it seems.

[heady ember]

should I TikZ an owl

[remote vortex]

Other than the cranks but those tend to get banned before they start digging.

[molten gulch]

I always think of you as a literal owl who spends his nights in a tree or burrow then comes out during the day, takes upon a human form as an owl in a trenchcoat teaches class, disappears again

[remote vortex]

That is fairly close

[heady ember]

I'm an owl that disguises myself as a human to teach them mortals math. I prey upon the chosen in the dark.
some ln title, probably.

Owlsider, what's the coolest diagram you have seen?

[remote vortex]

I honestly have no answer, nothing springs to mind.

Also, I've just noticed this is #book-recommendations

Also known as #discussion-4

[heady ember]

[molten gulch]

lmao yes

[round pelican]

Anybody read Hodel’s Introduction to Mathematical Logic. I have it but haven’t gotten around to reading it yet.

[dim pendant]

I like how this channel is 30% book recommendations and 70% #math-discussion2

Oh someone literally just said this

Wow

If I could go to school to learn from anyone it would be Borcherds or Gaitsgory

Or Conway, rip ❤️

[rose bronze]

Textbook recommendation for the variational approach to evolution PDEs?

[plain maple]

Does anyone know where I can get resources for calculus and functions for first years

[dim pendant]

Professor Leonard (YouTube), Khan Academy, and James Stewart's calculus books.

[pine tundra]

I've written down this list recently, if you wanna pin feel free <@&268886789983436800>

(of course it's not a virus, even if it's txt)

[pine tundra]

@plain maple I believe you can find something useful here

[plain maple]

Thank you so much

[grizzled niche]

Which book/resources or any material or any part of specific resource or anything that's available online of maths have the toughest and most challenging questions of calculus that can be done on the knowledge and theory of high school maths?

Same Qs for coordinate geometry (St lines, SOT, circle, Parabola, hyperbola, ellipse)
And for trigonometry..

I won't ask for algebra, because I know how tough it can reach ... 🙂

[vital bane]

Yea that's what I had in mind as well

[cunning elk]

HMMT (math competition run jointly by Harvard and MIT students) used to have a calculus round many years ago

try some of their old problems?

[topaz rampart]

Hey, does anyone know a very accessible book (because i live in greece) about complex analysis? I'd like it if it was from a really cool mathematician whose knowledge could be compared to god's (stupid joke because rn i feel weirdly happy)

[naive lava]

for the first kind, churchill and brown or gamelin might be it

for the second, ahlfors (has a fields medal)

[topaz rampart]

Hahah thanks mate, i'll check them out:)

[covert pike]

Hi, any recommended book on the philosophy of mathematics?

[real stratus]

rudin principles of mathematical analysis

[covert pike]

that book is about analysis

i'm looking for something like Russell's introduction to philosophy of mathematics.

[remote sparrow]

#book-recommendations message

[covert pike]

thanks, i'll check it out later

[iron pulsar]

ty~! i feel my money growing already

i think tomorrow once it goes through 😅

i used fidelity

[pale mica]

I was watching Eigenchris on youtube for tensor calculus and then some introductory differential geometry, but it wasn't quite complete enough for me and I would like a deeper and also more rigorous book on it

[heady ember]

Common recs:

1. Loring Tu
2. John M Lee
3. Jeffery M Lee

The last one requires some knowledge of category theory and functional analysis iirc

[vital bane]

Since you're coming in from a physics perspective

I would also recommend checking out

Manifolds, Tensors, and Forms: An Introduction for Mathematicians and Physicists by Paul Renteln

Also who can forget about David Tong the goat

https://www.damtp.cam.ac.uk/user/tong/gr.html

The first three chapters are about diff geo

[vital bane]

what da hail

no way func anal is required for a book on diff geo

[heady ember]

What

[vital bane]

Func anal for what

spectral geometry?

[heady ember]

Go get it yourself

I mean, its free

Everything is

[vital bane]

I'm looking through the ToC and I see nothing requiring func anal

But I do see Appendix A has Cat Theory

Grass when reading through diff geo and sees physics:

[heady ember]

That's not from Lee

[vital bane]

it is from Jeffery M Lee

[heady ember]

Oh yeah

[vital bane]

"Manifolds and Differential Geometry"

You gotta learn physics some time grass, it's goated as hell you're missing out 🔥

[heady ember]

Yeah I misremembered: you just need algebra (including cat theory) + analysis

#discussion message

[vital bane]

@remote sparrow

so true!

mfw printing each page costs 30 cents

that's why it should be dissemininated for free

[heady ember]

Is that FIS

[vital bane]

Yes

But I have accquired a pdf of the 5th edition

[heady ember]

I got my international fifth edition for like 40-50 bucks

[vital bane]

through completely legal means yes

[heady ember]

softcover

[vital bane]

50 bucks....

[heady ember]

But the quality is :/

[vital bane]

50 SG dollars or USD?

[heady ember]

Doesn't make much of a difference

,w 50 SGD to USD

[vital bane]

Oh damn really?

[hasty eagle]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by grass1977

[heady ember]

Ok maybe it does

That's why I print out and bind math books myself

[vital bane]

I didn't know SG dollar was doing well

from how much SG slander I hear from you

[heady ember]

Eh

I don't really give much SG slander

I just complain about my enslavement

[vital bane]

True

100%

[remote sparrow]

i only found crappy pdfs. i suspect the pages may have come from a software that rapidly takes screenshots from the vitalsource copy

[vital bane]

I see

this one is good

do you want me to dm the link?

[remote sparrow]

ok

update: it was not better than other copies i found myself

[vital bane]

It wasn't vector graphics

we'll just get grass to TikZ the whole thing

[naive lava]

a prof told me that seme "modern" results in diff geo comes from sobolev spaces and shi

[vital bane]

[naive lava]

also on this note

nicolaescu or smth

rigorous text

[vital bane]

Ah yes the famous footballer and differential geometer

[naive lava]

maybe a bit more advaced than jefferey m lee

[naive lava]

but has gauge theory in mind

https://math.stackexchange.com/questions/13575/teaching-myself-differential-topology-and-differential-geometry this stack exchange post makes it seem like it's intoductory

but i beg to differ

[vital bane]

Damn bro wrote this right out of PhD

[naive lava]

mf gives a 4 page proof of cauchy projective spaces(can't remember their name) are actually manifolds in first 10 pages or so

[timber mesa]

definitely not introductory but seems very complete honestly

[vital bane]

derivada, when I start my dynamical systems arc, I will ping you in my thread

be ready

[naive lava]

uhh

maybe taubes as a ligher alternative?

[timber mesa]

idk haven't read it

[vital bane]

Holy hell!

[naive lava]

yeah