book-recommendations

[quick hornet]

linear algebra is also handy just so understanding R^n and stuff is second nature

since that comes up frequently in examples

but its not really necessary at all

[primal summit]

I got some recommendations for algtop books (Specfically, I asked for something that isn't Hatcher). I was recommended Dieck, Spanier or Modern Classical Homotopy Theory by Strom. I'm mostly doing this to prep for my algtop course next semester which will be focusing mostly on homology, so idk how much strom would help, but between the other 2 what do you think would be better. I'll add that I looked a bit into dieck and it seems that he introduces categorical langauge right from the beginning without really explaining it which was kinda jarring

[sage python]

Rotman's the easiest algebraic topology book probably

It's pretty formal, it introduces categories from the start too but with a veeeeeery light hand (instead of tom Dieck basically assuming you know it going in)

[primal summit]

Sounds like what I'd need. Does it cover homotopy or does it go straight into simplical homology?

[sage python]

Homology is chapter 4 but chapter 0-3 can be done in like

A week

[primal summit]

Gotcha

I'll look into it thanks!

[sage python]

Arguably chapter 2 on simplices is part of homology

[primal summit]

oh ofc you need to understand simplices and simplical complexes to understand (simplical) homology. I just considered that as part of 'simplical homology'

[gray gazelle]

I need a good actuarial science book to study from

help lol

if you see this, please @ me or dm

[sage python]

ShiN yeah I just mean the organization in Rotman is slightly split up

Basically it's chapter 0 that sets the stage, so it shows you how once you set up "homology functors" you can prove e.g. Brouwer, then some basic categorical stuff

Chapter 1 is "Point-set you might not've seen yet"

Chapter 2 is simplices, chapter 3 is pi_1

4-9 is homology lmfao

[primal summit]

gotcha

cool, i'll check it out

[rough hawk]

for proofs do you mean induction and contradiction?

what other proof methods should I know

[quick hornet]

all of them? a topology course will expect you to be fluent

[rough hawk]

do you have a list

[timber mesa]

Part II and III of the Contents of http://www.people.vcu.edu/~rhammack/BookOfProof/

[quick hornet]

you should have no trouble proving, say, that a subset of R^n is compact iff it is closed and bounded

not that its an easy proof, but it should be doable

[primal summit]

@sage python Just got through chapter 0, very cool. Really gives proper motivation to homology and sets the scene nicely

It's a bit weird though that he defines a category explicitly as locally small

Like he says that Hom(A,B) must be a set for all objects

[sage python]

It's pretty common I think?

The category theory here isn't for its own sake in any event, it's for algebraic topology

[primal summit]

Yea, I figured non-locally-small categories don't have much use outside of category theory, but I haven't dove into the literature too much so I wouldn't know

[sage python]

And you'll largely be dealing with categories like groups, rings, R-modules, spaces, pointed spaces, pairs, chain complexes which are all locally small no questions asked

[rough hawk]

@quick hornet In the preface the book mentions experience with group theory. Is there a book recommendation for that? I have some experience with set theory, is there a more advanced set theory text?

[quick hornet]

oh youll need groups for the homotopy stuff

forgot to mention that

you dont need much group theory though, i think you can kinda put it off lmao

but any intro-to-abstract-algebra text will cover groups

see

#book-recommendations message

[timber mesa]

group theory in topology is one of these things where you need the language rather than the whole theory

[whole rain]

Don't you end up using group theory "big theorems" at some point ? Like finitely generated abelian groups structure theorem, Sylow stuff etc ?

[sage python]

Hmm, I don't remember using Sylow in topology thus far

[gray gazelle]

What’s the gigantic analysis book called, again?

Also, is Rudin recommended for func analysis?

[gray gazelle]

Any good books that focus on the maths for ML such as linear algebra and stats? I should note that I am still in high school and have some experience with rigorous maths texts

[remote ginkgo]

yeah

there are 2 books i like a lot

[tulip blade]

are you looking for a math for ML book or a book on linear algebra and a book for stats?

[remote ginkgo]

wasserman's All of Statistics and shifrin's Multivariable Mathematics

[tulip blade]

and what do you mean by rigorous math texts? Like writing rigorous proofs

id check out axler

[halcyon hornet]

Are Schaum's Outlines books good?
I plan to use their Elementary Algebra, Intermediate Algebra, College Algebra, Geometry and PreCalculus.
Is that a good book to use, also as a supplement, I am using KhanAcademy right now, and studying Algebra 1, then after completing it, will proceed.
Thanks, other suggestions for books are greatly appreciated.

[slim peak]

The only one I read was the one about Laplace Transform

a pretty good one

[rough hawk]

it says that group theory is fundamental to homotopy theory

thrift books is usually really cheap

i got some dover books for 5 dollars on there

it doesnt matter whether or not its in good condition if its not falling apart and you can read it\

[rough hawk]

does it matter which edition

[grave flume]

Any book suggestion for combinatorics? I am a graduate but Don't know that much about Combinatorics still. mostly with questions and theory as well

[broken meadow]

probably Bona, A walk through combinatorics

[grave flume]

Does this contains solutions as well? I know the basics but want to refresh them again.

[broken meadow]

i dont think it does

[karmic thorn]

It does, actually

Hints/solutions have been given at the back of the book for most problems

[broken meadow]

oh

okey

nice

[grave flume]

Thanks a lot

any other suggestions you guys have in mind?

[karmic thorn]

Some other standard recs seem to be Stanley's Enumerative Combinatorics and Brualdi's Introduction to Combinatorics

[livid ermine]

combinatorial problems and exercises also

by lovasz

[grave flume]

Thanks a lot guys

[timber mesa]

I don't think it does, but the latest edition is freely available as a digital copy there

[gray gazelle]

has anyone read this one calculus book by zorich?if so can you recommend it?

[hollow peak]

does anyone have a recommendation for an introduction to fluid dynamics geared toward mathematicians?

[ripe granite]

fluids for the working mathematician

[willow pecan]

[hollow peak]

ange do you have a recommendation

[willow pecan]

No

@glad prairie do you

My fluids is ~patchy~

I should probably fill in the holes this summer

[glad prairie]

i do not know of a good fluids book

[hollow peak]

https://books.google.com/books?id=9Iwrt0l0nFMC&printsec=frontcover&dq=Arnold+topological+methods&source=bl&ots=8EboHOnalu&sig=ZlmmgB8FyfZj9P_V-0YDtSMpFiE&hl=en&sa=X&ei=eqpeUK-tCoiA4gSq1YHoAQ#v=onepage&q=Arnold topological methods&f=false

holy fucking shit

[willow pecan]

No

[hollow peak]

yep

[willow pecan]

No

[hollow peak]

chorin looks really good so that's what i'm going with

[willow pecan]

Chorin is at Berkeley

Interesting

He sometimes drops by applied math seminars

[hollow peak]

this book appears to be more the pde speed

[willow pecan]

There are 3 chapters

......

[hollow peak]

sad

[willow pecan]

Gas flow in one dimension = inviscid burgers equation?

This book is a bit ~lacking~

[hollow peak]

how about this

https://www.macs.hw.ac.uk/~simonm/fluidsnotes.pdf

[willow pecan]

There is no table of contents...

[hollow peak]

[willow pecan]

Or problems...

[sudden kindle]

Ange just write a pde book already

[willow pecan]

And ruin my career?

I think not

I will be listening to the sage advice given to me by Gian-Carlo Rota

[hollow peak]

[willow pecan]

I'm going to be honest

It looks like these notes are just a laundry list of different flow types

[hollow peak]

didn't you take a course on fluids

what did you use in that

[willow pecan]

I attended the MSRI fluids workshop

It had no textbook

There was a topics course on free water waves as part of the workshop

It had no textbook

[hollow peak]

sad!!!!

[willow pecan]

@glad prairie let's write a fluids book once we know fluids

[glad prairie]

[willow pecan]

[gray gazelle]

Any big difference between Munkres first edition and second edition?

[whole rain]

the edition

[timber mesa]

I don't think I've ever seen the first ed., the second one is old-ish enough already

[gray gazelle]

i found the first edition of lee's smooth manifolds on the internet

it's so cursed

a whole chapter on lie derivatives

(not pirated)

[ripe granite]

,ban tterra

[hasty eagle]

You don't have the required permissions to ban members here!

Jun 14, 2021, 12:13 AM

[gray gazelle]

[broken meadow]

,ban tterra

[hasty eagle]

Please enter a reason for the ban, or c to cancel.

[obsidian valley]

[willow pecan]

[hasty eagle]

Reason prompt timed out, no members were banned.

Jun 14, 2021, 12:18 AM

[broken meadow]

c

[solemn mantle]

Yo @sage python ik u don’t remember this but thanks for recommending Jacobson I really like his style

[obsidian valley]

weak

[broken meadow]

the mods have no spine

[willow pecan]

[daring reef]

what are good ways to self study a math textbook? i feel like whenever i take notes i just rewrite the book, but when i don't take notes i don't absorb the material as well

[willow pecan]

If it has problems, you should do those

When taking notes, you should aim to, instead of copying the material, transform it somehow

This might mean summarizing

Or filling in details that are glossed over

[daring reef]

hmm yeah, i do try to do that, but i find that books have such concise proofs that half the time i just end up copying the whole thing 😦

ill probably just try to only write down things not explicitly in the book

[thorn finch]

maybe try to put the book away and try to use the method the book use to prove it again? I do that, and when I find out things I get confused with, I will look it up in the book again and label it in my notepad, or use my best logic to sort things out then write down my own "proof"

[static crest]

sometimes the books with the concise proofs arent the best for self learning

because it almost feels like the author is trying to flex how short they can make the proof

rather than give a proof that's more easily understandable

[daring reef]

ooh will definitely try that, that sounds like it fits my learning style

[daring reef]

haha i guess

[primal island]

does anyone have any calculus book recommendations?

preferabbly one that starts at basic derivates and integrals and goes into multivariable and vector calculus later

and ones with lots of questions and answers

ive been using khan academy for calc 1 and 2 and i feel like theres a limit to how much i can learn so

[sage python]

@primal island so are you focused more on gaining computational prowess or do you want theory? I guess if you're doing Khan more the former, in which case... Stewart is the standard and I think it's fine but

Idk a calc book is a calc book how amazing could it be to be worth that ridiculous price?

So yeah I wouldn't recommend buying Stewart full price. If you can acquire it for... < $100 by some means (e.g. buying used copies or [REDACTED])

Then sure. Or find some other calc book. If you already know the theorem statements and the rules it's basically a matter of doing practice problems

Also for an online source there's Paul's notes

[primal island]

ah okay

[primal island]

mainly studying so i can start studying physics

ill look into that stewart book and decide if i will use it

[sage python]

Yeah if you wanted theory I'd say Spivak but that's probably a bit of a distraction for you

[primal island]

Ah okay

Is khan academy still a good place to start?

[sage python]

Khan Academy is probably fine?

[primal island]

Oh okay cool

Thank you 🙏

[thorny helm]

any books to learn graph proofs for early uni

[tulip blade]

You can try introduction to graph theory by douglas west (standard book for intro graph theory).

I think its good

[thorny helm]

And that covers graph proofs or at least has questions on them?

[tulip blade]

Wdym graph proofs its confusing me

Its an entire textbook dedicated to introductory graph theory at the undergraduate level (it is not an easy book though). It is filled with proofs of results about graphs and has hundreds of questions.

If you find it too difficult then maybe try the book by Trudeau or Chartrand. If you just dont like it then I see the book by Bondy and Murty recommended some times as well.

[willow pecan]

Justin Trudeau is a graph theorist

[thorny helm]

I'm referring to if the textbook has graph proof questions to attempt

Like book of proofs

with its content

[tulip blade]

Yes its a textbook like most undergrad texts books it has many problems for you to solve.

[thorny helm]

Yeha ty

[tulip blade]

Very prominent one of the only politicians to have written a math textbook

[wise topaz]

Do you guys got good books that touches on maths for economics for undergrads?

[willow pecan]

Math for econ for undergrads is 1. linear algebra 2. multivariable calculus

[tulip blade]

Wb analysis and probability?

[willow pecan]

That comes in during grad school

[tulip blade]

Ive heard those are important if you want to do grad school in econ.

[willow pecan]

Trust me I was almost an econ major

[tulip blade]

I started as econ but switched to math bc everyone said you should do math instead even if you want to do econ you need analysis anyway

By everyone i mean reddit

[willow pecan]

Yeah if you want to pursue econ in grad school you def need a lot of math

[wise topaz]

so you got any? With books on analysis and probability i guess

[willow pecan]

But if you just want an undergrad econ degree then you don't really

At least in the US

It might vary in other places

[sage python]

Did someone say graph theory?

[tulip blade]

Me

[wise topaz]

Bros.....

[broken meadow]

Did?

[unreal star]

Does anyone have a book good for calculus, I'm starting calculus rn so it would be good if it covers all the basics and has good problems. Thanks

[gray gazelle]

spivak's book is solid, a little difficult though

[unreal star]

Thanks will see it

[gray gazelle]

How are the problems in Sheldon Axler's Linear Algebra done right?

[sonic vessel]

Which books do you guys recommend to self-study number theory?

[stray veldt]

what kind of number theory?

[sonic vessel]

Introduction

I mean, elementary

@stray veldt

[karmic thorn]

See the latest pinned message

[sonic vessel]

I do not know anything about number theory

do you still recommend this book?

[gray gazelle]

Check out Hardy-Wright book.

Oh, also, A Friendly Introduction to Number Theory by
Joseph H. Silverman is a good one and probably more beginner friendly and easier for self study

[gray gazelle]

Topology of numbers is pretty good too

[primal island]

does anyone know the difference between james stewarts calculus 8th edition textbook and the calculus: early transcendetals 8th edition textbook

[lofty sluice]

Is there any book/website that follows Euclid's Elements but present it with modern logical notation,rather than an line-to-line translate

[hasty turret]

Why would you want to do that

I guess you might wish to look at Hartshorne geometry book

If this looks interesting,read Hartshorne geo

Google "Euclid and Beyond"

You will get a free completely legal pdf

[quartz dome]

what type of text/practice book would u recc for an introduction to calculus?

assuming the student is a complete novice, fresh out of algebra I?

[cursive orbit]

You probably should know some trig and algebra 2 before trying to learn calculus, as many of the examples and problems in calculus concern those types of functions.

[quartz dome]

hmm..interesting, are there any suggestions you would have for algebra 2 books?

[willow pecan]

@hollow peak did you find a fluids book

I have my eyes on a few

[hollow peak]

I started reading chorin and I'm actually liking it so far

I think it's definitely above your level but for a noob it's a good

[willow pecan]

I see

These were the 4 that I picked out

(all legal copies)

[hollow peak]

sorry not above, below I meant

[gray gazelle]

(legal)

[willow pecan]

Yes

All legal

Springer Link

[hollow peak]

god bless springer link

[willow pecan]

Let me know if you want to work through one together

@glad prairie as well

[hollow peak]

anatole keeps raving about mycopy but my school doesn't have that service :(

[gray gazelle]

what are the prereqs

[willow pecan]

PDEs

Or at least

[hollow peak]

pdes and vector calc yeah

[willow pecan]

Familiarity with multivariable calculus

[gray gazelle]

I know 0 pdes

[hollow peak]

also real analysis is useful for understanding some of the trickery

[willow pecan]

You probably won't need serious pde knowledge

The books I picked out don't focus too much on the pde theory side of things

[lofty sluice]

Whats a Springer link?

[glad prairie]

i need to do that i guess

oh dear

[humble flume]

is there any book that covers all forms of geometry? like from Euclid to current? only best books thanks.

[stray veldt]

no

geometry is a very broad term

[willow pecan]

@hollow peak I think that Pozrikidis and Wendt might be a bit too computational/numerical for your tastes

On the other hand, Visconti doesn't have exercises

I'm probably going to use Kleinstreuer for a first pass

[humble flume]

I guess i'll just get a good book on Euclid then one on Non-Euclidean geometry

the search continues....

[hasty turret]

Just skip euclid

No one cares about that old man

[humble flume]

lol

[gray gazelle]

wasn't he pretty young when he died?

[hasty turret]

No one knows

[humble flume]

@hasty turret where would you start learning geometry if not for Euclid?

any book recommendations?

[hasty turret]

Hartshorne

[humble flume]

Geometry: Euclid and Beyond?

kinda seems like what I was looking for lol

[hasty turret]

Yes

[gray gazelle]

if it's less than 10k pages i-

[humble flume]

Advanced Euclidean Geometry goes into Non-Euclidean geometry?

or i need diff book for Non-Euclidean geometry

[uncut zealot]

Brannan, Esplen and Gray covers a fair bit of geometry at an undergrad level, including projective, affine, inversive, hyperbolic and elliptic geometry.

It won't get you up to research levels or anything.

It also contains the following paragraph in the "further reading" section, which is hilarious:
"In addition, the World Wide Web contains a massive amount of interesting and relevant information that can be accessed using a Search Engine (such as GOOGLE)."

[hasty turret]

You probably need to know analysis and some multilinear algebra to understand the other geometry fields

[uncut zealot]

Commalg is required for Hartshorne, I believe, though there might be books with more accessible alggeo out there. I don't know enough about diffgeo to know what you need for that, but probably at least vector calculus and complex analysis I would assume.

[hasty turret]

Sir,This is a different Hartshorne book

[rotund elbow]

B o o k s

N i c e

[uncut zealot]

Hartshorne wrote more than just Algebraic Geometry?

TIL

[humble flume]

@uncut zealot thanks

glad you guys helping out noobs like me

[uncut zealot]

No worries, everyone starts somewhere. I'm actually also planning on reading Brannan, Esplen and Gray soon, if you'd like to be my study-buddy on this one.

[hollow peak]

@willow pecan do you have a preferred intro numerical methods book as well?

LeVeque it is

[marble solar]

I heard ppl swear by atkinson

@hollow peak but I have no experience with that shit

are you gonna do some computational fluids bacono

[hollow peak]

i'm very curious about that kind of thing

also that knowledge is very high in demand I believe

[gray gazelle]

fluids

[willow pecan]

Yes I like LeVeque's Numerical Methods for Conservation Laws as an intro

It doesn't assume any numerics knowledge so it's fine as a first book as well

[uncut zealot]

I can no longer sit back and allow communist infiltration, communist indoctrination, communist subversion and the international communist conspiracy to sap and impurify all of our precious bodily fluids.

[gray gazelle]

[marble solar]

yuh

[marble solar]

Gotta love Dr. Strangelove

[willow pecan]

Once you read LeVeque, you can tackle something like Iserles

[rough hawk]

Any recommendations for some problem books and or textbooks for computational math competitions?

[gray gazelle]

for geometry just get Euclid's Elements.

That's fine.

[timber mesa]

depends on what you mean exactly by "computational math competitions"

[gray gazelle]

euclid's element is lost work and i highly doubt that you have a copy of it

[willow pecan]

http://farside.ph.utexas.edu/Books/Euclid/Elements.pdf this you mean?

[gray gazelle]

oh, I was reading the wiki page wrong

[sonic vessel]

What is the best book for introduction Combinatorics?

I don't have any knowledge about this topic

[heavy plank]

Any recommendations for a good book for probability and statistics?

[regal walrus]

Do someone have solutions of the book" Calculus of a single variable,10th edition"

[pale scarab]

If you want a nice easy intro at the high school level the aops book is good. You can get both for the price of a typical undergrad text. The problems are a lot of fun also.

[pale scarab]

Oliver byrne has a pretty euclids elements book I would recommend. It is just a aesthetic book to look through and is more true to how they probably thought about this stuff thousands of years ago.

[pale scarab]

Check out some math circle book collections. Typically junior high/elementary books are more computational. Once you get to even high school level you start to see more proofs. Though the amc is still mainly computational. There are some integral books that are mainly computational also.

[sonic vessel]

Which book are you talking about

Can you share its amazon link or thumbnail picture

I think I have it

[sonic vessel]

Oh, wrong comment, I was talking about this

This one?

[pale scarab]

The art of problem solving. I would go with the intro first and the the intermediate one. https://www.amazon.com/Introduction-Counting-Probability-Textbook-Solutions/dp/B0083C7A64

[sonic vessel]

nono I am talking about your question

[sonic vessel]

This

[rough hawk]

yes I do have a copy

I was just reading it last night

Green lion press reprinted it in a single edition on nice paper with nice margins

[rough hawk]

Definitely intro to counting and probability by AoPS. I took the course and it was the best math course I've ever taken

[rough hawk]

competitions that aren't proof based

basically the amc and aime

[gray gazelle]

I read the wikipedia page wrong, apparently. My bad.

anyone ever tried Oscar Levin's Discrete Book?

[gray gazelle]

Do you recommend that book for discrete mathematics?

Should I got for it?

[queen dove]

Any recommendations for something on programming language theory for an interested high-schooler with essentially no background beyond a basic level of coding proficiency?

[obsidian valley]

"Category Theory for programmers"

[queen dove]

it seems interesting and idk whether or not it has any hard prequisites

[queen dove]

Does that mostly stick to a category theory perspective or is that just how it markets itself?

[obsidian valley]

I'm mostly joking please stay away from that book

you are too young to take the red pill

[queen dove]

lol

I've consciously tried to not become a(nother) teenage category theorist

[obsidian valley]

I think the move for most people interested in PL theory is to learn some functional language first actually

if you don't already

[queen dove]

I know C at a basic level

[obsidian valley]

no I said functional

[queen dove]

oh

functional

wikipedia time

[obsidian valley]

xd

[queen dove]

ah I see

I'll probably give that a go then, thanks

[obsidian valley]

Your time would be well spent with Clojure or OCaml or Haskell or something

[tulip blade]

Where is category theory useful

[obsidian valley]

I suppose Haskell is the the language there but idk mniip would know more probably

[tulip blade]

In CS

[queen dove]

is it too tricky to learn?

I've heard from a friend that Haskell is a bit tough to pick up

[obsidian valley]

you can read this preface: https://bartoszmilewski.com/2014/10/28/category-theory-for-programmers-the-preface/

It is Shimmering but the community for Haskell is very strong

It's a completely different paradigm from what you're probably used to

[pale scarab]

Haskell is amazing I think most who study math would enjoy that programming language. I learned C++ in school and python on my own but got into Haskell last year and it is really great although yes much more difficult compared to say python.

[gray gazelle]

yea i thought of trying it but hundreds of MB install

[uncut zealot]

Does anyone know any good books for inter-universal teichmuller theory (IUTT), accessible to an undergrad?

[willow pecan]

[sudden kindle]

dont even try reading IUTT if you havnt learned the elementary theory of heights, at the advanced undergraduate/beginning graduate level.

[tight crag]

Scholze and Stix learned that the hard way

[willow pecan]

I imagine that you should also know anabelian geometry?

[karmic thorn]

Wait, is this something Mochizuki said in response to the Scholze-Stix assessment of his work?

[sudden kindle]

Yes

[karmic thorn]

[willow pecan]

Breath takingly (melo?) dramatic

[karmic thorn]

Indeed

LOL

What's the deal with weird italics and boldface lmao

[willow pecan]

It's Mochizuki's style

[karmic thorn]

very challenging task to document the depth of my astonishment
Definitely going to use this one for stretching word limits on English tests.

[willow pecan]

Indeed

[flint forge]

lmao english classes ruined my writing with word minimums

word minimums are such a bad way to teach good writing

[uncut zealot]

I was in a philosophy class that had word maximums, so I altered my writing style for that, and now I can't meet most word minimums anymore.

I'm too used to conveying information as succinctly as possible.

[flint forge]

yeah thats a good thing

strict word maximums teach you to write well

I just always go back after I write stuff and cut out half of it

[karmic thorn]

It is a very challenging task to document the depth of my astonishment when I observed how much exaggeration is a part of creative writing in elementary curriculum.

Goodness someone should teach Mochizuki the elementary theory of writing good LaTeX

[uncut zealot]

Gotta love Mochizuki

[willow pecan]

[uncut zealot]

Best source of mathematical comedy in decades

Also, any good reading on the elementary theory of heights? I know like two theorems about the heights of points on elliptic curves and that's about it.

I do actually genuinely want to be able to read Mochizuki's preprints for myself in order to see if he's as full of shit as people say he is or if he's as much of a genius as he says he is.

[obsidian valley]

you genuinely will not be able to tell what he's talking about I think

[karmic thorn]

Yes, jesse is right.

[gray gazelle]

have u even tried tho

[sage python]

@uncut zealot do you think that'd be a particularly productive use of time?

[uncut zealot]

Not particularly, no.

I think it would be funny.

[obsidian valley]

the point is that this is not worth it for the bit

[uncut zealot]

Okay fine I'll spend my time learning real math instead of crankery

[gray gazelle]

anyone?

[still jay]

Anyone have any notebook suggestions? For notes and scratch work

[flint forge]

anything cheap so you dont feel bad wasting it

even a legal pad honestly

i think fancy notebooks are probably not worth it?

[rough hawk]

LOL i read about this in an article about the abc proof

by some japanese guy

2013 best writing on mathematics

[timber mesa]

definitely, every time I buy decent paper I feel bad writing on it

[rough hawk]

composition notebooks

[timber mesa]

and my best stuff has been done in the most random paper lmaooo

[rough hawk]

i bought 10 for 5 books at target

[flint forge]

yeah compositions if you need organization

legal pads otherwise

i actually do have a penchant for small notebooks that fit in a (large) pocket

i like to take them with me places in case i am inspired or bored

[whole rain]

same lmao

[frosty ermine]

Anyone know of any good books/articles on hyperreals?

[tulip blade]

Wikipedia

[pale scarab]

Agreed but fancy pens are. I love my fountain pen

[flint forge]

eh

ill use pilot g2s until i drop anyway

[tulip blade]

Pilot g2s are great

[timber mesa]

they're lovely but I feel like they burn down the ink way too fast

[broken meadow]

i love my fountain pen

but i don't use it enough and i dont really wanna spend money on nice paper

i would rather just waste pilot g2 ink on printer paper

and that's what i used to do

until i got the ipad 😈

no more burning through paper and ink i guess

but i still do occasionally do scratch work with a g2 on printer paper

[flint forge]

honestly

i have come to dislike writing on my ipad

for everything except lecturing

it just feels inferior to paper still to me and i can't really explain why

[hearty steppe]

well its basically like writing on glass. You need to try a Wacom texture based surface device like Mobiscribe

[gray gazelle]

this reads like an advertisement

[hearty steppe]

or get a Wacom tablet for cheap and see if you like that texture. Don't mind the accuracy/precision of a cheap wacom tablet

I really like my e-writer tablet mate, I wouldn't go off about it if I didn't lol

and its way cheaper than a ReMarkable

[broken meadow]

i see max

[static crest]

it's true, I still only use paper for notes for that reason

paper just feels different, can't replace it

[gray gazelle]

Im a homeschooling senior year this year, what calc book should I use?

[willow pecan]

Steward probably

[gray gazelle]

,w steward

[hasty eagle]

Results provided by WolframAlpha

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

Requested by 88ddda#7872

[willow pecan]

Oh

Stewart

Oops

[marble solar]

spivak

[uncut zealot]

Openstax is free and online. I don't recommend using it as your only book if you can afford to buy an actual textbook, but it might make a good supplement.

(also skip calculus and go straight for baby Rudin)

[willow pecan]

No

[hearty steppe]

I am enjoying baby rudin but id recommend taking an initial two semesters of calculus first at least

Or learning the equivalent

And also some exposure to formal mathematics notation and proof writing

[ancient belfry]

CAN ANYONE SHARE A GEOMETRY BOOK WHICH STARTS FROM BASIC AND ENDS TO THE LEVEL OF MATHS OLYMPIADS PLS

[timber mesa]

why the damn caps

[gray gazelle]

IT'S URGENT

[timber mesa]

anyway, Evan Chen has a nice book on that

[hasty turret]

Not the damn caps

USE THE DAMN CUPS

$\cup$

[timber mesa]

this one https://web.evanchen.cc/geombook.html, as it say there it's literally meant to be a self-contained book that eventually teaches you stuff that's useful for comp math

I've skimmed over it and it seems nice

[pale scarab]

Evans book is good but if your not familiar with geometry already it can be quite challenging. The nice thing is that it has hints and solutions for the problems which can be brutal. Though geometry problems tend to be some of the harder olympiad problems imo. I would start with the AOPS geometry book first then go to evans book

[ancient belfry]

thank you

[ancient belfry]

oh ok

[sick plover]

Even two semesters seems too little

But then what do I know

[analog pollen]

Stewart

It’s got a lot of exercises

So it’s great for studying at home imo

[broken meadow]

i would not recommend reading the book totally in-depth because that's boring but the exercises are good

i would specifically encourage doing as many of the more challenging problems as possible

they would probably be in a section marked as such

[analog pollen]

Yeah

[broken meadow]

even if they're in a section you already know about, i would do them

[analog pollen]

The problems plus section is pretty good

[broken meadow]

like even the first section on functions or whatever

yeah i was prepping for an entrance exam for a calc 3 class

and i straight up did as many of the problems plus as possible

it worked wonderfully

[analog pollen]

Still think some of those problems are almost impossible

With the information given in the book itself

[broken meadow]

some of them are crazy indeed

[analog pollen]

But it has like 70 exercises per paragraph so it’s got a lot

[broken meadow]

yse

[forest blade]

I am new to this field of deep mathematics (at least for me is deep, I am in high school), would Stewart's books be a good recommendation for me too, or should I look for other more conceptual books first?

i say "conceptual" because theres a bunch of simple things i still dont master (like demonstrations of basic things, such as why (-)*(-)=(+))

i mean, (-)*(-)=(+) i know, its just a example

[analog pollen]

I wouldn’t recommend going into calculus without a good understanding of algebra and some basic trig

Idk if you already got that under your belt

I would say that around the level of algebra of 10th would cut it

Cuz you basically already got all of that and some basic trig

At least for me

@forest blade

[forest blade]

Hmmmm ok ok, I'm gonna search for something in this line

Because idk really now how far I already know

I would say I have a good understanding of algebra and got some topics do review in trig

[forest blade]

Im on the top of math on my class, but I don't live in the USA, and the education is probably different, so idk with in behind or above what you would expect from a "really good in math high schooler"

[analog pollen]

What year are you in

I’ll see if your year covers everything

[forest blade]

Im on my second year of the Brazilian high school (we have 3 years of hs here)

[analog pollen]

Oh then I think you are good to go

Stewart’s is a good book for beginners

[forest blade]

But for me is really really easy, even the third year (in my school you can watch others classes)

[forest blade]

Oh ok

[analog pollen]

It still does trig review and logs, exp

I would say Stewart’s will be a good intro then

[forest blade]

Alright, ty, im gonna try Stewart's, in somedays in gonna comeback with the results😔🙌

Ty ty

[analog pollen]

Buy it in the sale tho

In Some countries it’s expensive as hell

[forest blade]

that's why pdf-piracy exists

[analog pollen]

Ohh hahahah also an option

[sinful pewter]

@broken meadow #chill

[broken meadow]

🤔

[gray gazelle]

Any book recommendations for basic number theory? already had a class with very basic stuff like wilson and euler theorems and chineese remainder

[karmic thorn]

You could check the latest pinned message for some recommendations.

[gray gazelle]

carla check out ireland rosen

i could but i already had bad experience with recommended books already in here lol

ireland rosen fits you carla

thanks, i had a bf who was irish, she's a girl now

yeah the book is as dry as your humor

it's not humor it's true

I believe you, just in general

thanks you are a wonderful friend thank you so much

[kind sapphire]

can anyone recommend me a textbook for igcse additional maths

which is clear and covers all the topics

[gray gazelle]

what are the topics

[kind sapphire]

i'm not quite sure about it

[kind sapphire]

mostly the o level topics

[tulip blade]

@kind sapphire that means nothing to people from other countries

[tranquil granite]

Things to make and do in the fourth dimension

Great book for recreational mathematics

[broken meadow]

yeah that's a fun book

[dusty grail]

anyone have any recommendations for PDE books? I want to build a good basis of understanding of the topic so i can better understand some texts on fluid dynamics that i’ve been reading. I’ve currently read about half of Elementary Diff Eqs and BVPs by boyce so i’m not super experienced with DEs but i’m definitely up for a challenge if the book is good.

i’m also not saying i want a particularly difficult book just whatever would give me the best basis of understanding

[willow pecan]

Evans

[tulip blade]

Folland

[willow pecan]

The book is good and will give the asker the best basis of understanding

[dusty grail]

awesome thanks

[stark creek]

can anyone recommend a book on algebraic geometry? i remember that there exists some free book published by a renowned prof but i can't remember the name

oh nevermind, that one was on algebraic topology by allen hatcher

[crude geyser]

if you’re just getting started, fulton has good notes on plane algebraic curves

gathamann’s notes on algebraic geometry are nice

also vakil’s notes “the rising sea” I think are good

[stark creek]

alright cool

will look into these

[gray gazelle]

@hasty turret young's litetal translation, KJV, ESV for english. There are others which are okay too

But use multiple ones for a better understanding

[gray gazelle]

What's a good book for point-set topology?

[willow pecan]

Munkres

[gray gazelle]

Is there an alternative to Munkres

It's expensive

[timber mesa]

I think Stephen Willard's is good and it has a Dover edition

Dover books are inexpensive in general

[gray gazelle]

Thank you! This looks perfect.

Is Topology Without Tears any good?

[timber mesa]

too basic imo

it's a good introduction if like you've never taken a course resembling real analysis

probably the intended audience tbh

[mint tide]

Question what is a good book suggestion for mental math?

[gray gazelle]

Okay, thanks, I'll go with Willard, then

[mint tide]

Specifically ones that don't involve mental imagery

[flint forge]

wait

okay

[flint forge]

unless you really need a physical copy its very easy to obtain it for free

dont use a different book just bc of that

[smoky surge]

thats why I am using it KEK

Im not a math major though so i dont think i will ever need real analysis might go through it for fun

does anyone have any book recommends for a intro to diff eq?

I didnt see any in the recommendations

[willow pecan]

ODEs or PDEs

There is no good ode book

[broken meadow]

nagle saff snider/boyce diprima for ODE

neither books are good

[willow pecan]

The question is, which ode book is the least bad

[broken meadow]

but you can try learning from them

[smoky surge]

ODE's

fuck

ok hm whats the best way to learn ODE?

just khan academy and paul lamar?

[broken meadow]

i have no idea

[smoky surge]

KEKW

[broken meadow]

i mean those sound like good supplements

a book doesn't hurt either

[smoky surge]

I guess are there any books with good problems

[broken meadow]

like for exercises too

[smoky surge]

yyea

exactly

[broken meadow]

the ones i mentioned have exercises

a lot of them are kind of bad but like

idk

not a lot of good options lmfao

[smoky surge]

kinda interesting that there arent any good diff eq books

suprised tbh

[broken meadow]

after two semesters for me

i am not surprised

the content is just

Pain

[smoky surge]

poorly taught or confusing?

[broken meadow]

at this level

[willow pecan]

Undergrad ode is excessively computational

[broken meadow]

there's no good way to do it at this stage

[willow pecan]

There is some interesting theory but it requires much more background

[broken meadow]

like you will suffer

[smoky surge]

yea im just going through ODE for myself mostly cause apparently for some computational nueroscience you need it

[willow pecan]

Variation of parameters/undetermined coefficients is literally guessing the solution

[smoky surge]

wait would you recommend just skipping ode and coming back later?

[willow pecan]

And the proper way to handle odes in practice is numerically

[smoky surge]

like how much more background

[broken meadow]

im not sure

[willow pecan]

Well

[broken meadow]

what parts of ode do you think u will need for the comp. neuroscience

[willow pecan]

The theory that I mentioned is also useless in practice

SL theory doesn't solve anything in practice

[smoky surge]

honestly no idea just started going through it

was doing more imaging but im interested in comp nuero and apparently it uses dif eq alot

[willow pecan]

Are you doing odes because of that neural ode paper

If so

[smoky surge]

no

[willow pecan]

Then that's a bad reason

Ok

Good

[smoky surge]

idk what you are even talking about didnt see it

is it a bad paper?

[willow pecan]

It won the neurips best paper prize a few years back

It was a cool idea

But there have been no further results published in that direction

[smoky surge]

ahhh

[willow pecan]

Which suggests that it was not a fruitful line of research

[smoky surge]

i guess I can just half ass it ODE's via khan academy and paul lamar and see if I can make sense of what is going on

and find exercises to practice

[willow pecan]

In practice, the proper way to deal with odes is

1. Plug it into Mathematica to see if it has an explicit solution

2. If it doesn't you use numerics

You can frequently skip 1 as well

[smoky surge]

hahahahah ok

[pale scarab]

Probably better to just use a app to work on speed. Most is just practice keeping numbers in your head. Arthur benjamin has a decent boom that covers a few tricks. I had my mental math pretty sharp when I was tutoring a lot and tried to practice solving everything in my head before they worked out a problem. Its kinda useless though and in reality even in heavy computational classes(or science classes) you will still end up using a calculator anyways.

[pale scarab]

My least favorite class ever. I would just get a schaums outline book to practice a ton of problems. It was mainly memorizing a bag of tricks and applying them over and over.

[karmic thorn]

I would suggest taking a look at Shepley Ross' Differential Equations in any case

[broken meadow]

i wish this ode 2 course had idk like

analysis as a prereq

so that maybe i could understand some of the shit that was going on

[willow pecan]

[broken meadow]

rn it feels like a lot of computations but like they're Fancy™️

and deal with functional spaces and stuff

fancy words and fancy math but it's the same garbage

[karmic thorn]

I'm digging into dynamical systems hoping to find some motivation to learn about DEs

[gray gazelle]

dynamical systems

i took a course on this and learned literally nothing

[karmic thorn]

Tried it, couldn't bear with it

[karmic thorn]

Why????

Was it heavy on background?

[gray gazelle]

no

it was too light on background

the CS major math courses were the prerequisites

[karmic thorn]

Lmfao

So you actually learnt nothing because you already knew most of the stuff?

[gray gazelle]

no we just didn't really do much of substance

[karmic thorn]

Oh

[gray gazelle]

you could tell the prof really wanted to do some serious mathematics

but like 80% of the class were CS majors who've never seen anything past calc 3

so a huge chunk of it ended up being related to simulating very simple systems in python

python...

now this isn't a bad thing inherently

but it amounted to filling in code templates the prof made and that sucked balls

[karmic thorn]

Oofff

[gray gazelle]

the only things i remember from it are like

angle shifting on the circle

[karmic thorn]

DS would have been a fun class, and a valuable edition to your physics toolkit

[karmic thorn]

I see

What all did your class end up covering?

[gray gazelle]

consider the $\bR$-action on $S^1$ given by $$x \cdot e^{i\theta} = e^{i(\theta + x)}.$$ describe the orbits for $x \in \bQ$ and for $x \not\in\bQ$

[willow pecan]

[hasty eagle]

R2T2 ✓

[gray gazelle]

this is the only thing i remember

wait

i have it bckwards

dont i

[willow pecan]

Tbh I don't really know why dynamical systems are interesting

[karmic thorn]

[willow pecan]

It's just like

Worse odes

[gray gazelle]

ok i think i phrased it incorrectly but you want to rotate a point on the circle through an angle

[karmic thorn]

I can send some notes here, they're from the ODE and Dynamical Systems class Stefano Luzzato teaches ar ICTP

[karmic thorn]

Gotcha

[willow pecan]

I'm going to be honest I'm not going to read them

Even if you do send them

[karmic thorn]

Smh

[willow pecan]

Like it's just not going to happen

[karmic thorn]

I have no choice but to spread propaganda against ORV now.

[willow pecan]

[gray gazelle]

something something if the angle you rotate through is irrational you get a dense orbit

[ripe granite]

ORV?

[willow pecan]

ORV is a modern masterpiece

Omniscient Reader's Viewpoint

Irrational rotations are dense

Rational rotations give roots of unity

And are not dense

[gray gazelle]

[willow pecan]

You can prove this with Fourier techniques

[karmic thorn]

ORV is the most awful pieces of literature that have happened to the modern world

Million words of boredom and meh

[willow pecan]

Lol cope

[karmic thorn]

No u

[ripe granite]

no

[willow pecan]

Yeah I did I said that I didn't understand why they are interesting

Am I wrong

It is...

[ripe granite]

this is your applied math on brain

[willow pecan]

Anyways

A lot of people are saying I'm wrong

But no one is saying why

Ok

I don't understand why combinatorics isn't worse arithmetic

You're counting

[karmic thorn]

[willow pecan]

[steel viper]

applied math

not even once

[willow pecan]

No regrets

[narrow echo]

[sage kelp]

Hogg or Larsen for introductory mathematical statistics?

[karmic thorn]

I've seen a bit of Hogg and found it to be good

[silk shadow]

i second Hogg

[wicked nymph]

any IIT aspirants here help me pls

[inner mantle]

yes

[wicked nymph]

do u know resonance academy?

[inner mantle]

yes

but I am in fiitjee

[wicked nymph]

oh nice im in 11th in resonance

shall i do only the modules or shall i solve some books too

[inner mantle]

I am in 9th :p preparing for nsep, nsea and jee as well

[wicked nymph]

oh

nice

[inner mantle]

any tips?

[wicked nymph]

u are in fitjee?

[inner mantle]

yeh

[wicked nymph]

is it good?

[inner mantle]

yes bro

idk about 10, 11 and 12

[wicked nymph]

ohh

[inner mantle]

but 9th class they are comprehensive

I am there for 4 yrs classroom program

[wicked nymph]

oh nice

[vagrant sedge]

Has anyone here studied from David Bachman's "A Geometric Approach to Differential Forms"?

Just saw this from the book and got quite disappointed tbh

[karmic thorn]

Why so, is this incorrect?

[vagrant sedge]

well, it's sloppy, in a sense. Strictly speaking, sure, it is incorrect.

The example of cos(2t), sin(2t) isn't one-to-one

neither of the examples are functions defined on R, but on subsets of R

and \phi, there, doesn't have to be onto.. it's image is supposed to be C

a function from R to R^n onto is supposed to have R^n as its image and be defined on the whole R

I mean... it is sloppy writing

that looks like formal mathematics... that is kind of frustrating to me

The usual, afaik, definition of a C^k parametrization that I know of is a C^k function defined on an interval of R into (but not onto) R^n whose range lies in the curve.

[karmic thorn]

Oh, I can't believe I let so much sloppiness slide lmao

That makes a lot more sense, yeah

[vagrant sedge]

I was just wondering if the book is good (I've heard great things about it) even if it has these kinds of things in it.

[timber mesa]

I think it's a common thing in diffgeo, bit of a "you get what I mean" thing

not sure about the book never heard of it

[vagrant sedge]

Ahh ok. That is good news tbh 🙂

btw... @timber mesa Are you Brazilian??

[timber mesa]

nope

[vagrant sedge]

Ok. Thank you all 🙂

[silk shadow]

hmm for me a parametrization is a smooth mapping from a subset of R to R^n

[analog pollen]

Where can I find all the answers to questions in Stewart?

Is there some kind of Website for that?

[tulip blade]

For most of the calc questions you can use an integral or derivative or limit calculator to check

For the word problems try looking it up

Or search stewart calculus “your edition” answers

[halcyon garden]

Hey has anyone here used the G. Simmons differential equations book? Is it any good(from an applied math perspective)? Would I be able to learn it with one sem of LA and one sem of RA ?

[hearty steppe]

Gene Simmons made a diff Eq book?

[willow pecan]

Is it an ode book or a pde book

[hearty steppe]

You can try Slader

[willow pecan]

Ah I see

I will say that from an applied math perspective, it probably doesn't do enough numerics

Also power series solutions and special functions are of decreasing relevance

https://www.maa.org/press/maa-reviews/differential-equations-with-applications-and-historical-notes

Here's a review from the MAA

But I'm going to be honest, there is no good ode book

Because there is no good ode class

[gray gazelle]

differential forms textbook

[obsidian valley]

i heard tterra took a good ode class

[gray gazelle]

correct

[willow pecan]

[gray gazelle]

well maybe 75% good, the computation parts sucked balls

good thing the focus wasn't computation

[willow pecan]

What did it cover

[obsidian valley]

i met someone who is transferring to UTSG and is taking 257 and 267

im jealous

stupid me

[gray gazelle]

some stuff about linear systems and matrix exponential, behaviour of such systems (eg as dictated by eigenvalues). existence and uniqueness (picard lindelof) and behaviour of non linear systems. a lot of linearization and stuff. something near the end about lyapunov stuff

idr specifics

[willow pecan]

Sounds like a baby dynamical systems class

[gray gazelle]

tfw i took two baby dynamical systems classes at the same time

[willow pecan]

[gray gazelle]

[marble solar]

I dunno spivak seems good

[narrow talon]

Why is Kallenberg actually a better intro to measure theory than Rudin

Seriously, anyone who wants to learn measure theory quickly should just read the first two chapters of Kallenberg and then look at some examples since there are basically none

Oh jeez apparently there's a new edition of this published this year, seriously anyone learning measure theory next semester should take a look at the first section of the new third edition or the first two chapters of the second edition, they're quite good (if abstract as hell)

[marble solar]

I'm a big fan of the stein and shakarchi series

I like volume 3 for measure theory - I think it does a good intro w/out getting bogged down

[narrow talon]

Kallenberg is definitely much more terse and advanced than many measure theory books (outside of GMT texts), but surprisingly readable and possibly a good choice for someone interested in probability

[timber mesa]

ODE courses should be replaced by babby dynamics

[timber mesa]

in fact our department's undergrad ODE course is pretty much this + boring computational stuff the physicists need

[flint forge]

Are there good expository resources on differential forms and deRham cohomology that might be readable after a first course in analysis and measure theory

One of my mentees is interested in analysis and algebra and topology

are you referring to an entire textbook lol

that might be unavoidable I guess

oh nice

[lament sage]

that short text was suprisingly enlightening

[timber mesa]

is it Kallenberg's Foundations of Modern Probability?

[sinful pewter]

@broken meadow #chill pt. 2

||<#chill message>||

it's what I did last time lol

[willow pecan]

The correct thing to do is to message modmail

[sinful pewter]

idk this word "modmail"

[willow pecan]

It's at the very top of the list of server members

[sinful pewter]

Ah yes usually I feel bots are inferior so I ignore them 😔

[willow pecan]

[broken meadow]

modmail is preferred

because nothing gets buried

[narrow talon]

That’s the one

[warm glen]

does anyone know what resources i could use to learn about the erlangen program, and what the prerequisites would be for learning about it?

[wicked nymph]

is objective maths by amit m aggarwal good enough for jee preparation

[hasty turret]

Probably not

[pale scarab]

Any resources for condensed mathematics and the work by scholze and clausen at a non research level?

I guess a basic blog post or expository type paper on what they are trying to do?

Thanks thats what I was looking for

[flat bay]

Hey guys, i want to learn more about algebra/calculus any idea which books i could get? There are so many options and i am kinda lost. I know already the basics of both algebra and calculus but i want learn more and improve my skillz

[gray gazelle]

dummit foote for algebra and spivak for calc homie

[flat bay]

Is it advanced?

[gray gazelle]

starts from basics

[sage python]

There is no way the algebra he wants to know is D&F

If people pair "algebra and calculus" it means high school algebra I feel

[flat bay]

yea that's what i mean

sorry forgot to turn off ping

looking to study CS and i want to be ready for the math

[sage python]

So yeah idk about algebra books tbh

But I'll say that "Khan Academy" is overall a source people like for learning math

Spivak Calculus is a good book if you want to know theory, so learning math the way mathematicians learn it. Definitions are very formal etc

[flat bay]

i already know calculus not like crazy but i know derivatives and a little bit of integrals. And for algebra i would say i'm OK but there is room for improvement

[void sable]

does spivak get deep into analysis ?

[flat bay]

I want to have something that i can follow yk? Like a book so i can look up chapters etc

[sage python]

If you're in CS it's probably a bit 50/50 whether you care about that theory, more likely than not it's a bit of a distraction

[flat bay]

Otherwise i get super lost

[sage python]

Stewart is the standard calculus book

[glossy grove]

by studying calculus, you will improve your algebra skills anyway.

[flat bay]

ig :p

[sage python]

Buying a new copy at full price is not worth it though, I don't think any calc book differentiates itself enough to be worth fuckin $200 or whatever the cost is

(haha differentiates)

[flat bay]

so i should go with calculus?

[sage python]

If you've mostly got algebra down then sure you can use calculus to practice algebra

Simplifying the expressions that you get in calculus problems etc

[glossy grove]

what's biocalculus? 0.0

[flat bay]

that's the thing, my algebra is a bit rusty and i always find my self looking up the algebra rules

[sage python]

Well again I don't think buying full price Stewart is worth it

If you can get a used copy or something that's better, otherwise you can roll with any other calculus book in all likelihood

[flat bay]

yea that's what i am aiming for lol no way i am paying that much

[analog pollen]

There is always a pdf version of the book

[analog pollen]

Calculus with applications to biology

[glossy grove]

for what do you need calculus in biology?

[analog pollen]

Like rates of change of blood flow

Stuff like that

[flat bay]

I'm not sure which one i should start with. there are like 12 versions

[analog pollen]

PDF?

[flat bay]

Already got a book about derivatives but it's super simple and basic

this

[analog pollen]

9th edition is he newest

[flat bay]

Do they all cover the same thing?

[analog pollen]

Yea

Only like 6th edition got second order diff eq

[flat bay]

oh

[analog pollen]

But it’s all pretty much the same

[flat bay]

oh great

i got confused, i thought they were complementary books

[analog pollen]

But newer version I would say would be best if you are downloading the pdf

[flat bay]

do you know what that pirate website is called?

liber?

[analog pollen]

If you are gonna buy the book I would say find an older version

[flat bay]

or something lol

[analog pollen]

Yeah idk

You can just look the pdf up

No site needed

[prisma snow]

Love Indian Books: General Education Nourishment

[flat bay]

yea, you are right

[flat bay]

das a book?

[prisma snow]

No that's a hint

[flat bay]

[prisma snow]

Capital letters are capitalized for a reason

Grammar

[glossy grove]

[azure pagoda]

How's Niven's textbook for number theory? I'm taking a class that uses this textbook and am wondering if I need any other reference book besides it (for example Hardy).

[broken meadow]

i've only seem the first few chapters, it seems nice enough

i don't think you need another book to go with it if you have a professor i think

[azure pagoda]

thanks!

[tulip blade]

LIBturd GENeration

[hearty steppe]

I still don’t think pure biologists will understand the intuition behind this mathematically and that’s a problem obviously

[hearty steppe]

For biophysics, bioinformatics type of stuff obviously.

Mathematical biology too

[willow pecan]

Oh

I gave a talk that covered Poiseuille flow

I think you would be surprised at some biologists

[hearty steppe]

“Some”

Other than being like “oh I use this formula for this”

[willow pecan]

My undergrad advisor is currently collaborating with some biologists at UCSF about an artificial pancreas

[hearty steppe]

Nice

So you have interest in biology research as well?

I’m mostly spending a lot of time rn just learning enough to do something interesting with my blog

[willow pecan]

No

I don’t do lab work ~~~

[vagrant sedge]

Hi... sorry for the re-asking of this. I've asked this here already some time ago. I'm going to re-ask (sorry about that) just to see if maybe I get better answers...

What is a good book to learn about integration over differential forms? The "whole vector calculus" thing, etc.

Assuming, for example, one just finished bartle's elements of analysis book (which doesn't cover that sort of stuff)

[hearty steppe]

You don’t have to do lab work per se.

[willow pecan]

Biology is an empirical science

[sudden kindle]

Some possible books are: Spivak Calculus on Manifolds and Munkres Analysis on Manifolds

[hearty steppe]

Yes but there is also the aspect of analyzing the nature of biology through mathematics and physics

[willow pecan]

And doing biology without experimental validation is worthless

[hearty steppe]

So you can work with people that do the lab work but you wouldn’t be doing the actual lab work

[willow pecan]

Sure

I consider that applied math

[hearty steppe]

I suppose it depends on how you are working with biologists too.

Maybe you will be indirectly doing lab work

It would be nice if you decided to experience that effort and then tell me how it’s like working with biologists 😛

[willow pecan]

[hearty steppe]

Maybe your advisor can tell you more about it or something cause I’m curious about personal experiences

[willow pecan]

I’m not

[vagrant sedge]

@sudden kindle Ok. Thank you.

@sudden kindle I'm currently going through David Bachman's one. It seems kind of informal and more computation, which I guess is a good start for me since I've never studied that before.

I have already (without much understanding on many things I must admit) read through Spivak's Calculs on Manifolds (up to the chapter before the last one). I intend to go back to it later on.

David Bachman's one: https://www.amazon.com/Geometric-Approach-Differential-Forms-ebook/dp/B00FBG7T6G

[hearty steppe]

It’s cool mate I don’t blame you if that area isn’t your cup of tea

[karmic thorn]

You could also check out Hubbard & Hubbard

The book title is Vector Calculus, Linear Algebra and Differential Forms iirc

[tame coyote]

Tory Lanez vs the number 27 and 42

[flat bay]

Is arithmetic related to algebra? Any thoughts on book "Arithmetic the Easy Way"?

[flat bay]

is it good for learning algebra/improving in algebra?

[vagrant sedge]

Ok. Thank you.

[analog pollen]

He question that was asked was ‘what is bio calculus’

[gray gazelle]

The bible

[flat lantern]

Da broble

[languid shard]

Peter nimble and his fantastic eyes 👍

[warm blade]

anyone have recommendations for reading about , other functional analysis approaches to quantum mechanics? I've been reading Hall's book and like it, but id like to learn more about the func analysis stuff

[gray gazelle]

@sweet lotus

they probably know

[gray gazelle]

should i not have pinged

[gray gazelle]

pedersen's "analysis now" is a good book.

[worldly glacier]

The Green-Eyed Dragons and Other Mathematical Monsters
Does anyone have pdf version of this book?

[daring reef]

For ODEs, does anyone have thoughts on Arnold vs. Perko? I'm looking at the contents of both books and they seem pretty different, but I also don't really know a second thing about ODEs so idk. Here's the table of contents for Perko: https://imgur.com/a/7W7Tq5b, and here's the toc for arnold: https://imgur.com/a/bCNY4Hy. my background is an intro to diffeqs class (mostly computation of linear systems and other solvable first/second-order ODEs), and my goal is to just self study some of the important theorems and gain a decent intuition of ODEs since i dont plan on taking any more courses in the subject for my undergrad

[willow pecan]

They sort of go in different directions

What are your mathematical interests?

Perko heads in the dynamical systems direction

While Arnold seems to focus more on diff geo things