book-recommendations

[remote sparrow]

seems like a smart guy though

is it open source, or just free?

ah, yes, there is latex source code

[orchid mortar]

I never really built it but seems open source to me
https://bitbucket.org/ben-crowell/lm/src/master/lm/

[remote sparrow]

https://openstax.org/details/books/college-physics

not sure whether this is open-source, but it is free

[sturdy flame]

university physics from that same website is for calculus based physics. i used that one and it was pretty good

he also has a youtube channel where he’s solved a handful of problems if you are looking for physics problems -

https://youtube.com/@gajendratulsian4335

[dusk crater]

i'm tring to read a book called Algebra and trigonomety by micheal sullivan

but within a few min i get bored

what should i do

[meager path]

So I'm not sure where to ask this, this might be the most relevant place; I'm after a sort of chart relating to sets and Venn diagrams in terms of the union sign, similar signs and equations to reference to try and remember from. Any suggestions? 🙂

[swift dome]

read another author book

[fiery radish]

Anyone got any good books or pdfs on Number Theory?

Ping me or dm me if you have any

[finite gale]

what level of number theory are you looking for?

[fiery radish]

currently i know lcm, gcd, divisibility, modular arithmetic, division algorithm, remainders, multiples but i would like to know more number theory so that i can win math competitions that have number theory questions

[finite gale]

i don't know much about math competitions resources, but hopefully someone else will answer

might help to ask in #competition-math as well

[fiery radish]

ok

[thorn orchid]

Anyone into Group Theory? I've never been a big number theorist but it comes up a bit in finite group with prime powered cyclic groups.

[fierce hedge]

Do you want group theory book recommendations or want to talk to people who know gt? In the case of latter try #groups-rings-fields

[thorn orchid]

Oh sorry @fierce hedge yes any book recommendations would be great I love the Fraleigh book but doesn't cover lie groups so if anyone knows I good recommendation for that it would be great. I need a readable book introduction.

[grand thistle]

are there any resources on like topological results like homotopy, the fundamental group, and perhaps even (co)homology from a more analytical perspective?

[formal bronze]

Check out 'Elementary Number Theory' by David M. Burton.

[hazy elk]

Maybe Fulton? He starts the book with complex integration and winding numbers and ig leads to homology. But idt the material is analytic apart from the initial motivation

Fulton, algebraic topology btw

[grand thistle]

got it

i was thinking more of a

measure theoretic or functional analytic perspective rather than a complex analytic one

since i was actually looking for resources on these topological things for complex analysis itself (thinking of reading schlag or miranda sometime)

[gray gazelle]

hello what's a decent general purpose book to teach myself mathematics as a highschool student

[grand thistle]

lang's basic mathematics

[gray gazelle]

it would be nice if it included things like the binomial theorem and basic statistics like nPr and stuff like that

I need it

[swift dome]

#books

Might check it out, and see topic which you wanna learn and pick a book

[digital sandal]

I'm a pretty dumb engineer, but somehow my job has actually become extremely mathematical, and I need some books that I actually have the background to understand... Main topics would be numerical integration of systems of delay differential equations, non-linear regression (I need to fit model parameters to said ddes), and robust estimation of measurement variance.

My background: chemE undergrad with a minor in statistics

I've take all the normal calc. classes, linear algebra, odes, some pdes

[remote sparrow]

burton or dudley are good. you can just quickly pass through the topics that you've covered already. though like most math books, they are not designed to help you win competitions, but rather to build theory.

[orchid mortar]

These are some hard topics...

[pale scarab]

Are there any other books in the style of algebra by aluffi? Like areas of math but using the language of category theory more. I'm enjoying this book now and would like to relearn other areas in a similar way

[digital sandal]

Yes, lol

I have experienced that first hand

[orchid mortar]

Do you have to actually understand

[remote sparrow]

niven, zuckerman, and montgomery also has some elementary chapters on number theory, but i'm not sure whether you're in high school or college given you said you were doing this for math competitions @fiery radish

[orchid mortar]

what about 'just applying'

[digital sandal]

I don't need to understand everything

[remote sparrow]

i've only heard of tai-danae bradley's topology book

[digital sandal]

I just need enough context to use the right tools and diagnose problems

[orchid mortar]

For anything non-linear I recommend at least trying some 2 to 5 layer neural network

[remote sparrow]

where she does topology from a category theoretic lens

[orchid mortar]

For variance estimation, just use some econometric-derived variance estimation

That is at least a base

After that you can move on to more interested ways they do variance est

I can't say I have seen DDEs

Queues maybe

I know enough about queues to know I know nothing about queues

[digital sandal]

Mhmm, a neural network doesn't work exactly for my application. One of the goals is to have the underlying model reflect some scientific intuition.

[remote sparrow]

you might also get some recommendations in the physics discord (see #old-network for an invite link)

[digital sandal]

There's biological kinetics involved

[orchid mortar]

<- this is pain inside

Sorry I can't really help. I have 0 pharmacokinetic background

in fact IDK where you gonna find help

Have you tried the chem and medicine servers too

[digital sandal]

No, came here first

[orchid mortar]

I strongly doubt you can find help on discord

[digital sandal]

Everyone at my job (who are in chemE and biology) say the math is over their heads

[orchid mortar]

it's 'easier' if you get a footstep in

And ask more specific questions here

on specific mathematical questions

for example I think DDE would have some analysis on them

don't know if you need to read Stein Shakarchi

[digital sandal]

no

I've read research papers and found some books on ddes

But they all assume background knowledge that I don't have. I can get some useful information, but I don't understand 90% of it

[orchid mortar]

You'd probably need an introduction to control

[remote sparrow]

you could ask the appropriate subreddit

try explaining to r/math first

they might help point you in the right direction at least

[digital sandal]

Yeah, I might have to get my questions and confusions into better order

"introduction to control"

[orchid mortar]

ok

[digital sandal]

As in process controls?

[orchid mortar]

I was wrong about the control

no

(Optimal) control theory

That's one case they do DDEs

But it's not the only way

[digital sandal]

I had an engineering course on controls, and there's definitely overlap

[orchid mortar]

https://www.chebfun.org/examples/ode-nonlin/DelayDifferentialEquations.html
ODE nonlin

it's clearly in advanced stuff

[digital sandal]

Yes, this is the sort of stuff, but I have software working that can solve the IVP like in that example

But setting the simulation parameters over the whole parameter space has been very difficult

[orchid mortar]

Because of speed? Stability?

[digital sandal]

I can't seem to predict when I will need relax the tolerances to avoid insanely long simulations

[orchid mortar]

The 'lazy' way to do large parameter spaces is to use a random grid

[digital sandal]

Both

[orchid mortar]

so your parameter surface is crazy too huh

[digital sandal]

😦

I can usually make it fast by relaxing tolerances

But that can lead to non-physical results

Thanks for the help though

[fierce hedge]

I thought I replied but anyway, Artin has a bit of Lie Algebra. For more you can check Basic Algebra by Jacobson or his book especially on Lie algebras

[fiery radish]

@remote sparrowim in high school

[fierce hedge]

Fraleigh pdf mentions some type of videos as an aid but I couldn't really find any link. Is this some kind of paid feature of the newer Pearson copy

[crimson leaf]

If you know Linear Algebra you could probably read erdmann introduction to lie algebras from there you can probably learn a few more things then get into rep theory and lie groups. There's also hall intro to lie groups and lie algebras which is pretty good but iirc it only works over matrix groups ( I forget the exact name btw it's like lie algebras, lie groups, and representations by Hall)

[gray gazelle]

what are some good books on set theory?

[remote sparrow]

naive or axiomatic

[gray gazelle]

mix of two would be great

[remote sparrow]

i don't believe there is such a thing

naive set theory is about getting to some basic set theoretic results that are useful in further mathematics, but not necessarily for set theory itself

a set in such a book is defined as "a collection of objects" and it's called naive because such a definition falls prey to russell's paradox

an axiomatic book gives the axioms that define a set such that russell's paradox is not an issue

[gray gazelle]

so maybe axiomatic

since i want to dive deeper

[remote sparrow]

you can look at enderton, goldrei, or hrbacek and jech

[cobalt arch]

I think that is what enderton does with his book, he states:
It is nonetheless quite possible to study set theory from the nonaxiomatic viewpoint. We have therefore arranged the material in the book in a "two-tier" fashion. The passages dealing with axioms will henceforth be marked by a stripe in the left margin. The reader who omits such passages and reads only the unstriped material will thereby find a nonaxiomatic development of set theory. Perhaps he will at some later time wish to look at the axiomatic underpinnings. On the other hand, the reader who omits nothing will find an axiomatic development. Notice that most of the striped passages appear early in the book, primarily in the first three chapters. Later in the book the nonaxiomatic and the axiomatic approaches largely converge.

[gray gazelle]

i found that this book have very little exercises where could i find more of exercises on the exact topics?

[cobalt arch]

There is a book by schaum's for set theory that you could check out

It has solved and unsolved problems

[gray gazelle]

oke

btw why do more advanced math books have so few exercises?

[remote sparrow]

which book

i gave three books

[remote sparrow]

because they're not trying to bore you with 5000 drill exercises

there are fewer problems because each should require more thought

[gray gazelle]

ye that makes sense but still there could be a little more

[broken meadow]

If you can solve all the problems presented you should be okay

[gray gazelle]

yeah right maybe im too worried that this could not be enough for me too learn

[gray gazelle]

ye and i have a book that didn't even try to bore me with 1 exercise

lol

[remote sparrow]

btw there are lectures to go with the enderton book

[gray gazelle]

could link them or smth?

[remote sparrow]

https://www.youtube.com/playlist?list=PLjJhPCaCziSQyON7NLc8Ac8ibdm6_iDQf

[gray gazelle]

ty

[gray gazelle]

if i want to pick one which one do you reccomend?

[remote sparrow]

enderton is good

just try one and if you don't like one, go through another

[sterile harness]

I’ve got a friend who wants to self study Linear Algebra over the summer. His background is Calc BC (calc 2) with almost no exposure to proofs. What would be a good set of resources for him to study?

[remote sparrow]

#book-recommendations message

[ancient sand]

any recommendations for a modern introduction to number theory?

^ not, like, an entire textbook though please

[heady ember]

I have 1 section and 2 chapters left in Enderton, I throughly enjoyed it so far

I shill Enderton

[swift dome]

https://home.cs.colorado.edu/~alko5368/lecturesCSCI2820/mathbook.pdf

[swift dome]

just wondering if i get some recommendation on DSA / analysis of algorithms in python.

[fossil arch]

What’s a measure theory book with some exposition?

Like not just definition -> theorem -> proof dryness or throwing random ideas at you and you have to wait 40 years to see why they’re important, a book where the author is conversational and gives a preview of what they’ll do/builds motivation in every chapter/section

[remote sparrow]

axler or tao i guess

[fossil arch]

Particularly interested in eventually going onto stuff with differential equations and/or harmonic analysis, so anything that builds towards functional analysis would be cool too!

[marble solar]

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

So volume 3 of S&S real analysis would be fantastic

[fossil arch]

Yeah I’m skimming through S&S, it’s not awful but I would appreciate more conversation between the definitions 😛 though I’m still only early in so maybe I just need to give them more time to build up basics

[gray jungle]

Real analysis by Folland goes into some basic forier analysis and has functional analysis in it altho it can be a bit dry here and there but you can have it as a reference

Measure theory by Donald cohn is a more friendly book

[vagrant wigeon]

If you're started out in calculus, I recommend 'An Analytical Calculus' by E.A.Maxwell. He explains the basic concepts and some of the less talked about things as well. It's really old though, I don't know if you can find it easily

[fierce hedge]

How much measure theory is required at grad level assuming I won't be doing research level analysis or some measure theoritic in near future. Is the exposition in Browder enough or something like Folland is a requirement?

[grand thistle]

i like folland

[ocean mulch]

Tao?

[ocean mulch]

Oh, measure. Princeton's Lectures on Analysis, book III

[ocean mulch]

Yes! Book IV is functional analysis

And it's not dry at all. That series really saved my ass

[digital sandal]

Yesterday I was asking about books potentially on delay differential equations and non-linear regression (that were also hopefully introductory). I've realized since then that I need something easier to work up to ddes, for which I've found many detailed books/research articles (all of which I don't have the back ground to understand). Does any one have a recommendation to learn more about numerical solution to systems of differential equations, in general. I'm hoping for something that picks up where a typical ode/pde undergrad class would leave off and eventually get to stiffness, error control, RADAU IIA methods (and related concepts).

I haven't taken real analysis, but I wouldn't mind working through that if it was strongly recommended before moving to my interests above ^^

[dusk crater]

#resources

[swift dome]

Any book recommendation on algorithms in py

[wispy pebble]

mwahaahaha

[coral prawn]

Boom

[zinc crypt]

how can one self study analysis with no prior knowledge
people are tellign me how to prove it by vellman is a good proof intro book

[civic python]

Yeah. If you want to do real analysis, it would be advisable to have prior experience writing proof

(I personally believe "How to prove it" is pretty good)

[zinc crypt]

ohh okay

should i go thru the how to prov eit book?

and from then can i go straight into a analysis book?

[gray gazelle]

what can i do if my book has very little exercise?
try to come up with examples for theorems or maybe prove as much theorems as possible?

[remote sparrow]

have you tried attempting the exercises first?

maybe you will find the exercises given are enough

[sturdy flame]

.

[gray gazelle]

ye i looked at them and the problem is they occur in random subjects so and there is like max 2 of them i looked at one and it seemed kinda easy because i already know some of that subject

[vast raptor]

Does Vladimir Arnold's ODE's require analysis as a prereq

[remote sparrow]

i think so

[civic python]

I don’t really know you so I can’t really give you any solid advice. But, I thoroughly studied How To Prove It and found it immensely helpful. If you are a novice to proofs it should substantially add to your mathematical maturity. Furthermore, having done proofs, you will see math for what it is, rather than what school might have made you think.

[zinc crypt]

ohh okay for sure

shld i go thru every chapter

[civic python]

The first chapters are probably going to be the most useful to you. But I think almost everything is relevant

Try to do many excersizes

But yeah, I think its a good idea to go over "How to prove it". It essentially taught me how to think like a mathematician. Thorough understanding of the proof strategies will help you immensely later.

[zinc crypt]

ohh okay

[zinc crypt]

awesome

will this book help for intro to analysis

[civic python]

Yeah. I'd say you need previous experience with proofs before jumping into analysis.

But it depends of course, I'm assuming you don't have instructors? A book like baby rudin definitly requires experience with proofs, while abott's analysis might be a bit easier in that regard.

In "How to prove it", you will generally mostly be dealing with proofs in discrete math. Analysis proofs are a bit different in flavour.

(Altough, Vellman does actually include excersizes that cover the epsilon delta definition of limits)

[crimson leaf]

Schroder analysis could also be an option for you he introduces proof and stuff in the book. Also tao analysis you can read instead of a proof as the appendix along with early chapters contain everything you need.

The appendix in Schroder also has stuff you'll need

[heady ember]

I don't really think there's a need to read an intro to proofs book. If you use Rudin without mathematical maturity you will get slapped into oblivion. If you use smt like Schroder it'll probably be much gentler and he actually gives detailed explanations and explicitly tells you about some proof techniques used in earlier chapters. So really depends on the book

I read Enderton without intro to proofs and it worked out

[thorn cloak]

if uh, rudin is the book ur first proof class is using, would you then recommend reading an intro to proofs book 😅

[zinc crypt]

is there a pdf for that

[remote sparrow]

there are pdfs for both

[crimson leaf]

Yes if you know where to look

[zinc crypt]

oh okay

[zinc crypt]

can schroder be read by someone with little to no math knowledge

only a little bit of calculus

[crimson leaf]

Probably? You can certainly try

[zinc crypt]

what would i do if im confused on a section

wld i google like what the symbols mean etc

and whatre some good ways to review math books and rlly understand whats going on

[crimson leaf]

For questions you can ask on this discord. For symbols if they're not explained in the book or the appendix (I would suggest you read that first) then you can Google them or ask here. For me to really understand what something means I have to think about what's being said and doing as many exercises as I care to

[zinc crypt]

ohh okay

thank you

[swift dome]

Tao

But i think tao analysis is bit rigorous.

[gray gazelle]

I just read "humain, trop humain" a book written by: Friedrich Nietzsche, a great philosopher of modern philosophy, one of the best philosophy books I have ever read.

[fickle bough]

mastery over the basic proof techniques if you have any gaps they'll show up

I definitely recommend book of proof

even has a small intro to analysis part but don't expect too much it's just giving a very small taste

but yeah gets you to the level of proof writing you should have prior to attempting analysis

even knowing proof techniques some analysis books are difficult but atleast you'll have the tools to be able to understand what's going on

[full kestrel]

Any recs for statistics and discrete mathematics

[loud cradle]

do you know any probability already?

[full kestrel]

Well I’m taking an intro to stats and probability in the fall

So a beginner book would be great

And I guess whatever book to follow as well

[full kestrel]

So for a straight answer no

[hollow shore]

rosen is pretty good for discrete math

there is really nice lecture series which follows the book

[full kestrel]

That’s exactly what I’m looking for

Where can I find the lecture series or is it with purchasing

[loud cradle]

this book by freedman etc. is very introductory and doesn't require you to know any probability (they teach some probability as needed)

https://www.amazon.com/gp/product/0393929728

[full kestrel]

This is great thanks

[hollow shore]

https://nptel.ac.in/courses/106108227

it's free btw

[full kestrel]

Oh awesome

[modern crag]

What's a good book for supplementary algebra and trigonometry, I have encountered these subjects before, but I am just looking for good refreshers for a calculus course

[heady ember]

Yeah sure just have to have some level of perseverance, as standard for any math book

[bronze halo]

hello

any book recommendations for trig?

[fallow cypress]

This depends a lot on the professor tbh, you can go through rudin fast or you can go through it gentler

[fallow cypress]

If you're willing to accept a website recommendation, KhanAcademy is very good

[thorn cloak]

i think (at least for first sem) we are doing chaps 1-6, but then i think we transition to spivaks calc on manifolds as i (heard) rudin is bad for multi-variable functions. does that pace seem reasonable?

[coral prawn]

@heady ember sorry for the ping but I genuinely wanna consider delving more into set theory, so I wanted to hear your thoughts of picking enderton as my "starting point"

[hazy elk]

I can dm some set theory notes for a course I took last year, they assume familiarity with first order logic tho

They only cover basic stuff tho

We didn't get time to wrap up the course properly : (

But prolly good as a starting point

[heady ember]

Mind sending it to me lol, just curious on what yours are like

[heady ember]

Stop jumping from book to book smh, actually finish one.

[hazy elk]

Sure, I'll send it along when I'm free

[chrome yacht]

i can vouch for enderton

[dense elm]

I need some help. My mentor recommended that I read An Introduction to Information theory, Symbols, Signals, and Noise. I went out and bought some lower level elementary style text books on physics, mathematics, and engineering books because I'm often stopping every other paragraph to look up something i.e.: I didn't know who Claude Shannon was.

My question is for anyone who has read it, or has a background in mathematics and engineering academically. Should I put this book on the backburner until I get a better grasp on mathematical theorems and proofs? I've taken business calculus and have a remedial base in math, but would not say I'm anything beyond a super generous label of intermediate maybe.

[mellow wren]

Is it really important to know who Claude Shannon was to be able to read that book?

[dense elm]

I would argue it is if I want to read it critically, in the introduction the author states: "It would have been difficult to do this and give any sense of of unity to the account before 1948 when Claude E Shannon published 'A Mathematical Theory of Communication'."

[mellow wren]

If it's a book on math then it definitely isn't

Lemme search up what the contents of ur book actually are

[dense elm]

It's a revised version of the 1961 book on the study of information theory. The author sort of modernizes those theories to explain rapid development in communication.

[coral prawn]

Fair will ask next time

[hearty steppe]

Is this worth reading? https://books.google.com/books/about/A_Garden_of_Integrals.html?id=C0nInxo7y5MC&printsec=frontcover&source=kp_read_button&hl=en&newbks=1&newbks_redir=0&gboemv=1&ov2=1#v=onepage&q&f=false

[devout forge]

I’m taking algebra next fall for the first time…I have a first course in abstract algebra by Fraleigh coming in, anyone recommend that book or a better one?

[remote sparrow]

it looks fine

judson and pinter are good too

they're both super cheap

[finite gale]

fraleigh is fine, you can check the pinned message by dami on abstract algebra books as well

[devout forge]

Thanks y’all !

[modern crag]

How about Precalculus by Stewart, Redlin, Watson

[devout forge]

I used Precalculus with limits by Larson in high school but both are respected authors. Whichever is cheaper

[finite gale]

generally speaking, the textbook you use for stuff before calculus doesn't matter so much; you can also use/supplement with khan academy as needed

[humble rain]

plane trigonometry from the classic text series is good i think

i will have the paperback version of it soon enough

i havent started reading it yet cause i dont have it

i have heard some good reviews about it

[loud jackal]

Any like free resources for mathematical methods Grade 11 Aus??

[humble rain]

Many Australians here nice

[humble rain]

I'm in grade 11 too! But I'm from India so... Things are very different

There will be for sure

You can search specific topics in google

You can find PDFs for almost everything

[loud jackal]

Tyty!!!

[alpine rover]

did you find anything better than S&S?

[bronze halo]

ty

[humble rain]

No problem

[solid wadi]

Hello! I want to read something about logic of knowledge and belief. My goal is to model intelligent agents. I am reading Reasoning About Knowledge by Ronald Fagin, Joseph Halpern, Yoram Moses and Moshe Vardi right now. It is a fine book, but I want to get another perspective.

[hasty turret]

So you want to like do AI? Why not just read Norvig's book

[solid wadi]

I have read Norvig's book.

I assume you refer to Artificial Intelligence: A Modern Approach by Stuart Russell and Peter Norvig.

It talks about a lot of stuff, like constraint solving and path finding, that does not address the kind of problems I have on my mind.

I should maybe read again parts IV–VI though.

[ocean mulch]

Herstein all the way

[kind elm]

im using dummite & foote rn. I don't see it often reccomended. Are there any shortcomings of it that I should know of?

[ocean mulch]

Well, if u like it, it's good

[fierce hedge]

dnf is dry asf is the prevalent opinion. That said if you like it, then it's good

[ocean mulch]

Doesn't matter that much, what others think

[fierce hedge]

(dang beat me to it)

[ocean mulch]

Yeah, prevalent opinion is Hatcher for alg topo is good

But you can put a gun on my head, I'll still shit on it till my last breath

[kind elm]

Yea I didn't mean deficiencies in form, just in content

Thanks

[fierce hedge]

I will never not feel weird that Herstein does group actions without calling them group actions

[ocean mulch]

Just technicalities

[kind elm]

I don't really know how to compare books n find which suit me better, I just pick a popular one and go through it

[ocean mulch]

Read a lot, you'll have a taste

Like others, I suffered through Lang

[fierce hedge]

it's actually a decent strategy plus it's always better to use multiple books

you can always start with an easy read and then fill in the gaps

[kind elm]

I see. I am currently (trying to) alternating between dnf and Mike Artin's Algebra cause thats the one my advisor reccomended

[ocean mulch]

Didn't E. Artin also write some books on Algebra?

And Serre? I know Serre did for Analysis

[kind elm]

lots of artins in math

[ocean mulch]

Well, Emil Artin

One of the Gods

[sage python]

Serre wrote analysis?

[ocean mulch]

Foundation of Modern Analysis

[hearty steppe]

I guess the book I brought up is not really a big deal to check out?

[solid wadi]

Looks fantastic, I made a note to read it some time.

[hazy elk]

Ahaha a fellow Hatcher hater

Not hater ig, but definitely overhyped imo

Somehow it's not as precise and careful as I want

[hollow peak]

he gives exactly the wrong amount of detail every time

It's incredible frankly

I like Tom dieck

[hearty steppe]

Yea I did a quick skim. Some of the best visual graphical figures I’ve ever seen in a math book

[gray gazelle]

im reading naive set theory by halmos and i looked up solutions manual to check my answer to exercise but i found that in the manual there are actually more exercises with then exercises in the book anybody maybe knows whats going on?

[kind elm]

probably different editions?

[hearty steppe]

Skimmed more thru it, it doesn’t really go into the details I was expecting it to. Nice historical reference though

[crimson wolf]

Anybody read Quantum Theory for Mathematicians by Hall? I think I might pick it up to get a better understanding of quantum mechanics. I have a physics background, but I 'think' going in this direction will help me gain a better understanding.

[hollow peak]

I fucking LOVE that book

absolutely fantastic book for gaining an appreciation for the rigor behind QM

I use it as a reference constantly, and the sections on geometric quantization are particularly good if you have familiarity with gauge theory

[sand flame]

David Goggins wrote a pretty good book.

It’s called “Can’t Hurt Me”

[gray gazelle]

recommendations for a geo/trig book? pure

[wintry quartz]

like euclidean geometry?

[hallow belfry]

Could someone recommend me a book to learn about affine and projective spaces?

[tawny copper]

when does the springer sale end

[tawny copper]

Evan Chen

[mellow wren]

june 31st

[tawny copper]

Dayum I might sucumb the temptation 💀

[mellow wren]

I already did lmao

Arrived yesterday

very good quality too ngl

[tawny copper]

Yoo nice thumb

[mellow wren]

thanks

I wanted to buy Neukirch but that isn't on sale 😔

and it costs like 150$ lol

[tawny copper]

does the softcover look cheap? @mellow wren

like I have read softcover from springer, but not of that type

[mellow wren]

https://link.springer.com/book/10.1007/978-3-662-03983-0
Idk why it's so expensive

[mellow wren]

Not in the slightest

it's surprisingly high quality

[tawny copper]

👍

if you think about it

some of this books are not that expensive. They are not books you read in a week, probably takes more than a year to fully digest or even more. People used to buy videogames for like 60 bucks back in the day

[mellow wren]

I mean ppl still do buy games for 60$ lol

[tawny copper]

idk

but like I think you now have monthly subscriptions and stuff and lots of games available

[mellow wren]

But this sale is amazing
I can't believe everything is like <20$ lol

[coarse oriole]

im reading "How to prove it: a structural approach" right now and its pretty good, but its mainly about proof writing and not so much about logic.

What is a good book about logic that i should read aswell?

[cunning steppe]

What would you suggest me as a 9th grade student (finishing soon) .
I've reached equations' systems.

[summer raven]

Are you interested in competitions? Aops volume 1 is good

[cunning steppe]

I am not interested in any type of competition where I would surely fail but why are you asking it ?

[summer raven]

You said what this chat should you suggest you and said you've reached equation systems. You have to be more specific.

I am also in 9th grade who became interested in math recently so I bought this book. It is good for many reasons. It is mainly for competitions but also has an introduction to proofs and is a good supplement in general.

[cunning steppe]

I've done first and second grade equations, inequations, systems (equations and inequations) and some geometry proof

The last arguments

[summer raven]

I meant specific as in what you want the book to teach you.

[cunning steppe]

I surely cannot skip from a beginner topic to an advanced one so the book that teaches the next "layer" of what I'd have to learn

I enjoy both math and geometry so consider both if that's your doubt

[summer raven]

The book starts from the very beginning. I'll send you the table of contents

https://s3.amazonaws.com/aops-cdn.artofproblemsolving.com/products/aops-vol1/toc.pdf

It is for competitions from 9th to 12th grade. It has some stuff you've already seen but everything is more challenging than school. The problems are much tougher.

If you've already seen it you can just skip those chapters

[cunning steppe]

I covered most of this stuff

Actually everything but a long time ago

It may be nice to review it

[summer raven]

You've covered number theory and combinatorics?

Those topics are usually not taught in school

[cunning steppe]

Not deeply but I think yes

Middle school level

But as I mentioned, I forgot most of it

Because I haven't used them in a long time

[summer raven]

Damn. What middle school you went to? Do you know nCk notation? Binomial theorem? Diophantine equations?

[ocean mulch]

Was about to say something racist, but I held myself back

[summer raven]

Why?

[wanton yew]

Does anyone know any good intro books for discrete math and linear algebra?

[ocean mulch]

Ironically Lang's LA isn't too bad iirc

I have a copy myself

[summer raven]

Why?

[ocean mulch]

It'd be a good guess that the school be in Asia

But again, that's racist

[wanton yew]

Is it by a Serge Lang with a yellow cover?

[summer raven]

I wouldn't say that's racist

[ocean mulch]

Idk man, I have a copy, not the book. A pirated copy, if must specify.

[devout forge]

Otto bretscher’s intro to linear algebra is good, if it’s your first course in linear algebra. Or Howard Anton elementary linear algebra

[ocean mulch]

Also never opened it so...

[cunning steppe]

Can you give an example of nCk notation ?

By the way, I've done the binomial theorem

[ocean mulch]

6C3 = 6 choose 3 = 20

[cunning steppe]

No, never seen such thing

I read briefly the summary. My bad

[ocean mulch]

It's an old notation, you can still find it on calculators, books, and papers, but it's really old.

[wanton yew]

What math are you taking in highschool, im actually curious?

[summer raven]

Does an n on top of a k with them inside parentheses ring a bell?

[cunning steppe]

@wanton yew

[wanton yew]

Ahh I see

[cunning steppe]

And generally polynomials

[summer raven]

Thats the modern notation. I thought n choose k was required for binomial theorem but I realized my school taught without?

[cunning steppe]

Then in physics vectors and trigonometry

I'd count it as math

[wanton yew]

Around precalc /geometry bordering calc

[cunning steppe]

(Added to acceleration, friction, Archimede's principle, lever, etc...)

[summer raven]

Does an n on top of a k with them inside parentheses ring a bell?

[cunning steppe]

Is this a joke ?

[summer raven]

No. Just surprised you learned combinatorics in middle school

[ocean mulch]

Maybe the one that does not involve binomial theorem

[cunning steppe]

It's just a pyramid (you know what I mean)

Isn't it ?

[ocean mulch]

Prime numbers, dirichlet theorems, proving inequalities, invariances. Those are combinatorics of a different breed

A harder breed

[ocean mulch]

Pascal's triangle?

[wanton yew]

I’m sure it’s not that incredibly advanced stuff

[cunning steppe]

Yes

[ocean mulch]

Well yeah, that's it

[cunning steppe]

Indeed

[wanton yew]

basic combinatorics isn’t hard to understand

[ocean mulch]

Or maybe they just skip the terminology

I have seen that before

[cunning steppe]

They do

At first glance I didn't recognize the specific term

[summer raven]

I learned a version without pascals triangle.

But with n choose k. Weird

[orchid mortar]

Intro to discrete math = Rosen

[wanton yew]

Is this a book?

[orchid mortar]

It's probably 'too much' which is typically better than 'too little'

[cunning steppe]

Anyways, let's go back to the previous topic

[orchid mortar]

Google it

[ocean mulch]

Combinatorics is a strange subject. You see tens of pages on nCk, and you think "really? this shit gets hard? You gotta be kidding me"

[cunning steppe]

Which book would you suggest me ?

[ocean mulch]

And somewhere on the way, it gets ridiculously hard

And it's impossible to say exactly where it gets hard

[orchid mortar]

Just teach the 12 ways, which is what HS 'only needs' tbh

Problem recognition is all HS students want typically

[ocean mulch]

You certainly don't know my HS

[wanton yew]

Thanks for this, I’ll look into this book!

[orchid mortar]

What did your HS do

[summer raven]

In how many different ways can you rearrange RAMANUJAN?

[ocean mulch]

Olympiad stuff. Pell's equations, ring theory, combinatorics, Diophantine equations, etc.

[orchid mortar]

naah not standard

[ocean mulch]

I spent my first two years in college learning nothing in CS because of it

[orchid mortar]

Well it's advanced stuff

[wanton yew]

What is Olympiad stuff?

[cunning steppe]

F*ck... I did it but I forgot about it

[ocean mulch]

Not even that. They want formulae, and how to use formulae, and how to plug them into calculators and get the answers as fast as possible

[cunning steppe]

I mean..I once knew how to do that

[summer raven]

@ocean mulch Was it a public school. What country? I am envious.

[summer raven]

Do you know diophantine equations?

[wanton yew]

Yeah my school didn’t even have a calc class….im surprised that other schools have so much more to offer

[ocean mulch]

I'm not gonna reveal myself here, but I'll say it's a public school 😄

[orchid mortar]

It's a country which places more emphasis on math early in education

[cunning steppe]

@summer raven can you please remember me how to do it ?

[orchid mortar]

TBH that doxes him if you know the country

[ocean mulch]

Well, it's an odd school anyway. Technically it is a university faculty.

[orchid mortar]

But it's fine.... probably

[ocean mulch]

Literally all schools in Asia and Russia

[wanton yew]

So your highschool had professors?

[ocean mulch]

[wanton yew]

That’s crazy

[orchid mortar]

Not really true, gaokao's syllabus is not supposed to be hard IIRC

[ocean mulch]

Yes. They are all lecturers who got bored with uni students. It's a must to have PhD I think.

[orchid mortar]

Same with CSAT

[cunning steppe]

Here they are called professor since middle school

Teachers are just elementary school teachers

[wanton yew]

I’m a little envious on how other countries put emphasis on education

[orchid mortar]

Are you in US?

[wanton yew]

Yes

[orchid mortar]

US education is known to suck

[ocean mulch]

At the end of the day, it's a pissing contest.

[cunning steppe]

Here they usually reject half of the students in 9th grade

[wanton yew]

I literally had to self teach calc just to be ready for university

[ocean mulch]

I wish it were done more carefully. I got lucky because Olympiad stuff did become useful later on.

[orchid mortar]

Education isn't supposed to be about teaching it's supposed to be about learning

[ocean mulch]

And here we had integration bee

[wanton yew]

Something so many forgot nowadays lol

[wanton yew]

?????

That’s crazy

[cunning steppe]

Self taught math is hard in my opinion

[summer raven]

I'll give you a differwnt one. In how many ways can you choose 3 of the 5 colors of m&m's to eat?

[wanton yew]

It definitely isn’t for everyone, unless you have some uncanny determination to learn

[ocean mulch]

Nah. Put a bunch of math kids in a room, sooner or later they'll get bored. Integrals are just a convenient way to kill time.

[hollow peak]

it definitely does not take uncanny determination to learn math on your own

most math math students learn is on their own

[ocean mulch]

Like literally any other things, it is hard

[wanton yew]

Depends

[hollow peak]

i think that kind of mentality drives people away

[cunning steppe]

Sorry but without the formula it's too hard for me

[hollow peak]

it doesn't take a super genius to do math

[wanton yew]

Im not saying that

[ocean mulch]

No, but you have to be very stubborn

[summer raven]

The formula is n!/k!(n-k!) where n is the number of objects to chosen from and k is the number of objects to choose

Oops. Formula is actually

[ocean mulch]

Imagine grinding through category theory, Eilenberg-Steenrod axioms and exact sequences to get to do fun stuff in alg topo

You definitely need to be very determined

[wanton yew]

I know engineering students who really only care for their engineering classes for example, they aren’t as determined to learn all the math

[hollow peak]

yes, I agree that you need persistence

[summer raven]

The formula is n!/k!(n-k)!. Have you learned this?

[hollow peak]

but if you want to learn, that's pretty much all there is to it. self motivation is key more than anything that's unique to the individual

[wanton yew]

If I gave someone a book and told them to learn they would have to be somewhat determined to learn something or they’d just procrastinate and slack off

[cunning steppe]

No. It was in a different way

[ocean mulch]

And that's what I said 😄

[cunning steppe]

But that does not count as far as I have a way to do it

[wanton yew]

I know a smart kid who wanted to do physics but wasn’t determined to learn math so he switch his major

[summer raven]

I highly doubt a middle school actually taught combinatorics

[ocean mulch]

You definitely didn't know middle schools in Asia

No, actually, most of them don't

[orchid mortar]

They teach prob/counting problems yes

[ocean mulch]

But it still comes up in exams

[orchid mortar]

But not combinatorics like the Pell stuff you saw

[summer raven]

South Asia definitely isn't like this.

[ocean mulch]

Well, who am I to say anything? I don't know all of them 😄

[summer raven]

Thats like a third of Asia

[cunning steppe]

I still haven't got the book

[ocean mulch]

probably AoPS

I know a good book in Combinatorics that I used 7 years ago, but for that, you kinda need to brush up the dirt first, i.e. all these basic combinatorics problems

[summer raven]

I'm in 9th grade like you who is interested in math. Aops vol 1 and 2 were both interesting books. Vol 2 is more advanced and assume knowledge of proofs

[cunning steppe]

I am doing geometrical proofs

Is it enough?

[summer raven]

Probably not. Vol. 2 also has proofs in non geometry stuff

[ocean mulch]

Like, Euclidean stuff?

[cunning steppe]

The principles are there

[ocean mulch]

You'll need more than that. The degree of rigour is different

[summer raven]

Vol. 1 has an intro to proofs

[cunning steppe]

Yes

[summer raven]

I think you should check that out first

Vol 1

[ocean mulch]

Yeah, AoPS is probably best shot

[cunning steppe]

Complete name?

[ocean mulch]

The Art of Problem Solving, Volume 1: The Basics

[cunning steppe]

Ok

Thanks y'all !

[summer raven]

Do you know proof by contradiction, induction, pigeonhole principle, using words instead of step by step, converse, inverse, contrapositive?

[ocean mulch]

Maybe not by those names 😄

[cunning steppe]

Not contradiction

But yes

Explain everything using both math and words

[ocean mulch]

Strange...

[cunning steppe]

Theory , hypothesis, demonstration

[ocean mulch]

You know what, I'm gonna follow my gut, and say you can also try out Engel's Problem Solving Strategies.

[cunning steppe]

Why?

Isn't it supposed to be done like that ?

[summer raven]

If that is too hard do vol. 1

Contradiction is a very standard proof technique. You seem to have learned induction before contradiction

[ocean mulch]

Because you didn't know how to solve the combinatorics problem above 😄

Like, you have all the prereq, but are really, really, really rusty

[cunning steppe]

It's what I've said at the beginning

That's why I need to revise

[ocean mulch]

Yeah, maybe try Engel, I think you'll like it.

But AoPS first to brush up the dirt

[cunning steppe]

Ok

The aoPS saga basically ?

[summer raven]

Not all of it. Just vol. 1 and 2 which is like a condensed version of the saga

[cunning steppe]

Of course, I was just joking

What is the advantage of doing it like this and not in school?

[ocean mulch]

Advantage: you have no one to tell you what to do
Disadvantage: you have no one to tell you what to do

[cunning steppe]

🤣

[ocean mulch]

Figuring out how to learn math by yourself is hard

But you get all the freedom in the world

[cunning steppe]

My ego drives me

I just want to be better than anyone else

[summer raven]

Do vol 1 and skip stuff you already know but even if you already know something, still try the problems in the back. Aops problems are usually deeper than how its taught in school

[cunning steppe]

If I know it problems shouldn't bother me so I'll do them anyways

[ocean mulch]

You'll learn that this mindset won't make you go very far, but it's OK, you'll learn it one day.

A better mindset is to want to be better than your yesterday self

[cunning steppe]

It would be hubristic to skip them just on my feelings

[summer raven]

I've also found aops to usually be more fun than school math

[cunning steppe]

I mean... it makes me want to learn stuff

Actually mostly annoying people

Like the class top student which is actually a total idiot

And often shits on me

[ocean mulch]

Use it while it's still useful, but trust me when I say it's not sustainable, I've been there and done that. Try to find an alternative in the mean time.

[summer raven]

You both seem elitist

[summer raven]

I mean you and your classmate

[ocean mulch]

Oh these kids...

[summer raven]

Streckeuy

[cunning steppe]

Just a bit of revenge

But I like art too

[summer raven]

Lol

[ocean mulch]

Revenge will escalate revenge, and burnout comes sooner than you'll think

[cunning steppe]

And automation

But I already top art

And automation of any kind isn't treated in school

[summer raven]

I want to say something poetic about elitism, hubris, and revenge

But I'm not creative enougj

[cunning steppe]

Who wouldn't want to get revenge ?

Be real

[ocean mulch]

Not here where I live

[ocean mulch]

Me. I don't.

[cunning steppe]

Too kind

[ocean mulch]

No, that's called being wise

[summer raven]

I guess no one's ever been really mean to me before

[gray jungle]

how is this relevant to books?

[ocean mulch]

No, it's not

[summer raven]

Scroll up

[ocean mulch]

I'm out actually

[cunning steppe]

Epic exit

Anyway

I can use it for my own hobbies

The revenge part is just a additional motivation

I just need a path to follow

Self learning can be often misleading

For now I know what to do

There's no need for further help at the moment

[summer raven]

After aops you have many options. Calculus/analysis, discrete math, linear algebra, abstract algebra

[cunning steppe]

I am following you

Keep going

[summer raven]

So yeah. You can pick any of these after aops

Many different books

You should come back here after aops

[tender river]

#book-recommendations message

[mellow wren]

why do you have a month

OK let's take a step back

is the uni gonna like test you on these topics?

OK cool
Then for the topics you mentioned khan academy is your best bet

it gives you lots of problems and you can do it at your own pace

it doesn't but idk what he really means with that
Number theory is a very wide area of math lol

[ocean mulch]

I'll recommend Holy Bible, King James version. Because only God can help you with this.

[mellow wren]

OK in that case I can (probably) imagine what they mean
I think that shouldn't be too much of a worry
First focus on everything else
Because khan academy covers basically everything else

[crimson leaf]

Yeah that's a very broad list

[ocean mulch]

Well, it's never too late to start having faith, because for this one you'll need a ton of it

[crimson leaf]

Well yeah but you also don't know the distribution of the questions

[mellow wren]

it's not as bad as it can be

you should probably start with khan academy haha

[ocean mulch]

It depends on what you know. Like, you know the gist and only need to revise... or you need to speed run High School in a month

[mellow wren]

Since he's serbian I think he already covered most of this stuff

[ocean mulch]

oh... brate 😄

[mellow wren]

at least as far as I know the balkan education system

[ocean mulch]

No, but I have a Serbian roommate

From all the Serbs I know, you'll be fine

[crimson leaf]

If you don't mind me asking Megumi are you from Czechia by any chance?

[ocean mulch]

It's OK, you know everything and just need to brush off the dirt.

[ocean mulch]

Not an ounce 😄

[ocean mulch]

I'll say pick a good collection of exams/exercises, and cram your way through it

By the end, you'll master it enough to teach HS math yourself

[mellow wren]

ye

[ocean mulch]

Not for you

Pick a good collection of hard exams/exercises

Preferably those who resemble what you'll be tested on the best

make sure it comes with babushka's blessing

Do a test, try your best. See what you've missed/didn't know, patch the gap, Repeat.

Trust me, you have the basics

This will come out sarcastic, but just channel your inner Serb

Just like "channel your inner Asian"

trust me, you can do it

To be fair... they all kinda are

[gray gazelle]

Good books on the philosophy of mathematics?

[remote sparrow]

hamkins has one

[gray gazelle]

anything by wittgenstein

Thanks

[viscid sun]

any book recomendation for stoicsm?

[gilded lagoon]

@viscid sun 12 rules for life

[gray gazelle]

Don't read that. You'll turn into a lobster

[gray gazelle]

Not its biggest fan but Marcus Aurelius

[meager path]

Do any of you have suggestions for a book, Youtube channel etc for the way I learn? I have a particular process I find that works best for me which is to try to solve a problem, if I'm unable to, I compare it to the answer in my attempt to find the process and if I still can't get it, then I read the relevant text so I immediately know and understand how I can apply it (basically learning in reverse xD)

[rapid lily]

This is a good way to learn. You can just get a book on the topic you are wanting to learn about. Have a go at proving the statement or solving the problem on your own, then look at the book if you are stuck for a while. It works best if you just look enough to give you an idea about what you can try and then stop looking while trying that method. Not all books have solutions though, so be mindful of that.

Has anyone looked at the book "Distributions, Partial Differential Equations, and Harmonic Analysis" by Mitrea? I'm looking for a book (preferably a Springer book) which covers some amount of harmonic analysis to give a rough idea of that area while still containing and using a lot of functional analysis. This one seems to work well for that, but I don't know if anyone else has any other suggestions.

Link: https://link.springer.com/book/10.1007/978-1-4614-8208-6

[viscid sun]

nah man💀

[void ridge]

Yo

[gray gazelle]

Aye bro that's my profile

[ocean mulch]

insert spiderman meme

[viscid sun]

any recommendation book about classical physics or modern physics

[ocean mulch]

Feynman's Lectures on Physics?

The saga is really good iirc

Although there are better books, but you have to be more specific

Yeah.... Feynman

[coral prawn]

feynman my beloved

[ocean mulch]

At that level, you'll see that indeed you're ordinary

Because you forget what "ordinary" means to the mortals

[heavy pelican]

“Excuse me Mr Feynman, but what does integrating x^2 from -infty to infty mean?”

(Thats my caricature of a path integral)

[inner token]

If your calc/de's are solid kibble's "classical mechanics" is good

[gray gazelle]

Can anyone help me
How can I start a best approach for self study in higher mathematics.

[crimson leaf]

Just start doing it if you don't know any proof start by reading the pinned thing in proofs and logic then move on to linear algebra or really whatever you want

[heady ember]

Set theory

[crimson leaf]

Yeah I wouldn't recommend that as a first book to most people

It's very steep for someone who knows nothing

Some courses use Rudin as an intro to proofs books

[fierce hedge]

Artin is basically the algebra equivalent of Rudin

[heavy pelican]

Rudin is much terser

No diagrams! Opposite of Artin

[fierce hedge]

A proff can probably use Artin for a intro proof course but there are much better book out there for intro to proofs

[cerulean cypress]

isn't herstein more like rudin

[heavy pelican]

Agree

[fierce hedge]

I felt Artin was worse, Rudin at least has good exercises

[fierce hedge]

oh yeah, that'd be much more fair

[cerulean cypress]

i mean I'll never understand why rudin is used for first exposure to analysis

like the author explicitly states that the book is intended for advanced undergrad& 1st year grad students on the preface

and the book is meant to be a review

[fierce hedge]

Like I said few lines above yes it's not as bad as Rudin, something like Herstein is probably more like Rudin but there is no way Artin is slow. Chapter 1 is pretty decent but it goes fast asf from chapter 2 to the point that it's exhausting.

[cerulean cypress]

herstein was quite more challenging than say, fraleigh

like much more

which is I guess 1950s

I mean I"m fine with rudin but at least they should fix up the design

like the design feels outdated and ugly

needs some cleaning up

people will come out and say that content is what really matters and yes I agree but it wouldn't hurt to just clean things up a bit wont it?

[fierce hedge]

The exercises in Artin are decent but nothing great plus there aren't that many to being with. In fact in most places, Artin is considered for more matured audience. Again, not like it's not doable but it'd require supplementary theory as well as extra exercises.

[inner token]

I just got a copy of Herstein! And here you guys are talking about it

Someone on reddit said the exercises were good

[cerulean cypress]

which one did you get? I recommend topics in algebra

[inner token]

That's the one

[cerulean cypress]

but let me warn you: the book is quite challenging and concise

[inner token]

Used hardcover for 15 dollars

[cerulean cypress]

it fortunately has solution manual though so use it wisely

don't get me started with lang

[inner token]

Thanks

[cerulean cypress]

I gave up reading that book after like 2~3 chapters

[inner token]

My school library had a Lang, but I already disliked him after complex analysis

[cerulean cypress]

whats wrong with his complex analysis book though

[void ridge]

Its there since I saw that anime
More then 6 months i guess??

[inner token]

Very dry like a lot of his stuff I understand, and I just gelled better with conway

On top of other more modern pdfs on the internet

Conway complex analysis of one variable reminded me a lot of baby Rudin in style and exercises

[cerulean cypress]

i've heard good thigns about freitag

[inner token]

But rudin has a complex book too doesn't he

[cerulean cypress]

is complex analysis more difficult than say, rudin(i mean the answer to this question is most likely yes but just asking)

[wintry hornet]

tao 1 or baby rudin (the age old question yes)

[inner token]

I like baby Rudin. Great exercises imo

[cerulean cypress]

uh why does your profile have this warning:ⓘ User is suspected to be a part of a cybercriminal organization. Please report any suspicious activity to Discord staff.

[inner token]

I don't think complex is more difficult per se

[wintry hornet]

after extensive googling, im told that tao presents his ideas in a much more intuitve manner

[wintry hornet]

dw about it sir

ah fair enough

[inner token]

Maybe Tao for the literature, rudin for exercises. I never read Tao though so I should shut my mouth

[wintry hornet]

yeah zlib goes so hard i can get both if needed

[inner token]

I have Abbott and Pugh and they're both good. Abbott is great for a first pass at analysis

Pugh has a lot of good pictures

[cerulean cypress]

pugh might be an excellent book

if it wasn't for the lack of exercise

solution

[wintry hornet]

buy? boy im graduating high school next week. do i look like i have that sort of money 💀

oh

[cerulean cypress]

wish I was as young as you two

[wintry hornet]

damn imaigne being able to buy those books

[cerulean cypress]

i'm 23 and it f-ing sucks

[wintry hornet]

imma j 🏴‍☠️ them

[cerulean cypress]

5 years passed like it was nothing

though 2 of those were wasted on conscriptoin

[wintry hornet]

eh who cares about legality :D

but imma get both

[cerulean cypress]

tbh textbooks without solutions are worthless for e

me

[wintry hornet]

and read tao + do exercises in rudin

[cerulean cypress]

since I self study

[wintry hornet]

i kinda already started on tao cuz i found a pdf of the first few chapters

and i like the way he presents his idea and explains the intuition

yuh fs

where r u going to uni

:O

nice

im already here

so im staying in america lol

:O

no idea atm

probably nt

i did that for math oly and stuff

[tender river]

ugh not kids having out of topic discussion in book rec again

[wintry hornet]

oop

okok

[cunning forge]

Does anybody have any Springer book recommendations recommendations for diff geo and math phys?

[heavy pelican]

name checks out

[cunning forge]

too bad the server doesn’t have a Witten emoji

[heavy pelican]

https://link.springer.com/book/10.1007/978-93-86279-00-2

I recommend this

Big Witten stuff

[cunning forge]

Ah, it’s not on sale. That’s mainly the reason I’m restricting the question to Springer books.

Thanks anyway

[heavy pelican]

Ah OK

[cunning forge]

What background does it require btw? I’m pretty sure I don’t have it yet, as I’m still a newbie when it comes to diff geo, but just curious

[heavy pelican]

It’s pretty terse, I was just recommending it for the memes. Probably some serious amounts of Riemannian geometry and algebraic topology

[cunning forge]

Oh yeah, not there yet. Maybe one day…

I’m mainly looking for introductory stuff, I know of Lee’s trilogy but I’m looking to see if you guys know any alternatives that you think are better

You know what, they don’t even have to be Springer books, one can always get lucky online these days :p

I also know of Tu’s intro to manifolds and would love to know what people who’ve gone through some parts of it think

[mellow wren]

I think it's excellent

Tu's writing style is very nice

Lee is more in depth than Tu but idk Lee is a bit drier

[heavy pelican]

Are Universitext books up for sale also?

[mellow wren]

what the fuck is geometry.org

Oooh interesting

[cunning forge]

I have read a bit of Lee’s top mfds and I felt it was too dry too, and took way too long to just go through 1 page of it

[heavy pelican]

Lee is very very meandering

[mellow wren]

It requires a lot of topology

[cunning forge]

Does Tu provide me with all the basics I need?

[heavy pelican]

It takes him ages to do anything

[mellow wren]

yes
He has a very comfy introduction

more like 2500 lmao

[heavy pelican]

Lang lol

Peter B Petersen is too postmodern for me

Cheeger/Ebin is nice but only for someone who knows a decent amount of Riemannian geometry already

[cunning forge]

and is it enough for mathematical physics purposes? Does it allow me to basically jump into gauge theory or the likes without much trouble?

[heavy pelican]

I was going to recommend Gallot-Hulin-Lafontaine

Oh, you want to do gauge theory

[cunning forge]

Not specifically, but sure it’s an interest

I should clarify I’m a 1st year undergrad (starting 2nd year in August)

I’m generally interested in mathematical physics

I know a bit of diff geo from Schuller’s lectures, though I recognize they’re very surface level and I also did not complete them all yet

[mellow wren]

Well not like in medias res but you will be able to learn abt gauge theory

[heavy pelican]

Tu is probably the most sane recommendation

[mellow wren]

ala gauge theory uses a lot of vector bundle stuff
Which I don't think Tu covers

[heavy pelican]

Its quite accessible although I never read through it

[mellow wren]

realistically idk of a single diff geo book that talks abt vector bundles only algebraic topology books

[heavy pelican]

Yeah lol

Horrendous notation but quite in depth

Literally cannot keep track of notation

If you ever read it, start making your own notations

[cunning forge]

doesn’t Lee do that?

[mellow wren]

I don't believe so but I could be wrong

[heavy pelican]

“Geometry of Differential Forms” by Morita. More accessible “From Calculus to Cohomology” by Ib Madsen etc

[mellow wren]

Ahh well good to know haha

[cunning forge]

Just checked, he does. Chapter 10

[mellow wren]

hmm well good then

[cunning forge]

In general, would you recommend Tu to actually first learn this stuff from, and then maybe I could pick up something like Lee and just scan through certain things whenever I need them or something like that?

I will probably buy Tu as it’s on sale actually

softcover for $16 lol

Oh that’s cool

I guess I’ll try to continue with Lee and see how it goes, if it’s still too terse for me I’ll switch to Tu

I have went through chapter 2 of top mfds

[hollow peak]

lee is really not great for a first time learning

if you've seen the basic material before I would say it's great, but it's not really a soft intro

[cunning forge]

I see

And what do you guys think of Nakahara?

it seems a bit more gauge theory oriented

[heavy pelican]

loooong

[hollow peak]

nakahara is great book

[heavy pelican]

seems good tho

[hollow peak]

the physics is kind of hardcore

but the math is very solid, not particularly rigorous but he lays out good framework

and the gauge theory is excellent if you have some exposure to classical gauge theories

but yeah, I really do think tu is the best option for an absolute beginner to smooth manifolds, perhaps with some supplementary exercises from lee

[cunning forge]

Thanks, I will go through it

I’m also currently (just started) reading Baez and Muniain on gauge theory

[hollow peak]

baez has been on my reading list for a while now

[cunning forge]

so maybe (hopefully) by the end of summer break I’d be able to handle something like Nakahara

[hollow peak]

just for your knowledge, nakahara starts off with VERY difficult physics

you can safely skip it entirely and just go to the math

[cunning forge]

I know, I was told that haha

yeah I was told the book basically starts at chapter 2

[hollow peak]

exactly

[heavy pelican]

I didn’t know of this, looks amazing

[cunning forge]

yeah it doesn’t actually assume knowledge of diff geo either which is great

[hollow peak]

and, as I now know: fwi, what physicists call "global gauge transformations" are not global automorphisms of an associated bundle

[ocean mulch]

Sternberg's Differential Geomery or Taubes' Differential Geometry: Bundles, Connections, Metrics and Curvature

[hollow peak]

remember this, for it will be confusing

[heavy pelican]

Oh man I have to read Taubes as well

[hollow peak]

yeah, also Tu's DIfferential Geometry: Curves, Connections and Characteristic Classes

[heavy pelican]

Too much to read

too little time

soon we all die

[ocean mulch]

Lmao

I basically cram the books as fast as possible, then come back and repeat

[hollow peak]

i read the same books over and over for multiple years lol

i need to otherwise it doesn't fully sink in after first reading

[ocean mulch]

I don't wish for much. Just that I can fully master May.

[hollow peak]

now that is one fucking dense book

[ocean mulch]

I don't know, just happened to find it in the library.

[hollow peak]

i feel the same way about analysis now by pederson

absolutely banging book

ridiculously concise though

[ocean mulch]

I also wanna master Lang

But def won't work for me

[heavy pelican]

Then there’s More Concise

which is worse

[heavy pelican]

is that the postmodernist neo marxist one

[hollow peak]

it's a very concise GTM book on modern functional analysis

[ocean mulch]

One concise book on Measure Theory is one by Tao

[heavy pelican]

oh ok

https://link.springer.com/book/10.1007/3-540-28890-2

[hollow peak]

i fucking hate that book on measure theory

[ocean mulch]

Man, I don't doubt Tao is good, but pls someone remind him that we are but mortals

[hollow peak]

I really dislike tao's exposition

[heavy pelican]

postmodern neo marxism is by jöst

not petersen

[hollow peak]

wait seriously

[heavy pelican]

yeah

[hollow peak]

oh my god

jost is so based

i love him for his geometric analysis book and geometry and physics

my respect has just skyrocketed

oh wow i'm just gullible you were joking

[ocean mulch]

Banach fixed-point theorem from page 43

This is very, very concise

[hollow peak]

jost is such an excellent author

[heavy pelican]

the neomarxism part may be a stretch

[hollow peak]

https://link.springer.com/book/10.1007/978-3-642-00541-1

this book was my bible this year in particle physics

[orchid bridge]

planning to start working on analysis abit more rigorously with tao's series on analysis, I started off with abott's book. Anyone knows of any online supplements that revolves around his books?

[ocean mulch]

What's in Abott again?

I'm thinking of Abott and Tu, but that's for alg topo

[orchid bridge]

understanding analysis

its much of same content but much easier than rudin's,tao and others

from what I understand*

[dry pike]

Guys i want something some discrete mathematics books, any suggestions

[ocean mulch]

what kind, topic, and level?

Discrete math is huuuuugggeeee

[dry pike]

Probably like

Intermediate books on discrete mathematics

Where all the basic topics are listed which are important

[remote sparrow]

did you finish abbott already or are you just switching to tao?

[orchid bridge]

covered till just before integration

was following an online lecture series

[fiery radish]

Hey guys, so someone recently suggested me this book on number theory and I think it's a great book. Right here is the name of this book: Modern Olympiad Number Theory by Aditya Khurmi.

I was wondering if anyone has a link to a real paperback book version of this book rather than a PDF. Thanks!

[dim forge]

this book looks interesting. I'll recommend some books too.
Bertlmann - Anomalies in QFT
Hori et al. - Mirror Symmetry
Isham - Modern differential geometry for physicists
Schlichenmaier - Riemann Surfaces, algebraic curves, and moduli spaces
Huybrechts - Complex geometry

The book by Baez and Munian - Gauge Fields, Knots, and Gravity is probably the best intro to differential geometry, at least as far as I can remember

[analog lava]

can you start number theory from ireland rosen

[hollow peak]

yes, it's very intro friendly

if you know the bare minimum about rings, you'll be very prepared

[uncut zealot]

Ireland Rosen should honestly be a utm or a universitext instead of a gtm. The only prereq is undergrad level algebra and, later on, undergrad level complex anal.

[long wren]

Does anyone have any recommendations for philosophy of mathematics? In particular, I'd love to learn more about platonism, formalism, logicism, their similarities, differences, and historical development. Maybe also about which one is the most popular.

[remote sparrow]

hamkins has a good intro

and he has yt lectures for his book

[long wren]

oh, I follow him on twitter, he looks super smart

[remote sparrow]

stewart shapiro's Thinking About Mathematics is a popular choice too

[long wren]

thank you, I'll check them out!

[long wren]

this one? "Lectures on the Philosophy of Mathematics"

[woeful ravine]

does anyone have any recommendations for graduate level books on category theory?

[remote sparrow]

yeah

has anyone read General theory of functions and integration by angus taylor? is it any good? it's available as a dover, but i first saw it as a nice hardcover at my community college's library. it's supposed to be a measure theory textbook

[remote sparrow]

i found some reviews for buck's Advanced Calculus:
https://doi.org/10.2307/3610424
https://doi.org/10.2307/2309776

i also happened to find some reviews for hubbard and hubbard's multivariable calculus book:
https://doi.org/10.2307/3647874
https://doi.org/10.4169/amer.math.monthly.124.6.572
http://www.jstor.org/stable/20454184

[dapper root]

Categories for the working mathematician by Maclane

[woeful ravine]

other than that?

[dapper root]

I don’t know of graduate level ones. People just tend to learn it as they need it

[woeful ravine]

hmm alright, i have maclane i was just wondering if there any well known books on category theory

besides introductory books

[sage python]

@gray gazelle how's your linear algebra?

[fierce hedge]

please remove this link, it voids Discord ToS

[sage python]

^

Yeah don't post links here. It's ofc an open secret that you can find the stuff for free at this point

I'm sure Discord doesn't care except for possible liability, but nonetheless it's part of TOS

Anyway, in analysis the year before mine

They used Edwards

I'm not super familiar with it personally, though I'm certain it's miles ahead of Buck

Munkres I've heard bad stuff about. Spivak is harder (more concise) but better problems and less time wasted on some unimportant matters

Shifrin Multivariable Math is good but does the linear algebra from scratch which you may not need

Hubbard is Shifrin but screwy

Fleming does measure theory within, which I endorse

If you wanna go hard, and this does build up to diffgeo, you could read Duistermaat and Kolk

[oblique apex]

are introduction to algebra and intermediate algebra from art of problem solving good books for someone learning math from scratch on his own? (I'm using khan academy to supplement)

[ocean mulch]

In general AoPS are top-notch, well-written

[kind elm]

Nature of mathematical knowledge by kitcher

[mellow wren]

I mean Maclane is already very in depth
But if you're familiar with 1-categories then there's always Higher Topos Theory

[mellow wren]

Idk
There's prereq knowhow definitely (mostly in AT imo and like some stuff on simplicial sets) but if you know the stuff in working mathematician you're already a good way there

(Tho maybe my choice of book wasn't the best as I am heavily biased towards HTT since I like it a lot)

[remote sparrow]

fun piece of trivia, spivak recommended it in the bibliography of the fourth edition of Calculus

[primal jacinth]

hi can someone point me to a resource where I can read up spatial integration? my google search keeps giving me stuff about policies and what not.

[ocean mulch]

what spatial integration?

Multivariable calculus?

[primal jacinth]

honestly? I have no idea.

There's a function I saw in a fluid mechanices textbook that was integrated spatially. I'm guessing that's integration w.r.t space instead of time. I want a refresher, cuz I can't remember how to do that.

[ocean mulch]

😄 what the hell is integration wrt space instead of time?

We talk only about integration wrt to a variable

@heavy pelican any clues? You're expert in path integrals

[heavy pelican]

nope

[ocean mulch]

It's always the physicists that make up these sorts of shenanigans

[tender river]

ck_'s probs talkin' bout multiple integrals

[ocean mulch]

So indeed multivariable calc?

[primal jacinth]

nah.

[primal jacinth]

probably? I'd check it out.

[marble solar]

Not surprising because Spivak knew Shifrin

[ocean mulch]

They all know each other I think

[primal jacinth]

Yea, I can't articulate my issue properly, or I haven't understood what the text meant by "...we integrate this distribution spatially to find..."

but, I guess what I was interested in is if there is a topic involving spatial integration (like integration by parts for eg) and where I can read up on it. Seems there isn't 😔.

[sturdy shore]

it's just integration in spatial variables

there is nothing special about integration in spatial variables, sounds like you just need a more general resource

[primal jacinth]

please share?

I've spent 3hrs ish trying to crack that. I'd appreciate any resource

[steep badger]

it's your normal Euclidean coordinates. dx dy dz or whatever instead of dt. For sure you know integrals are not only defined on dt?

[inland elm]

any good pde theory books
i have taken 2 computational pde courses so i have had exposure on that side but nothing really building the theory

[narrow relic]

I've looked through it lightly! Let me know if you have a question about it

[inland elm]

i think i'm going to look at evans

[primal jacinth]

aye, for sure. from what I read so far, double, triple integrals are solved sequentially. For the equation I'm trying to re-derive, they are two boundary conditions (b.c). Would it mean using them as the integral bounds and intergating the equation twice w.r.t the two variables contained in the b.c?

(guess this falls under help, but I got kicked out and sent here)

[vague granite]

Whats a good introductory ode book to self study? I did multivariable calc and I'm pretty comfortable with proofs.

[inland elm]

are you looking for application, computation, or theory?

[vague granite]

all three, but I think theory would come first

computation you can just like toss it into wolfram right?

[inland elm]

ah i just read the part about multivariable calc. do you have any background in linear algebra (proof based) and analysis?

[heavy pelican]

Taylor has three large tomes that I want to read at some point

[heavy pelican]

Hirsch-Smale

Fantastic book, even for nonmathematicians

[vague granite]

awesome, thanks! :)

[vague granite]

just making sure, "DIFFERENTIAL EQUATIONS,
DYNAMICAL SYSTEMS, AND
AN INTRODUCTION
TO CHAOS" right?

[heavy pelican]

yup

[vague granite]

cool, thanks

[molten marlin]

Anyone knows sources for plane geometry exercises for university prep?I need to focus on circles and triangles

[worthy venture]

Anyone know a good book on more advanced probability/ statistics theory

Hopefully ones in relation to data science and/or finance