book-recommendations

[coarse frost]

this year

i am giving jee

lol

[gray gazelle]

Aye

Senior

https://tenor.com/view/salute-gif-21949953

[gray gazelle]

I will be giving in 2024

[coarse frost]

oh

well good luck

[gray gazelle]

You too lol

[coarse frost]

ty

[night knot]

Thank you!
So I guess for right now it's safe to skip the module theory?

[dapper root]

Ah shit, no

You don’t need the classification of stuff over a PID I think

But you want to know some basics I think, I forget if Eisenbud covers that

[night knot]

ah, alright

[limber swan]

Hi. I recently read Steven Krantz's 'How to teach mathematics', and I would like to know what other books about math/teaching/education would you recommend?

[gray gazelle]

does anyone know of any mooc's that can introduce me to analysis

[pliant stream]

Mit analysis?

[pliant stream]

At what level? @gray gazelle

[shell geyser]

Is Hvidsten's Exploring Geometry a good book for a first college-level course in geometry? For reference the chapters are:

Geometry and the Axiomatic Method, Euclidean Geometry, Analytic Geometry, Constructions, Transformational Geometry, Symmetry, Hyperbolic Geometry, Elliptic Geometry, Projective Geometry, Fractal Geometry
If not, any other book recommendations?

[pliant stream]

Yes, but at what level do you need to know it

And what book ar you using now that you find inadequate？

[subtle mango]

thoughts on "An Introduction to Analysis," 4e by William Wade? my real analysis 1 prof is using it this fall, so i just wanted to get an idea of what it's like

i'm using Tao Analysis rn for self study

[zealous timber]

Is there a book that exists which goes through all the foundations for higher level math? (up to like calc 2/3)

I want to refresh from the very beginning, from like basic arithmetic, to algebra, to derivatives and integrals and then discrete/finite

[quick hornet]

if you want an "elementary math in the style of higher math"-type tome, there's lang's basic mathematics

im not exactly sure what youre asking for though

if you want 1 textbook that covers literally years of mathematics, you will not find that.

[flint forge]

Higher algebra

[quick hornet]

i read higher algebra in 2 nights

[flint forge]

Damn

Too smart for me

Infinity operads are namingtons bedtime story

[quick hornet]

just a warning that it's very dense (relative to other textbooks that cover said material, that is) and assumes a lot of fluency

it doesnt necessarily expect you to know anyhting going in insofar as it explains everything, but if you dont get an individual part, youll likely just be straight unable to progress

its still lightweight in comparison to higher math textbooks but

you know how it is

those are written for dedicated students majoring in math/sci/whatever, not a general audience of high schoolers

[tropic dock]

PTSD intensifies

[vital bane]

awesome name

[grand thistle]

what are the prerequisites to this book?

this is the table of contents

[loud cradle]

i don't know the book but based on the table of contents and looking at a few random pages in the Amazon preview, calculus should suffice

[grand thistle]

ah i see, thank you

[main void]

Though i dont know the book, for probability theory, knowing multivariate calculus (especially bariable substitution for higher dimensional integrals) is quite useful.

That being said, you should just start reading the book, this type of calculus is best learned through a few examples rather than a complete course + you’ll save some time

[grand thistle]

yeah i’ve decided to read it along with munkres analysis on manifolds once i’m done studying baby rudin first 8 chapters

[main void]

I’ve never heard of this book from munkres, though if your end goal is to just learn introductory probability theory you most definitively do not need to know what a manifold is

[grand thistle]

yup ik, but it's probably something i would eventually have to learn anyway and i also want to learn it for it's own sake, since i have 0 experience with multi and i wanna do it as thoroughly as possible

i've heard baby rudin -> spivak calc on manifolds/munkres is a very comprehensive coverage of the real analysis i need to know to learn other more advanced topics

[main void]

Sure, then this seems to be a nice program. Good luck

You probably need at least some basic point set topology for manifolds btw, though, again, i dont know these books that well

[grand thistle]

yup, i think i can mostly learn along the way, which is what i'm doing with rudin

[fading wave]

Anyone got a good book rec for game theory

[gray jungle]

what kind of game theory? combinatorial or math-economics
if its combinatorial then i like Lessons In Play by David Wolfe, Michael Albert, and Richard J. Nowakowski
im not familiar with the other type

[gray gazelle]

Lmao Y

😂

[vital bane]

guys

does anyone have a link to a solution manual to "linear algebra done right" by sheldon axler?

[tropic dock]

Yea... Reminds of my jee days . Rough times

[gray gazelle]

[tropic dock]

You a jee student too right ?

[gray gazelle]

More ptsd

[tropic dock]

Cengage innit ?

[gray gazelle]

Yeah

[gray gazelle]

Ye lol

[tropic dock]

Yeaaaa.....

Pls no more of this

[gray gazelle]

😂 😂 😂 😂

[tropic dock]

Lemme ask u the question all jee students hate

[gray gazelle]

Ok

[tropic dock]

How the preparation going ?

[gray gazelle]

I have just started

In 11th lol

[tropic dock]

11th ya 12th ?

[tropic dock]

Oh okay

By the end of jee ull understand why that question is hated

Baarvi is 12th

[gray gazelle]

यारवी कक्ष

[tropic dock]

Lmao

[gray gazelle]

Lmao short circuit in brain

[tropic dock]

Anyway all the best dude

Give it your all

[gray gazelle]

Aye thanks yo

[tropic dock]

You might or might not get into IIT ,
But in the end it'll be worth it

[gray gazelle]

I will man i will

[tropic dock]

Nice to hear brother

[gray gazelle]

If i wont get into an iit

I will apply for mit

😂 😂

[tropic dock]

Just make sure where ever you end up , you just don't stop learning

That's it

Wishing you the best

[gray gazelle]

[gray gazelle]

Ty yo

[tropic dock]

Welcome brdr

[tame plaza]

still 2 years to go

[lapis sundial]

Are there any particularly good places to get started with complex geometry?

I've been recommended Voisin's books but think I need to do more basic stuff before lol

[sudden kindle]

Maybe start with a book on riemann surfaces ?

Idk actually

[lapis sundial]

Yeah I mean stuff like looking at complex manifolds and almost complex structures and all that jazz

[gray gazelle]

Zes

[near peak]

I recently started learning calculus and got a pretty good grasp of derivatives, but am away from my textbook now since I couldn’t fit it in my luggage. Any recommendations for relatively cheap ebooks that I might be able to learn from/work through in the meantime? Ideally something non-calc that would still be stimulating and doable, looking towards further math education.

[vital bane]

there's a free open stax calculus book

https://openstax.org/details/books/calculus-volume-1

[gray gazelle]

https://tenor.com/view/irodov-wtf-irodov-irodov-wtf-what-irodov-irodov-what-gif-21299485

irodov be like:

[sage python]

@lapis sundial Maybe try Huybrechts? I think I know people working on complex geo using that book

[lapis sundial]

Ah okie ill check it out, thanks!

[gray gazelle]

@woeful marsh

[primal mica]

I know it isn’t this kind of book recommendations channel, but does anyone know what is best to do about this:

I was thinking about just swapping it out for another new one, but I didn’t know if there was an easy fix with low odds of damaging the book.

It seems like you could just get a certain glue and kinda shove it down in there and let it dry, but I don't know if there's a chance it could make some other things awkward.

[timber mesa]

you mean gluing the book spine to the cover? any decent white glue can do that, though you can also look for types of glue that are better suited to book binding, e.g. https://www.thecreativefolk.com/best-glues-book-binding/

[primal mica]

Thank you, have you done this, and would it be easy to clump the glue or some other issue causing pages to bulge or not turn properly?

[timber mesa]

I do have some tiny experience with book binding, basically make sure to distribute it evenly, not get any outside of the spine etc.

since it's a hard cover (so it seems) you don't want to spine to turn anyway so it'll be fine

[gray gazelle]

U can just get a thick needle

[primal mica]

It is indeed a hardcover, okay, thank you very much :)

[gray gazelle]

And then u can use it to make holes

And then u can use yarn to

Bind it up

[sage kelp]

Thoughts on the Calculus I-III books of Marsden and Weinstein?

[timid owl]

what is a good book to start learning calculus and get a true understanding but not be a doorstopper.

[flint forge]

I think Spivak is doable as a first pass but it’s probably pretty hard

If you don’t have any speed requirements tho I think it is a pretty good way to really understand what’s going on

[timid owl]

I took ap calc bc in high school and have done some basic proofs from doing a bit of self study in discrete math, is that enough of a background? Im starting college soon and my first semester is calc 1 then my second is calc 2

[pliant stream]

Why are you repeating calculus?

At any rate, I wouldn’t read a “rigorous” calculus book

I would just read an analysis text if you’ve already seen calculus

[timid owl]

I missed the bc exam, I was 4 hours late to the exam.

[pliant stream]

Your school might have an exemption test for the calc sequence

But if you have already seen calculus, just start reading an analysis book

[loud cradle]

i think there's merit to reading spivak or apostol as an intermediate step if you've only seen completely non-rigorous calculus (never heard of epsilon-delta, total handwaving definition of limit, etc)

otherwise the likes of rudin will likely be impenetrable

[pliant stream]

Then just read like abbot

Or mit also has a analysis ocw with videos too now

Might be worthwhile

And personally I’ve tried to read Apostol initially to learn, but I understood nothing and had a really hard time

i think there really isn’t much of a difgerencebeyeeen Apostol and say Abbott

Obviously Apostol will teach you calculus better and Abbott analysis better, but difficulty wise, I think they should be pretty similar

[crimson leaf]

They're okay I had the calc 2 book as a course text

[sage python]

Abott is similar to Spivak imo, phrases things slightly more topologically

APostol is more old school

[coarse frost]

and is also very good

[timid owl]

I wouldent think im ready for something like analysis

[runic hatch]

I’d say to give it a try

If you feel like you’re going too slow you can downgrade

[shell geyser]

Woah didn't know this. That's epic.

[lime sapphire]

When ppl say apostol do they typically mean calc or analysis?

[sage python]

This setting was calc

And I think that's the one that's generally more well known

[warped stump]

Does somebody know if there are solution to Basic Mathematics by Serge Lang?

[tender cedar]

YEAH

yeah

I'm trying to find it for you

I think they have it in the springer website

couldn't find it, mb

[hearty steppe]

I bet you guys don’t happen to recommend what I can look at to learn more about what’s going on with Ruliads besides Wolfram’s take

Seems like that’s gona be exploding in the math community

Rule space*

Seems like a bunch of functional based sets and operator specific stuff with combinations of outcomes

[flint forge]

I am not an expert or anything

but my understanding is very few people take wolfram's work very seriously at the moment

[hearty steppe]

Well he does have a nice sandbox model of playing with stuff like molecular structures

And see whether or not what he says has weight

I have nothing to lose working on a literature review publication that can criticize his ideas alongside with Kolmogorov’s when it comes to complex dynamics. It is gona kick my ass too

This is a very nice take https://writings.stephenwolfram.com/2021/11/the-concept-of-the-ruliad/

I don’t mind trying to criticize it with what I’m working on if I can and get publication experience at the same time

[flint forge]

I would recommend learning something more main stream, to be honest

I am not even certain that original work about ruliads has been published outside of wolframs own website

[hearty steppe]

So the context of this would be molecular structural dynamics and bond integrity, mainly looking at what’s going on with electrons

Yea I’m mostly gona look into Kolmogorov’s ideas

Wolfram is just extending at scale computationally what Kolmogorov is saying

Is there anyone besides Kolmogorov though I should look into in terms of these ideas?

[warped stump]

Ooh thanks for the help!

There are other problem books with answers

[gray gazelle]

I generally like this type of course syllabus for following along a book, lots of problems for you to focus on
just I can't find one for chapter 1 to 4 of friedberg, the instructor doesn't teach linear algebra 1
http://www.math.toronto.edu/payman/mat247/main.html

[timid owl]

Note that I plan on majoring in electrical engineering, so would I really get a benefit from studying calculus in a rigorous way?

[solemn rover]

I am an electrical engineer and I would say that formal epsilon delta style arguments are probably not useful in engineering most of the time. However, I would say the better your understanding of mathematics, the better you'll understand the basic building blocks of engineering. For example, a thorough grasp of the Laplace transform and the Fourier transform is an essential part of the engineer's toolbox

That said, studying epsilon delta arguments and more generally learning rigorous mathematical proof will open up an entire different world.

[timid owl]

Alright thanks for your advice, Im going to go for it then.

[novel obsidian]

So do you do maths only for your work or is this a hobby for you?

[lilac girder]

I wanted to know how do you decide what questions to do. I decided to only do odd questions

[gray gazelle]

anyone have any syllabus' or courses following zorichs mathematical analysis by chance?

[viscid citrus]

Has anyone here tried Terence Tao's Analysis 1 and can recommend it?

[subtle mango]

i am on chapter 10 of tao analysis 1

i started at chapter 6 since i already knew construction of reals and whatnot

i think it’s nice

good problems, things are laid out pretty clearly

[viscid citrus]

Ok, thanks. Sounds nice.

[solemn rover]

I personally love proof-based mathematics and so I would encourage you to give it a shot.

[solemn rover]

I am engaged in mathematical research and I hope to publish some papers soon. I wouldn't say it's purely a hobby. Having publications on your resume is good.

[timid owl]

personally in your opinion do you think that spivak is good for self study though?

[fading wave]

thanks

[hearty steppe]

I can probably use Ruliad spaces for different bond arrangements for molecules that are pretty much almost identical that’s what I’m thinking

Like we have these molecules that are pretty much identical and then when we pair them with some different molecules we gotta figure out why different things can happen

Especially at scale when you have patterns of chain-like arrangements

Or lattices

Kolmogorov might be the goat tbh. If I had to pick a mathematician that was the most important to mankind right now, it’s probably him.

That and Riemann

[lilac girder]

Has anyone ever done a curriculum that does basic math to higher level math?

[blazing canopy]

In a single year?

I've seen some math crash courses, mainly for students attending college who were out of school for a long while, and they often do a fast review of basic math going all the way up to the end of high school math in a single year

[lilac girder]

more of something for the average person (me) to go from doing basics to advanced math

[blazing canopy]

I don't feel that this is enough information. What makes regular courses that go through high school-level, and then early college-level math unsuitable?

[flint forge]

You might also describe what "advanced math" means to you

also what basics means

[solemn rover]

I have not studied spivak. I think it's worth trying and putting effort into.

I was a teaching assistant for a course that used Apostol's book on calculus, which is similar to spivak, and I thought it went well.

For an engineering student I would recommend heavier priority on computational fluency in calculus than epsilon-delta arguments. Both are important and I do encourage you to study rigorous proof-based calculus. But computations and hands on experience will help with the intuition for abstract concepts of real analysis. So please consult Stewart's book on calculus as well, which is more focused on computational fluency than rigorous proof.

[lilac girder]

true, since what i think is hard you guys might think its basic

real analysis/topology/Stochastic calculus?

[flint forge]

And basic?

Like what do you currently know well

Because learning those three subjects in one year is by itself very hard

let alone one course lol

Oh unless you just mean like

a pathway

I think that planning too far ahead isn't important

its better to take it one book / subject at a time

[lilac girder]

Currently doing work on Stewart's calculus and Discrete Mathematics with Applications Susanna

[blazing canopy]

as an undergrad we used Apostol's course Calculus Vols I and II (one year course) as a bridge between calculus at the level of Stewart, and more advanced mathematics, you could look at that

[lilac girder]

Thank you!

Did you use Apostol after taking a calculus class?

[blazing canopy]

Yes

Apostol's course is a lot more than just "calculus" despite the title.

It would be a very bad idea to use it as a first course in calculus

It was used as the first-year mandatory math textbook when I was an undergrad and it was famously unpopular, but specifically for the purpose of preparing students for higher level math, it is not b ad

[vital bane]

woah so you're an engineer but you're doing actual math research? niceee lol modern day oliver heaviside

[sonic sparrow]

Which is better: Book of Proof by Hammack or How to Prove It by Velleman?

I want to read Spivak afterwards 🙂

[vital bane]

I'm doing "Mathematical Proofs: A Transition to Advanced Mathematics"

it's pretty good so far!

[sonic sparrow]

I'll take a look at it

[grand thistle]

idk the first one but how to prove it was pretty good

but i didn’t read the whole thing, i found doing proofs in linalg/group theory really helped solidify my understanding

i only really read chapter 1-3

[zealous bane]

Vouch for How to Prove It!

[sonic sparrow]

Does anybody with experience of both How to Prove it and Book of Proof have a preference?

[novel obsidian]

How'd you find balancing your job and research?

[shell geyser]

I doubt many people would read both books since they likely cover similar ideas. I thought Book of Proof was pretty good, which was the one I used. Though seeing the number of people vouching for How to Prove It, surely you can't go wrong with either choice.

[gray gazelle]

Algebraic Geometry with minimal prerequisites

[rich harness]

any book recommendations for competitive programming...

I am new to this space..

[gray gazelle]

Goes to a math server and asks about competitive programming books, sigh

[alpine pulsar]

maybe check out a server more geared to the subject at hand. 😁

[rich harness]

isnt this a math server..?

hmm.. ok.. thanks for suggesitng

[alpine pulsar]

Yes, math, not computer programming, sure may go hand in hand at times, but, a server dedicated to your subject may be more likely to help, and you're welcome.

[timid owl]

alright, I actually have a copy of stewarts book although its a total doorstopper 😅

[heady ember]

Just find math books in pdf form on the internet for free lol

[timid owl]

Although couldent I just get my dose of rigourous math from discrete math though instead of calculus and focus on calculus more in terms of computation? Because I have been working though Discrete math and its applications by Kenneth Rossen.

[heady ember]

Just do Enderton
(Jk)

We do love staring at definitions / questions for hours

[timid owl]

Hmm I did find apostol which I think has a better mix between rigor and computation, but ill figure it out, thanks for your advice.

[mystic verge]

Any good books that you can find at the library that are just good to read?

[heady ember]

"you can find at the library" is way to unspecific for anyone to answer properly imo

unless you're referring to zlib

[timid owl]

what genre do you like?

[timid owl]

if you like political philosophy or have any interest in it then the works of Karl Marx, Fredrick Engels, and Vladimir Lenin are pretty interesting to read.

[solemn rover]

bro i've got a book recommendation for you

this book will knock your socks off

are you ready

"Essays on Marx's Theory of Value" by I. I. Rubin

Don't sleep on it man

[vital bane]

[gray gazelle]

CCCP flashbacks..

[vital bane]

the good old days

[brittle latch]

anyone have a good set of algebra lecture notes by any chance?

[gray gazelle]

We have just started with algebra

Basic stuff

But yeah i have handmade notes

[brittle latch]

oh i meant like prof notes like hatcher with topology lol

[foggy relic]

Shin has very nice Galois lecture notes

I don't think their prof gave it to them, but rather they wrote them from lectures

(it's more of a reference of definitions/results than exposition though tbh)

[brittle latch]

yeah im just looking for a refresher tbh

[foggy relic]

Ok yeah it's probably perfect then

You should ask them if they can send it to you

[brittle latch]

@primal summit sorry for ping but hi

[primal summit]

I live-typed them during lectures

@foggy relic you can share them with nitezba (I just don't have the file on hand)

[primal summit]

Yea the lectures didn't have too too much exposition. I wrote pretty much everything

[foggy relic]

Alr

On mobile rn I'll send it when I'm back home

[fervent perch]

people who can live type notes are so goated

[livid ermine]

What are prerequisites for Kashiwara's categories and sheaves?

[astral cape]

Hello world, any book recommendations for calculus and GRE quant test preparation ...

[solemn rover]

What are you trying to get out of it? I don't really recommend it as a first introduction to anything it's talking about. More of a reference work to somebody who's already comfortable with category theory and homological algebra

Kashiwara has another book, "Sheaves on Manifolds" which is more accessible

[gray gazelle]

how to get comfortable with category theory and homological algebra

[dapper root]

Read the last two chapters of Aluffi no cap

[foggy relic]

its amazing

[dapper root]

Yeh

[primal summit]

Read rotman homalg if you want a very gentle introduction

Rotman cradles you so gently

[mystic verge]

Sorry so late, but any genre

[timid owl]

I enjoyed this one, A bit sorrowful, but a very good book. I may be a bit biased since im a bit of a history buff, but give it a read, Im sure you will enioy it.

[balmy flume]

does spivak's calculus on manifolds require some analysis or can I read it with just some linear algebra?

[gray gazelle]

You’re gonna need some R^n analysis and point set topology and linear algebra and (arguably/optional) group theory

[queen badger]

Hiiii

Does anyone have book recommendations for practicing and learning algebra1? Like quadratics factoring linear equations and stuff at that level? Thank you!

[oblique quarry]

If you ask me I think you should go to ESA publication online! They have all sorts off books for any subject! From maths statistics, algebra, to even art, pe, and geography ect! It's helped me quiet alot! You should try it :)

[queen badger]

Oh wow Thankyou so much!

[oblique quarry]

No worries :D

[pliant stream]

The book covers diff and integration in Rn, so I don’t think Rn analysis is a prerequisite

[sharp latch]

This is a great book

[solemn mantle]

Has anyone read “Mathematics Made Difficult”?

https://www.amazon.com/dp/0529045524#aw-udpv3-customer-reviews_feature_div

[quick hornet]

why do you ask

[crude sage]

This isn't a book, but does anyone know the name of the blog post that describes the differences between learning math in undergrad and grad school? I don't know who wrote it, but it mentions how undergrads are taught math with a bottom-up approach while grad students get exposed to jargon and gradually come to learn what it means.

I've been looking for this for a while, but no luck so far

[heady ember]

One difference i read about before is that

In one uni the depression or mental illness rate (can't rmb which) is like 47% among graduate students

[crude sage]

Wow I hope that's not representative

[balmy flume]

sorry for the ping, but would you have any idea what the pre reqs for it are then?

[sage python]

Spivak Calc on Manifolds mostly needs proof-based calc/analysis on R + probably some linear algebra

[grand thistle]

what abt topology

[vital bane]

it was terrance tao's blog

https://terrytao.wordpress.com/career-advice/theres-more-to-mathematics-than-rigour-and-proofs/

based on how you define it, i dont think this is it

but it's similar! also it's terance tao, who doesnt like tao :D

[crude sage]

Oh yeah that post gets quoted a lot

[karmic thorn]

The book develops the topology it needs

[pliant stream]

If you read the prefacs

spivak says the only formal prereq is the usual mathematical maturity and a good course in calculus, at the level of Spivak's calculus for example

and I would probably agree with that

[river tangle]

Guys any good books for beginners on abstract algebra?

[inland hatch]

@river tangle Undergraduate Algebra by Serge Lang and A Course in Algebra by Vinberg. I’m reading both but the second is a very fluid, conversational book.

The author stated in his preface: “following my conceptual point of view on mathematics, there are almost no technically difficult proofs in this entire book. Exercises are interspersed with the text and flow naturally out of discussed concepts.”

I agree with his viewpoint

It’s published in the “graduate studies” series but don’t let that scare you, it’s definitely a first algebra book

He has a really beautiful chapter that motivates determinants as area functions of boxes and deduces their properties from that perspective

[neon tiger]

so can any one reccomend then

yes i need it for high school and olympiad stuff

[oblique quarry]

Best place of I'm being honest is ESA study guide publication

It has everything thetr

*there

[hearty steppe]

I actually really like this paper

Almost forgot about it

[neon tiger]

which one

for geometry

[river tangle]

Do u think it is beginner friendly and what are its prerequisites?

I am still a highschooler

[grand thistle]

usually abstract algebra books require only mathematical maturity as in like proof writing, etc

if you've never seen proofs maybe try discrete math or something first

dunno about beginner friendly since i've never used those books

[grand thistle]

i think a motivated high schooler can do some abstract algebra with some effort

i'm in the same boat and i'm about 8 weeks into a group theory course

it's pretty managable

it does take some effort and banging your head against the table at times though

[halcyon garden]

I've heard "Visual Group theory", Nathan Carter is a good book for high schoolers. There is also an online course http://www.math.clemson.edu/~macaule/classes/s22_math4120/ based on the same. It's more advanced than the book though. The lectures are on yt.

For a more standard but still gentle intro, there's Gallian.

[tropic dock]

Anybody here uses Arthur Engel -problem solving strategies ?

[oblique quarry]

I don't really know what ESA books are there but I know there is a geometry one.

@neon tiger

[river tangle]

Hmm

[river tangle]

I am doing discrete maths from a few weeks lol

[grand thistle]

yeah that's good

maybe try some abstract algebra

and see how it is

[tropic dune]

does anyone know to find the pdf form for this book? I've been searching everywhere

[tropic dock]

You do ?

[crisp river]

Thoughts on griffiths and harris principles?

[river tangle]

Well tbh I tried it and it's really a good one but needs high mathematical maturity which i still lack atm

[next storm]

Book recommendation for learning proofs?

I have Book of Proof by John Hammock but found it too simplified and at the section on Cartesian Products it defined Cartesian Products in terms of 2 sets which wasn't a very general def.

[karmic thorn]

I don't think extreme generalities should be a goal in a book introducing proofs

Better, if you feel that you can generalise one of the presented ideas, it gives you room to come up with definitions and general versions of theorems, etc. on your own

[pliant stream]

Defining an infinite Cartesian product is problematic anyways

[karmic thorn]

Which can be rewarding

[pliant stream]

Because then you need choice

and plus, defining the Cartesian product of two sets is identical to defining for any finite number of sets

[still panther]

you can still do stuff with the general definition, like proving commutativity/associativity or proving that it coincides with finite product

or like, exponentiation as repeated multiplication

[pliant stream]

How is infinite cart product commutative

or cart product in general

And it’s only associative assuming your operations you define on your cart product are suff nice

[still panther]

if you have a bijection f between the index sets of $\{x_i\}_{i \in I}$ and $\{y_j\}_{j \in J}$ such that $x_i = y_{f(i)}$, then $\prod x_i$ is equinumerous to $\prod y_j$

hmm does latex bot refuse when you type in ```

[still panther]

wdym, its finitely associative if you split your index set into several parts, thats what i mean by associativity

[heady ember]

Why is choice "problematic"

[still panther]

i dont see much purpose to explaining what choice is in an intro book to proofs

i guess you would like to have choice to prove that countable union of countable sets is countable

[next storm]

What’s good book for learning proofs?

https://tenor.com/view/puss-in-boots-cat-cute-kitty-begging-gif-11691445

[still panther]

book of proof seems like a nice resource now that i am looking through it

if you are comfortable with the kinds of proofs it presents, i would move on to just regular math books?

[gray gazelle]

@next storm I haven't read it but

introduction to discrete math by scheinermann

[crisp river]

I suggest not doing book of proof ever

[gray gazelle]

@crisp river why

actually I want this answerd too

do I read the discrete maths book I mentioned or book of proof? @crisp river

[crisp river]

Why do you want to read book of proof

[gray gazelle]

to learn proof writing

[crisp river]

For what purpose

[gray gazelle]

to learn discrete math/analysis/linear algebra

[crisp river]

In my opinion its better to start there

at a certain point math learning isnt linear

you can try to learn how to proof write by learning linear algebra for example

[gray gazelle]

that's what I thought too about the discrete math book

it says it can be used as an intro to proofs

[crisp river]

it should be in my opinion

you linear different proof methods as you learn

[gray gazelle]

feels a bit redundant to me read book of proof THEN à discrete math books

[crisp river]

it might be

[gray gazelle]

alright do you think reading the discrete math book then skimming book of proof for things that I missed a good idea? @crisp river

[crisp river]

yeah probably

[gray gazelle]

alright

[crisp river]

also asking people to read your proofs

[gray gazelle]

so I can verify that they are correct?

[crisp river]

thats a part of it

also you learn how to communicate which also helps you write proofs better

early on you will be able to know when you are correct by yourself

you develop a sense of absolute confidence when you get to a certain point in math and you can sort of gauge how confident you feel in your answers

[gray gazelle]

I see, thanks for the advices

[crisp river]

no problem

[foggy relic]

Look up solutions manuals

Sometimes you might find someone’s solutions manual on GitHub

[vital bane]

but how do I know that it isn't wrong?

[gray gazelle]

By people to reread your proofs, reread your own proofs

[vital bane]

[gray gazelle]

*asking

[vital bane]

*forcing

[next storm]

I wanted to learn proofs, Burton's Elementary Number theory, and Predicate and propositional calculus book so I could start doing abstract algebra and analysis. Book of proof is pretty good tbh. But not rigorous enough for my purposes which is why I'm looking for a second book to add that.

I have Rosen's discrete math but it doesn't go in depth enough on any given subject to care to go through the whole book.

On page 11 book of proof so far pretty good intro level material.

Book of proof has a chapter on counting btw which is great for CS.

[viscid citrus]

Any books that could be an introduction to CS/programming?

[next storm]

How much programming have you done?

Depends what you want to do with programming. Python is always a good starting language.

[whole anchor]

i recommend humble pi by matt parker if you want to have a chill read related to maths

[viscid citrus]

I know Python and Java basics

[next storm]

There's more material on youtube than there is in books.

[next storm]

I bet that was fun learning to program Java.

[crimson leaf]

I know people like SICP (if you feel up to it) not sure about SICP JS

[crimson leaf]

You should be ready to do analysis after book of proof tbh

You maybe could do some LA if you don't have any of that though

[gray gazelle]

where is general

wait it goes away with studying role

[next storm]

wha?

[next storm]

No I wasn't planning on it.

[next storm]

It's a good book tbh

[pliant stream]

Suggestions to learn the prerequisite material in 30 days?

Reading royden right now, perhaps a list of exercises to do?

[gray gazelle]

Try finding a course syllabus online

[glad prairie]

Oh I took this last year

Paul will go over measure theory very quickly and very abstractly

Unless he changes that

I didnt know any probability theory going in and that wasn't a big deal

But being comfy with real analysis and measure theory is important

Royden is probably fine

The class is quite hard and quite work intensive

It was a lot of fun imo

But I also know a lot of people who did not have a good time

[pliant stream]

💀

sounds good thank you lol

[forest sleet]

you could pick up a probability textbook that starts with defining measures if you need to catch up fast

they'll probably get to radon-nikodym a lot faster than a usual real analysis course

[pliant stream]

do you know approx. what section of royden i'd need to be reading through

I'm at the part where he just introduced lebesgue measure lol

[unreal minnow]

Can anyone recommend me books on mental math, speed math and geometry?

[pliant stream]

ah i see true that's a good idea

[forest sleet]

I'm not familiar with Royden but you will need measure theory in general that is not on R

[sage python]

Ah washingbear actually what do you think is a good source for probability? Let's say I wanna see measure theoretic treatment but don't need to go into super detail on technical matters (e.g. I know Durrett has n different forms of the LLN with slightly different hypotheses, that might be a bit much, though I don't stress on this point)

[forest sleet]

I'm not sure unfortunately, but not Kallenberg lol

[sage python]

And ideally it gets into interesting problems (prob some practice with finite probability/combinatorial stuff), connections with other areas of math

[forest sleet]

I got that book

and uh I tried to look up defn of Poisson process

let me see if I can find it

I was going to take a look at Cinlar at some point

[pliant stream]

ah shit

okay lol

so like "abstract measure"

[forest sleet]

yeah just general abstract measure

in some ways it is simpler than Lebesgue measure on R

since they just give you the definition

and you don't go through a ton of time showing it works the way you want, or defining outer/inner measure, etc.

[analog lava]

@forest sleet what u just said is amazing

[pliant stream]

so i guess basically need to know all of 3?

[analog lava]

i dont think so]

i think ur just going to need uptill 18

the rest just seems like functoinal analysis

u should ask

u might need 20 tho

[pliant stream]

ah okay

i can't ask otherwise it will be really weird

💀

[analog lava]

just ask man

its okay

[forest sleet]

that book might be a bit overkill, although I don't know the specifics of the class

[forest sleet]

from what I remember Durrett might actually be ok for that, I remember they had a lot of examples for discrete-type things

The topics in Cinlar seem very nice

so I guess I would recommend trying out Durrett or Cinlar

both are used for standard measure theory probability class

[glossy yarrow]

Hello
I need good introductory textbooks for -
Combinatorics
Number theory
Graph theory
Trigonometry
Calculus
Linear Algebra
Probability Theory

I am 16 and currently using Spivak's Calculus (which I feel I am able to understand with some effort), SL Loney's Trigonometry. Any suggestions would be greatly appreciated.

[sage python]

@forest sleet sory I was out, but hmm

[sage python]

@glossy yarrow so, overall I don't think there's much of a point in having a stack of books well in advance. If you're not gonna get around to some topic for a while, your goals (and thus what the best book for you to learn that topic is) may very well change by the time you start studying it, and what book you eventually use for, say, linear algebra, doesn't likely have much influence on how you go about studying calc now. That said, to entertain your curiosity and because I like hearing myself talk/give opinions, I'll provide some commentary.

I'll assume based on the topic selection and your use of Spivak that you're probably at least somewhat interested in theory and if anything are biased more toward CS than physics.

Spivak is good for calculus, if you're handling it and not on a rush I'd say no reason to change it. Let me know if you're also thinking multivariable calculus, since that is its own complication.

Trig to me doesn't need its own book, but if you're enjoying Loney then sure keep it up.

I like Weil's Number Theory for Beginners for a short/sweet intro.

I learned linear algebra first from some lectures not tied to a reference, followed by reading/doing a bunch of problems from Hoffman-Kunze. I like the book, but it's a bit long, slightly on the hard end though not excessively so imo, and a bit old school (dinosaur-era typesetting, starts with an awkward treatment of matrix row reduction that I imagine used to be common). Friedberg-Insel-Spence seems more modern and a bit easier. I wrote a longer review of books in pinned messages.

For the other topics, I didn't learn much out of books. Ross seems to be the most common book for probability. http://people.cs.uchicago.edu/~laci/20comb/ and http://people.cs.uchicago.edu/~laci/21graphs/ give some mention of books on combo and probability.

Hope this helps

[glossy yarrow]

I'll assume based on the topic selection and your use of Spivak that you're probably at least somewhat interested in theory and if anything are biased more toward CS than physics.

I am very interested in theory however I am biased more towards physics.

Let me know if you're also thinking multivariable calculus, since that is its own complication.

I do want to learn about multivariable calculus, differential equations among other topics but I have little to no idea how to go about it.

Hope this helps

This was very helpful. Will definitely read your book reviews and check out all the mentioned books and links. Thanks a lot😄

[frank lava]

What are the bookreccomendations for Linear Algebran problems? Only interested in books with lots of problems

[heady ember]

A lot of ppl will disagree on that

LADR being bashed is like breakfast here

Look at pinned to get an opinion on several LA books

By dami iirc

[steady wagon]

is understanding analysis by abbott good for a first course in real analysis?

[halcyon garden]

What my uni did, is spend the first 2 weeks on the computational part with gaussian elimination and other stuff (Matrices chapter of Artin) then we went to Axler

I really liked Axler eventhough it was used in a first course (maybe because it was my first intro to proof based math)

[karmic thorn]

Yes

[hearty steppe]

anyone familiar with this text? https://link.springer.com/book/10.1007/978-0-387-22464-0#toc

i forgot i had it buried in my notes

also I had THIS guy buried in there too https://en.wikipedia.org/wiki/Leslie_Valiant#Research_and_career

[gray gazelle]

Fuck you

[pale sapphire]

lol

[solemn rover]

Somebody has published an actual linear algebra textbook called "Linear Algebra Done Wrong" btw, it's meant to be a satirical comment on Axler's book. It focuses heavily on matrices from the get go

[gray gazelle]

That's funny haha, didn't know that

[timber mesa]

drinking game take a shot everytime LADR is bashed in this channel

[rapid flame]

any (literally any) old-fashioned/rigorous precalculus textbooks? looking for ones around 1950s-1980s thank you

[vital bane]

idk any but im curious why you're looking for old ones

[gray gazelle]

Sheldon Axlers precalculus

well

Idk if it's from that era

But

It's rigorous (technically) and precalc

[pliant stream]

I mean it's basically impossible to be rigorous without actually discussing calculus

For example, what does multiplication of real numbers even mean?

[cyan yarrow]

2 * 2

[remote slate]

Any book recommendation for learning set theory?

[gray jungle]

halmos

[remote slate]

Naive Set Theory?

[gray jungle]

yes

[remote slate]

Thanx man

[remote slate]

But no questions for practice? Like exercise questions...

[gray jungle]

there is usually 1 question given within each section if i remember correctly , dont really need more but if you want you can use exercises from another book like enderton's elements of set theory

[remote slate]

Okay

[sand temple]

Any books to prepare for Mathematics Admission Test (MAT) for Oxford University.

?

[gray gazelle]

best introductory real analysis tb?

[vital bane]

understanding analysis by stephen abbott

and then mathematical analysis by tom apostol

[shell geyser]

From my experience with the MAT, there is no real book to prepare you for it, since the content you need is already covered in school. I'd recommend just working on past exams. A similar test is Cambridge's STEP, which does have a support site (https://maths.org/step/welcome) but do note STEP covers a lot more than MAT so not all of this is useful, though might still be a good source of problems.

[lapis sundial]

Yeah TMUA is probably helpful too for the shorter answer questions, more so than STEP, though I guess it really depends what you wanna focus on lol

[hearty steppe]

Anyone familiar with computational origami and where I can learn more about it?

[solemn rover]

I second Enderton

[near peak]

could someone recommend me a book on equalities? I’ve looked at spivaks calc but found that when it came to doing proofs and shit with inequalities my base was completely lacking

[loud cradle]

you mean practice with specific inequalities like cauchy-schwarz, holder, jensen, etc?

[cursive orbit]

there's the cauchy-schwarz masterclass

[sage kelp]

When I found out about that inequality book I was vey surprised

[pliant stream]

I skimmed through the way of analysis

It’s probably the best book I’ve seen

[timber mesa]

you probably want something more basic, grab a precalc book or watch Khan Academy

[timber mesa]

this is a good book if you want to do more adv math though -- it motivates many of the most well known ineqs, provides historical context and usually generalizations

[gray gazelle]

That happens to everyone, shit my biggest fear when starting analysis was inequalities

Just do the chapter 1 exercise of spivak and inequalities and keep at it

*of

[karmic thorn]

What are the prerequisites for Bredon's Topology and Geometry? I want to use it to go through the bare minimum necessary of general topology, which it seems to cover in its first chapter.

[stray cloud]

good morning, is anyone know statistical learning book? I find the book from Gareth James is pretty hard for me to understand. Thank you

[loud cradle]

have you tried Bishop's Pattern Recognition and Machine Learning (PRML)?

[stray cloud]

no. I will check it 🙂 Thank you.

[loud cradle]

if that one's too math-heavy you could also try Duda's Pattern Classification

both are pretty nice

[stray cloud]

Thank you :))) I will check it

[pliant stream]

Wait isn't intro to stat learning oretty bare bones on math

[loud cradle]

iirc, a bunch of pictures and R code, not a lot of math

that's why it's hard to understand maybe

[pliant stream]

Id think it's unlikely for someone having trouble with ISL to have more success with those books, no?

[loud cradle]

😁

[pliant stream]

Oh lol maybe

[loud cradle]

well tbf, @stray cloud didn't say why it was hard to understand

my eyes glaze over when i try to look through ISL, but I like PRML and Pattern Classification quite a bit

[stray cloud]

yes, it was hard for me especially I am not from Europe and the book was pretty different (more easier to understand)

[pliant stream]

Tbf it's mostly just some intuition handwaving and then formulas thrown at you, so if you don't know basics of inference already, you'd probably be lost, like i was

[gray gazelle]

Linear Algebra Done Left

[tawny copper]

Enderton is very readable and doesn't demand background. Look at the pinned comment on list of Logic books, there are other recommendations for set theory you might like

[heady ember]

I get slapped by Enderton when i try to read it/ do the exercises in it

But i just continue anyways

[remote slate]

Buddy me too prepping for MAT

[sand temple]

How's the prep going?

[brazen jungle]

nois

[remote slate]

You too Prepping for MAT?

[lapis sundial]

Ah best of luck for MAT

[bitter raptor]

In my experience the best practice for these kinds of tests is practice

Ie doing previous papers

For the format obviously use MAT papers but for the questions I’d use STEP, they’re harder and all around more varied

[hidden sparrow]

Can someone recommend a book(s) for precalculus + early calculus + linear algebra problems with solved solutions? I already know the material and don't need introduction but rather I want to grind a thousand practice problems to internalize what I know (my book ran out)

[gray gazelle]

Hi, great question! I am also interested in origami. I think there are some MIT lectures on origami by Eric Demaine. There is also a blog called abrashiorigami exploring some origami related theorems, but its more about designing origami as art. There is a famous book by former NASA physicist Robert Lang about the theory of origami, its called Origami Design Secrets. It talks about origami as an art but has also a mathematical perspective. There are also some origami related discord server where many people are studying mathematics or engineer realted subjects. DM me if you want to join, these people know probably a lot more than me about origami. What exactly do you want to learn about origami? There are a lot of things that can be done with origami.

[errant heath]

I’m looking for a book that either references how to read proofs or a book on how to read proofs. Assume low level of math understanding

[analog lava]

vellemans how to prove it

[dusty grail]

Does anyone know of a book which has a good exposition on functions, their formal definition, and how that definition is commonly applied?

[pliant stream]

given that functions permeate just about all of math

just about any book on math?

[errant heath]

Wow! Thanks

It’s noted that only HS math is assumed

So would that include calc?

[analog lava]

no

you do not need calc

probably has some examples involving calculus identities

but no you can just skip

[errant heath]

Okay!

[remote slate]

Which book will provide me with problems on special series

Like (2+3+5+8+12+...
Find the sum of n terms) this kinda problems

[ornate badge]

is it worth reading both a lin alg book and an algebra book (and which books are recommended?)

more specifically, I'm looking to learn analysis & algebra over the next couple of months (for background, I've worked through the entirety of spivak's calc and I know multivar, although I'm also on the lookout for a book that would provide a more rigorous treatment of the subject; I've also taken nt, discrete, and set theory courses)

are there any books that y'all would recommend (for any subjects mentioned above)?

[final magnet]

Have you covered APs, GPs, etc might just help you out Nd give you a pretty good approach to such questions

[loud cradle]

for linear algebra my default recommendation would be Friedberg Insel Spence, and also check out Treil's Linear Algebra Done Wrong (the latter is freely available as a PDF on the author's website)

[heady ember]

Check out the pinned messages

[loud cradle]

for algebra I guess dummit and foote but it's a pretty dry read, and somewhat encyclopedic

[ornate badge]

ty! I'll take a look

[ornate badge]

mm yeah I read through them before posting but I was a bit confused abt a couple of points; i.e. a number of the recommendations recommend prior lin alg knowledge, so would it be better to pick something more self contained (/ that introduces lin alg in it) or try to learn lin alg (before? concurrently? I'm not sure) starting books on analysis and algebra?

also didn't parse the whole message on real analysis books very well (... I draw that one of the first 2 in the list would be the most recommended for me? 😵‍💫 )

would also like to find a good text to brush up on multivar at some point since I feel like im sorta shaky with it

[ornate badge]

yeah! a couple of ppl have told me that they used d&f in their classes, but im not sure if it's the best for self study and/or how much motivation the text provides :0

[loud cradle]

beware, there is no pinned message for introductory analysis books, all of the ones in the first message are for basically a second course in analysis (with measure theory and lebesgue integration)

[loud cradle]

i find it super boring myself but it does have good exercises and good coverage of material

[ornate badge]

oh really 😵‍💫

[loud cradle]

but if that was my only exposure to algebra i would probably hate algebra

i'm not sure what 1 and 2 refer to, but a good introductory book is abbott's "understanding analysis"

if you've already had rigorous calculus (with epsilon/delta proofs as in spivak's calculus) you can go straight to rudin's "principles of mathematical analysis"

[ornate badge]

mm what other books did you read?

[soft spruce]

I’m trying to get the solutions manual for the book Proofs and Fundamentals by Ethan Bloch. Do you think it is possible, or do you have it?

[ornate badge]

oh also are there any reccs for a multivar book?

[remote slate]

Yeah covered that, but want to solve some good amount of questions of this kind

Where will I get them?

[heady ember]

~~John Lee ~~

[vital bane]

Multivariable mathematics by theodore shiffrin

there's even a playlist of videos of him teaching that class on youtube

which follows that book

[whole anchor]

“Things to make and do in the fourth dimension” by matt parker is great if you wanna have a chill read about parts of math that are actually fun

[sand temple]

Like could someone explain me in simple terms what additional thing does a 4th dimension have to 3rd dimension?

In 3-d we have length, breadth and height. What does 4d encompass?

[still panther]

nothing? its just a dimension

[sand temple]

But how to visualise it?

[still panther]

you can visualise projections of it into 3d

[sand temple]

Is hyperbolic geometry that?

[still panther]

no, hyperbolic a non-euclidian geometry

[alpine plover]

Latin...

[sand temple]

Sure but what dimension would you say hyperbolic geometry is in?

3d only?

[alpine plover]

2.5D

[still panther]

you can make a hyperbolic space of any dimension

[sand temple]

So to define hyperbolic space

Any space with negative curvature?

[still panther]

i dont think so? im out of my depth on this one though

[gray gazelle]

Hello.

Any good texts for getting an introductory treatment, but with some depth on the algebra and geometry regarding:

1. The General Linear Groups ( and special linear group )
2. Affine Algebra / Affine Maps / Affine Geometry
3. Projective Algebra / Projective Maps / Projective Geometry

*Ideally at a early grad or late undergrad level please.

[river aurora]

need a book recommendation for analytical geometry
i have read jee level books and now wanna learn the abstract things like plucker's μ

[gray gazelle]

Please recommend some good beginner level books for Game theory

[fickle whale]

It doesn't really work like this but you can think of 4D as duration

As an example

[hearty steppe]

Hey I figured I’d ask about some computational origami book recommendations

Nobody seemed to bite last time I asked

[vital bane]

it encompasses a 4th dimension

think of 2d being asking the same questions as you, but instead of asking about the 4th dimensions it's asking about the 3rd dimensions

it's asking "In 2-d we have length and breath. What does 3d encompass?"

explain that to that 2D being

and remember it has literally no notion of "height"

all it knows is length and breadth

also this might be helpful to you

it's a fun book

the books is about

"In a two-dimensional universe populated by a hierarchical society of geometric figures, a square is persecuted for attempting to reveal its new knowledge of a third dimension, learned from encounters with a sphere."

[sand temple]

oh wow, thanks a lot!

[vital bane]

you can generalize the same line of thought to n-dimensions, any arbitrarily large number of dimensions

except infinite dimensions

They don't make sense to me

they're weird

[trim solstice]

How is langs undergraduate algebra and linear algebra?

[subtle mango]

prereqs for Quantum Theory for Mathematicians by Hall?

[hearty steppe]

Huh I have not heard of this book?

I am currently working through Griffiths and it’s a great read so far. I am only on chapter 2 tho. I been focused on learning complex dynamics atm

[vital bane]

griffths QM? yeah it's great!!

[hearty steppe]

Complex dynamics I think might help anyone understand QM or GR/SR

[primal mica]

I feel like I always understand subjects best when I start working on more advanced subjects, so my recommendation is to skip all prereqs, ezpz

[hearty steppe]

Complex dynamics involves a lot of stuff like logic, probability, combinatorics, dynamical systems, linear algebra

It’s a beast

[forest sleet]

in the preface of Hall he writes

I do not assume, for example,
any prior knowledge of spectral theory or unbounded operators, but pro-
vide a full treatment of those topics in Chaps. 6 through 10 of the text.
Similarly, I do not assume familiarity with the theory of Lie groups and
Lie algebras, but provide a detailed account of those topics in Chap. 16.
Whenever possible, I provide full proofs of the stated results.
Most of the text will be accessible to graduate students in mathematics
who have had a first course in real analysis, covering the basics of L 2 spaces
and Hilbert spaces. Appendix A reviews some of the results that are used in
the main body of the text.

[hearty steppe]

Differential geometry is gona be one of your best friends

Because partial differential equations

I feel like I’m mostly gona be picking a lot of the stuff up I didn’t learn super rigorously

I spent about 2.5 years studying pure math

[primal mica]

Why is diff geo going to help with PDEs?

[hearty steppe]

Like pretty much nothing but pure math

And some foundation in physics

Huh I mean Diff geo involves PDEs

But like your gona be doing stuff like playing with tangent bundles

On manifolds

I might be recalling my GR texts mostly I been reading

Infinite square well problem is trippy tho in Griffiths

[hollow peak]

Almost nothing for the first few chapters

[cinder cave]

So I'm a CS major minoring in mathematics. My university's minor program requires you choose either an analytic or algebraic track for your final few courses. For practicality, I have chosen the algebraic track. However, I regularly run into concepts in real and complex analysis that i wish I understood. For a person trying to learn analysis as an extracurricular study, can anyone recommend good resources/books?

[hollow peak]

Some familiarity with classical mechanics is good, and a strong knowledge of analysis will be useful for the perspective hall takes

Frankly you can get by checking the appendix

[coarse frost]

[hollow peak]

I love pugh's real analysis book. For complex analysis stein and sharkachi is quite good, but people have wildly different preferences for complex analysis books

If you check pinned messages in this channel there are some good recs

[coarse frost]

For intro analysis, you can try schroders book, i personally really like apostols book

[cinder cave]

Thank yall. Sorry if this is a frequently asked question. I'm great at choosing courses but not so experienced with self-study

[orchid mortar]

I think Dami's post is more grad-level though

[coarse frost]

damis post is for measure theory

not intro analysis

[coarse frost]

when u say familiarity with CM, what do u mean? Like an intro course worth? or more familiarity with lagrangian and hamiltonian stuff

[loud cradle]

abbott's "understanding analysis" is a good intro and would be my default recommendation

[cinder cave]

Thank you! I think this seems appropriate for my plebian undergraduate understanding of the subject.

[pliant stream]

I like the way of analysis, though I haven't read it

[loud cradle]

what do you like about it if you haven't read it, just curious..

i have read part of it and found it very wordy

[pliant stream]

I think it's way better than Abbott, but I don't know why Abbott is so popular

I mean that's literally why people suggest Abbott

The exercises are easy and he writes lots of words

[loud cradle]

he writes a lot less words than Strichartz, who as i recall often has long paragraphs where a couple of equations would be clearer, but admittedly it has been a long time that I looked at Strichartz

Strichartz does cover more material though, which is good

[pliant stream]

I think the main issue is strichartz is published by someone I've never heard of and Abbott by Springer

[cinder cave]

For extracurricular study, easy exercises can be pleasantly reinforcing. While i appreciate exhaustive coverage, it does encourage me to keep reading if I make tangible progress

[pliant stream]

And yeah, Strichartz writes lots of words, but they are all quite insightful

[loud cradle]

what does that mean in practical terms? is it harder for you to get a copy of Strichartz?

looking at amazon i'm wondering if it's out of print

[pliant stream]

I mean when you first read analysis you lack maturity, so it's very nice to have lots of exposition

[loud cradle]

for sure, particularly if you are self-studying

[pliant stream]

And I don't think there's any downsides tbh

[loud cradle]

it's a question of personal preference how much verbiage you want

[pliant stream]

Like I've seen people say stuff like it's condescending if the author is too wordy, but I literally have no idea why anybody would think ghat

[loud cradle]

i have never looked at any of these books as a newcomer to analysis, i got to learn from rudin

[pliant stream]

Same

[cinder cave]

I'm not afraid of flowery language. I just want problems that are positively reinforcing

[pliant stream]

I think, looking at abbott quickly, the problems are too easy

[loud cradle]

that's absurd imo, it's much more condescending to be proud that you published an analysis book with no pictures, as rudin was

[pliant stream]

I read somewhere that rudin meant them as lecture notes, though not quite sure to be honest

But it definitely needs to be accompanied by a lecturer or some kind of supplementation

[loud cradle]

yeah agree, it's not a good choice for self study

[pliant stream]

I think like if a major publisher publishes it, it will be more famous?

And I feel like, many professors tend to use springer texts just by virtue of universities paying for e-access

Like at my school, and a few others, the text of choice for analysis is jiri lebl's, and I honestly don't know why except that its free

[loud cradle]

springer tends to be somewhat sane with their pricing too, compared with people like wiley

[pliant stream]

To be fair, as long as I get a book that is printed okay, Im fine

[cinder cave]

Yeah i am, sadly, terribly poor

[pliant stream]

The most recent book i got from springer was printed ass quality

and Royden 3e too lol

[loud cradle]

they've been using print-on-demand for some years now, for most of their titles, and the quality is uneven at best

i mean it's good that they can keep a lot more titles nominally in print that way

but i wish the quality control was better

[pliant stream]

some people care about the quality of pages. Personally i dont care, i just want the book to lay flat when you open it

[loud cradle]

and the binding not to fall apart

[pliant stream]

Exactly lol

[loud cradle]

but most importantly to not have faded print like someone forgot to change the toner in a laser printer

[pliant stream]

Which is...not the case many times

[loud cradle]

or missing pages or whatever

i've had all these issues at various times

[pliant stream]

Wait the amazon pricing for abbott makes no sense

[loud cradle]

AMS has quite a few good titles

[pliant stream]

Why does a used book cost more than a new one

[loud cradle]

and their physical quality is a bit higher than springer

amazon sellers make no sense to me period

yeah, but it's nice to have a reasonable durable cover and binding if you're gonna carry it around a lot

i guess you can get that if you take it to a print shop

[pliant stream]

My bookstore is trying to sell me a 85 dollar ebook

[loud cradle]

i've seen some pdf's that were much poorer quality than a physical copy too though

especially for older books

like someone used a shitty photocopier

[pliant stream]

True 💀

[loud cradle]

fuck that, $85 and no printed copy?

ha, or you can rent a digital copy for $54

[pliant stream]

Forgot to mention there's a 4 dollar fee "To support the delivery of digital content to you"

[loud cradle]

hahahaha

those bits ain't gonna send themselves

it's like they want people to just download pirated copies

[pliant stream]

You can get a 72 dollar brand new physical copy from amazon

I literally don't understand

[loud cradle]

meanwhile there are authors who make their stuff available for free

with quality just as high in many cases

[pliant stream]

Yeah it's insane

[loud cradle]

i made the mistake a couple of times of buying a cheap used copy a few months before the course started, only to find that a new edition was published a month later and that's the one that the instructor required

great fun

"do problems 3, 7, 11, 16 and 24"

"uh, mine only goes up to problem 21 in that section"

[cinder cave]

I'm 100 percent unwilling to buy a textbook prior to the first lecture

[pliant stream]

LOL

[loud cradle]

good policy

[pliant stream]

dude new editios man

Like Ross probability just adds exercises for every edition or?

[cinder cave]

I wouldn't put it past them

[pliant stream]

Anyways I'd say just use two texts for analysis @cinder cave

For example, this is the treatment of lim sup/inf in abbott, which is not the greatest

[loud cradle]

yeah he's on what like edition 10? how much could he possibly be changing each time

his "intro to probability models" (which is a good book btw) is on like edition 12 now

[pliant stream]

I wonder if so many courses use his book because it's good or just has so so many exercises

Like the instructor will never run out

[loud cradle]

he does have a habit of making basic and key results exercises more often than i would like

[pliant stream]

Never read prob models though, not a fan of a first course

[loud cradle]

i haven't read all of prob models either, but the markov chain stuff is pretty well handled

it would be better handled if he would assume people know a bit of linear algebra though

[pliant stream]

I did not learn markov chains at all in the probability class I just took 💀

Barely learned anything actually

[loud cradle]

you would probably cover them in a second course, or maybe one called stochastic processes or similar

[cinder cave]

Markov chains aren't actually that wacky

[loud cradle]

intro courses don't usually have time to get to markov chains i don't think

even though they're pretty easy

[pliant stream]

I think it was probably my fault I didn't learn much though

[loud cradle]

and very useful

[pliant stream]

yeah I'm not really sure what we did tbh. Something about markov chains --> wiener process

[loud cradle]

wiener process is a lot harder to do in an elementary way

not with any rigor anyway

[pliant stream]

I'll probably take stochastic processes in the spring assuming I pass the prob class this fall im taking

[loud cradle]

but a nonrigorous first pass is probably not a bad idea anyway

[pliant stream]

Yeah I was completely lost though, unfortunately

Actually i was lost basically after we stopped talking about cards

[loud cradle]

computing the probabilities of various poker hands was kinda fun

and random walks are fun

(given that we're using a definition of "fun" that applies to math)

[pliant stream]

Honestly discrete probability is pretty fun

[loud cradle]

nonrigorous handwavy "proofs" of the central limit theorem, not so much fun and kinda pointless

just punt that stuff to a rigorous course

[pliant stream]

Hmm we proved some version via char. functions

[loud cradle]

yeah that's the normal proof (no pun intended)

[pliant stream]

The class im takinf this fall will probably prove it some other way

[loud cradle]

but char functions aren't really done rigorously at that level

[pliant stream]

yeah i just ignored it lol

like in grimmett and stirzaker there was some stuff about them that I just ignored

[loud cradle]

and then there's the kind of annoying way you have to deal with random variables when you don't have measure theory

you can't even properly define a random variable without it

[orchid mortar]

Ross newer editions should be easy to find though?

Ross really needs to reprint the Stochastic Processes book

or make a nice digital edition available

[pliant stream]

Yeah I have the eight edition for under 10 dollars

[loud cradle]

isn't his "probability models" basically the replacement for that? i've never seen the older stochastic processes book

[pliant stream]

Maybe that's the only good part of new editions

[loud cradle]

yeah, the ability to get a version that's only a few years old, for cheap!

[orchid mortar]

Probability models is a slightly easier book

[loud cradle]

you can get a usable calculus book (usable for anything except a required textbook) for basically free

[pliant stream]

yeah but unfortunately a used calculus book is useless

imo at least

[loud cradle]

ah, i'd like to see that stochastic processes book someday then, the closest equivalent i own is probably karlin and taylor's first course in stochastic processes, i'm guessing

(which is also a pretty good book)

[loud cradle]

for self-study? why?

as long as it's not full of writing or highlighting

[pliant stream]

well def for college classes since webassign access codes. For self study, I can't imagine someone would choose to use a book over youtube videos

[orchid mortar]

Yup, similar

[loud cradle]

aight it's 4am here, i'm gonna head out

cheers

[pliant stream]

like when I was in high school taking calculus, I never once read a calc book,

[shell geyser]

Reading Ross' First Course right now and so far I'm enjoying it. I think it offers a decent amount of theory (at least more than those probability & stats books that aren't for math majors), while still being accessible enough without measure theory.

[pliant stream]

Based on Amazon reviews, people seem to think Ross is only suitable for math majors!

[cinder cave]

Books are physically pleasing. I love youtube and all but only as supplementary material

I like being able to carry my obsessions around easily

[shell geyser]

To be fair, I think it does delve into some relatively in-depth examples early on. I think a lot of intro books often only go over very basic examples. Though I could be overgeneralising here.

[orchid mortar]

Ross writes multiple books. First Course is definitely not a math major-only book

[pliant stream]

That's fair, some examples are quite involved and there's also proofs, which well...

[pliant stream]

Well yea

But I mean a lot of people, on Amazon at least, seem to find the book very chalkenging

[shell geyser]

I was going to read Myers and Myers' Probability and Statistics for Engineers and Scientists and uhh... that is an intro book that is very light on proofs. Not a big fan.

[pliant stream]

There are countless reviews talking about how they have engineering degrees or whatever and have taken so many advanced math classes, and bash about how inpenetrable ross is

Yeah, imo even though the book says it's meant for everyone, I really doubt it

[shell geyser]

Could be that their advanced engineering math is very computational. Ross feels more conceptual than some alternative intro books.

[grand thistle]

whats the probability equivalent of spivak for calc?

like i also wanna get into probability once i do rudin

[pliant stream]

Ross is definitely not easy...

at least the discrete stuff isn't

[grand thistle]

it has a lot of proofs and is written more like a math textbook than an engineering one right?

[pliant stream]

Yes

[grand thistle]

this one?

[pliant stream]

But if you want something more rigorous, but not measure theoretic, try grimmett and stirzaker

Ayo I literally have that book

[orchid mortar]

Great recommendation.

[grand thistle]

hmm

this looks like exactly what i was looking for

[pliant stream]

Very difficult book ime

[grand thistle]

thank you

[pliant stream]

there's also a solutions manual by the authors

[grand thistle]

baby rudin should be enough background though right?

[pliant stream]

And the third edition is like 10 bucks on smazon?

[grand thistle]

first 8 chapters*

[pliant stream]

i don't think so but you can ignore the stuff you don't know

[grand thistle]

oh...

what other background should i have?

[pliant stream]

I mean it kind of depends on what exactly you want to know

Like I only really have exoerience reading the first 5 chaoters of GS

Which is more or less a first course in probability

[grand thistle]

i mean i guess i kinda just want a working knowledge of probability, since i have like 0 atm

i'm interested in delving further into measure theoretic probability in the future, so i guess the more the better

[pliant stream]

Well for me, I just ignored the things I didn't know

Like if you look at chapter 5 on char functions, there is a certain amount of complex analysis that would be helpful

Which I just ignored lol

[grand thistle]

well i guess ill just do the same

and if theres any really significant hole in my knowledge ill just review what i need to know when i come to it

[orchid mortar]

I think GS is great both as a learning book and as a reference text

[grand thistle]

yeah it looks like an amazing text

doesn't waste any time

[heady ember]

Measure theory

[spice stag]

Can someone recommend some resources to learn determinants

[gray jungle]

anything thats not axler

[tardy walrus]

Lol

[spice stag]

Something specific would help 🐍

[tardy walrus]

Look up a linalg book and skip to the determinant chapter

Any linalg book except for axler should suffice

[heady ember]

Look in pinned

E.g.: Friedberg, Insel, Spence

[hearty steppe]

Is it necessary to read Hall? I’ll check it out. I think I should be fine with the books I have. I don’t have a super strong analysis background but I might be able to work through it

[tardy walrus]

…incel

[heady ember]

isn't it spelled with an s

[tardy walrus]

Nono

Incel

[livid ermine]

its pronounced the same

[tardy walrus]

Like the word. I can’t make stupid puns if you don’t get them D:<

[livid ermine]

Do anyone know any good book or series of papers on the intersection of algebraic geometry and combinatorics? Like the stuff june huh works on? I tried to read his paper about rota conjecture but couldn't understand anything 😭

might be because I don't know anything about homological algebra and almost nothing about algebraic geometry, but in 1 years time I will 😤

[vital bane]

enumerative geometry?

that's the field I've heard of that seems close to the intersection of AG and combo

[heady ember]

I see no pun

Not punny

[livid ermine]

Is that what June Huh does?

[proud lantern]

Is there an online pdf exercise book on first-year analysis with just a load of questions and answers?

[hollow peak]

definitely don't HAVE TO, but I personally like the book

[hearty steppe]

Yea it doesn’t seem necessary

I have so many books and paper to read, sometimes I don’t realize how many I have to read

Cuz sometimes you get done reading some shit just to find out you gotta read about some other shit

[vital bane]

nvm I don't think so, anyway you should learn AG first

[sharp latch]

Anyone know where I can find a large supply of practice problems for the math subject GRE? Using the Princeton review book now and it’s great but I would like some more questions to practice. Thanks!

[warm glen]

this person made a list of recommended books to prep for the gre subject test

https://www.mathsub.com/resources/

it's not exactly what u asked for since its not a supply of problems but it tells you where u can find some

actually i stand corrected there are literally practice tests on that website

[sharp latch]

Tysm!

[primal mica]

Zweibach gives a fun twist on the infinite square well problem in his undergrad string theory text, providing an extra dimension but making it closed and thus a “compact” dimension.

I think it’s rather illustrative for low level students. Tried talking the undergrad quantum professor into providing it as a handout/alternative to 2D well with regular dimensions but he was not interested.

[warm storm]

I want to get a thorough understanding of single-variable calculus and also prepare for the AP Calc BC Exam. (Which I want to take in end of 7th grade, which I'm going into, or beginning of 8th.)

Already, I have the AoPS Calculus textbook and I will take the respective course with AoPS as well. However, as I've understood, AoPS goes a bit deeper than is needed for the AP Calc BC Exam, and a supplemental textbook with more routine calculations that prepares for the exam would help.

Any recommendations for which textbook would be good for me?

[sharp latch]

Honestly, I wouldn't rush learning all of calculus from a book like that especially if you havent learned it yet. The best way to learn calculus is to have a really strong foundation, and for that, I would check out "calculus made easy" by silvanus thompson. It introduces you to a bunch of fundamental concepts without blowing up in your face with math. and then after that pretty much any textbook about calculus will be fine. Khan academy is also really good for getting practice

[crisp river]

tropical geometry

is exactly this

[sage python]

Also the work of June Huh

[dapper root]

Did you even fucking read the message?

They mentioned that and then said they tried to read a paper and couldn’t understand it

[flint forge]

Algebraic geometry is not a subject that lends itself well to like

Casually reading before you understand the basics

So studying algebraic geometry's intersection with X will be hard if you don't know basic AG

[sage python]

@dapper root yeah I was being ironic, like

The guy was asking for stuff that helps him understand June Huh

And someone's like oo tropical geometry

And I'm like yeah also... The thing he actually asked about

[crisp river]

[proud gazelle]

is there any book that discusses Lagrange multipliers and the Lagrangian in detail?

I saw this video

https://youtu.be/b9B2FZ5cqbM

and I want to take a deeper look

[crisp river]

Yeah it is really interesting stuff but I know nothing

[proud gazelle]

a video will rarely give you a deep look

[pliant stream]

any optimization text or analysis text

[proud gazelle]

I prefer a book, if someone has a suggestion please tell me

[pliant stream]

for example, tom apostol analysis

[crisp river]

Sorry I am not an expert but someone here is.

@grave thorn

[loud cradle]

serge lang's "calculus of several variables" covers lagrange multipliers and is good in general for (nonrigorous) multivariable calculus

[proud gazelle]

will check it out, thanks

[fallow cypress]

wait do you want information on lagrange multipliers or the lagrangian?

the lagrangian as in physics?

[proud gazelle]

no not the lagrangian that is in physics

[fallow cypress]

ah okay

https://www.youtube.com/watch?v=5A39Ht9Wcu0

[proud gazelle]

the one that relates to optimization and constrains

[fallow cypress]

here is a good visualisation of lagrange multipliers

[proud gazelle]

I actually understand lagrange multiplers

https://youtu.be/m-G3K2GPmEQ?t=248

right here, he introduced some function and called it the lagrangian

it's like some kind of generalization/packaging

[proud gazelle]

and then introduced in this video another extended lagrangian function

and from them he got an interpretation for lambda

I know the idea and the proof of lagrange multipliers, but these functions and generalizations seems more deep than that, and 3b1b didn't explain them very well imo

[fallow cypress]

ah I see, that is the same lagrangian as used in physics, I didn't know they were connected haha

I have been enlightened

[proud gazelle]

they do look related

I don't know a lot about physics, but I've seen some lagrangian mechanics

[gray gazelle]

Is there any beginner level book to understand Linear Algebra?
I want to learn it myself but somehow, I found Strang somewhat complicated
Isn't there an easier book?

[pliant stream]

Unfortunately not really

Note Strang is written as accompanying lecture notes to what's on mit ocw, or at least I think it is

You can also try like larsen linear algebra or something

Or manga guide to lin alg?

[brittle breach]

Linear Algebra done wrong

[shell geyser]

Like mentioned by Andrew above, Strang is already considered to be one of the easier books. Though as he also mentions, it is not meant to be used on its own, but rather with the accompanying lectures from MIT. If you still have issue with following that, other introductory texts at that level would be something like Howard Anton's book or David Lay's book.

[idle tendon]

I love linear algebra if you ever have any questions or want to talk about a concept feel free to message me, I also can give you a brief overview.

[radiant relic]

has anyone read "The Moves That Matter: A Chess Grandmaster on the Game of Life" yet? if so can i get a review plz

[gray gazelle]

Thank you!! I'll do that!

[gray gazelle]

Are those accompanying lecs free?

[pliant stream]

Yes go on youtube and search 18.006

[shell geyser]

Yes. MIT 18.06 on YouTube or on their OpenCourseWare site.

[gray gazelle]

Okay
Thank you!!!!

[gray gazelle]

Thank you!!!!

[forest sleet]

Is the physical copy of Atiyah's book on K-theory the same as the lecture notes https://ncatlab.org/nlab/files/AtiyahKTheory.pdf ? (both content and typesetting)

[hollow peak]

yes, this also has additional content at the end

[red sentinel]

Hi everyone! I'm currently writing a thesis on simplicial homology groups, and I wanted to incorporate a chapter fully dedicated to examples and computations of homology groups. For now I've included zero-dimensional homology and the homology of surfaces (I'm reading Munkres' Elements of Algebraic Topology), and I saw some yt videos titled "homology on graphs". Does anyone know any book which talk specifically about homology on graphs? It would be fantastic if it used just the definition given for simplicial homology (for example I've found a book that talked about homology on graphs but used terms like "cell complex" which I've not treated in my thesis, and I don't want to develop a whole new theory for just a section of a chapter, it should be like a class of examples).

[stray veldt]

might also be worth to ask in #point-set-topology

[red sentinel]

I'll try that, thanks, I realize it's an oddly specific request😅

[subtle mango]

do I need to know diff geo for Brezis’ Functional Analysis?

[warm glen]

graphs, surfaces, and homology by peter giblin

[gray gazelle]

Any good resources for adult learners basic algebra? I wasn't taught any of it in school. If this is in the wrong channel, please advise and I will gladly move.