book-recommendations

[gray gazelle]

unless you have a cartridge printer

[remote sparrow]

https://press.barnesandnoble.com/

this works too

do be aware that they only accept very specifically formatted files

[tawny solstice]

Fairly cheap, too

[remote sparrow]

if you don't know what you're doing (like myself), it's pretty much luck whether a file is permitted to be printed

[gray gazelle]

can these do paperback like printing on yellow creamy paper too?

[remote sparrow]

sometimes

i like white paper

[tawny solstice]

Me too

[gray gazelle]

say I wanna print a novel or smth

[tawny solstice]

Lulu has option for cream, but it doesn’t specify yellow cream

[gray gazelle]

altho for me it would be difficult to import it from north america

[gray gazelle]

I see

[tawny solstice]

Yeah, probably a lot of shipping fees

[remote sparrow]

well you can check yourself

i would presume lulu and barnes & noble have international reach

[gray gazelle]

I have ordered some BluRays from Barnes and Noble before

cost me a fortune lmao

[tawny solstice]

That’s why I’m looking at Amazon, able to find books for ~$20 or less

[remote sparrow]

by emil artin? that's michael artin's dad btw. i wouldn't recommend that book for a beginner. this book is better: https://www.amazon.com/Galois-Theory-David-Cox/dp/1118072057

[tawny solstice]

$83.95 though 😬

[remote sparrow]

i saw a used copy go for ~$40 before

unfortunately i didn't have money at the time or i would have snatched it up

thankfully several months later i got a used copy for ~$60

[tawny solstice]

Cheapest I’m seeing is ~$75

[remote sparrow]

yeah i just got lucky

maybe wait a while, or save some money

you won't need to read this book until you finish most of artin anyway (or some other book if you change your mind)

#book-recommendations message

here are some other good abstract algebra books

pinter and judson are both cheap and beginner friendly

[tawny solstice]

Fair enough. Only other good Algebra book I found was “A Book of Abstract Algebra” by Pinter

[remote sparrow]

aluffi is reasonably priced but not the cheapest option

[gray gazelle]

notes from the underground?

[remote sparrow]

yeah

[gray gazelle]

that's an interesting book

[tawny solstice]

What about books on number theory?

[remote sparrow]

#book-recommendations message

[gray gazelle]

I liked Silverman from what I read last night

he takes a conjecture building approach

[tawny solstice]

What do you mean?

[gray gazelle]

do you know induction?

[tawny solstice]

A little

[gray gazelle]

say you wanna prove a predicate that's true for all natural numbers

predicate is written in the form p(x)

for example

p(x) : x is even

p(1) is false

p(2) is true

etc

so let's say to get a feel for it you plug in a lot of values

and you see a pattern

based on the pattern you form a conjecture

[tawny solstice]

Right, but doesn’t p(1) being a counter example destroy the entire proof or conjecture?

[gray gazelle]

it was just an example to motivate what a predicate is

[tawny solstice]

Got it

[gray gazelle]

in case you didn't know

so if you wanna prove the conjecture, you have a method at your disposal

that's induction

[tawny solstice]

I’m more familiar with proposition and conjecture than predicate

[gray gazelle]

lemme leave you with a problem

oh i don't have image perms

#chill message

[remote sparrow]

Mathematical induction is distinct from induction used in the ordinary sense. Mathematical induction is actually deductive, despite the name. Induction, in the ordinary sense, is summed up in this article. A conjecture is an unproven mathematical statement. You may arrive at your conjecture by your intuition, previous experience with ostensibly similar problems, observing patterns, or looking at numerical data.

Point is, I think it's a little misleading to immediately associate mathematical induction with inductive reasoning when discussing a "conjecture-building" approach. A "conjecture-building" approach is not only applicable to statements that can be proven by mathematical induction. Stating a conjecture need only involve non-deductive reasoning. It suffices to prompt the reader to observe some patterns and form a guess as to a possibly true mathematical statement.

[tawny solstice]

You can DM it to me, if you’d like

[gray gazelle]

deductive means you have a chain of statements which go from a set of hypotheses to some conclusion

inductive means you observe empirical evidence which are premises from which we generalize some conclusion

I think mathematical induction being deductive means that you have an implication where you go from the premise (inductive hypothesis) to conclusion

[gray gazelle]

what other methods exist to prove conjectures?

I am curious

[remote sparrow]

any method of proof you can use?

a conjecture is any unproven mathematical statement. a conjecture is not any unproven mathematical statement that must be proven by mathematical induction. one may arrive at a conjecture by inductive reasoning.

[gray gazelle]

I see

can you give an example to help me understand better?

say a conjecture we arrive at that is proven through direct proof or contradiction

[remote sparrow]

well, some ancient greeks (incorrectly) conjectured that the square root of 2 was rational

then someone conjectured and proved it was irrational

the proof proceeded by contradiction

[gray gazelle]

hmm right

perhaps the rational approximations were not sufficiently convincing enough

thank you for the insight sour drop 😄

I would read up on this more

[remote sparrow]

i don't think decimals existed in ancient greece. i think the conjecture was more based on a religious belief that all numbers were commensurable (which is supposed to mean that numbers are either whole or rational)

https://www.britannica.com/science/Pythagoreanism

[pliant wadi]

Oh dang, it looks a bit more general than I was looking for but I'd check it out after this one def!

Oh thanks, I'll check it out 👍

[sullen raptor]

thx

[buoyant halo]

https://csclub.uwaterloo.ca/~pbarfuss/18093757-Fuckin-Concrete-Contemporary-Abstract-Algebra-Introduction-by-Nicolas-Bourbaki-Junior.pdf

[distant spear]

[lusty ermine]

how to get started with standard distribution of probability or geometric distributions, any readings

how to get started with probability theory

[remote sparrow]

https://stat110.net

all you need is three semesters of calculus

[lusty ermine]

mmm

is calculus a prerequisite?

[graceful moon]

Pretty much yeah. You can do really basic stuff without it but any reasonable stats course requires calc

You can do a decent bit of basic probability without calc, but again you will eventually need calc, and more so analysis, as you go on

[shut grotto]

Any good books to start linear algebra?

learning it for the funsies, heard it's used in programming sometimes but I'd preffer a book that doesn't care much about that aspect of it

[tribal crow]

if you’re looking for proof-based books, check the pins

#book-recommendations message

[shut grotto]

ah, found the lin algebra post. Thanks!

[junior isle]

What do you guys think about Serge Lang's calculus of several variables?

Good for a first course?

[slender cargo]

What is with the love for Serge Lang here, even for earlier courses?!

[loud cradle]

i think it's pretty good

[junior isle]

I liked his lin alg book

The abstract one

Used to his writing

[loud cradle]

i definitely don't love most books by lang, but his several variables calculus book is quite nice

[slender cargo]

Ah okay, well... more power to you!

[autumn spire]

guys I really wanted to start doing calculus during vacation

where should i start

I am at level 0

[graceful moon]

Khan academy if you want a complete package, something like James Stewart’s calculus if you want a book

[autumn spire]

thanks

both are helpful

[graceful moon]

I’ve never actually used it, I just learned it at highschool, but their other stuff is decent afaik so I had no reason to assume the calc wouldn’t be.

But there’s also no shortage of calc resources so yeah other stuff could work

[violet shuttle]

i want my khan academy course covering the proof of the poincaré conjecture

[tribal crow]

When will Sal Khan teach me how to prove the hodge conjecture

[violet shuttle]

he actually has a solution to all the millennium problems

but the world couldn't handle it yet

"with ai"

?

??

[tribal crow]

I didn’t know he possessed such power

no wonder we put the education of our children in his hands

[violet shuttle]

this is not sufficient to make exercises or to teach content even at an advanced undergrad level.

Using current technology.

[graceful moon]

Yeah no. You want standards so why appeal to AI lmao

[violet shuttle]

For lower level stuff you don't need AI, you use computer generated exercises that just change numbers or do computer algebra

[tribal crow]

uhh, AI is not very good at math atm

I don’t think it could reasonably be used to teach math at the grad level

[graceful moon]

It can’t even at the UG level so it 100% couldn’t handle grad level stuff

Yes like if you put in maths and expect anything helpful you’ll be disappointed

[tribal crow]

as far as I can tell, AI can’t teach math at all rn

it constantly gets things wrong

no matter how much you refine input

[violet shuttle]

I would expect current LLMs to be significantly worse at anything higher than calculus.

[gray gazelle]

But… why would you? There are plenty of (free) resources available written by actual people

[tribal crow]

it couldn’t help me with my basic analysis questions at all

I don’t have high expectations for it anytime soon

why’s this wrong?

[violet shuttle]

this I full heartedly believe.

Higher level maths is qualitatively different from examples like these.

I am not good at prompt engineering and only used the ChatGPT based using GPT 3 (the free version)

it failed to help me with exercises from Hatcher's Algebraic Topology

[fallen terrace]

Probably wide news already

but Akira Toriyama (the real GOAT) died

[tribal crow]

I guess I should have clarified: it can’t teach UG math and above properly atm

I think it’s going to be a while before it can

[marsh ingot]

Lol

Also here is for book recs

[reef jay]

Hey all, I'm a physics guy. Wanted to know what would be a good book on research level matrix theory (like spectral theory, random matrices, statistical properties etc). Interested moreso on normal matrices.

[marble solar]

For Random Matrices, you can start with Terry Tao's book

[reef jay]

Thanks, although im looking for a book that's more general than just that

[marble solar]

It's hard to find a book that's at the research level in multiple domains like that. At the research level, you usually have to read a bunch of stuff

A more general book could be Advanced Linear Algebra by Steven Roman

Although I'm not sure it's at the "research level"

(Although, neither is Terry's RMT book, eh only so much one can do)

[loud cradle]

horn and johnson may be worth a look

"matrix analysis"

[reef jay]

yes im looking into that one now 👍

i guess i just don't have the vocabulary rn to describe whats relevant to my research; it's along the lines of understanding perturbations of matrices and decomposition proofs

horn has some interesting topics including a "perturbation of eigenvalues" chapter so maybe it's the right one

[remote sparrow]

#book-recommendations message

[remote sparrow]

#book-recommendations message

[hallow pivot]

I would like an extremely rigorous logic or metamathematics book that would make me jump off a bridge

recommendations pls?

[remote sparrow]

#book-recommendations message

[tribal crow]

for those of you who study/have studied chemistry, what organic chemistry textbooks do you recommend?

(I'm asking on behalf of my friend)

they are considering Clayden et al, but are looking for possible alternatives

[crimson leaf]

Does anyone have a good set of homeworks or a course page for Conway's complex analysis book?

[remote sparrow]

@marble solar

[marble solar]

https://mathweb.ucsd.edu/~m3xiao/math220a/index.html

UCSD uses Conway Complex analysis as their main text, and has been a good resource for me

It's the 220ABC sequence there, and often time if you snoop around you can find some problem sets, solutions, practice exams, etc.

[gray gazelle]

Any book recommendations for computability theory?

[crimson leaf]

Thank you! Actually you talking about the book mad me check it out. My analysis isn't the strongest specifically power series so Conway seemed perfect since he seems to go over the proofs again

[marble solar]

No worries! Try not to get bogged down into "the best" book. Everyone is coming in from a different point of view, and these books are there to help people with a variety of backgrounds

[crimson leaf]

Yeah I'm not worried about best book but I picked up Frietag and Busam and it was a bit too terse for me right now I think and Churchill Brown was too slow but Conway s I ma nice so far

[molten mason]

When I did my original research everyone had something negative about Conway, but the last few weeks it's been pretty positive about Conway

[marble solar]

I'd say Conway's Complex is exactly like Munkres' Topology

It's slick, it's clean, it's dry

There's good stuff in there, and it's well thought out and more logically sound/rigorous than books like Ahlfors

[rigid flint]

anyone know of any good linear algebra textbooks with lots of questions?

[finite gale]

See pins

Newest edition of ladr should be decent

[rigid flint]

thanks

[remote sparrow]

you can look at cooper, cutland, enderton, or weber

[remote sparrow]

marshall begins with power series

[spring marlin]

Theres also LG wade, let me know if you find some good alternatives

[vital bane]

conway seems really nice

[lusty ermine]

books to get started with graph coloring? undergrad.

[hallow oriole]

book recommendations for proving if something is maximal or minimal?

like

an optimization book

pretty please!

[left cloud]

proving if something is minimal, or algorithms to find mins that may have some necessary or sufficient conditions for ‘working’? the latter is what comes to my mind with optimization books

[covert zealot]

I like Stillwell's "Reverse Mathematics" as background reading for a good exposition of the link with mathematics (given the topic of this server).

[gray gazelle]

What's a good book to learn elementary number theory? preferably one with lots of examples and exercises

Even better if the exercise solutions are available online

[remote sparrow]

#book-recommendations message

[gray gazelle]

Thank you

[verbal gull]

Hi guys! I found one website with amazing math books: https://openstax.org/subjects/math but I don't know whether or not they've covered all the necessary school math topics. I'm not that good at math so can anyone check these books in terms of content?

[dusk wind]

its pre university but other books are better

[daring lake]

I haven't read it after that
Been too busy , sorry

[proud junco]

Reccomendation for beginner high school trigo book? Preferbably able to be found online.

[sour current]

S.L Loney was a nice one

[proud junco]

isnt this a pretty old book?

[sour current]

I mean why does it matter high school trigo is what you want to learn

It's not something which has 'evolved' or changed or something

[proud junco]

ah

I forgot about the part about self study

sry

[gray gazelle]

https://open.umn.edu/opentextbooks/textbooks/trigonometry-2018

[heady ember]

Most book can be found online if you look in the right places

[verbal gull]

what books you would recommend? I need to learn school math program altogether.

I found many books and it's a bit confusing to choose

[dusk wind]

Pick one for what you want to learn, as I don't know what that is for you I can't recommend anything

[halcyon wasp]

So I want to buy a physical copy of some algebraic topology textbook

I heard that conflicting remarks about Hatcher, what would be good alternatives?

[heady ember]

Some recs I've heard people here mention

• Bredon
• laurentiu maxim, algebraic topology: a comprehensive introduction
• Raoul Bott, Loring W, Tu Differential Forms in Algebraic Topology
• Rotman An Introduction to Algebraic Topology
• Tom Dieck AT

[halcyon wasp]

Hmm, I cannot decide..

What would be a good book to learn basic cohomologies and cup product?

[violet shuttle]

Hatchers Algebraic Topology

[sage python]

Absta asked for a good one smh

[tough egret]

I just bought Johar’s Big Book of Real Analysis, it has about 300 pages dedicated to the construction of N, Z, Q and R

[random folio]

what are some good reccomendations for discrete math

[vital bane]

"concrete mathematics"

[hallow oriole]

both!

separate books would be fine as well

or just one or the other

[modern ruin]

davis and kirk lecture notes in algebraic topology (at least the first few chapters) if you are already familiar with some topology

I have been meaning to read the rest of that book

very very well-written

[slender wasp]

Bloch real analysis chapter 1 starts with Peano for naturals, then builds up to Dedekind cuts. Its main feature compared to others is it's very clear and easy with modern notation.

[left cloud]

soz forgot to reply. a class i'm taking now uses nonlinear programming by bertsekas and convex optimization by boyd and vandenberghe. they are alright to me

[hallow oriole]

tyyyy ur great

[left cloud]

i know

[hallow oriole]

[hallow oriole]

this emoji scares me

[tribal crow]

you get used to it

and then it becomes funny

[left cloud]

no it's scary

because i'm scary

[hallow oriole]

ill take ur word for it fr

[hallow oriole]

ill take ur word for it fr

[tribal crow]

lol

[left cloud]

good

[violet shuttle]

boo

[left cloud]

i'm not scared

[violet shuttle]

you totally spent the last 4 minutes freaking out and this is just you covering it up

[left cloud]

the only things i'm scared of are chmonkey not liking me, large cardinals, and mniip

[violet shuttle]

it is at this point that I realize that you are two different people

[gray gazelle]

im very brave and so none of those things scare me!

[left cloud]

what are you talking about

[violet shuttle]

i had been confusing you with chmonkey

[left cloud]

i'm really perplexed by how people keep doing this

[gray gazelle]

Maybe they use compact mode

[violet shuttle]

@left cloud what led to your simpery?

[modern ruin]

[wicked fractal]

[left cloud]

he's so hot and funny and silly and good at math and... other things

before i knew it

[violet shuttle]

...other things?

sitting in chairs?

monkeying around?

[left cloud]

no that's me

[modern ruin]

lmao

[tawny copper]

does anyone know good books on Euler, his life and work? I'm not so interested in the mathematics, but his life, historical context and personality

[remote sparrow]

https://press.princeton.edu/books/hardcover/9780691119274/leonhard-euler

[halcyon wasp]

Is this published as a book?

[modern ruin]

yeah it is

[cedar flume]

Any recommendation of books for topological dynamics please

[north wedge]

guys any books on pre-calc?

[remote sparrow]

try the search function. type "in: book-recommendations precalculus" without the quotes for some previous comments

[tawny copper]

Thank you

looks pretty good

[tawny copper]

the same but with Kummer

I can google myself, but in case anyone knows some good reference

actually it's hard to find these, if you google keywords "kummer", "book", "biography", etc. you almost exclusively get wikipedia-style short biographies

[wary compass]

can someone recommend an introductory textbook for self studying PDE? my advisor suggested that I read Evans but I find it too advanced (I only had an undergrad ODE class and I forgot most of it)

[finite crane]

have you learned harmonic analysis, functional analysis, differential geometry?

[wary compass]

ive taken a course in measure theory & diff geo and currently learning more about functional analysis

[finite crane]

ideally you want to know about distributions, tempered distributions, Banach-Alaoglu and Fourier transforms before you jump into PDEs

[wary compass]

distributions?

[finite crane]

you should read Folland's Real Analysis if you want to learn about distributions and Fourier transforms

Folland analysis skills will stay with you throughout PDEs

[wary compass]

oh im using folland but i only got to chapter7

i see

[finite crane]

chapter 8 and 9 then

[wary compass]

ok, I just feel like evans assume that I'm already familiar with some concepts but I'm not, and sometimes im confused with an approach without any intuition.
I take a small example here, why do we seek such a mu with "special structure"? and what is the idea behind dilation scaling?

so im wondering if I should read another PDE text before I read Evans or I should have another more introductory text just to familiarize myself with stuff

[finite crane]

after Folland and diff geo (at least up to knowing Stokes' theorem and Riemannian geometry), I think it will be perfect to go back to PDEs
In which case there are 2 main books:

• Evans: elementary writing (without diff geo), more hands-on so even an undergrad can read it, but the price is that you do a lot of calculations and one can easily forget / lose sight of the big picture
• Taylor's PDE series: absolutely elegant writing in the language of diff geo and Fourier analysis, and everything is explained in a natural way, but the price is that you need to know diff geo / analysis prereqs to understand the language

[finite crane]

the heat equation is very elegantly solved by Fourier analysis (it's just a polynomial)

but when you have to simplify to write an elementary textbook, the tradeoff is that the reader might not know where the ideas come from

as for what evans is doing here specifically
it's called an ansatz
fancy word for making an educated guess
there are some justifications for it, such as observing the symmetry of the equation, but in the end it's a guess, so it's up to you whether you feel convinced by it

the proper way to solve it for me is still the Fourier transform

[wary compass]

yeah I'm aware of the approach using fourier transform but I just did not understand what dilation scaling means. But I guess I could just skip it
also did not realize it has so many prerequisites 😭 I definitely need to review some stuff / relearn..

[finite crane]

dilation is a concept from geometry, rescaling vectors.
here you are rescaling time (time dilation) which happens a lot in PDEs

usually when you learn any new PDEs you will come across such change-of-variables tricks

also called symmetries

[wary compass]

what do I need to know in diff geo? because I dont remember much about my diff geo class but I did pretty well in my multi calc class and that's where I learnt stokes and gauss theorems

[finite crane]

discovering such symmetries can be their own art forms, but usually for the most famous equations, the symmetries are all known

[finite crane]

Stokes theorem, differential forms, tensors, connections on vector bundles, Riemmanian geometry, Hodge Laplacian, covariant derivative

[wary compass]

cool! thank u

[finite crane]

make sure you already know general topology (like first chapter of Bredon's Topology and Geometry)
if you are short on time read Jeffrey Lee's "Manifolds and Differential Geometry" to learn diff geo
if you're even shorter on time read some physicist's book on diff geo but hopefully it won't come to that

[wary compass]

I took a pointset topology course, i never learnt what general topology is

how do they differ

[finite crane]

can you prove Tychonov's theorem and stuff
compactifications etc.

[wary compass]

I'm not that short on time, I'm going to begin my master's in September, I would like to just prepare myself for PDE because my advisors are doing PDE

[finite crane]

partition of unity / paracompactness is the big one

[wary compass]

yeah we learnt tychonov theorem

[finite crane]

cool, you can review first chapter of Bredon to refresh it then go straight to Jeffrey Lee

PDE analysts don't need to count holes so Jeffrey Lee's book is all you really need

[wary compass]

I think we used munkres for topology when I learnt it

[short violet]

oh hows the book so far?

[short violet]

i see
The Real Numbers and Real Analysis by Ethan D. Bloch
Is this the book you are talking about?

[slender wasp]

yep

[molten mason]

When you go through it come back and let us know what you think of it!

[glad rose]

Which one of the two would be better for a highschool graduate learning proof writing, or any opinions: Mathematical proofs- A transition to advanced mathematics v/s How to prove-it a structured approach?

[tough egret]

Excellent so far for a self-learner. I was going through Abbott, although he explains very well the concepts, I felt that the book lacked in the use of fundamental concepts (from commutative algebra for instance) and in providing examples. Johar’s has lots of it, which helps build mathematical intuition and improve proof writing. It also features lots of exercices and some hints at the back for the harder ones.

The construction of R from Q is done using Dedekind cuts. The book also has chapters on introductory measure theory, applications of calculus, topology and double integrals as well as a section on differential equations.

[tough egret]

Will do ! I hope to get done with it by june to get on ODEs and complex and functional analysis for the summer

[molten mason]

I don't know the first book, but How to Prove It is extremely popular and a good portion of this server has gone through it if you need help or have questions.

I'll wait to see if anyone knows anything about the first book though.

@vital bane has gone through A Transition to Advanced Mathematics

[molten mason]

Ooh, all that does sound nice.

[glad rose]

Oh, I didn't know that. I'll see if Neamesis has anything to say for now. Didn't know the first book was so popular. Thanks.

[vital bane]

how did you remember that? Even I forgot I did this book

but yes I started with this before I got started with Abbott

[heady ember]

Hi Name

[vital bane]

The book is well written, but I only have gone through the first 2 or 3 chapters

[molten mason]

Leave all you want. Your old messages still come up in search

[vital bane]

then I dropped it and continued on my way with Abbott

that's actually my previous account with the same name

[vital bane]

because Abbott is so well written for people who are new to mathematical proofs

that I had no trouble learning how to write a proper proof in anal

[vital bane]

Hello glass

[heady ember]

How did you know the name of my mind

it breaks quite easily

[vital bane]

your mind is like glass because it breaks easily

[heady ember]

Exactly

[vital bane]

jinx

[heady ember]

[vital bane]

my mind is like supersymmetric bosons

because it doesn't exist

just mindlessly scrolling through stuff and not doing much

[heady ember]

You're a bot confirmed

You: Mum can we have skynet at home?
Mum: We have skynet at home
Skynet at home: Neam

[vital bane]

Honestly if you wanna get better at writing proofs a dedicated proofs book I would say isn't the best approach, just pick up an intro analysis book (Like Abbott) and start working through it

the best way to get better at writing proofs is to actually write proofs in the real setting of learning actual math (real math because it's "real analysis" note it, not "fake analysis")

But going through that book isn't bad either because the latter half of the book is actually proofs from real mathematics

[molten mason]

"Fake analysis"

[vital bane]

https://tenor.com/view/real-and-true-cat-walking-gray-cat-gif-14865986020845776272

[molten mason]

How to Prove It was great for me because of getting all the logic, set theory, and other nonsense without all the real math lol I enjoyed that.

[civic python]

What is "fake analysis"?

[molten mason]

Was a nice introduction.

[tough egret]

Not the best way to abridge “analysis” 💀

[molten mason]

I have more fingers than that gif has pixels

[civic python]

Yes. I agree. How to prove it was my first real math book

[molten mason]

Wait until you hear about fun anal (functional analysis)

[vital bane]

and harm anal

[molten mason]

Harm anal best anal

[vital bane]

(harmonic analysis)

[civic python]

Harmonic analysis is about sequences that are harmonic? In that they fluctuate?

[tough egret]

What about complex anal ?

[vital bane]

it's basically like a generalization of fourier analysis

Like doing fourier analysis on topological groups and insane stuff like that

[civic python]

hmmm. Wierd stuff

[vital bane]

very cool stuff

[molten mason]

That's where the real fun begins

[civic python]

Why is a dedicated course on numerical methods a thing

People should just learn numerical analysis

[molten mason]

I need to find a professor at my university that does HA and convince them to take me under their wing

[vital bane]

complex fun you mean

[civic python]

What country is that?

[molten mason]

I'm in the USA. I won't get any more specific than that.

[civic python]

oh i see. Its just that I don't think that's how it works in europe

[vital bane]

Time to track down Salagos using his time zone

[civic python]

Wait. This is #book-recommendations. Thought this was general chat

[molten mason]

Do it

That would narrow it down to like 50 schools lol

[civic python]

I already have his IP-address, no need to go through the trouble

[heady ember]

why stop at his IP address?

[civic python]

Oh yeah. I forgot to mention i used his IP-address to hack his laptop camera 👏

[vital bane]

and hack into his neuralink™️ brain chip

[glad rose]

what do you mean by "fake analysis" if i may ask?

[lime vessel]

Calculus

[chrome tide]

Best introductory and challenging physics book. I don't want like young and freedman or fundamental of physics those are way too easy.

[short violet]

i am a self-learner! , whats Abbott btw?

[remote sparrow]

a very good introduction to real analysis

[remote sparrow]

the third edition of halliday resnick is more difficult

[short violet]

? is that a book ?

[remote sparrow]

halliday resnick krane is also challenging

[remote sparrow]

yes

[chrome tide]

Physics by hallidag resnik and krane (not fundmentals) is good kinda but I am open to suggestions

[short violet]

oh whats the full name ?

[remote sparrow]

Understanding Analysis by stephen abbott

[short violet]

okay so u r using this book for more fundamental concepts , u say right ?

[remote sparrow]

fundamental concepts in what?

[short violet]

" fundamental concepts (from commutative algebra for instance) and in providing examples"

[remote sparrow]

https://www.amazon.com/Introduction-Mechanics-Daniel-Kleppner/dp/0521198119

also ask the physics server in #old-network

[remote sparrow]

it teaches you single-variable real analysis

also a misquote

[short violet]

oh i see i will buy that too

[remote sparrow]

it's on sale

https://link.springer.com/book/10.1007/978-1-4939-2712-8

only $29.99 for a hardcover

[gray gazelle]

You can go through dedicated books on different topics in that case. So for example physics of waves by georgi or introduction to mechanics

Halliday teaches you the basic concepts though so you might want to go through that first if you can

[chrome tide]

I am sorry that I am asking a physics question in a math discord however physics discord are somewhat dead and full of toxic people for some reason

[chrome tide]

Ur right

[tough egret]

Abbott is very good as a first introduction to real analysis. It presents all of the essential concepts in a way that’s both rigorous and understandable.

However, it does not build up the reals from commutative algebra, neither does it presents many concepts in topology. Also, it does not consider multivariate stuff.

[short violet]

Understanding Analysis by stephen abbott , right ?
good for a beginner too ?

[tough egret]

Having some knowledge of single variable calculus will definitely help you

Like having some understanding of what differentiation and integration is, how to manipulate sequences and series

But it’s not a firm prerequisite IIRC, it just makes the concepts of RA less hard to understand

[short violet]

and those topics are taught in Johar's big book right ?

[tough egret]

Yes

[short violet]

yeah ik them !!

[short violet]

are u a self learner too?

[tough egret]

Like the field axioms and ordered field axioms are never mentioned in Abbott

[tough egret]

Yes

[short violet]

i felt like i have mugged up all the concepts of maths i have learnt so far , so just decided to learn every concept from the beginning

[tough egret]

Where do you find yourself at atm ?

[short violet]

tbh i am clueless
thought real no. would be a great place to start

[tough egret]

Are you familiar with some advanced topics like linear algebra, complex numbers, abstract algebra, topology ?

[short violet]

just complex numbers and a bit of linear algebra

[slender cargo]

imo deriving the real numbers is a better exercise later on, when you can appreciate it more

[short violet]

Is it really necessary to know these to understand real numbers?
and what do u think , Is it a good idea to start with real numbers in the first place?

[tough egret]

Depending on how deep you want to delve into RA, Abbott can do the trick, and Johar can do it as well

[short violet]

one thing i realized is that i can go as deeper as i want theres not limit

[short violet]

oh really ?

[tough egret]

No, it’s not at all. It was to gauge your level of mathematical maturity. Some maniacs on Reddit or elsewhere recommend baby Rudin as a good resource for RA for instance, which is suicidal

[short violet]

lol , what should i do then ?

[tough egret]

Depending on the time you have to allow, either go for Abbot’s Understanding Analysis (smaller option) or, if you want to have an exhaustive and deep look at RA with lots of examples and exercises, go for Johar’s Big Book of Real Analysis. These are the two books I own on the topic, there are lots of other that could be considered intermediate options.

[short violet]

i see , what are u studying btw?

[dark obsidian]

do I need topology to study tensor fields?

[tough egret]

I have a master’s degree in law lmao

Right now I’m working my way through undergrad mathematics to get into a master’s in applied math

[modern ruin]

epic

[hot dagger]

is this a scam?

asking 15 eur for ebook is fishy

because many universities have this pdf listed for free on their site

[tribal crow]

Springer is not a scam

[hot dagger]

why would they charge for something available free then?

or official universities are pirating books which is unlikely

if you want ebook of abbott I have a copy and can send privately

[earnest wolf]

usually it's ~100 tho

[hot dagger]

What are you saying?

100€ for ebook?

💀

In what kind of Monaco world do we live in

Where one gives 100€ for an e book

[earnest wolf]

ah. e book

i meant hard copy. sry

[hot dagger]

Hardcover and softcover are the same price as ebook on that site

Yeah yeah

But doesn't make sense

Both hardcover and softcover are 20$ and ebook is 15$

Who the hell would buy that ebook

[gray gazelle]

im sorry i dont like sweet tea, i prefer bitter tea

[earnest wolf]

I mean...I personally like ebooks MUCH more than hard copies

[gray gazelle]

also hi sergeEmbedding, long time

[earnest wolf]

exactly

[hot dagger]

Then get one for free at least duhh 💀💀💀

[manic cairn]

...hi

[hot dagger]

Why is it forbidden to send files in here this is literally book recommendation

Admins think

[tribal crow]

lots of books from Springer are free if you login with your institutional email

that's also likely how the universities are getting the pdfs

[hot dagger]

I don't think they gonna accept my institutional mail

[hot dagger]

Free for all

Doesn't require mail

[tribal crow]

yeah not every institution does

and not all books are going to be free either

even if they did

[hot dagger]

Mine has my specific domain

True

But those that are available for free why pay for them

[tough egret]

Why so?

[earnest wolf]

in my tiny laptop i have hundreds of them

try to read in bed / position the book vertically / read in public transport / take at least one such book with you to college assuming on average they are 2-3 kg

[molten mason]

"on average they are 2-3 kg"

Do you even lift bro

But same lmao, PDFs = for out and about or in bed. Physical books = when I'm in my office at the desk.

Right now I'm using a PDF on the computer so my desk has room for me to aggressively slap as drums along to my full blast study music lmao

[lusty ermine]

graph theory introduction, and pidgeon hole principle intro pdf ?

[dusk wind]

me with any book that exists

[hot dagger]

Yeah well laptop makes sense

[dusk wind]

you're right, it is a scam

[hot dagger]

Lmfao

I have 2 Spivak calcs, abbott and ross books so if you need I can send

[dusk wind]

I'm good

[hot dagger]

The spivak is not full tho

[dusk wind]

my library is rather decked out

[hot dagger]

One is 600 but looks really nice and one is 700 pages

[hot dagger]

Yeah same but I have mostly stuff in my own language I rarely use eng literature idk why

Maybe because they're all PDFs

So i have to sit to read them

I'mma post this here because nobody gave a fuck in another channel

Im looking for help, this semester I got analytic geometry course (university level) and lecturers are really bad to a point where both calculations and theory are just red from the existing scripts/presentations. I dont know how to learn this because this geometry is mostly proof based, doing vectors at the moment and have experience from LA but this is way too different with every calculation task being something to proof or to express somehow. Where can I learn this easily and what books are really easy to understand and fast to learn?

I had logic last semester and its professors were 10x better both on calculation and theory field but this is a completely differnt story

Basically it's everything but a regular geometry I've seen

Everything requires some sort of proof although it's really basic formula-wise there's not many transformation rules

[steel cloud]

Can someone suggest a way to learn physics independently?

[hot dagger]

Book, youtube, discord, forums, colleagues

Undergrad math is hell, can't imagine physics ☠️☠️☠️

[steel cloud]

Which book?

[hot dagger]

What book is recommended by your college/professor idk really, are you in college?

If you're not in college/school why would you want to learn physics? That is a really hard topic to learn by yourself and you don't have any guidance on what to do + that knowledge is useless if you don't have a diploma

[modern ruin]

for sport

[steel cloud]

No I haven't physics course therefore I said independently

[steel cloud]

No actually I do mathematics and want to do physics

[hot dagger]

Then try with YouTube and people there might suggest good literature

Like math sorcerer does suggestions for mathematics

[steel cloud]

Okay thank you

[hot dagger]

But bear in mind physics is much more niche topic and probably less information available

[tribal crow]

hm?

[hot dagger]

Uhh

[modern ruin]

bruh

[tribal crow]

I don't really agree

[hot dagger]

I meant less popular than math for example

[tribal crow]

there's TONS of resources for physics

[modern ruin]

you have no idea

[tribal crow]

no wth

physics is more popular by a long shot

[hot dagger]

For real?

[modern ruin]

for realsies for sure

[hot dagger]

Here physics is almost forgotten lol

[tribal crow]

math is not nearly as popular as physics

it's not even close

[hot dagger]

Most you'll get from physics is electrical engineering related subjects

Here*

[tribal crow]

I see

that's a bit unfortunate

[hot dagger]

True

Here both math and physics faculty are in a downfall

Because they're too hard

[tribal crow]

what a shame lol

[hot dagger]

True

So many many kids actually ask for math private lessons rather than physics

I remember myself few years back and many others, I don't think anyone ever went to physics private classes

Mostly mathematics and english

I had no idea physics was so popular damnnnnn.....

[dusk wind]

its crazy to me how one schools curriculum can vary so much for the same courses

[ancient sand]

recommendations for books for introduction to abstract algebra?

[tribal crow]

#book-recommendations message

[ancient sand]

artin, then, thanks

[earnest wolf]

what could one study after half a course in real analysis and a full course of linear algebra?

by half a course I mean basically the whole Abbott's book (which would be pretty close to the first volume of Tao's)

the second part will be about sequences of functions, differentiation in R^n and Riemann integral

For fun I mean ofc.

Probably not functional analysis (yet) — more stuff about sequences of functions needs to be studied first ig

i think maybe abstract algebra will widen the option list

[gray gazelle]

Topology?

[remote sparrow]

abstract algebra, multivariable calculus, measure theory on the real line, metric and function spaces, fourier analysis with riemann integration, complex analysis

these courses will use either your real analysis or linear algebra knowledge

of course, there are courses that don't depend on real analysis and linear algebra as much or even at all, like combinatorics, mathematical logic, axiomatic set theory, computability theory, problem-solving courses on ODEs and PDEs, calculus-based probability and statistics, elementary number theory, etc.

[modern ruin]

second on topology pick up munkres

[heady ember]

More set theory

[molten mason]

Complex analysis

[digital harbor]

There are fairly advanced physics books out there specifically intended for mathematicians.

[digital harbor]

Have you studied Measure Theory? There is more out there than just Riemann-Stieltjas integration.

[gray gazelle]

Any books recommendation for discrete math?

[digital harbor]

There are lots of discrete mathematics books out there. How tough of a book are you interested in? Have you studied enumeration yet?

[gray gazelle]

No, I want Introductory

Idk what enumeration is

[digital harbor]

OK - Then I don't recommend Roberts book as it is suitable for an introductory graduate course. Let me think a bit.

[gray gazelle]

Sure man

I appreciate the help

[digital harbor]

If you want an overview, try "Combinatorics and Finite Geometry" by Dougherty. It includes graph theory and finite geometry which are both fun as well as an introduction to enumeration.

[digital harbor]

Doughtery also introduces coding theory, cryptography, and games.

[digital harbor]

Enumeration is all about how to count things that are difficult to count.

[gray gazelle]

Is it a good introductory book?

[digital harbor]

Go take a look at the preview and tell me whether you think that you can handle it. It is intended for undergraduate mathematics majors. https://www.google.com/books/edition/Combinatorics_and_Finite_Geometry/LGMGEAAAQBAJ?hl=en&gbpv=1&printsec=frontcover

[gray gazelle]

Thank you it's only 22$ I'll order it

[digital harbor]

The book does expect you to have previously taken a course which included "informal" mathematical proofs.

[gray gazelle]

Oh Damm I have not taken that

I need like intro intro shit

[digital harbor]

Go read through about page 5 or 10. That is the level that they are expecting. Ultimately, mathematicians prove theorems for a living. So, proofs are something that you will need to cut your teeth on at some point.

[gray gazelle]

Will do

Appreciate the hell

Help

[digital harbor]

You might want to pick up a copy of "Pure Mathematics for Beginners: A Rigorous Introduction to Logic, Set Theory, Abstract Algebra, Number Theory, Real Analysis, Topology, Complex Analysis, and Linear Algebra" by Steve Warner. The first two topics are foundational for studying mathematics at the college level. It has pretty good reviews and introduces a bunch of other topics.

[gray gazelle]

I'll look it up

There is one for pre beginner too

[digital harbor]

Take a look at this one. It is an introduction to abstract mathematics including proofs for freshmen in mathematics programs. It is also currently on sale for 50% off. https://link.springer.com/book/10.1007/978-1-4471-0603-6#toc

[gray gazelle]

How many books do u know lmaoo

[digital harbor]

I have a PhD in discrete Geometry from the Combinatorics Group at Northeastern University. I also have rather a lot of books about a rather a lot of subjects. Now then, I should give you the discount code for the last book I recommended as it is not showing up automatically in the link.

[gray gazelle]

It's okay I'll order from Amazon

[golden salmon]

Just wheeling in to simp for the Amann and Escher trilogy

[gray gazelle]

What is discrete geometry ?

[golden salmon]

https://www.amazon.com.au/Analysis-I-1-Herbert-Amann/dp/3764371536 great great great series

[digital harbor]

Discrete geometry is the geometry of things like points, lines, and similar higher dimentional items. This is in contrast to differential geometry which is all about being smooth.

[golden salmon]

It does measure theory in an interesting way (it skips mentioning rings of sets entirely and introduces sigma algebras in book 3, but does include algebraic rings in book 1. sounds weird but it works)

[gray gazelle]

That's awesome

[digital harbor]

You will get a much better price from: https://link.springer.com/shop/springernature/highlights-sale/en-us/

[heady ember]

Why did you reply ping me for that? It isn't even that related to what I said

[remote sparrow]

#book-recommendations message

[digital harbor]

Sour Drop just told me that I replied to the wrong person. Sorry for the mistake.

[remote sparrow]

that wasn't him though

that was Sweet Tea

[digital harbor]

oops!

You can currently buy Amann's Analysis I directly from Springer for $42.49 US (paper) or $32.49 US (electronic).

[golden salmon]

alright book gods I got a spicy one for ya. y'all think you're so slick with your tasteful analysis books and your elegant discrete maths books WELL I'VE HAD ENOUGH.

Please recommend to me a selection of free networking and homelab books and video series.

(yes I'm aware this is a maths server and not an IT server but someone in here is bound to have good suggestions)

[dusk wind]

the best ones are paid or on youtube, pick any of them

[gray gazelle]

books are expensive

[gray gazelle]

32$ for an ebook?

Any book that does multivariable calculus but uses lebesgue integral rather than riemann? i need to review multivar calc but already learned lebesgue integration

[cedar ridge]

Still a Hall of famer

He deleted his account shortly after

[heady ember]

On a random note, how important is the smell of your books to you guys?

[daring lake]

hmm, somewhat, like 60%

I prefer the old book smell the most, like old novels, old papers. The new smells often irritate me. If it doesn't give off any smell that's fine too.

Texture of paper is also important to me. Too glossy and its again not comfortable for me.

or maybe I am just too jaded

[heady ember]

Yeah the smell of Schroder makes me want to read it more

The smell of my copy of FIS is not pleasing, though.

[heady ember]

Dover enjoyer?

[daring lake]

Yea, dover is good. I hate Hindustan TRIM papers though since they are too smooth.

Well, its not as smooth as clairefontaine, but something about its texture is just too off putting (I have the Tao books from TRIM)

[heady ember]

I see

[analog spruce]

I'm looking for a second course in linear algebra style book

one with more reference to the decompositions one would learn at graduate level

like SVDs and Polar Decompositions

[remote sparrow]

amann escher volume iii, schroeder, browder, mikusinski. i know hubbard introduces the lebesgue integral so that it's easier to state fubini's theorem, the change of variables theorem, the monotone convergence theorem, and the dominated convergence theorem, but i'm not sure if lebesgue integration is used in a significant way much later. the appendix should have proofs.

https://link.springer.com/book/10.1007/978-3-7643-7480-8

https://link.springer.com/book/10.1007/978-1-4612-0715-3

https://www.amazon.com/Mathematical-Analysis-Introduction-Bernd-Schröder/dp/0470107960

https://link.springer.com/book/10.1007/978-1-4612-0073-4

[remote sparrow]

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

https://www.amazon.com/Matrix-Analysis-Second-Roger-Horn/dp/0521548233

roger and horn is more of a reference but it complements garcia and horn well when you want more generality and detail

[remote sparrow]

https://math.stackexchange.com/questions/3673352/book-that-uses-measure-theory-to-develop-multivariablee-calculus

some people don't appear to be a fan of amann but ymmv

[fierce hedge]

Smell is the one of the things that makes me wanna buy an actual book rather than getting is printed for much cheaper

[daring lake]

he is so real for that

[snow flower]

Truly a man of the people

[remote sparrow]

https://www.mdeetaylor.com/?page_id=264

https://maa.org/press/maa-reviews/an-introduction-to-multivariable-analysis-from-vector-to-manifold

[vital bane]

analysis that's fake

[glad rose]

😭 👍 alright thanks

[languid bloom]

anyone know much about "Basic Algebra 1" by Nathan Jacobson? Got sent the wrong book by accident so now I have it in my collection

[finite gale]

I mean what kind of comment are you looking for

it's a commonly used text for a first course in abstract algebra

[languid bloom]

just mainly seeing if its a good book for what it covers to see if I'll go through it much

I probably will go through it though seems decent

[finite gale]

you can read the bit here: https://discordapp.com/channels/268882317391429632/716264872018706443/718931426346795099

[languid bloom]

thanks!

[rigid hare]

Any good books that have matrix problems involving Eigenvalues and Eigenvectors?

[remote sparrow]

you can't return it?

[remote sparrow]

most introductory linear algebra textbooks?

[languid bloom]

no they're going to either send me the correct book for free or refund it

[finite gale]

any precalc text should work

or you can try khan academy

[trail hemlock]

my goat

what the fuck they made into a real person!!

[thorny cloud]

It's either going to be basic or hard

spatial geometry is too easy until it becomes analytical

[heady ember]

Yeah it can enhance the experience a lot or make it worse

[violet shuttle]

just get a multivariable calculus textbook, a linear algebra textbook?

"Cross product" is in some sense really broad. At a most basic level it's basic. But then you get things like the lie bracket and the wedge product and the theory of clifford algebras.

I always felt that the cross product was surprisingly rich

I don't understand what you are saying.

I was asking for clarification about how much depth you wanted.

And also recommending you a couple books

And also making a tangential statement about how cross products seem surprisingly deep to me.

I am well aware of how to compute a cross product in R^3.

However, I don't know German.

I wouldn't have read what you posted anyways.

...that's not German, is it?

my bad.

Look, please explain in English, without just pictures of a book, what you want.

I am asking at what level. Be more specific.

So, Calc 3 is a no go.

Linear algebra, also a no go?

Oh, great, tada

I have never understood what "analytical geometry" means.

...?????

"linear algebra, but not with the stuff that linear algebra is about"

all the conic sections can be obtained from a bilinear form in the projective plane

in homogenous coords

[gray gazelle]

I mean, determinants and matrices are natural constructions to do with vectors. And they’re useful for geometry

[violet shuttle]

https://en.m.wikipedia.org/wiki/Conic_section

...you mean the one saying that L^p spaces are normed spaces?

I thought calculus was off limits.

But functional analysis is a yes?

[gray gazelle]

I mean, here’s the thing. You can probably find some text which takes entirely elementary approaches to geometry in Rn. For instance, Apollonius’ Conics. However, the start-up cost of learning some calculus and LA and using that for geometry is well worth it

But you haven’t taken linear algebra?

[violet shuttle]

I think you are seriously incorrect in your beliefs about what you should learn in what order. This seems ridiculous to me.

[tribal crow]

hm?

functional analysis but no calc 3?

what

[gray gazelle]

Well functional analysis is a generalization of linear algebra using methods from real analysis… typically a grad level course

Why not just read a multi variable or linear text?

Both would cover the stuff your interested in from different angles

[violet shuttle]

Linear Algebra Done Right (or, Linear Algebra Done Wrong)

[gray gazelle]

Finite-Dimensional Vector Spaces

[violet shuttle]

(i haven't read a single linear algebra textbook (besides some numerical ones), actually - so don't take my suggestions that strongly)

[gray gazelle]

or Gil Strang’s book for a computational text

[gray gazelle]

Did you just learn it from an algebra book?

[violet shuttle]

I first learnt it from Shankar's Principles of Quantum Mechanics.

[gray gazelle]

Interesting

[violet shuttle]

After Baby Rudin, it became pretty easy to go and understand the rigorous proof of the finite dimensional spectral theorem

[tribal crow]

FIS!

Friedberg, Insel, Spence

if you're more interested in the computational stuff, Strang is a good idea

[gray gazelle]

Published by Springer, author is Paul Halmos

[violet shuttle]

The downside is that I just cannot remember how to compute a Jordan normal form.

[tribal crow]

despite my being tested on this a week ago, neither do I

(actually, I do remember how to get a JCF; it's the Jordan basis which I've forgotten how to compute again)

what an odd course

[violet shuttle]

There are things that in the course of self studying I never properly learnt.

[tribal crow]

isn't that true, self study or not?

I don't know how many people fully learnt and understood every last detail they were exposed to

[violet shuttle]

Yeah, it's just that I self studied

[tribal crow]

but I'm not guessing a lot

[tribal crow]

you clearly did a very good job with that though!

[violet shuttle]

Thanks!

So, clearly everything about me must be unique to autodidacticism.

[remote sparrow]

geometry on coordinate planes

[remote sparrow]

it's a dover too

[gray gazelle]

It’s more rigorous that stewart

[slender wasp]

It's mid-way between a computational calc book like Stewart and an intro real analysis book. Which means a lot more focus on proofs and proof type problems.

[finite gale]

You can choose to work on it alongside Stewart or just in place of it but go look at Stewart for some computational problems

[marble solar]

It's the way a mathematician would teach math to math majors/math nerds

It has most of the caveats a mathematician would think about, and interesting problems to work on, even for the instructors

[heady ember]

Seconded. But I wish there were more exercises that slapped me

Also, sometimes the authors wrote in excruciating detail that felt a bit unnecessary, for me. But for someone new to proofs, that might be something nice/beneficial.

[heady ember]

Abbott or Schroder are good intros to analysis

The Good

Why Schroder is nice #book-recommendations message

Some pages of it #book-recommendations message

The Bad

Whilst I like Schroder, I also have had times where I didn't.

1. In chapter 5, his proof of the Riemann's Condition felt a bit handwavy and was hard to parse.
2. In chapter 6, he presented a proof that absolute convergence holds iff unconditional convergence does. There was seemingly unnecessarily complicated notation involved. I proved it myself and I didn't seem to find that necessary.

Page in question for point 1.

The parts in question for point 2. I think its a bit

Personally, I wrote this instead.

[vital bane]

Yoooo fellow physics enjoyer and a Shankar enjoyer on top of that! based af!

[tribal crow]

physics is awesome

[vital bane]

[vital bane]

"absolute convergence holds iff conditional convergence does"?? what? conditional convergence doesn't imply absolute convergence

[heady ember]

Typo...

unconditional

[vital bane]

RIP

[heady ember]

Obvious smh

[vital bane]

what is unconditional convergence?

btw check out my proof in my thread

[heady ember]

Aren't you reading abbott

flip it open

[vital bane]

tell me if it's correct or not

[vital bane]

there is no mention of it in Abbott

[heady ember]

are you sure

[vital bane]

yup checked the index

I dont think that's a thing

or maybe it's an outdated term for something

[heady ember]

[vital bane]

Lol nevermind

https://en.wikipedia.org/wiki/Unconditional_convergence

yea it's in Abbott but he never used the term "unconditional convergence" for it

[heady ember]

Now who's outdated? (idk)

[vital bane]

what is an advanced inequality?

holder inequality and stuff like that?

or do you mean like more complicated algebraic expressions involving inequalities?

[remote sparrow]

https://maa.org/press/maa-reviews/the-cauchy-schwarz-master-class-an-introduction-to-the-art-of-mathematical-inequalities

[wise moth]

guys i need a book on precalculus can you like tell me some topics i should cover before that? and based on my knowledge could y'all reccomend a book?

[violet shuttle]

It's one of my favorite books!

First textbook I read for funsies. First advanced book I read.

Analysis is just applied triangle inequality

[vital bane]

of course

"wait it's all triangle inequalities? Always has been 🔫 "

[vital bane]

same! it's my favorite QM book! super well written

[violet shuttle]

(thus the best place to learn advanced inequalities is to get a dozen books in analysis)

[golden salmon]

Hello chat, I am here to give an unsolicited physics textbook recommendation for anyone curious

I think for the individual interested in quantum mechanics, they should decide if they're mathematicians or physicists in style (to grossly oversimplify, are you primarily interested in the behaviour of the theory or the way the theory describes experiment). If you're a mathematician, read feynman+gasiorowicz then shankar. if you're a physicist, read townsend then shankar.

this isn't to say griffiths bad or sakurai bad (they're both great) but I think that this progression makes the most sense because:
-early exposure to bra-ket notation
-clear language used
-finish on shankar (which has the necessary level of abstraction to feel "done" with it)
-doesnt have cohen-tannoudji's problem of TOO much detail

[violet shuttle]

why not start with Shankar?

[hot birch]

I want to learn logic

From start to like, halting problem, 2nd order logic etc

What good book(s)

?

[golden salmon]

You could! But I've been told its good to learn at least 2 ways to think about QM and better to finish on a high note

[remote sparrow]

#book-recommendations message

check pins as well

[hot birch]

ty

Why does everyone here have a hot pfp

[gray gazelle]

infinite regex? explain your coding experience in #discussion always happy to meet a fellow coder

[hot birch]

I was glancing at

A concise introduction to mathematical logic by Wolfgang Rautenberg

and it looked nice. What do you think of it? You didn't mention it in your recommendations.

[tawdry thistle]

could someone recommend a book about number theory?

[orchid nacelle]

if you haven't already, skim over the pins in this channel. maybe there's something in there?

[tawdry thistle]

i forgot those existed, thanks 😄

[gray gazelle]

Ireland & Rosen is good

[finite gale]

person who asked is preuni

pinned message is also not so elementary books i think

[hot birch]

should make one big wiki-entry pin tbh, it's hard to find past scattered recommendations here

[finite gale]

you could also just search stuff up

in book recs

[sacred ingot]

go drink some water

[finite gale]

thanks for reminding :3

[sacred ingot]

no problem xD

[slender wasp]

Assuming you are looking for an intro to elementary number theory: #book-recommendations message

[rain crescent]

in:book-recommendations maff you want

[hot birch]

@remote sparrow
What do you think of this project
https://github.com/OpenLogicProject/OpenLogic
https://builds.openlogicproject.org/open-logic-complete.pdf

The Open Logic Project is an open source, open access collection of materials on advanced logic, aimed mainly at philosophers, ...

Is logic really this useless?

i hope it's not just a semantics maze

[dusk wind]

no just that project

[dusk wind]

this the only thing that should be pinned tbh

[hot birch]

where do you draw the line in logic where it becomes more philosophy than useful things? how can i know if my textbook of choice is philosophy?

[dusk wind]

this is philosophical

if it's useful then go for it

[hot birch]

i just can't tell about this because the project looks to have the same topics as the ones discussed in other logic books recommended

[dusk wind]

pick any text, literally any other text (even one recommended here)

[storm zinc]

"more philosophy than useful things" youre hurting me

[hot birch]

sorry

[dusk wind]

that project is whats painful tbh

[hot birch]

i just wanted a bit more elaboration

on why it's obviously philosophy and not math

but w/e

[dusk wind]

also philosophy is useful (if it can be applied)

[hot birch]

yea but you get what i mean

[dusk wind]

in general it's useless, but academics can make anything seem useless if they write it for themselves

Sour Drop has some good reccs I think

[violet shuttle]

Well, Shankar has a last chapter on path integrals, which I think counts as a second way.

[remote sparrow]

not beginner-friendly

[tribal crow]

anything is beginner friendly if the beginner is brave enough

[remote sparrow]

#book-recommendations message

[remote sparrow]

why would a logic book be useless if it's aimed at philosophers?

[remote sparrow]

i'd probably recommend something else for the more mathematically sophisticated but that doesn't mean formal logic for philosophers is useless, bad, or necessarily nonmathematical

[hot birch]

well you know what i meant by "useless" come on

[covert mauve]

Dumb question, but why do authors love giving 50 repetitive questions instead of 10 hard ones? it doesn't even make me learn any better, and just exhausts my time which I could use to learn more.

It's not like they can't use the topic in later questions and have muscle memory build over time.

[tribal crow]

of course it’s best to know everything in Stewart… but that would take way too long!

[remote sparrow]

you don't have to do all the questions

[marble solar]

You can learn it from Spivak, but you might have an easier time if you roughly know how to compute limits, derivatives, and integrals

[tribal crow]

spivak is friendly enough that one can read it without too much calculus background

[tribal crow]

but I completely agree with this

[marble solar]

Even if it means you learn how to do the stewart problems, then you go read the corresponding section in Spivak

[covert mauve]

yes, I dont have to, but FOMO caused by it is pretty bad.

[tribal crow]

I have the urge to solve every single problem in a textbook too lol

[marble solar]

You can interlace it actually

I learned in a combined class that used a book like stewart and spivak at the same time

We'd learn the basic problems then do deeper dives in spivak

That works, if you have something in plan down the road

[remote sparrow]

well you can either have fomo or be bored by doing problems you're confident in

[gray gazelle]

Recommendation request: Ultimate non-measure theoretic Probability book combo? Three books at most which cover the topic from different appreciable perspectives.

[earnest wolf]

i mean, it really depends on the level of the book

honestly, I haven't seen such such exercises in ages since high school (except in some shitty books mb)

[covert mauve]

I am only doing "basic math" books so far, and most have an absurd number of problems, specially pre calc ones. the only one I found that didn't was serge lang's basic mathematics.

[violet shuttle]

what about from profs?

what about 5 instead of 50?

[earnest wolf]

u mean lec notes?

[violet shuttle]

that, or homework

[earnest wolf]

oh boy, u better don't see our homeworks ☠️☠️☠️

again, depends on the lecturer really much

[covert mauve]

my high school math books have 200 problems per chapter.

[earnest wolf]

I have had some that gave us homeworks of the type 'solve or die trying'

and some who just gave simple verification stuff

like the things which are 'left as an exercise to the reader'

[violet shuttle]

...don't

I don't do enough exercises, because the content of the later chapters always beckons me

[earnest wolf]

and as for lec notes, that also largely depends on the lecturer

[covert mauve]

oh, I dont. if I did, i would spend the entire year doing 3600 problems.

[dusk wind]

you definitely dont need to do all of those

but do 10% of them at least

[earnest wolf]

but that's a valid point tho – why 500 and not 5 hard ones?

ig mainly because those are computation-based subjects and students are expected to solve algorithmic problems?

[covert mauve]

I do all the "terminal exercises" at the end, 35 or so questions covering all the topics in the chapter.

[dusk wind]

would actually recommend serge lang over a typical high school book

[violet shuttle]

which Lang?

[covert mauve]

I hardly have enough experience to recommend anything, I just like serge lang because it's not dry and has proofs.

[dusk wind]

basic mathematics which I find dry

[violet shuttle]

...

"lang" and "not dry"

[covert mauve]

definitely doesn't cover everything from my high school book, though.

[violet shuttle]

i use lang's algebra because i have it, it has the content, and i didn't like Dummit and Foote.

[covert mauve]

isn't that an abstract algebra book?

[violet shuttle]

yes

[covert mauve]

is that really relevant to a discussion about high school math books?

[violet shuttle]

Yes

It's written by Lang.

[covert mauve]

basic mathematics by serge lang is way less dry than any of my high school books

(atleast in my opinion, but what do I know)

[violet shuttle]

What does it cover?

[covert mauve]

trig, geo, and algebra

[violet shuttle]

How rigorous?

A title like that makes me hope that it has things like the definition of the integers.

[covert mauve]

I haven't really read enough rigorous books to compare it to

[covert mauve]

it does

[violet shuttle]

Does it prove things formally? Do you get definitions of things like "equivalence class"?

[violet shuttle]

as equivalence classes of ℕ × ℕ?

[covert mauve]

no, not that

[violet shuttle]

Oh, okay.

[remote sparrow]

blitzstein/hwang and grimmett/stirzaker plus the companion 1000 exercises in probability

[remote sparrow]

variety so you can pick and choose. also, odd problems typically have answers, so professors may only assign some subset of them.

[gray gazelle]

Blitz doesn’t develop approximations to the Binomial, specifically not the Normal, he just defines them. Does Grimmett does that?

[ashen axle]

Good afternoon, can someone recommend me a book pls? I am currently learning Alberta but I wanna get a head. Thx!

[gray gazelle]

A book on what?

[gilded notch]

Alberta

[ashen axle]

Oh, me goal is to learn calculus but, I don’t know how to start. I was thinking about something that could help me to understand more about algebra or t Trigonometry or something like that. Thx

[maiden glen]

Can Edwin E. Moise's book "Elementary Geometry from an Advanced Standpoint" be a reliable resource for self tutoring geometry like that; in schools? if not, then possibly an addition to existing knowledge? (assuming the term "elementary geometry" refers to the geometry taught in school, modern or classic)

[full pier]

would baby rudin be a good text to work through in an introduction to analyis

[violet shuttle]

yes

[full pier]

thankyou

[violet shuttle]

others may disagree, though.

It is hard.

My biggest complaint is that he doesn't give the names of some of the theorems, which led me to think that I hadn't learnt the Arzela Ascoli theorem for years after I had learnt it.

[full pier]

oh i see, yh, i was going though the first few pages yesterday and was very confused on example 1.1 where it just looked like he did an asspull where q=p-(p^2-2)/p+2

[remote sparrow]

https://math.berkeley.edu/~gbergman/ug.hndts/#Rudin

here are supplements to rudin

[full pier]

thankyou som uch

[remote sparrow]

https://www.youtube.com/playlist?list=PLldiDnQu2phvYtwJBwauXuT9UbNfMYrhF

https://www.youtube.com/playlist?list=PL0E754696F72137EC

[full pier]

thankyou!

[maiden glen]

response please

[lusty ermine]

book with lots of transpose of matrices hard exercises

mathematical rigurosity

undergrad

[violet shuttle]

...hard exercises...at finding...the transpose??

[remote sparrow]

have you read any of the linear algebra books that have been recommended to you? you're being a bit paranoid about being underprepared tbh

you're not going to be expected to know everything perfectly

[violet shuttle]

Look, write a short python program that'll ask you to find a transpose of a million dimensional matrix.

[hallow oriole]

i disagree for the record

i think for a new student going into anal pma is not it

if you've done spivak or something similar beforehand then sure

but dry?

no

[violet shuttle]

It works great for someone that was exactly like I was.

YMMV if you aren't literally my past self.

I was waiting for someone to give a different recommendation to them

[hallow oriole]

right but i'm gonna go out on a limb here and say that you had one or more of three things: natural intelligence, mathematical maturity, or just really really hardworking

[lusty ermine]

yes I read a bit. I what do you recommend apart from HK, LADR, LADW, Anton's, for this matter?

[hallow oriole]

someone without any of those going in is gonna have a bad time

for an analysis intro use abbott

[tribal crow]

why do you need so many LA books the heck

[violet shuttle]

first, replaced the last with obsessiveness and interest.

[lusty ermine]

I just want to practice transpose before clases start

[violet shuttle]

...the transpose?

[remote sparrow]

you can google "matrix transpose examples" and "matrix transpose exercises"

it's a very simple concept

[violet shuttle]

look, do you want me to literally write the short python code?

[hallow oriole]

if ur going to buy a book to learn the transpose buy me a book of my choice instead and i'll js teach the transpose to u 🙏

[lusty ermine]

I am just not satisfied with any of the algebra stuff I have seen

is lang any good, in that regard? (algebra)

[fallow cedar]

I'm making a collection of (legally) free resource on mathematics.
Although the field is biased, I hope this will be of some help.
https://seasawher.github.io/free-math/index.html

[tribal crow]

how is getting another book going to help with that

[remote sparrow]

if you ever decide to give up on rudin, take a look here: #book-recommendations message

[heady ember]

Don't like his proof? Just prove it yourself

[magic spade]

What's your goal? Moise is good but I don't think it has exercises. I think Lee's axiomatic geometry is the best college level book covering high school geometry topics

[remote sparrow]

this is page 475 of blitzstein

[lusty ermine]

maybe the author doesnt elaborate enough

[maiden glen]

To cover as much of elementary and school geometry as I possibly can through pdfs

[lusty ermine]

i have same goal

[magic spade]

Try Lee

[maiden glen]

Thank you.

[dim sierra]

are you open to anyone else contributing? im not sure if i have concrete stuff off the top of my head i can give but i’d love to contribute in the future

[fallow cedar]

Yes, contributions are welcome.
but lecture notes or textbooks are more helpful than lecture videos.

[full pier]

bet haha, hopefully i will be fine

[maiden glen]

Is there a PDF I can find?

[molten mason]

Basic Mathematics by Lang is probably your best bet.

[glass oracle]

I have obtained a copy of stewarts book. Im still starting calculus so il probably get a spivak one when im more understanding of everything. Thats what someone suggested i do

[molten mason]

Slightly, but it works.

I would supplement the trig with this.

https://mecmath.net/trig/

It'd perfect for a review, or to get quickly started and running through it. Them afterwards finding resources like exercises books or YT to strengthen weak areas.

[steel cloud]

Any review on Groups rings and field by D A R Wallace

[hot birch]

@remote sparrow hey, can i get your opinion again? what do you think of Introduction to Mathematical Logic by Church, Alonzo ?

[hot birch]

hmm, found this

[oblique girder]

Hey, looking for an undergrad level book/resource to familiarise myself with the p-adics, any exercises would be nice too. Not really sure how deep it goes as a topic, so no real expectations on what level of detail the resources are so far too. Any resources giving a nice overview of the -adics and how they're used would be nice too. Or if this is actually pretty small and suited to a conversation that'd be nice too

[finite gale]

Gouvea has a book on the p-adics

But otherwise you can get a brief introduction to them in whatever topic book you're interested in probably

[oblique girder]

I'll take a look at this, thanks

[oblique girder]

I don't have a particular motivation for learning them now, other than the fact that I feel like they come across tangentially in many things I'm learning about is all, and I'd like to be able to understand more context in the things I learn, if that makes sense

Because of that I'd like a little more than just a brief introduction if possible, but I'll take your recommendation for a spin

[finite gale]

I haven't used gouvea too much besides to reference a couple times but I've heard that it's quite good

[oblique girder]

I'll take a stab at it, but just having skimmed the table of contents and the introduction it seems like it'll cover all I need, thanks!

[remote sparrow]

no clue. don't think anyone currently uses it as an introduction though

[versed coral]

can someone please help me decide a pathway when it comes to math like im so confused and wasting tons of time. I'm a high school student and i missed grade 11 and grade 12. Now, I desperately need math bc imma major in comp sci and im trying to study on my own. i got no teachers to help. im following the turkish high school diploma and its curriculum is so bad.

someone suggested me to try IB curriculum

and then another one sıggested me that i start with pre-calc books instead ofIB

I'm so confused

[gray gazelle]

What’s the last math class you took?

[versed coral]

in turkey we dont seperate classes like that its just math

the last chapter we saw was analytical geometry

i have some gaps because of the stupid curriculum we got

for example idk rational root theorem things and i think i need it but i want to learn in order

i got james stewart's pre-calc book

and haese maths ib

where do i start

i started to both of them but its confusing

i wanna stick to one so that i feel less stressed about the orders of chapters

[gray gazelle]

Honestly, I don’t know much about the IB curriculum. I would opt for the stewart

[versed coral]

hold on

I cant add images dude

[versed coral]

i sent u the overall of curriculum check ur dm

[finite gale]

You can try to work through whatever pieces of khan academy to fill in the gaps

[versed coral]

i filled gaps using khan academy for alg 2 but someone stated for precalc and calc, khan academy is not enough

i still love it and will use it tho. however, i need a real source to study

[finite gale]

I think a lot of the precalc texts cover the same stuff, so if you work through one of them, it's probably enough

[versed coral]

yeah but ib math is kinda different

im between a regular pr-calc book or an IB math curriculum