book-recommendations

[violet shuttle]

well, gradually fades

[quick hornet]

that behaviour is a subset of disappearing yes

[placid oriole]

the algebra of the baldor is a good book?

[quick hornet]

not sure this server has many spanish speaking users unfortunately

[molten mason]

Sí

[trail hemlock]

well according to math sorcerer's review its a really good algebra book

and he is a fluent spanish speaker so i would say yes

[molten mason]

Really? I did not know that

The book is fairly popular, and quite a few people in this server have or are using it.

[trail hemlock]

https://www.youtube.com/channel/UCWXTWXKpkDk7LJfurtPHb6Q
https://www.youtube.com/watch?v=kNFMoj0_Gnw

[molten mason]

This feels illegal. Like a whole section of lore just got unlocked.

[molten mason]

That book review lmao
"It has the hardest math problems ever for an algebra book"
Based Cuba

[trail hemlock]

wait til you hear abt the fitness arc

math sorcerer getting buff arc

[molten mason]

That should be everyone's arc

[trail hemlock]

im currently on "dont fail the ap world history exam" arc

its not going very well

[molten mason]

wdym, how do you not know world history, you're part of history, and you live in this world

[trail hemlock]

what da hell are historical thinking skills

[violet shuttle]

i never took ap world history

[trail hemlock]

lucky

[coarse arrow]

I looked at it but it doesn't look like an introductory book and I have just completed highschool and graph theory is a fascinating subject to me so idk

[violet shuttle]

i had a choice

[tribal crow]

I took world history (we didn't have AP) and I liked it a lot!

[molten mason]

Lmao I looked this up. What the hell

I've never taken a single AP course

[trail hemlock]

material is interesting

leq and dbq is hard

well i guess only leq

dbq is easy

[violet shuttle]

$\leq$

[hasty eagle]

Xela

[trail hemlock]

😭

[violet shuttle]

order theory is very hard yes

[tribal crow]

mfw when I didn't have a choice

[trail hemlock]

✨ triangle inequality ✨

[tribal crow]

my hs didn't do AP (they discarded it in 2016)

[violet shuttle]

no order theory

[trail hemlock]

real analysis try not to spam triangle inequality challenge (impossible)

[violet shuttle]

dcpo

[molten mason]

The books builds up from the basics. Try and give it a shot.

[violet shuttle]

no not c3po

[fresh skiff]

Hello!
Which of the following books is more friendly for the first course in probability?

Sheldon Ross
Or
Blitzstein

[versed cipher]

same but with ap euro

[heady juniper]

Anyone have a recommendation for a good resource (book, website, or video) specifically dedicated to handling matrix operations better? For example, I regularly get a little mixed up when doing Gaussian Elimination. I know how to do it, but I know that I'm not efficient. I'm doing unnecessary operations that get the right answer, but with extra steps. Which means more steps for simple arithmetic mistakes, etc.

Any good resource for strategies to solve them more systematically, prettier, patterns, etc.? Basically, totally computational.

[remote sparrow]

blitzstein

he also has a website

https://stat110.net

[fresh skiff]

Oh understood.
I was thinking that Sheldon Ross's book is friendly.
Thank you so much for your help and this link.

[remote sparrow]

maybe look at Linear Algebra: Step by Step by kuldeep singh

there are complete solutions on the companion website, as well as brief solutions in the back

[thorny tangle]

Anybody have a book recommendation that covers philosophy of math and how it relates to logic and proofs? Specifically, written down for the laymen person?

[wheat trout]

You may look at this.

https://www.mcmp.philosophie.uni-muenchen.de/students/math/index.html

[trail hemlock]

fuckkk that shit

[spring jacinth]

hey, does anyone here have any suggestsions for out of print or rare books i might want to check out from my university library? maybe something like this: https://www.reddit.com/r/math/comments/7yj2us/what_is_your_favorite_secret_out_of_print_math/

[gray gazelle]

based

[next condor]

I have "Lectures on the Philosophy of Mathematics" by Joel David Hamkins and I really like it.
Professor Hambiks works at the intersection of philosophy of mathematics, set theory, and mathematical logic, and he extensively discusses proofs and logic. He also has a great blog at substack called "infinitely more".

in his substack blog, look for the post's series "A Panorama of Logic"

His recent posts have been discussing the "theory of truth," which I believe converges with yours objectives.

[earnest wolf]

If anyone is interested, that's how I ended up doing it (for Apple addicts)

No need for any extra software at all

[next condor]

I also have the book "The Story of Proof: Logic and the History of Mathematics," which I haven't read yet because I'm not prepared for it, but it seems to be a good source for understanding the evolution of the concept of "mathematical proof" and the tools that pretentiously legitimize it.

[novel obsidian]

Does anyone have any recommendations for any short basic ring theory notes? something similar to j.s. milnes group theory notes is what I'm looking for

[heady juniper]

I'll take a look at it. Thank you.

[oak hazel]

any recommendations for something related to the stock market?

I liked "The Big Short", so I want something similar

[gray gazelle]

How to Make Money in Stocks by William O'Neal

birkshire hathoway reports are also good to read

warren buffett said the language of business is accounting and you can't know which business is winning if you can't understand their balance sheet income statement and cash flow statement

if you don't want to spend a lot of time on the economy and stocks you might as well just invest in s&p500, many people including warren buffet believe you can't beat the market

[graceful moon]

Just like read tea leaves and your horoscope and you’ll do basically as well as you would after learning all the analysis anyway

[woven quail]

are there any textbook that takes more "geometry/topology" approaches for linear algebra?

[gray gazelle]

yea idk why people do

[remote sparrow]

https://www.youtube.com/playlist?list=PLg5tKDNI_a86OO6J9HuIngyROBsUqcf_z

there is a playlist following his book

@thorny tangle

[remote sparrow]

https://link.springer.com/book/10.1007/978-0-387-48744-1

this book is good

[thorny tangle]

Thank you!

[orchid echo]

can anyone give a good recommendation for learning some commutative algebra?

I know Atiyah and MacDonald is (one of )the standard textbook but I'm curious if there are any others. I'm also interested in understanding more what the point of learning it would be. I was told that after a course in abstract algebra one of the reasonable things to study next is commutative algebra. From there where might I go next/what topics should I be looking to get a good understanding of

[gray jungle]

algebraic number theory ofcourse

[violet shuttle]

algebraic geometry

[maiden glen]

I NEED good group theory books. May multiple people please suggest something I may read?

[orchid echo]

Armstrong is alright

Dummit and Foote is good too for the basics

Aluffi's undergrad and grad textbooks are both fantastic as well at an undergrad level

I'm not sure if there are any grad group theory only textbooks

[maiden glen]

implying that there exist books that contain group theory "Explanations" on the graduate level, I want those too.

[gray jungle]

i like "The theory of finite groups" by Hans Kurzweil

[maiden glen]

thank you both

anything else?

something i can download online 🙆‍♂️

[graceful moon]

I’m currently working through Cox Little and Osheas book, it’s decent but quite slow, and (according to one of my lecturers) proves a much less general case of everything for the first few chapters even through the more general proof is the same, and is seemingly scared of the algebra

So he wrote like a 40 page introduction for the commutative algebra course here which in his mind is better. I’m not far enough in to really comment, but it seems like a fair criticism based on what I have read.

Other than that, he and a few others I’ve seen have recommended Miles Reid’s book. It’s much more terse than IVA is (which really might not be bad) and more pure maths focused (IVA, spends a decent bit of time on the computational angles) but I haven’t personally done more than skim it

[orchid echo]

I don't know anything but at that level you are usually looking for groups with a particular behaviour (amenable, residually finite, surjunctive (these are so cool)). At least at my school the first graduate abstract algebra course follows Aluffi so you can probably find explanations of group theory concepts at the grad level there as well. I think the book recommended above is also good

[crimson leaf]

Check Milne's notes

[maiden glen]

what do i need as prerequisites to read this?

[orchid echo]

Not much to be honest, it would be good to know some linear algebra since matrices make good examples of groups

Also good for grounding some intuition

[maiden glen]

ok, so i read something like ladr first?

[orchid echo]

But strictly speaking you don’t need linear algebra

[orchid echo]

I think this would be helpful

[graceful moon]

That’s the usual path yeah, but you could do D&F first, you just might not get some examples

[orchid echo]

That’s just my opinion though

A lot of stuff you do in algebra is similar to what you do in linear algebra. Define objects, look at maps, explore the properties of those maps, sub objects etc

Most group things have linear algebra counter parts (morally speaking) that can be helpful for guiding intuition at first

But you probably could just start reading dummit and Foote

[maiden glen]

are you sure that there's nothing else i may need before reading this book?

(Excluding the obvious; undergraduate school "algebra", calculus, etc.)

[orchid echo]

Not to the best of my knowledge/memory

Another decent introductory group theory book is by Armstrong

It’s at an undergraduate level

And it’s just group theory

It is very slow (even compared to dummit and Foote)

[remote sparrow]

https://link.springer.com/book/10.1007/978-1-4612-4176-8

[graceful moon]

If you want an all in 1 book artin works, I’ve heard it’s linear algebra isn’t great but it is there

[remote sparrow]

the material in this book might already be contained in various editions of Advanced Modern Algebra by rotman though

[orchid echo]

This is neat

Thank you

[maiden glen]

thank you

[loud cradle]

this one is excellent for finite groups https://bookstore.ams.org/gsm-92

[maiden glen]

thank you

[maiden glen]

thank you aswell

[graceful moon]

That’s the book my group theory course next semester is based on, good to see it’s recommended

By the one and only sour drop, resident recommender, no less

[gray gazelle]

best book on algebra and best book on trigonometry?

I will be happy if you tell me

[foggy relic]

Lang pt 1

[vocal violet]

any easier books than basic mathematics by lang or is that easiest

[remote sparrow]

most precalculus books

[tacit walrus]

any competition prep books for high schoolers?

[trail hemlock]

aops

well what competition?

[tacit walrus]

like precollege competitions in university?

[dapper fossil]

any books for intro counting/euclids etc

[gray gazelle]

I would like to suggest combinatorics through guided discovery by kenneth bogart, it's lovely and very fluid for anyone looking for a first book in combinatorics https://bogart.openmathbooks.org/pdf/ctgd.pdf

[gray gazelle]

the book below is good for intro counting.

[next condor]

It seems really great 👀

[main hill]

Hello there! Does somebody know where I can find the sullivan's precalculus books? I'm thinking about some older editions (from the 80's or 90's) because the new ones are too colorful for me and filled with some random shit like baloon photos or graphical calutlators output which greatly helps me not to focus. I'm looking for something better. Tried archive org and see there are some older versions but sadly those books are not available to be borrowed. There is a note "Book available to patrons with print disabilities." I once even made a donation hoping that this will grant me a rank of patron and be able to borrow these books but that didn't work out. 😦

[hallow oriole]

oh, really interesting

it seems to miss a good amount of topics sadly but otherwise i really like it

[gray gazelle]

I would love if somone suggested a second more advanced (maybe even graduate level) combinatorics book and the required pre-requisites to study it.

[wise dew]

hey, guys! I kinda want to buy generating functionoly. do you guys recommend it for someone in high school?

oh, what a pair of questions, sathya :)

[gray gazelle]

🙂

[gray gazelle]

somone here can correct me if I'm wrong but it looks like the last parts require a little complex analysis?

[wise dew]

yeah, I'm pretty sure it does, actually

but I would just skip that last part

now, if the rest of the book used calculus, then it's an impossibility for me to study

[flat marten]

Does anyone have any curt concise multivariable calculus textbooks? I'm vaguely familiar with the ideas and terminology I just need theorems and proofs (although I won't complain about nice exercises) and im sick of "introductory" textbooks

[ancient mist]

Here are some concise textbooks on multivariable calculus:

1. "Vector Calculus" by Jerrold E. Marsden and Anthony J. Tromba: This textbook provides a clear and concise introduction to multivariable calculus, emphasizing both the geometric intuition and mathematical rigor.

2. "Multivariable Calculus" by James Stewart: Stewart's textbook offers a balanced approach to multivariable calculus with concise explanations, examples, and exercises.

3. "Multivariable Mathematics" by Theodore Shifrin and Joel R. Hass: This book covers multivariable calculus in a concise yet comprehensive manner, suitable for students with a solid foundation in calculus.

4. "Calculus: Early Transcendentals" by Soo T. Tan: Tan's textbook presents multivariable calculus concepts in a straightforward and concise manner, making it suitable for self-study or as a supplement to classroom instruction.

5. "Multivariable Calculus: Concepts and Contexts" by James Stewart: Another concise offering from Stewart, this textbook focuses on conceptual understanding and real-world applications of multivariable calculus, making it accessible and engaging for students.

[dim sierra]

ChatGPT?! LOL

[flat marten]

Lmao Marsden is not concise

[dim sierra]

This dude just used ChatGPT lmao

[flat marten]

Yeah I can tell

Still looking at them ig cos I'm desperate at this point but like

[dim sierra]

What kinda MVC r u familiar with, like do you know implicit or inverse function theorem

[flat marten]

Perhaps? I might not know them by name

[dim sierra]

do you wanna learn the more rigorous MVC or just master the undergraduate material

[flat marten]

I just need undergrad stuff so I can pass calc and get back to algebra

[dim sierra]

yeah honestly i dont rlly have a recommendation

[flat marten]

Idk... The lecture notes at my uni are pitiful and the books the recommend are almost as bad

[dim sierra]

i just found this website th o

https://www.calc3.org/previous-examsquizzes

nvm it looks like “introductory” 😂

[flat marten]

Lel

Yeah I literally haven't been able to find anything that isn't either introductory or just straight up diff geo

Which I'd love to do at some point but don't have the time to master before exams

[dim sierra]

check out https://tutorial.math.lamar.edu this maybe

each of the notes are pretty concise

[flat marten]

I was um. Already recommended that lel

OK I'll give it a proper shot

[dim sierra]

oh mb

[heavy pelican]

@flat marten if you want a shit treatment, Rudin "Principles of Mathematical Analysis" ch 9,10

there's nothing better if you want to just learn the bare minimum to pass the course

The best book by a long shot is Shifrin. Next in the list of my favorites is Duistermaat-Kolk's two volume tome. Of course, neither are concise.

[flat marten]

i think at this point shifrin is my best option, rudin/tao are too threadbare sadly

[gray gazelle]

If you have previous experience with some basic combinatorics (and power series), go for it. Also, the book is available for free (digitally) through the author's site

[gray gazelle]

It doesn't directly use calculus, but it assumes familiarity with power series, which involves some calculus. It might be tricky to get through if you haven't seen them previously

[wise dew]

thanks

well, that's probably not the right fit for me, then

[gray gazelle]

If you’re interested in combinatorics, there are lots of good introductory books on it

[trail hemlock]

we love to hate on rudin

[gray gazelle]

Calculus on Manifolds, maybe?

[remote sparrow]

#book-recommendations message

[hallow oriole]

!nogpt

[hybrid sparrow]

Please do not trust ChatGPT or similar AI tools for mathematical tasks, as they often generate output which "sounds correct" but has numerous factual or logical errors. Use of these AI tools to answer other people's help questions is strictly against server rules (see #rules).

[hallow oriole]

i wouldnt call most of these "concise"

[ocean mulch]

cough Bourbaki cough

[sacred sorrel]

Which book is the best for learn how to prove something in mathematics?

[graceful moon]

There’s a book called how to prove it by velleman that I’ve seen recommended (haven’t personally read it, but people say it’s decent)

There’s also a concise introduction to pure mathematics by Liebeck which is ok

Overall I’d recommend just picking up an introductory book in like linear algebra analysis or “discrete maths” and learning as you go

Why is it that you’re looking to learn proofs? Do you have a specific goal in mind?

[sacred sorrel]

It's because I'm in the maths course, and I really want to know how to prove a proposition before seeing the book solution

And thanks for those books recommendations

[graceful moon]

I’d personally recommend just getting a book for the specific topic you’re learning

The mechanics of a proof are usually pretty simple, the hard part is familiarity with the tricks of that subject, and your own understanding of the material

And you’ll only really improve that by more exposure to that subject area

[trail hemlock]

i wouldn’t call a james strwart textbook concise. chatgpt does ig

[trail hemlock]

spivak calculus on manifolds

[earnest wolf]

imo gpt-generated advice should be moderated and removed

[earnest wolf]

hm, check out Zorich and/or Tao (vol 2)

[trail hemlock]

!nogot

!nogpt

[hybrid sparrow]

Please do not trust ChatGPT or similar AI tools for mathematical tasks, as they often generate output which "sounds correct" but has numerous factual or logical errors. Use of these AI tools to answer other people's help questions is strictly against server rules (see #rules).

[trail hemlock]

really? is tao vol2 good as a first intro to multi?

[sick river]

Is asking for books on a topic really a mathematical task though?

[flat marten]

this isnt a first intro lmao thats the whole point

also tao/rudin are both nice but too threadbare

sadly

ill check out zorich

[sacred sorrel]

Thanks for the advice :)

[gray gazelle]

It is a mathematical task if the books are related to mathematical concepts

GPT also can’t read the book and give advices like how a person would

[graceful moon]

You just quoting GPT isn’t adding anything, anyone can do that

And you clearly don’t have the prerequisite knowledge to check the output it gives you so in general you shouldn’t be using GPT for it

Like it’s not worth anything if you can’t sense check the output, because it doesn’t think, most of what it spits out is nonsense

[trail hemlock]

i meant for me

[trail hemlock]

i dont think he was the one who used chatgpt

[graceful moon]

Oh oops, my point is the same though

[flat marten]

ohhh sorry i cant read lmao

[worldly garden]

any books for calc I and II

pdf preferably cus im broke

[graceful moon]

Stewart’s calculus is the standard choice at a lot of places, there’s PDFs online

The openstax calculus books are also free and apparently decent

[orchid echo]

openstax is pretty good

[trail hemlock]

https://schtschenok.github.io/calculus-made-easy/
this is a good one

pdf is here: https://www.gutenberg.org/ebooks/33283

[reef escarp]

are there any books focused on helping you build the intuition to approach problems? i am not looking for a 400-page book, rather something short.

[remote sparrow]

https://www.amazon.com/How-Solve-Mathematical-Princeton-Science/dp/069111966X

[slender wasp]

Also, Shifrin course lecture videos (2 semesters worth) are on youtube.

[fresh thicket]

Does anyone have recommendations for a introductory abstract algebra textbook that also helps with learning proofs

Or maybe 1 of each

& please ping if you reply

[robust portal]

Is the course Introduction to Mathematical Thinking (on Coursera by Stanford University) worth it? I’m a 10th grader and I’ve found it pretty challenging, even at the start

[signal swift]

Yooo

Anyone done aops by Paul zeitz

[gray gazelle]

What are the prerequisites for Qing Liu’s Algebraic Geometry and Arithmetic Curves?

[earnest wolf]

is there like a computation-based book (like calculus is to real analysis) on complex analysis?
I want to learn some computation techniques to work with Möbius transformations (aka linear fractional transformations)

[prime oak]

opinions on conway's complex analysis?

[formal bronze]

Dummit and Foote is a good introductory textbook for abstract algebra

[fresh thicket]

Ok thank you

[remote sparrow]

have you looked at pins?

[mortal mountain]

is mathematical circle a good book?

[remote sparrow]

#book-recommendations message

[remote sparrow]

Complex Analysis for Mathematics and Engineering by mathews and howell

[trail hemlock]

omg i LOVE this book

[fresh thicket]

Thank you and if you don't mind, which one would you say is more "beginner friendly" for the proofs or is it safe to assume they are all on the same level

[iron tangle]

Havent read that first hand but i have heard that the problems are extremely good even for olympiad level preparations

[fresh skiff]

any one please provide material in real analysis! (abbott)! if anyone has, Also if possible is there some university course on real analysis and the book of abbott. I am asking for university course bcz i will solve the assignements and exams and homework

i will appreciate thank you

[remote sparrow]

pinter, judson, and saracino are the most beginner-friendly, but they're all good

[remote sparrow]

#book-recommendations message

[fresh skiff]

Ah thank you so much. Sorry for asking the same question for a couple of time

[gray gazelle]

do these work

[remote sparrow]

only the reader can say

many people found it worked for them though

[gray gazelle]

i see i wonder if they'd be better than just learning more math

[lusty ermine]

which book explains completeness axiom easily

[remote sparrow]

abbott

[trail hemlock]

why you look sm like sour drop

[round shore]

Not much in fact. Basic commutative algebra (ideals, noetherian rings ,PID etc and modules) and you'll be fine. Iirc Liu even recalls tensor products so you don't need much. You can learn the necessary commutative algebra for the rest of the book in the meantime. Like, at some point you'll need to know what a Dedekind ring is, but you'll learn then.

Also Liu has made the choice to make a category theory-free book (to show that it is possible lol) so you don't even need that

[dapper root]

Kind of an L-decision IMO

But there’s a niche for that

Preach to the capacities of the people

[round shore]

Yeah I don't really get it but that's the argument he gave

[violet shuttle]

undergrads, i hear, get scared by the ⊗ symbol

[round shore]

Postgrads too 🥶

[dapper root]

I never struggled with the tensor product tbh

Maybe I was just lucky

There’s some random times it surprises me, but I already have the expectations that it will do that at times, and know in which situations things can get kinda funky

But I feel like once you learn a few of the basic rules you get really far just combining those

[round shore]

Yeah, master the formal rules and you're good. But sometimes you have to do +/- explicit computations, eg: when you first learn them, something like Z/nZ ⊗ Z/mZ

But in practice the basic properties suffice

[dapper root]

I mean this too gets subsumed

This is an application of M (x) R/I = M/IM

[gray gazelle]

I first encountered it in Halmos, and his definition of it is confusing as hell

[violet shuttle]

i struggled with the definition for a little because the first one on the wiki page was not good

once i saw "all things of the form v \otimes w such that \otimes is bilinear" it was easy going

[round shore]

Once you understand the proof of the existence you understand it all I think

"ok let's quotient by everything such that this thing becomes bilinear"

[violet shuttle]

oh yes these things do get me and likewise the clebsch gordon/plethysm problem but i meant just like the utter basics

[violet shuttle]

yeah but you can also explain it to someone that doesn't understand quotients yet

not rigorously sure

but you can indeed teach how it works to a nonrigorous la class

the only thing being missed being existence

[heady juniper]

Anyone know if there's a good lecture series on competitive math? Usually the most I see is someone going over random problems, but it's not structured in any way. I'm obviously working through books as well, but it's nice to have a lecture series.

[lusty ermine]

similar anime pictures I guess, not sure.

[remote sparrow]

next best thing is watching evan chen's streams: https://web.evanchen.cc/videos.html

they're obviously very unstructured

[gray gazelle]

Does anyone have book recommendations for a 13 year old who is turning 14?

[gray gazelle]

That depends on what you want to learn about

[gray gazelle]

Im more into sci-fi books

idk which one is a good one tho

Dune maybe?

[gray gazelle]

Author?

Frank Herbert

Found it

[noble swan]

anyone has a good precalc textbook ?

[gray gazelle]

Basic Mathematics, Lang

[noble swan]

mmh

[trail hemlock]

baby rudin

[noble swan]

the prince

from machiavel

it teaches you how to be a ruthless leader lol

[trail hemlock]

jk but 20000 leagues under the sea is a fire book

[gray gazelle]

hartshorne is also pretty good

builds maturity

[gray gazelle]

alr

[trail hemlock]

enders game, fahrenheit 451, asimov’s foundation series,

all good books

[trail hemlock]

i was just kidding abt that one

[gray gazelle]

when i searched it up i saw some kids books lol

[gray gazelle]

ive heard of enders game

[trail hemlock]

it’s good you should check it out

i read those books when i was 13-14 and i enjoyed them, you might as well

[gray gazelle]

Alr

i probs will

ty for the recommendation bro

[trail hemlock]

👍

[earnest wolf]

i'd strongly suggest to read Sumon's series called «Hyperion Cantos». Those are four relatively thick books

Honestly, this is one of the greatest books I've read recently

It's mainly sci-fi, but I wouldn't say it's a 'conventional sci-fi'. He managed to include thriller, romance and many more into one piece

[gray gazelle]

Sounds Interesting.

[earnest wolf]

the full name is
«Harry Potter and the Principles of Mathematical Analysis» by Rudin ||</jk>||

[gray gazelle]

Lmao

[violet shuttle]

but like you could do this to anything and it's not funny

it's not like the name matches particularly well

[gray gazelle]

“Harry Potter and the Elements of Algebraic Geometry”

[violet shuttle]

again the only neat part here was the font

[trail hemlock]

new jk Rowling pseudonym just dropped?

[earnest wolf]

ig it sounds fun to me bc the title is very reminiscent of the suffering I've experienced while (trying) to read it

it's like stress-induced laughter ig

[violet shuttle]

harry potter made you suffer?

[earnest wolf]

exactly

no

[violet shuttle]

really giving me mixed messages here

[earnest wolf]

like, 'the principles' part suggests that you have to navigate thru the hell of rudin's 'ways'

but maybe that's just me

[pale scarab]

It actually doesn't cover a lot of topics.

I think Sheldon axlers precalculus book is one of the better ones. It also has problems at all levels which is good for self study, along with full solutions to many of them.

[earnest wolf]

anyway, trying to explain why a joke is funny to someone means completely destroying the joke

[earnest wolf]

I mean, I wasn't trying to make fun of you.

Just said it in a way that I liked

[violet shuttle]

what

[violet shuttle]

what?

[violet shuttle]

what??

[earnest wolf]

https://youtu.be/yW5me_l9FL4

[heady ember]

lmao w h a t

[gray gazelle]

yo

is book of proof by richard hammond meant to be similar to "How to prove it"

[molten mason]

What

[molten mason]

This was peak humor

[heady ember]

Harry Potter and the Elements of Set Theory

(Enderton)

[remote sparrow]

Harry Potter and Basic Mathematics by Serge Lang

can i get a

wait wait i have an even better one

Harry Potter and Calculus: Early Transcendentals by james stewart

amazing

praise my cleverness

[molten mason]

Those weren't as good tbh but A for effort

[violet shuttle]

all of these are fucking terrible you all get F-'s

[molten mason]

Harry Potter and the Detestation of Xela

[trail hemlock]

Harry potter and calculus for the practical man wizard

[gray gazelle]

by Aluffi*

[twilit siren]

does anyone have any good resources/textbooks on learning complex analysis

also a good intro to statistics (uni level) cuz i wanna refresh myself

[gray gazelle]

#book-recommendations message

[twilit siren]

thank u!

[gray gazelle]

Harry Potter and the prison of Math Academia

instead of azkaban

[crude sage]

Harry Potter and the Rising Sea: Foundations of Algebraic Geometry

[vital bane]

Harry Potter and Ricci flow with surgery on three-manifolds

[reef escarp]

what are some good science fiction books with politics? (something that has unique plot)

[flat marten]

What about leviathan wakes and the expanse series?

Or basically any Ian M Banks book will do too

There's tau zero which has internal ship politics

But imo the expanse has the best space politics

Avasarala 🫶

[ruby prism]

Hey guys recommend me a book for quantum physics i am complete beginner

[graceful moon]

What maths do you know

[ruby prism]

i know basic maths

but i will learn linear algebra ,abstract algebra and calculus too

[graceful moon]

So you know like basic DEs and linear algebra?

If not you’ll need to learn those first before you can really do much with quantum mechanics

[ruby prism]

idk what is linear algebra

[gray gazelle]

Google is free

[ruby prism]

i know

[graceful moon]

Then you’re definitely not ready for quantum physics, you’ll need to learn those first

Use the search function or look at the pins in here for recommendations

Differential equations and linear algebra are just unavoidable prereqs, some group theory is helpful but like you can mostly ignore that

[ruby prism]

so i have to learn linear algebra and calculus first?

[graceful moon]

Yes

Tensor products are key to like quantum computing problems and you can’t understand tensors if you don’t have a solid grounding in linear algebra

Similarly for quantum mechanics, you need to understand mechanics hence you need to understand differential equations

[ruby prism]

ok

[dapper root]

THE TENSOR PRODUCT IS ESSENTIAL TO THE EXISTENCE OF BLACK HOLES

[versed coral]

can someone give me any advice on trigonometry? like i dont understand this thing and idk where im doing wrong tbh

[pliant wadi]

Harry Potter and the Prisoner of Abstract Algebra

Harry Potter and the companion to analysis

Harry Potter and the Calculus on Manifolds

[pliant wadi]

what sort of problems are you stuck on?

[violet ore]

hey i looking to self teach myself calculus

can anyone recommend me some good books to do so

[violet shuttle]

false

I mean true but

Shankar will teach you

[violet shuttle]

you need calculus. after that just pick up Shankar's Principles of Quantum Mechanics. He will teach you linear algebra.

[graceful moon]

I mean if you don’t know calculus or linear algebra you should not be starting quantum physics imo

[violet shuttle]

Shankar will teach you the linear algebra.

It worked for me when I had only known multivariable calculus and some lagrangiand

[graceful moon]

That’s possible yeah, it’s not a book I’ve seen or used, but im personally of the opinion that it would be better to get a solid foundation in these things rather than just trying to pick up what you might need as you go

[violet shuttle]

Shankar gives you good foundation

[ruby prism]

Ok , btw what I need for calculus ?

[violet shuttle]

wdym

you need to know calculus

[ruby prism]

What knowledge I need for calculus?

[violet shuttle]

(except for his explanation of tensor products)

[violet shuttle]

I don't understand

Oh

Learn basic algebra

[ruby prism]

See I need calculus knowledge and linear algebra knowledge for quantum physics, right? But what I need to learn calculus?

[violet shuttle]

basic algebra

[graceful moon]

Just basic highschool algebra and knowledge of functions really

[ruby prism]

a+b² stuff?

[violet shuttle]

what

i mean like a familiarity with basic algebraic manipulations

[ruby prism]

Ok , Where I can learn calculus from ?

[scarlet pewter]

Khan Acadamy

YouTube

A calc textbook

[violet shuttle]

paul's online math notes

a calc textbook, of which one can find recs in pins probs

[hearty steppe]

Anyone heard of this book? https://link.springer.com/book/10.1007/978-3-030-61871-1

Definitely trying to take advantage of the best linear algebra, abstract algebra, and measure theory/probability gems I can find. Figured I’d ask about it here. Just found out this book existed and not sure anyone here worked through it yet

[trail hemlock]

https://schtschenok.github.io/calculus-made-easy/

good free resource

[violet shuttle]

kallenberg?

shankar will teach you it

[high heath]

This is amazing

[violet shuttle]

indeed

[graceful moon]

Sure, I wasn’t really getting at a full course but knowing some mechanics matters and that requires you to know how to solve some DEs and seperable PDEs

[violet shuttle]

I don't think Shankar solves a single PDE.

This is a very popular graduate quantum mechanics textbook.

[graceful moon]

The Schrödinger EQ doesn’t appear anywhere in a QM book?

[violet shuttle]

That's not a PDE

...wait is it?

shit

Okay yes he solves many PDEs

[graceful moon]

Also this person doesn’t know calculus recommending them a graduate QM book is not helpful

[violet shuttle]

oh right and separable for that thing

lol oops

[graceful moon]

Yeah I mean seperable PDEs are really just ODEs but still

[violet shuttle]

Correct. But once you know about partial derivatives it's a great choice.

[violet shuttle]

yeah that's why I was like "what?" because in my mind I had casually conflated them

[versed coral]

well the thing is i know the majority of the things or at least i suppose i know but its so hard to graph the functions and like today i tested myself on my own and im stuck on exercises. but when i do a quick revise or check my notes for a second i can continue but i dont want this

i actually want to learn

i suppose i need practice

im doin pre calc atm

trigonometry chapter in the pre calc book makes me this mad and i dont even wanna think of uni so i gotta fix this

[remote sparrow]

according to the statistics server, it's better as a reference than something you should learn from the first time

[timber copper]

yeah kallenberg is good if you already know the subject lol

[hearty steppe]

Is Kallenberg comparable to certain texts that come to mind?

Im imagining it’s one of those inconsistent exposition based books that has its moments

[hallow oriole]

any chance u can dm me an inv btw

[remote sparrow]

it's publicly discoverable

[hallow oriole]

oh, nice

[remote sparrow]

just type "Statistics"

[violet shuttle]

any chance someone could dm me an invite to the math server

[molten mason]

...this server?

[violet shuttle]

that's the joke yes

[gray gazelle]

there are other servers

[molten mason]

Xela...makes... jokes?

[gray gazelle]

xela talking about smth other than adv math?!

[hallow oriole]

no chance at all sorry

[violet shuttle]

physics

programming

what a friend of mine calls "schizoposting"

idk how one gets into math research besides asking profs. what do you want to do?

i note the lack of advanced math. you have real analysis and linear algebra (at what level is the linear algebra?)

so what math do you want to do?

order? things are really unordered early on.

normally the "basics" include a course in algebra (up to galois), topology and algebraic topology, real analysis with measure theory, complex analysis, differential geometry

I'm not familiar with any courses in linear algebra as I originally learnt it from a quantum mechanics textbook. Is it rigorous?

Nope

Oh. You'll want to rigorify

Would you say you are mathematically mature?

You have real analysis on there

Mathematical maturity is more important to any of these subjects than already knowing any of the others

Pick something and go with it is my recommendation

If you like analysis more, learn complex analysis or measure theory stuff

If you want to do differential geometry you can do what i did and try to beeline to Stokes

If you want to learn why quintics can't be solved in radicals, learn algebra

I don't see why any of them would be different in this regard

Just grab books until you find one you like

[gray gazelle]

actually do you know a link to the reasoning, i've always wanted to understand why

[violet shuttle]

Lang.

I can explain much of the proof

[gray gazelle]

not the proof, just the solutions not in radicals

nah don't

ok

[violet shuttle]

Or even just the sketch

That's what I mean

The point is that if your galois group is solvable, then you can do it via extensions that are cyclic

Hilbert's theorem 90 lets us characterize cyclic extensions as long as we have an nth root of unity

[gray gazelle]

ok

[violet shuttle]

So the point is that any extension with solvable galois group is a subfield of an extension obtained by, at each step, adjoining (for n coprime to the characterstic) either an nth root of unity, an nth root of an element in the previous step, or a solution to X^p+X+a (i may have fucked this poly up)

Hilbert's theorem 90 is actually representation theoretic

https://mathoverflow.net/questions/21110/is-there-a-natural-way-to-view-the-proof-of-hilbert-90

So suppose L/K cyclic order n with galois group generated by \sigma

Well yeah, do you know how to read a proof, would you have some idea of how to go about proving something, can you understand definitions? Another way to put it is that for someone with mathematical maturity you can just give them the proof in enough detail and they'll eventually understand it

It's like they already know English

[violet shuttle]

Now suppose the field norm N(a) = 1

define \tau(b)=a\sigma(b).

this is a K-linear map L->L

we see that \tau^n = multiplication by N(a) = id

This means that we have a representation of \Z/n\Z on L.

Thus we can look at the projector onto the trivial subspace

1/n (1+\tau + \tau^2 + ... \tau^{n-1})

One then proves this is nonzero.

Now the proof actually still works with p = char but this way of thinking about it doesn't quite work

which is weird and i don't entirely get it

now, the point is that this provides us the X^n-a thing when there's an nth root of unity

[crude sage]

Does anyone happen to know any sources with worked examples of proving non-regularness/non-context-freeness using the relevant pumping lemmas?

[gray gazelle]

Sipser has several examples for each

[crude sage]

Thanks!

[violet shuttle]

uh since N(\zeta^{-1})=1 so \exists b : \sigma(b) = b \zeta

now uh \sigma(b^n)=\sigma(b)^n=b^n

so b^n is fixed by the galois group

[violet shuttle]

so \sigma(b)^n-b^n

ritht point is

\sigma(b) is a root

and b^n is actually in the base field

and so obviously the other parts of the field extension come from the conjugates of \sigma(b) which are also roots

and you can manage to do similar with the trace and X^p-X-a

Does this make sense?

[dapper root]

No

(I did not read it)

[violet shuttle]

you, the esteemed chmonkey, don't need to read it to understand

[remote sparrow]

https://ocw.mit.edu/courses/18-404j-theory-of-computation-fall-2020/

there might be additional worked examples in the lecture videos and notes

[crude sage]

Thanks you!

[remote sparrow]

he wrote the book that eigenpuppet mentioned btw

[burnt mauve]

Hello I am college student writing my papers and I need the help of a profsssor. My paper specializes in prime number distribution randomized.

[crude sage]

I see, neat

[burnt mauve]

However because of my young age it is unlikely that some professors accept my thesis

Any advice from anybody

[molten mason]

No this isn't the right channel. #serious-discussion would probably be the best starting point for in-depth convo, maybe #advanced-lounge . Then pop into here for books.

"Math research" is a wild field. What you need to do research in set theory would be very different than math for signal procressing.

There's always room for more Linear Algebra, it also seems like you haven't done Abstract Algebra. You can check the pinned messages in this channel as a starting point for books in those two fields.

[molten mason]

This is the book recommendation chat. Are you looking for books on writing a paper? A book on prime numbers? What book do you need.

If you don't need a book then this is not the correct chat and ask elsewhere.

[slender cargo]

Key difference is that Abbott sticks purely to the real line. Rudin introduces metric spaces and complex numbers, which generalize some of the material in his book more than Abbott. Also Rudin's book is more terse and supposedly has harder exercises.

[trail hemlock]

draw a number line

these questions look very googleable im ngl

[slender cargo]

Oh... the messages are gone

[molten mason]

I'll ask for them. They were all Googleable but one was appropriate here:

Differences between Abbot and Rudin

[lusty ermine]

it*

[trail hemlock]

theres no objective best book

try tudin

if its too terse and you cant undersand it, move to abbott

[remote sparrow]

tudin

https://tenor.com/view/minor-spelling-mistake-gif-21179057

[remote ginkgo]

Browder.

[heady ember]

Damn it you sniped me ||by exactly five hours ||

[ruby prism]

Ok

[rigid folio]

Hello, I am currently studying math and I am struggling with distributions. Are there any books that contains lots of practice questions with written explanations? Specifically I want to practice Geometric, Gamma, Erlang, and Poisson distributions. Thank you!

[lusty ermine]

https://www.amazon.com/-/es/Kit-Wing-Yu/dp/9887879711?dplnkId=3049404c-bb52-4682-be63-9c38239e3889&nodl=1

Should i read pma with solution guide or without?

Are in general solution guides a good idea?

[trail hemlock]

without

don’t ruin it

problems are v fun

[remote vortex]

My view is that you shouldn't read PMA at all if you're just starting out, I'd recommend Abbott much more.

[slender cargo]

Rudin seems like it would be really hard to self-study from, particularly if you do not have much prior experience with proofs.

[remote vortex]

Absolutely

[small stirrup]

hey any pre university book for trigno and algebra

[marsh ingot]

Fr fr

[small stirrup]

ayo

[small stirrup]

ayo

[pliant wadi]

Darn, sounds rough

There's this pretty little book that I loved when I was a junior in highschool

Titled 'Play with graphs'

You can try looking through it

Trigonometry at that level is all about practice.

Hang in there it'd get better, trust me.

Don't think about University, take one step at a time.

[pliant wadi]

Idk trigo but try Hall and Knight's for algebra?

Oh S.L Loney has a book on trigonometry....I think? Never used it but you can look through it maybe.

I used some recs from AoPS back in the day. Look through the website, you'd find fun stuff.

[small stirrup]

@pliant wadi thanks man

[narrow relic]

They're a bad idea and are not necessary if the book is written well.

[lone wave]

Can you guys recommend me a playlist on YouTube about soild geometry

[reef escarp]

are there any good books(preferably short) on introduction to proofs? i see a lot of books spending 40 to 50 pages on very basic set theory, when they could have just introduced it in a few pages. (i am just not really a big fan of reading 600 pages)

[pseudo bramble]

I agree. I am also having issues with set theory. I kind of dont understand the ven diagrams of sets and how they find the area to shade.

[lusty ermine]

books for order theory?

[graceful moon]

What is it that you’re struggling with? I tend to think it’s better to just pick up an introductory textbook in whatever subject you’re doing and pick it up as you go

By and large the hard part of proofs is knowing the tricks and ideas of that field not like knowing what induction or contradiction are

[remote sparrow]

https://www.amazon.com/Introduction-Lattices-Order-B-Davey/dp/0521784514

https://link.springer.com/book/10.1007/978-3-319-29788-0

[lusty ermine]

damn

its kinda advanced but i’ll take it

the first one i mean

i will check the second later

[violet shuttle]

the one thing that seems neat: all non modular lattices are not modular because they contain one of two basic nonmodular lattices

likewise for some strengthening of modular

kinda like the thing for nonplanar

[still panther]

one of two? i thought all nonmodular contain N5

[still panther]

I would also try birkhoffs lattice theory book, personally i found the very casual and leisurely pace of "introduction" to be insufferable

[reef escarp]

i am just looking to enhance my math skills, i dont want to study any particular topic currently, just mess around with proofs.

[fresh skiff]

A Problem Book in Real Analysis by Mohamed A. Khamsi

Is this suitable to use as a supplement for problems for Abbott?

[graceful moon]

A concise introduction to pure mathematics by liebeck could be worth a look

[tawny crater]

looking for an analysis textbook that discusses arzela-ascoli theorem. Baby rudin kinda does it but it feels like an aside

[versed coral]

Thanks a lot dude

[grand thistle]

maybe big rudin?

[remote vortex]

Papa Rudin doesn't mention Arzela-Ascoli.

Folland does briefly, takes up about two pages

Royden devotes a similar amount of space to it

[grand thistle]

it does, refer to thm 11.28

[rich sun]

what should i compare it to?

[grand thistle]

lmaoo mb wrong terminology

[remote vortex]

My version of Papa Rudin doesn't even have thm 11.28

[grand thistle]

oh what i have the third version of papa rudin

[remote vortex]

Oh yes

Still, that's even less than in PMA

So I can't think of any book that discussed Arzela-Ascoli in depth

Maybe there isn't much depth to be discussed, it's just a nice theorem about when a family of functions is precompact.

[vast jackal]

Is introduction to algebra by AOPS covers algebra 1 and 2?

Or no

[graceful moon]

I think my metric spaces book spends a page or 2 on it, I’m not sure how much there is to say about it

Which could be utterly ignorant btw, it wasn’t really used in my course it could maybe be a massively deep theorem and I don’t realise

[narrow relic]

I would check out Chapters 1-5 of this online book: http://intrologic.stanford.edu/public/chapters.php

You can integrate the set stuff on your own, I wouldn't worry too much about the "formality" of that.

[pliant karma]

complex analysis (random word to check my roles)

[fresh skiff]

anyone please

[gray jungle]

epsilon of room briefly discuss why its useful in PDEs, tbf most useful applications of the theorem are not simple.

[forest forum]

I want an algebraic number thry book to read after I’m done with a commutative algebra course and reading Marcus on the level and with same focus of langs algebraic nt but with exercises. Any recommendations?

[hallow oriole]

it's probably fine, i wouldn't stress about what your exact choice is too much

[serene vine]

Hey, val

Didn’t expect to run into you here.

[hallow oriole]

dia??????????????

wild

tf u doin here

[fresh skiff]

Oh ok got it. Thank you

[serene vine]

I’ve been self-studying a lot more recently. Figured some outside help may be of use.

[hallow oriole]

ah

well

best of luck

[fresh skiff]

Btw is there any book suggestion to learn LaTeX. Maybe in particular Amsart class

[hallow oriole]

you can learn latex by doing it

[hallow oriole]

see u around tho

[fresh skiff]

But I am facing issues.
Like attaching local pdf ( downloadable)

[serene vine]

Yes, I’ll see you. Goodbye for now, val.

[hallow oriole]

byeeeeee

[hallow oriole]

ah

is this in overleaf?

[fresh skiff]

Yes

[hallow oriole]

hmm

https://stackoverflow.com/a/2739710
this may work

[fresh skiff]

Isn't it including the pdf?
But i am looking for a way to attach a file (pdf).
Such that if I click the link the desired pdf opens

[honest bluff]

does anyone have a reccomendation for a calculus book for people who are beginers ( i only know how to find derivatives of functions)

[lusty ermine]

you mean beginner like pre calculus or calculus

maybe thomas calculus is a decent choice

[honest bluff]

pre calculus

ok

[fresh skiff]

I have already taken a course of discreet mathematics. But due to low quality education, I have learnt 5 − 10% if subject as compared to a standard undergraduate student.
So i wanna study the subject again as a beginner.
I found the following book on internet
"A course in combinatorics
Book by Jacobus Hendricus van Lint"
Is it suitable for beginners? If not then any recommendations for beginners please.

[lusty ermine]

I heard rosen is used for discrete math, is it any good?

[slim crescent]

I would appreciate any book that covers the fundamentals of computation, not necessarily a coding book, but things like ALUs, multiplexers, CPUs, GPUs, etc

doesn't necessarily have to be super academic

im mostly just looking for a good read

[remote sparrow]

https://www.amazon.com/Walk-Through-Combinatorics-Introduction-Enumeration/dp/9811277842

[remote sparrow]

it's fine

[earnest wolf]

tannenbaum?

I mean, unless you want to really dive into this şħĩț all the way, like, x86 architecture instructions, CUDA, or how to physically make an ALU, you are much better off with just watching some youtube videos

they will give you almost identical big picture in much shorter time frame

[slim crescent]

hm, do you have any specific channels in mind?

i actually just found a lecture series

[slim crescent]

appreciate it, might look at books later too, ill keep it in mind

[earnest wolf]

i mean, try both and see what you like more

[violet shuttle]

yes i think that's what i mean

if you can name it then you are right and i am wrong

[violet shuttle]

so just like baby rudin he doesn't fucking give you the name?

[grand thistle]

wdym look at the screenshot it has the name

[trail hemlock]

wait ppl actually read beyong chapter 7

[deep moat]

Any good math books that I can read - specifically those that're part in contests' and olypiads? epub or pdf files are good.

I think I can already handle the problem solving from here haha.

[remote sparrow]

https://www.amazon.com/gp/customer-reviews/R1GKKOK6STZ7JJ/ref=cm_cr_getr_d_rvw_ttl?ie=UTF8&ASIN=0070006571

a classic review of ahlfors

[narrow relic]

Haha:

Pivotal concepts are treated awkwardly in a rushed, conversational jumble that is rather like talking to a jet-lagged researching professor during office hours on a Friday afternoon minutes before he needs to catch a train.

[velvet flume]

There are many PDFs regarding latex. They are available online. I mainly use the latex stack exchange community. You may check this book https://link.springer.com/book/10.1007/978-3-319-47831-9

[civic python]

Does anyone have any recommendations for books on probability and statistics that is not too deep/heavy but also does not shy away from real analysis. I covered a large part of baby rudin and the book i'm currently invested in makes no attempt to connect real analysis and probability & statistics. I have not covered measure theory though.

[brazen grove]

any fun and historical course book for abstract algebra ? especially one that tells why the definitions were chosen the way they are chosen

[remote sparrow]

have a look at grimmett/stirzaker for probability and casella/berger for mathematical statistics

note that grimmett and stirzaker have a companion volume that i believe has more problems (and some problems repeated in the main text so that they are technically independent of each other) and solutions

however i do want to let you know that there are gentle measure-theoretic treatments of probability, e.g. rosenthal

i believe rosenthal develops the requisite measure theory

[mild rover]

Exceptionally well-written lmao

[cyan epoch]

Hey all, I wanted to ask if anyone had any recommendations to sources or books on logic that they found helpful to them? Particularly concerning natural deduction proofs, semantic tableau and or sequent calculus. Any help is greatly appreciated! 🙂

[pliant wadi]

Any book recs for an introduction to Non-Archimidean geometry?

[round shore]

Do you have any AG background

For a short introduction to rigid -analytic theory, there is a course by Ben Heuer
For adic spaces, Sophie Morel course is good too. You can also check Huber's original articles (same for Tate)
For the more recent approach, a go-to is Scholze-Weinstein "p adic geometry"

[pliant wadi]

Nope

[round shore]

Oh.

That might complicated then

[pliant wadi]

I have pretty much all preliminaries for AG tho

Maybe that's where I should start ig....

Thanks anyways!

[round shore]

I don't know how reasonable it is to directly learn non-arch geometry, but you can always check lol

[pliant wadi]

Oh yea I just went to a talk on it

I found some of the stuff pretty amazing

[round shore]

What was the talk about precisely?

[pliant wadi]

Ofcourse it was dumbed down

For undergrads

But

[round shore]

Oh I see

[pliant wadi]

I thought maybe I could check it out

[pliant wadi]

Oh one sec here's some part of the abstract:

....begin with an introduction to non-Archimedean fields and their properties. Further, we will introduce the notions of rigid analytic spaces, formal schemes and Adic spaces which are spaces over non-Archimedean fields relevant to Arithmetic Geometry.

[remote sparrow]

are you looking for introductory material?

[mild rover]

I would want to ask about recommendations about Statistics. I need an advanced textbook that is self contained, I haven't got much down but would like to challenge myself with the difficulty of the book.

[graceful onyx]

American Mathematical Society has pretty descriptive textbooks on logic and proofs

[graceful onyx]

Have any prerequisite knowledge of calc or linear algebra?

[hallow oriole]

@subtle violet are you gonna do those too

[subtle violet]

if it’s the “one thousand problems in probability”, I already own it. though I thought it was the same problems as the textbook

just with solutions and without the reading

[hallow oriole]

wow

that sounds awful

[trail hemlock]

theres a good chance i will never read that

[subtle violet]

i think it’s for people who already know probability and need to practice for interviews/exams/stuff

or for people who own the main textbook and need the solutions

[upper plover]

LOL

[hallow oriole]

But Ahlfors often manages terseness without elegance and hand-waving without intuition. It's breath-taking -- how does he do it? He couldn't have typed the book in the dark because there are very few typos, so it must be some special skill one acquires through life-long study of the Obscure Arts.
this review is great btw lmao

[remote sparrow]

van dalen uses a natural deduction system

you can look on https://logicmatters.net/tyl/ for other books related to your query

[trim kayak]

Hey guys. Haven't been here in awhile. I'm not looking for recommendation but rather a suggestion. I have so many math books and pdfs that I've found that I want to read through and learn more about. I also have A LOT of professional development and teaching books I want to get through too. I plan to read alot over the summer. This may be subjective, but how do I even get through all of these books? I'm afraid to read more than one at a time as I may get confused. I'm learning about topics and want to apply the info without forgetting where I read it and where it came from.

[trail hemlock]

take a lot of notes

and do all the practice problems

i think thats the only way to really fully remmever smth

[slender wasp]

Elements of Algebra by Stillwell

[molten mason]

Good book, along with Elements of Number Theory

[trim kayak]

@trail hemlock What about all of the books that don't involve math problems? I want to read through alot of those too.

[crude sage]

Looking for a book for a friend. I've seen it recommended here before. It's called something like a physicist's introduction to topology, groups, and geometry (one of those three may have been replaced with "symmetry"). I've heard it's well-written

[heady ember]

If you want to learn, exercises are essential.

[trim kayak]

@heady ember I understand that. What about my PD books that don't have math problems?

[heady ember]

Oh I thought you meant math books

[limber moat]

do any one now mtg

maths books

??

[trail hemlock]

just write down all the stuff you think is important

at the very least, you will remember it for future reference

[sullen kernel]

can anyone recommend me books for A/As level maths since I am going to die due to me learning late the A math since my school dont provide them but im joining it

[gray gazelle]

https://www.harpercollins.com/products/writing-to-learn-william-zinsser?variant=42347013505058

[reef escarp]

does anyone have a vulkan book thats updated to vulkan 1.3 and goes in depth about everything?

i could read the spec, but eh

[cyan epoch]

Thank you so much!

[remote sparrow]

see pins

[fresh skiff]

Ah wao this book contains bunch of exercise questions

[fresh skiff]

Thank you so much, really amazing and easy to read book.

[brazen lake]

Anyone know good books for category theory and representation theory

[brazen lake]

Thanks

[lusty ermine]

Book with easy proof exercises and examples

E.g prove that sqrt2 is irrational

[brazen lake]

How to Prove It: A Structured Approach
Book by Daniel J. Velleman

[stray veldt]

there is also a book called "proofs from the book" or something that showcases a few standard proofs that are considered very beautiful

velleman is more heavy (too heavy in my opinion) on the basic set theory stuff

its kinda annoying

[brazen lake]

I'd agree with you there

[desert moat]

I wanna self-study some math before starting a math bachelor. Does anyone have recommendations for books/topics I should go over? I started working on the Book of Proof by Richard Hammack a while ago and am thinking about looking into Elementary Number Theory by Gareth A. Jones and J. Mary Jones. Is this a good point to start my math journey or should I look into different books or topics all together?

[twilit nacelle]

Higher Algebra, Barnard and Child. Covers a decent range of algebra topics with an emphasis on proofs

[slender cargo]

That seems like a good start to me! I'm not sure about the Number Theory book, but I think getting an earlier grasp on Elementary Number Theory can only be helpful. Did you go through Introductory Calculus?

[desert moat]

Thank you! I'll definitely check that out

[desert moat]

I learned some calculus in high school

Could for sure brush up on it though

[slender cargo]

My only other thought, if your college accepts transfer credits for Calculus, is to maybe take Calculus courses over the summer so you don't have to do them at the university. I'm not sure if that's the best use of your time but that's something to consider.

[desert moat]

My college does not seem to offer that option ): Is Calculus in college generally something that is harder to get a grasp on?

[slender cargo]

Nope! It's the same as high school, unless you're taking an Honors version. I think going more through Book of Proof or Elementary Number Theory would be your best option then.

(I'm speaking from a U.S.-perspective. Calculus can mean something a tad different in other countries.)

[desert moat]

What's an Honors version?

[slender cargo]

An Honors version would focus more on why Calculus works, as opposed to simply applying Calculus. So, a (much) higher emphasis on proofs.

In high school Calculus classes you learn the integral and are then told to go integrate a lot of functions. In an Honors Calculus class you would be given a lot more emphasis on how integration actually works.

[desert moat]

Yeah, fom what I can tell the courses will more likely resemble the Honor version in the US with a focus on theoretical foundations etc. and less application.

[slender cargo]

Oh, excellent! Then I think continuing to work through Book of Proof will be the best option.

[desert moat]

Great! Thank you!

[remote sparrow]

Standard references for category theory are Awodey, Leinster, McLane, Riehl, and Simmons.

[brazen lake]

Thanks

[molten mason]

Much-awaited... by whom in this chat?

[remote vortex]

<@&268886789983436800> Is this kind of thing fine?

[fallow cypress]

Banned for advertising

[trail hemlock]

by me of course

[mild rover]

Yeah I have studied both calc and linear algebra

[crude sage]

I'm trying to convince my mathematical physics friend to read Spivak's Calculus on Manifolds with me. Does anyone have any words of advice for him?

[tribal crow]

well, why does he not want to?

it might have nothing to do with the book :p

[crude sage]

He is choosing between many books

[tribal crow]

what else is he considering?

[crude sage]

Some basic group theory, CFT, maybe measure theory?

I just thought that mathphys people are into DG and a "how do I do lots of kinds of integrals in R3" course isn't all that great as your only background

Though apparently that will get you through the electricity and magnetism course

[tribal crow]

I'm certainly not qualified to say anything about this lol (I'm reading CoM myself soon)

perhaps someone else can say a few things?

[heady ember]

I don't think an intro to proofs book is necessary, if you know the basics --- conditional/biconditional statements, basic quantifiers, etc.
You can probably jump straight into a (proof-based) linear algebra book (e.g. Linear Algebra by Friedberg, Insel, Spence), or intro analysis (e.g. Understanding Analysis by Abbott 🤖, or Mathematical Analysis: A Concise Introduction by Bernd Schroder).

Both Abbott and Schroder should be excellent picks for someone new to proofs. Similarly for FIS, as its quite pedantic and many of its exercises are very doable.

Pros and cons of Schroder: #book-recommendations message

[heady ember]

Why did you choose COM? Just curious

[tribal crow]

the primary reason would probably be the fact that I have an analysis course which uses CoM next year lmao

another reason would probably be it's short length; I, being foolish as usual, subconciously believe that a shorter book means that I can learn the subject faster or something

besides those two reasons, I've also been recommended the book by a few, both on and off this server

[heady ember]

Ah I see

I wonder if I can get through enough Schroder to avoid taking a class in multivariable calculus (the handwavy one) in uni.

[gray gazelle]

Well, it is quite required for most degrees in STEM and on a state level in the US, excluding private schools of course so even if you know proof-based Multivariable on the level of Spivak, I doubt you'd just never have to take it

[heady ember]

I see :c

Just curious: Why though? If a student has learnt multvariable analysis, surely mvc shouldn't be a big problem for them?

[gray gazelle]

is anyone familiar with Halmos' Finite Dimensional Vector Spaces?

I have a reasonable math maturity and want to teach myself Linear Algebra over the summer.

is it too advanced or should I go with something like Hoffman Kunze?

and btw I dislike Friedberg and can't seem to progress in it

[desert moat]

Thank you very much! To be honest do not know any of the basics. I'll for sure look up those concepts though and see if I can handle some of the books you mentioned.

[gray gazelle]

@desert moat https://store.doverpublications.com/products/9780486453064

I think I find this quite illuminating than your average intro proofs book

[desert moat]

Awesome, thanks!

[stray veldt]

pretty good intro book but iirc some of the terminology is a bit outdated

probably on the level of hoffmann kunze tbh

[royal remnant]

I need a book recommendation for DE's (ODE's specifically)

[graceful moon]

Boyce di Prima and Mede is a solid enough and pretty standard introduction

[royal remnant]

Neat

This?

[lusty ermine]

is this any good "problems in real and functional analysis", by torchinsky?

[graceful moon]

Yes, there’s about 47 editions but they’re largely the same

[royal remnant]

Neat

[lusty ermine]

damn

[formal bronze]

'Differential Equations and Dynamical Systems' by Perko is a good introductory book

[royal remnant]

Uuhhh I don't think I understand this

https://www-users.cse.umn.edu/~scheel/teaching/8501-fall18/perko.pdf

[vital bane]

lol you should probably mention that you want a non-rigorous computation oriented books, or else people will throw arnold ODEs at you

[royal remnant]

Arnold ODE's ?

[formal bronze]

Yes, one would presume that someone asking for a book on ODEs is familiar with the required topics in linear algebra

[formal bronze]

Then I guess this book isn't the right one for you at this moment

[gray gazelle]

hey guys

can someone please suggest a good calc 2 practice book ?

all books i've found are trivial and silly

[vital bane]

what do you want to practice?

integration?

[gray gazelle]

yup

[vital bane]

then I know the perfect book

[gray gazelle]

Nice
what's its name?

[gray gazelle]

thx
imma try it

[vital bane]

it's name you ask?

"Inside Interesting Integrals
A Collection of Sneaky Tricks, Sly Substitutions, and Numerous Other Stupendously Clever, Awesomely Wicked, and Devilishly Seductive Maneuvers for Computing Nearly 200 Perplexing Definite Integrals From Physics, Engineering, and Mathematics (Plus 60 Challenge Problems with Complete, Detailed Solutions)"

I'm not even kidding that's the actual name of the book

[gray gazelle]

XDDDDDDDDDDD

thx btw

[fresh skiff]

tbh yesterday i took a view of this book, damn everything was going above from my head even i have taken ODEs course upto series solution lol

[vital bane]

yea it's supposed to be challenging

since they're all "Interesting integrals"

oh nvm you're talking about that book

[fresh skiff]

yes it was (the book)

[vital bane]

yes I suppose it is, since it's a pure math book

[fresh skiff]

yes lol (odes by arnold)

[vital bane]

so automatically assumes like real analysis and linear algebra at the very least

though it's very interesting!

since he introduces group theoretic stuff

and manifolds

[fresh skiff]

ah and currently i am studying analysis from abbott (still on chapter 2)

[fresh skiff]

wow seems like it will be challenging.
i am crious to read it but have no proper background

[vital bane]

Abbott gang!

I just started chapter 4

[fresh skiff]

yes abbott

[fresh skiff]

oh wow, doing selfstudy?

[vital bane]

yeess

[fresh skiff]

same (in university TA has been completed the real analysis 1 course lol)

[opal spear]

abbott mentioned
im on chap 3!

[slender cargo]

I thought you were in college now? Just studying it before you take the class?

[vital bane]

I'm in a very bad college so I have to teach myself because only a few profs in my college know their stuff

the whole system is very bad, you can't really expect to learn anything besides "marks = good"

[slender cargo]

Oh gotcha

You got this

[vital bane]

Yoo niceee

chapter 3 is very fun!

[slender cargo]

I'm at the tail end of my Real Analysis class and have been using Bartle Sherbert + Jay Cummings

[vital bane]

especially the last section on Baire's theorem

[vital bane]

Noicee

[fresh skiff]

👀 ch 2 here

[calm dew]

can anyone recommend a website or a book to practice linear algebra?

[void acorn]

um for website

aops

on alcumus

or like

cemc waterloo courseware?

idk abt book tho

[fleet glen]

Can you guys suggest a cheap affordable calculus book?

[opal spear]

awesome, i actually got pretty burnt out with that one

[opal spear]

There are less than legal ways to obtain pretty much any calculus textbook

[fleet glen]

I see

Silly me

How about algebra books?

[gray gazelle]

taking grad linear algebra next semester potentially, and rly interested in numerical linear algebra. Is there any numerical linear algebra textbooks i could take that would also help prepare me for grad linear algebra next semester? To be clear taking a theory based grad linear algebra class, but just like numerical stuff on the side for fun. so it would be cool if I could find a book that would prepare me for both

I'm already familiar with the basics of numerical methods i guess also. took a class on undergraduate numerical linear algebra , though it was pretty surface level

[gray gazelle]

This seems standard:

https://www.amazon.com/Numerical-Linear-Algebra-Lloyd-Trefethen/dp/0898713617

tyy

[slender cargo]

https://calculusmadeeasy.org

This book is free online. It is very old (1912) but John Baez of UC Riverside highly recommends it. It gets straight to the point; only about 212 pages long. I haven't read it, but it's supposedly good.

[remote sparrow]

if you can't progress with friedberg, you might not fare much better with hoffman kunze. have a look at these recommendations: #book-recommendations message

[trail hemlock]

!introcalc

this must become a command

theres like 90 peple per day asking for intro to calc books

[gray gazelle]

Halmos is very concise, you should have seen either computational linear algebra & abstract algebra or a more simple course in abstract linear algebra before reading it

[coarse osprey]

Hi there! Someone out here that if, don't mind to, would like to talk with me in DM's? I'm a student from Argentina of "systems engineering", and I would love to hear about some books and comparisons between my country and yours. I fundamentally study from English-speaking books, so if you know books in this language that would be nice!

[gray gazelle]

Great book, I learned both LA and proof writing by reading it

[lusty ermine]

which book cover how to find absolute extrema of a function on a closed interval?

Also i wanted to ask, is Terrence tao anal 1 and 2 a good read?

[vale bloom]

What is the best book for all algebra? I’m thinking of getting Algebra I or II for dummies because it comes with workbooks in certain bundles

[quick hornet]

do you have conditions on the function? because in general this is a very hard problem and falls under the realm of mathematical optimization and global search

but if you know that its "well behaved" in a certain sense (e.g. differentiable a.e. with a "reasonable" number of extrema) then it should be covered in any calculus textbook's chapter on optimization/the first derivative test

find all the relative extrema by solving for the values that make the derivative 0 (or the jacobian determinant 0, etc.)

and then take the max (wrt your metric)

[quick hornet]

it's fine, i think it suffers from pretty severe pacing problems

it spends a lot of time sauntering about on the early "easy" stuff like the construction of ℕ and ℝ

and then the treatment of the actual analysis topics is fairly rushed

i think this is because it's also meant to serve as a first introduction to proofs/rigorous mathematics

so it starts slow to give students time to get their feet wet

but it still results in the actual content feeling a bit crammed IMO

i think spivak does that job better, though admittedly with a bit less depth

the actual writing of the book is fine though

i will say that i sometimes get a... condescending vibe from the prose

but that might just be me idk

also IIRC the exercises are overly easy

[quick hornet]

whats your background and what do you want to learn? "all algebra" is kind of vague lmao

are you studying for an exam? or to catch up on knowledge for a future course? etc

[vale bloom]

I am a high school student who has fallen down in grade exclusively because of a lack of understanding of algebra

Trigonometry and Physics aren’t a big problem for me, but Algebra makes me fall behind

I want to know it and love it so I don’t feel swamped or like I’ll fail when I get to university

My main goal is to be well versed in algebra to the point needed prior to taking engineering in university

[lusty ermine]

Is tao’s anal 2 too hard for someone fresh out of highschool?

I will give a read to taos anal 1

Seems good

[naive cove]

Hey guys, are there any good pre algebra/algerbra workbooks with many exercises?

[vale bloom]

I also would like an answer to this

[slender cargo]

After going through a construction of R with Goldrei's book, and finishing up the introductory real analysis sequence at my school, I now think it's odd to put the construction of R at the beginning. I just don't think a student would recognize why constructing R would be worthwhile if they don't see why the least upper bound property is important, over many examples. And I feel like it leads to a rushed treatment of Cauchy sequences without seeing them in other contexts. Just imo. I'm still only doing undergraduate math and have only glanced at his book.

[remote sparrow]

they're supposed to be read sequentially.

[lusty ermine]

Sorry

[slender cargo]

Yeah, you will not understand Tao's Analysis 2 if you do not go through his first book.

[lusty ermine]

Sorry

[remote sparrow]

I can agree that for most students, the construction of R (and of number systems in general) is not critical to teach. Most students aren't very concerned with whether something really exists, and a "specification" approach has the advantage that you are explicitly told what properties that you need to care about. Doing a construction first can obscure this.

[slender cargo]

Yep. 100% agree.

Rudin knew what he was doing lol

[remote sparrow]

in the first two editions, he did the construction first

in the third edition, he remarked that he moved them to an appendix for pedagogical reasons

[royal remnant]

Could I get a different book recommendation? Usually, this book is jumping to conclusions and I do not like that.

I want a book that teaches you DE's, and this book down here doesn't...meet the criteria really.

[tribal crow]

Arnold’s Ordinary Differential Equations

[royal remnant]

... I've heard that's complicated

[tribal crow]

I guess Neamesis was right

[royal remnant]

xD

[tribal crow]

idk many ODEs books, perhaps someone else can help you?

[royal remnant]

What I'm specifically looking for is an DE book that guides you, from basic to complex

and, well... Hightens your understanding and problem solving

[remote sparrow]

https://tutorial.math.lamar.edu/classes/de/de.aspx

try supplementing boyce and diprima with these notes

alternatively, you could read tenenbaum and pollard

[royal remnant]

Do you mean, like

combining?

[royal remnant]

Wait hold on, what am I sacrificing if I choose either of these?

[remote sparrow]

linear algebra doesn't really figure in tenenbaum, and the wronskian is introduced pretty late

[remote sparrow]

yeah

[royal remnant]

I think I could use the notes to help me here, yes

[remote sparrow]

#book-recommendations message

[royal remnant]

Oh cool

[vale bloom]

Anyone able to find a 2 in 1 textbook workbook bundle for Algebra II? I can’t seem to find it

[lusty ermine]

are you looking for highschool algebra?

maybe openstax algebra 2 is decent, at least is free.

[slender cargo]

Oh I keep forgetting about OpenStax. That should just keep getting recommended here. It's free!

[vale bloom]

Yeah, I just like having the books so I don’t have to go online for the information

[trail hemlock]

tao's analysis I and II are very approachable for someone in HS imo.

[gray gazelle]

If you know calculus and what inf and sup and the epsilon-delta definition of continuity, you can read rudin

[lusty ermine]

I know inf sup, lower boud, upper bounds but I cant read rudin since I dont know how to proof

exactly

epsi delta or any kind of proof I dont know

[gray gazelle]

You can learn proofs by doing them

A proof is really just like hey use the tools you have, without breaking their conditions, to show this problem

It's more of a way of thinking than a class you take in my opinion

[abstract copper]

Baby Rudin for intro is probably not a good idea

[trail hemlock]

use abbotts analysis for real handholding

[marble solar]

I fail to see the issue with this book. What is your issue? What is the book?

[hexed warren]

is Linear Algebra and its Applications by Gilbert Strang a good intro book for lin alg?

[tribal crow]

if you want to focus on computational linear algebra, I hear it's a good source

if you want something more theoretical, check out
#book-recommendations message

[hexed warren]

hmm, I think that's what im looking for, considering I want to learn the basics before jumping into something like machine learning. Thanks for the input!

[hexed warren]

this very helpful, ty!

also by computational do you mean focusing more on the calculation and applied aspect of lin alg as opposed to a more theoretical overview?

[tribal crow]

yeah

[hexed warren]

got it

[balmy crown]

I'll be taking discrete math this summer. Does anyone have any book reccomendations for it?

I just finished foundations of mathematics course so I've read through Book of Proofs and Introduction to Abstract Math

[rigid forge]

Same, I am looking for a introduction to discrete mathematics book.

[lusty ermine]

Rosen maybe

I would like to hear answers aswell

[royal remnant]

https://s2pnd-matematika.fkip.unpatti.ac.id/wp-content/uploads/2019/03/Elementary-Diffrential-Aquation-and-Boundary-Value-Problem-Boyce-DiPrima.pdf

The issue is, the book jumps around to conclusions without explaining how they got to a certain step in the first place. Then, when it does explain it doesn't get to the point, in other words, there's too much text and babbling.

Paul's notes are more optimal for pedagogical learning here. You can see how he teaches you how to do every step, instead of making massive jumps that throw you off.

[vital bane]

this kinda stuff is classic, we need a thread in #「the-obsidian-twink-jesus」 just for posting screenshots like this

[naive cove]

Hey guys are there any good books with many excercises mostly to train foundations like fractions, exponents, roots, algebraic manipulation etc?

[vital bane]

"concrete mathematics" is a good book

[tawny crater]

textbook that does just enough fourier?

the prof likes a lot of terminology and baby rudin and tao don't go into all of that. dini criterion is mentioned for example but doesn't show up in the texts. the "ergodic theorem on the circle" as well which is ???