book-recommendations

[exotic belfry]

ok

[undone pine]

For lee’s book, would learning about topology be recommended prior to taking on this book?

Tu’s book didn’t mention anything about topology for the first something pages I read, while Lee does

[tribal crow]

Yes. Lee states in ISM that the reader should "have a solid acquaintance with undergraduate linear algebra, real
analysis, and topology."

you can find all of the prerequisite material he assumes in his appendices

[gray gazelle]

Is there anyone who can recommend a resource on Euclidean geometry in multi-dimensional space?

[native cradle]

any number theory suggestions?

for someone who knows nothing

[remote sparrow]

oh, i meant lee's Introduction to Topological Manifolds. the requisite topology is covered within

[gray gazelle]

At a basic level. I am struggling to relate mathematics with geometry. I think this might be because I am just familiar with it. I want to learn geometry in a more mathematical way any suggestions?

[undone pine]

Ok just wanted to make sure the pre reqs in the appendix is sufficient

[tribal crow]

see what Sour Drop said

[undone pine]

I think his previous message said lee’s introduction to smooth manifolds but meant lees introduction to topological manifolds. Smooth assumes the pre req of the latter.

[tribal crow]

yes, that is what he meant

[rigid forge]

not really book recommendations, but how do I avoid procrastination. After completing a few books, I feel burnt out, and will read like 20 pages over a week.

[formal bronze]

Elementary Number Theory by David Burton

[narrow relic]

I would do something different for a few days. You'll feel a kind of impetus to get back to math, at least that's been my experience!

[sudden kindle]

<@&268886789983436800>

[maiden glen]

<@&268886789983436800>

May someone suggest books which concern axiomatic foundation, and formal perspective of arithmetic?

[left pasture]

thank you very much

[gray gazelle]

I recommend a dog's way come

[hollow peak]

Does anyone here have a good combinatorics textbook?

[tribal crow]

@hallow oriole your time to shine lol

[hallow oriole]

hi okay so it depends on your level and what you want to do

for a beginner i recommend a walk through combinatorics by bona

you can supplement it with bijective combinatorics by loehr if you want

for graph theory diestel is standard

[hollow peak]

I'm a graduate student but idk much combo beyond high school stuff

[hallow oriole]

start with bona then

[sage python]

DID SOMEONE SAY COMBO

[hallow oriole]

ewwwwww dami

[hollow peak]

swag money, thank you

[foggy relic]

no bona is too low-level for you

stanley enumerative combnatorics

[bright epoch]

I read stanley vol 2 and it was very good

I assume vol 1 is good too

[drowsy nacelle]

thoughts on the do carmo books?

[sage python]

Is there a particular one you're thinking of? I feel like the audience for the curves/surfaces book is not the same as the audience for the Riemannian book. As for forms, it seems alright?

[drowsy nacelle]

mainly the diff forms and diff geometry of curves and surfaces ones i suppose

I've just heard very polarized opinions about them

[sage python]

So, the only books I know on curves/surfaces are Shifrin and Do Carmo. I didn't like Shifrin and it kinda turned me off from diffgeo entirely, though friends of mine have said they taught out of Do Carmo and it was way better

Forms book I know less about, my analysis prof recommended it as a reference for the forms part of our class, online I saw one review which mostly complained about the notation

[drowsy nacelle]

By the shifrin one are you referring to the diff geo notes

i've studied out of shifrins vector calc textbook

[sage python]

Shifrin multivariable calc is quite good

[drowsy nacelle]

Yeah i really enjoyed it

[mossy flume]

who mentioned combo

[mossy flume]

If just standard combo stuff

Douglas West - Combinatorial Mathematics

Bona is UG level but good

Stanley has a good UG level algebraic combo book

Stanley's EC I and EC II are great but also more algebraic and maybe a little on the reference material side

Although idk of a better non-reference like text for alg combo

[dapper root]

So many exercizes

[maiden glen]

response please?

[mossy flume]

OH Fulton's Young Tableaux is my favorite text for getting into the more combinatorial side of algebra

How could I forget

[mossy flume]

In which text lol

[dapper root]

Stanley

[mossy flume]

Ah yea

[willow merlin]

which book introduces axiom of choice for dummies

[trail hemlock]

hey yall. is the book "Advanced Calculus: A Geometric View" by callahan a good standalone text for multivar calc?

from my brief glance over the table of contents and the Maa Review it seems nice

[willow merlin]

is marsen tromba decent for multivariable? does someone reviewed this?

I wanted to ask for a real analysis book that is not Pugh, Abbott, Taos, Bartle nor Cummings

[trail hemlock]

rudin?

[willow merlin]

im not good enough for pma

[trail hemlock]

neither am i, and yet here we are

nah but whats the problem with abbott or tao? those are like the two most populat analysis books ive seen

and cummings is super super motivated

[willow merlin]

I like them, but I like reading a bit from all of them, they introduce anal in very different ways all of them

and I wanted to have more references to check

[willow merlin]

agreed

[trail hemlock]

at some point having 10 reference books starts hurting more than helping

because the solution to exercise 10 in book A is a theorem in book B

[willow merlin]

which one should I stick with then!??

[trail hemlock]

go fot abbott. ive heard great things about it, and it has good motivation

it is the most popular for a reason

[obsidian pasture]

is the book "an introduction to dynamical systems and chaos" - G.C Layek a good book to start off learning dynamical systems ? I just finished my ode class im a bit interested in this subject.

[remote ginkgo]

it's not popular. try strogatz

[drifting fern]

Hi, does anyone have any resources on finite groups of lie type (and the conditions under which they are simple)? I've found some, but I really don't understand what a group of lie type is (and the resources I've found for that aren't helping).

[junior isle]

I'm with you

[tribal crow]

@violet shuttle might know a few.

[slender cargo]

@tribal crow how's Spivak Calc on Manifolds going?

[trail hemlock]

😭😭😔😔

[fresh skiff]

Where is Rudin?

[fresh skiff]

I am also with you guys (oops sorry I thought it was a discussion channel. Sorry)

[tender river]

no more with us

[violet shuttle]

I don't

finite groups of lie type are a group theory thing that has some connections to lie groups

[native cradle]

could I have a number theory book suggestion

for elementary number theory

[cyan crane]

A book which you really liked.. With good explanations and visualization

maybe not an 'advance' book but a beginner friendly one...

[hard gorge]

Guys, could anyone recommend me a math book, which is at my level, like I know practically all basic math with the exception of some geometry content, I would like to delve deeper and learn complex things, like Taylor's theorem

[gray gazelle]

I mean if I will say what the math sorcerer is good at, it will be only recommending books I guess lol

he makes a review about books so you could the content and talks about it

check his youtube channel for advanced things

[young grove]

Any good book for set theory. I referred to the book of Charles Pinter but it seemed to skip some important parts. I am not a student of mathematics but I want to learn this, so I need a proper book for understanding notations and other concepts

[still adder]

If you just need set theory to rigourise your arguments, I think chapter 1 of this suffices:
https://link.springer.com/book/10.1007/978-1-4612-0903-4

[young grove]

I want to understand the concepts of classes

[still adder]

you mean equivalence classes?

[young grove]

Because in case if I study another math topics, they introduce the topic from classes in a very general sense

[slender cargo]

Those books will introduce that topic in the book itself though. I don't think you need a separate book, unless you're trying to skip far ahead in material

[young grove]

I have a book called "mathematical proofs" of 3rd edition, there were no classes there

[slender cargo]

What book do you have in mind that uses "classes"?

[still adder]

https://en.wikipedia.org/wiki/Class_(set_theory)

Is this what you mean?

[young grove]

Advanced calculus texts sometimes uses classes

From starting

[young grove]

I think yes

I know sets, did those things several times

Like in school, and In my own like several times

To know the basics

[still adder]

I can't imagine this being a very widely used concept/term in calculus

[young grove]

Hmm. Guess I will skip it for now

[still adder]

I mean, set theory is definitely important as the foundation of mathematics, but once you've put some rigour into your thinking, you don't really use non naive set theory all that much in my experience

[slender cargo]

If an Advanced Calculus text does use the concept of a class, it will be introduced and taught in the text itself.

[charred inlet]

sl lonely for jee

or cengage? (trig)

[strange sentinel]

I can't imagine classes show up at all in a calculus or even real analysis course?

[foggy relic]

lmfao

[snow valley]

What's a good beginner matrix algebra book that is easy to follow

[granite viper]

Definitely not strang's introduction to linear algebra, fuck that shit.

[granite viper]

I second this question, but with a focus on engineering mathematics

[granite viper]

@gray jungle you got a problem?

[trail hemlock]

using lang's linear algebra atm and i like it

[granite viper]

does it also have a stupid sub-chapter on derivatives and finite difference matrices early on? wondering if it's only Strang

[trail hemlock]

i am not that far in yet

[gray jungle]

to be so aggressive about a good book with no justification is sully worthy my friend

[granite viper]

what chapter are you on?

[narrow relic]

I've read up to the middle of Chapter 5 and I haven't seen a sub-chapter like that yet.

[narrow relic]

For a total beginner I'd recommend the first three chapters of Poole's Introduction to Linear Algebra, the visualizations are great and helped me a lot.

[granite viper]

a "good book" by who's standard? First of all, it says it's supplementary or complementary to the lectures found on MIT opencourseware. But there isn't a lecture on derivatives and finite differences on where it appears in the progression of the concepts. Secondly, it throws in terms like "basis" and "rank" very early on, without giving definitions. It justifies this by saying "there are so many good ideas ahead, so why not jump right into it"

[narrow relic]

I did not like Strang either, it was one of the first linear algebra books I picked up due to all the hype

[granite viper]

While in the relevant chapter, it uses different terms to describe the same thing

[granite viper]

Then I'll be buying that one. The pdf online looks promising too. No fluff or bullshit, just straight to the point

Thank you

[narrow relic]

Yes, it's a very low on bullshit book. Can I give you a couple of recommendations about it?

[granite viper]

Please do

[narrow relic]

There's a good companion PDF here: https://www.math.columbia.edu/department/pinkham/LangCommentary.pdf
I recommend reading Chapter 1 of that PDF before reading Chapter 1 of Lang, and reading Chapter 2 of that PDF before reading Chapter 4 of Lang.

[trail hemlock]

wow that looks nice

[narrow relic]

Also, here are the homework problems I have been doing: https://math.ou.edu/~forester/5373F09/homework.html
(syllabus is here in case you're interested: https://math.ou.edu/~forester/5373F09/)

[granite viper]

So before every chapter?

Or wait

Chapter 2 of the pdf before chapter 4?

[narrow relic]

To be clear: Chapter 1 of PDF, Chapters 1-3 of Lang, Chapter 2 of PDF, Chapter 4 of Lang.

[granite viper]

Ah got it

[granite viper]

Thank you 🙏

[gray jungle]

i think its good with the MIT course, its not my favorite but its not a bad book either in terms of LA standards.

[narrow relic]

You're welcome 🙂

[gray jungle]

at least for applied LA

[slender cargo]

For a first introduction that is more computational, Gilbert Strang's book and David Lay's book are popular. For something more proof oriented as a first introduction, I think Friedberg Insel Spence is widely used across universities. Axler's LADR is perhaps the most popular proof-oriented book but it positions itself as a second course in linear algebra (you're probably fine taking it as a first course though if you're motivated).

[granite viper]

Looking forward to starting with this book. Which chapters or subchapters did you find particularly enjoyable?

[narrow relic]

Well, I got a lot out of basically every single section up through the middle of Chapter 5. I stopped at the point since I got sidetracked onto some stuff involving the complex numbers that I didn't know very well, and haven't gotten back to the book yet.

I was really enjoying what I did though.

[granite viper]

Nice. Yeah I saw that complex numbers was used further on as a means of matrix decomposition. Would you recommend preparing for those topics using an external source?

Like, a refresher course on complex numbers?

[narrow relic]

I was over-thinking matters. I think any basic reference on complex numbers would do the trick.

Not a whole course. Just the basics.

[granite viper]

By the way, what is the exact title of the book? Is it "Linear Algebra", or "Introduction to Linear Algebra"?

[narrow relic]

(how to add them, the DeMoivre thing, etc)

[narrow relic]

I'm talking about Linear Algebra, 3rd Edition (1987).

[granite viper]

Got it

[narrow relic]

Were you talking about the Introduction one?

[granite viper]

In what context?

[narrow relic]

you flipped through a PDF that you thought looked good.

[granite viper]

Ah, the pdf I opened was the "introduction to linear algebra" one, yes

I can't imagine his writing style differering too much between works

[narrow relic]

Oh okay. That's the more basic one but the style is really similar

[narrow relic]

Yep.

[granite viper]

Less proof focused?

[narrow relic]

No I think it just starts at a more basic level (e.g. if you've never seen a vector, etc.)

So you could always read some of that one and then go for Linear Algebra, 3rd edition before you get too far.

[granite viper]

I'm already at the 3rd chapter of Strang's. Probably acquainted enough, so I'll go for Linear Algebra

Anyway, thanks for the suggestion, and giving me relief that I'm not the only one that doesn't particularly like Strang's book

[narrow relic]

You're welcome!

[narrow relic]

Let me know how it goes. It'll encourage me to keep moving forward too

[granite viper]

Happy to do so, once I get started on the book

[narrow relic]

Thanks 🙂 Looking forward to it!

[fresh burrow]

i used "elementary linear algebra" by larson/edwards/falvo and had a really good time with it

it has so many exercises

also applications that i skipped

[desert crown]

hey, I have been studying calculus for a while, and I was wondering if I should go for the book "Calculus for the practical man"... its by JE thompson and it is quite famous for how good it is in terms of self studying... Should I consider taking the book, or there is something better for self study and leisure time purposes?

[prime blaze]

After watching the last Theory of Everything video discussing Grothendieck I'm interested in trying to study math as a hobby.
In the video they mention how "self-contained" the book Elements of Algebraic Geometry is and how you don't need to have a big background in math to understand it.
I'm wondering how true that is for someone with only a high school level in math and how long it could take me to understand the book, I'm used to watching vulgarization about maths but I haven't touched any real math for more than a decade now.
If anyone has done something similar successfully I'm really interested to hear about your experience.

[gray gazelle]

You need a good background in proof writing and abstract algebra/commutative algebra before reading EGA, and some background in differential geometry will help as well

[prime blaze]

I guess that answers my question then 😄 It's always hard to judge what these guys mean when they say "basic", thanks!

[gray gazelle]

EGA requires a great amount of mathematical maturity

[strange sentinel]

EGA will assume more mathematical maturity than you probably have, and it will definitely assume more knowledge of abstract algebra than a high schooler has

[gray gazelle]

if you’re interested in a first step towards EGA, check out Artin’s algebra book

or Cox’s “Ideals, Varieties, and Algorithms”

[prime blaze]

I've seen these words before but my next question was about finding an introduction video describing the difference branches of math and what they study so you are totally right

[strange sentinel]

One might also consider Fraleigh for a first algebra text, given you probably aren't very familiar with pure math

[strange sentinel]

Hmm, I'm not sure if there's a good youtube video for this

[prime blaze]

I don't even really understand what the stuff even is about in general outside from what I've learned in that video but I find hearing people talk about math really interesting so I'll abandon this idea and will look for resources on this discord (I just joined and haven't had the occasion to yet)

[prime blaze]

noted, I'll have a look at them, thanks!

[prime blaze]

I'm keeping the name for later, thank you!

[strange sentinel]

Here's a good resource imo (that admittedly isn't a video) https://web.archive.org/web/20150516025735/http://www.math.niu.edu/~rusin/known-math/

[prime blaze]

sorry I wasn't clear, I can read too it's just that I was thinking about introductory lectures for example but that's fine too

[slender cargo]

Most people start with calculus and linear algebra. Perhaps look into proof-based introductions to those subjects.

The higher level books tend to assume you know those two subjects at a deeper level.

[slate marlin]

Looking for a good calc one book. I’ll be taking Ap calc AB next year but the teacher sucksss so I’m gonna have to self study basically the entire course.

Not necessarily looking specifically for a Ap calc book just one that would good me a good foundation in calc one before university

[remote sparrow]

a typical calculus book is designed to cover calc I-III

[strange sentinel]

Stewart and Thomas will both give you enough for AB, but both will cover up through calc 3 instead of just 1 so you'll kinda have to figure out what you actually need from them

[slate marlin]

Is this the correct one?

https://www.thriftbooks.com/w/calculus-with-tools-for-enriching-calculus-video-cd-rom-ilrn--homework-and-vmentor-_james-stewart/247235/#isbn=053413212X&edition=1866801

[strange sentinel]

Yeah

[slate marlin]

Got it for $6 used pretty good deal

[mossy flume]

IVA mentioned

Love it love it

[still adder]

Yea idk why that guy hates Strang so much. It's a good applied LA book. In fact, one should always read theory and applications in tandem. I started off with Hoffman and Kunze in undergrad, and I never saw much of its use until Strang showed me. Things like how recurrence relations can be written in matrix form, and therefore easily solved by all the exhaustive theory of LA, is a very useful thing to learn. It shows up even in stochastic processes with transition/stochastic matrices.

[still adder]

Can second this, Artin >> Dummit and Foote imo

[magic leaf]

good luck!

by any chance does anyone have any good calc 3 textbook recommendations?

[gray gazelle]

Hello
Function, equivalence relations, Trigonometric functions, explicit and implicit function, domain, range, co-domain, etc comes in set theory and pre-calculas right?

So can u suggest a book for it

[stark turret]

anything for basic stats and probability? i just need to brush up on it for internships because i haven’t touched it since high school.

[molten mason]

Most math textbooks, in regards to topics such as Set Theory, will teach you what you need, and what/how notation is used, for that specific textbook in either the very beginning such as the first ten pages or somewhere in the end, as in the appendix.

You're always welcome to browse through Naive Set Theory by Halmos to get a nice easy introduction to Set Theory. I would also recommend Elements of Set Theory by Enderton and Introduction to Set Theory by Jech and Hrbacek for real introductions into Set Theory.

You can also check out Category Theory although I don't have any book recommendations.

[molten mason]

That entirely depends on what you used for Calc I and II

[young grove]

Thank you!

[vocal violet]

Does not understanding basic mathematics by lang mean im stupid and im not cut out for college

[tribal crow]

no.

[slender cargo]

No. Math is difficult, and this just means you need to orient yourself to concepts you are not familiar with. The fact that you're struggling means these concepts are valuable and new.

[hard gorge]

Guys

I want to learn more about algebra, can anyone recommend a good book about it? I have a little knowledge about this on a scale that is 4/10, but I know the sufficient to don't be classified like a beginner.

[vocal oracle]

Wassup, I would like to learn more about set theory but my knowledge of it is minimal. Are there any good introductory books that people know of on the subject?

[tribal crow]

I hear that Enderton's Elements of Set Theory is a standard choice.

I've never read it myself though

[hard gorge]

Could you help me too?

[vocal oracle]

Thanks! I'll look into it!

[slender cargo]

What math have you gone up to?

Calculus?

[hard gorge]

Algebra

[modern ruin]

roitman’s set theory was the book we used (with my professors notes). i wish i had typed up notes to share with others tbh

[slender cargo]

High school algebra, I take it? So you want to learn more about that stuff? Most of the material at that level is about preparing you for Calculus. There's tons of books and resources for that. People here often recommend going through Khan Academy. Lang's Basic Mathematics is a common recommendation here if you want something more oriented towards understanding why things are true.

[modern ruin]

i wanna type up more notes so that i can share them tbh

i feel like i have so many takes on pedagogy but i should put my $ where my mouth is

and actually try to create a style of notes that i feel is good

for subjects other than algebra

because i already think that aluffi already has a good enough book on algebra that i don’t feel like i need to spend the effort improving it

[strange sentinel]

Does this mean you've made notes for algebra?

[modern ruin]

no

[strange sentinel]

Damn

[modern ruin]

but if i were to do so it would be too similar to algebra chapter 0

like it would follow too closely to be useful i would just tell them to read that instead.

even though it’s not perfect and has some typos

[halcyon trail]

Here
https://tutorial.math.lamar.edu/
http://ko.mujica.org/

[hard gorge]

thank you

[magic leaf]

I used the Calculus for the AP course (3rd edition) by Sulivan and Miranda

[halcyon trail]

@strange sentinel which topic are u studying rn

[molten mason]

It's a very terse book and for the advanced learner, also GREAT as a refresher.

Supplement with YouTube for parts you don't understand. A lot of the "theory" and proofy abstract nonsense you can just skim and skip over. Also use the #precalculus channel for questions.

[strange sentinel]

Why do you ask

[trail hemlock]

hi arti why are you perm study

[molten mason]

There's three different textbooks. One has a last name of "Stewart", one has a last name of "Anton", and one has a last name of "Thomas"

Any one, any edition, from anywhere. They're all the same. They all contain Calc I, Calc II, and Calc III. I would review the Calc I and Calc II material first because it goes into it more than your AP textbook.

[trail hemlock]

spivak?

[strange sentinel]

Spivak barely qualifies as a calculus book

[strange sentinel]

I'm trying to be less degen than marlins and jay

[tribal crow]

but his book is called Calculus

[floral lantern]

I'm literally perma studied

💀

too busy to be a discussier rn

[strange sentinel]

You're still above me in messages

[strange sentinel]

Same

What r u busy with

[halcyon trail]

It's a genuine question

😭

[strange sentinel]

Uh.. ok I guess? I’m currently working through a paper about how we can construct “finite equivalents” to analytic and coanalytic sets and how in theory we can use this to try to approach showing that the polynomial hierarchy doesn’t collapse at the first level

[trail hemlock]

me too 🫶🫶

[trail hemlock]

what do these words mean arti 😭🥲

[floral lantern]

Ross is cooking me alive

Flash broiled

[strange sentinel]

Uh, are you familiar with the classes NP and coNP

[strange sentinel]

Lmao skill issue fr

[halcyon trail]

computational complexity theory at 14💀😭

[trail hemlock]

haha nvm 😅😓

[halcyon trail]

@trail hemlock what is ur latest topic

[trail hemlock]

reimann Stieltjes integration

i’m still on real analysis lol 😔😔

[halcyon trail]

Pretty advanced

Bro ur still in high school

Others don't even know about that

[trail hemlock]

ur learning functional analysis in hs hush

[halcyon trail]

No?

[trail hemlock]

help i thought u said that

i might be cooked

[halcyon trail]

😭🤣

I meant that it's a side quest

[trail hemlock]

oh nah

[halcyon trail]

That's not what hs teach me

Hs teach algebra and geometry

Trigs

Pre calc

[trail hemlock]

yeah that’s what i mean

as a hs student

[halcyon trail]

Yup

[floral lantern]

💀

[molten mason]

You're literally turning my beloved book recommendations into discussy 3

[tribal crow]

we did this a long time ago

[strange sentinel]

This has happened to #bots as well lol

[tribal crow]

wherever I go, discussification goes.

[strange sentinel]

Am I allowed to ask for non math books here btw

[tribal crow]

yes

[strange sentinel]

Like can I ask for stuff by Murakami since I liked Kafka on the Shore

[tribal crow]

people have asked for children's fiction here before

nothing wrong with that

[fresh skiff]

A topology book recommedation please (general top)
I have background of first 4 chapters of abbott

[strange sentinel]

The standard rec is Munkres

[tribal crow]

there's some people here who would recommend Munkres; other recommendations I've seen include ITM and Bredon's chapter 1

[fresh skiff]

I am not sure about prerequsities for munkers

[fresh skiff]

ITM?

[tribal crow]

ah

Introduction to Toopological Manifolds by John Lee

[strange sentinel]

Nothing really

[slender cargo]

No strict prerequisites. But I’ve heard you should complete Abbott first

I haven’t taken topology yet but I’ve heard it’s good to get introductory real analysis finished first to understand why you would study topology

[modern ruin]

just read it

or Bredon

you don't need that much to get into topology since it's entirely different from the stuff before it anyways

(opinion)

[dapper root]

You don’t need much

You just need to have swag (some familiarity with proofs and logic and shtuff)

Or you could honestly have it BE YOUR SWAGGENING

[drowsy nacelle]

any recs for automata theory?

[remote sparrow]

for basic coverage, you can look at sipser. for something more in-depth, see kozen

[drowsy nacelle]

thx

[strange sentinel]

Munkres has a section that swaggens you at the beginning doesn't it?

[dapper root]

Yeah

[normal crystal]

The Wind-Up Bird Chronicle
Norwegian Wood, if you're feeling sentimental
The Elephant Vanishes if you want short stories

[strange sentinel]

I think I’ll try Wind-Up Bird Chronicle, thanks

[gray gazelle]

anyone, thoughts on Garrity's *All the Mathematics You Missed But Need for Graduate School"?

[narrow fiber]

its cute but the placement of "all" is imperative here lol

its an extremely strict subset of what one should know for grad school 😭

[dapper inlet]

woah is that chmonkey from twitter?

🧎‍♂️

[junior isle]

Isn't it similar to analysis?

[modern ruin]

only if you want it to be

your analysis mind will certainly help you if you know it, but by no means is it absolutely necessary to begin learning about the subject (note the word begin) (opinion)

[cold tusk]

Anybody have any short (<500 pages) casual math books? Can be a little technical but should be able to read it in my bed, no exercises or anything

[strange sentinel]

Uh, Four Colors Suffice is a math history book about the history of the four color theorem that actually shows you most of the graph theory, though idk if that's what you're looking for

[cold tusk]

I know nothing of graph theory, but I will check it out thank you!

[knotty jewel]

Hi guys! Can anyone recommend me any book about Groups and Rings?

[mossy flume]

I like Artin's Algebra

[strange sentinel]

Depends on your background

How familiar are you with proofs and how much proof based math have you done

[knotty jewel]

Yes, I have already taken two two courses on Lineal Algebra and two on Introduction to Real Analysis, both proof based

[strange sentinel]

Ok then Dummit and Foote might be good, you could also check out Aluffi (which I think is probably one of the most fun of the intro algebra books)

[tribal crow]

this is precisely my background, and so I'm getting suspicious that we go to the same school...

could just be my paranoia though

[knotty jewel]

Most probably it is your paranoia hahah

[mossy flume]

Dummit and Foote bad!

it's so dry

Artin better

actually enjoyable to read

[strange sentinel]

I used to think this but I think I like it more now

But I think Aluffi is quite fun, which is why I recommended it

[mossy flume]

never looked at that

[tribal crow]

why not Lang

[mossy flume]

but I've heard good things

[strange sentinel]

Banned

[mossy flume]

Lang too hard

[tribal crow]

I'm joking!

[knotty jewel]

With "dry", what do you mean exactly?

[strange sentinel]

He likes his textbooks soggy.

The real answer is that "dry" basically means boring in the context of books

[knotty jewel]

Ok, I got it haha

[tribal crow]

like eating very dry food, reading a very dry book sucks

[molten mason]

[molten mason]

Do you want to be told straight facts or do you want storytelling and tons of examples

[brave lotus]

i want the whole saga

[junior isle]

What do you guys think of charles Pinter's algebra book?

[tribal crow]

@strange sentinel this is literally for you lol

[junior isle]

I read the intro and first chapter and seems to be well motivated

[strange sentinel]

I really love Pinter

It's probably my favorite algebra text

[junior isle]

Does it have challenging problems?

Its quite nice to read

[strange sentinel]

It does have challenging problems but in general it's more gentle than most other texts

Though I suppose that depends on your definition of "challenging" (ie, some other "intro" texts will have graduate level exercises)

[drowsy nacelle]

how would you compare it to aluffi?

[strange sentinel]

Depends on the reader

Like, from my perspective at the time I was first learning algebra, I like it much more

If you've done algebra you'll probably like Aluffi more but I'd suggest something more advanced at that point actually

[drowsy nacelle]

oh alright

[strange sentinel]

You might consider Lang, depending on what that first course was like

[drowsy nacelle]

i was gonna go through aluffi cause of the category theory stuff

[strange sentinel]

I mean yeah, this is also valuable

[drowsy nacelle]

Artin

[drowsy nacelle]

yeah i heard it was a valuable perspective

whats the controversy with lang btw?

many people seem to have mixed opinions

i havent read anything of his before

[strange sentinel]

I mean, category theory is pretty vital to algebra the farther you go, but you don't necessarily need Aluffi to learn that

[tribal crow]

if Lang is controversial, what does that make Axler?

[drowsy nacelle]

ah ok i think it was just to put it in a familiar context

[strange sentinel]

It's just not really fit for a first exposure, and it's also pretty hard

[strange sentinel]

How's your linear algebra

[drowsy nacelle]

pretty good id say

idrk how to quantify it

[strange sentinel]

You'd probably be fine with Lang

[drowsy nacelle]

aight ill check it out

[junior isle]

How does hoffman compare to lang in terms of dryness?

[narrow relic]

Are you talking about Linear Algebra?

[junior isle]

yessir

[drowsy nacelle]

@strange sentinel https://link.springer.com/book/10.1007/978-1-4613-0041-0 this one right

[narrow relic]

Hoffman is more verbose, if I remember right. It may have more details/material too.

[strange sentinel]

Yes

[gray gazelle]

whats the difference between aluffi's chapter 0 and underground?

[drowsy nacelle]

iirc underground is like a lite version of chapter 0

[snow valley]

What's a good proof book for beginners. I tried vellemans how to prove it and everything is confusing. The only one that makes a tiny bit of sense is book of proof but am I really stuck with that only

[gray gazelle]

no

[fresh skiff]

" How to think like a Mathematician " sorry I didn't remember the author's name.
I used this book to teach myself proofs.

Also I am using velleman's book and it's enjoyable.

IMO velleman is better, since he has provided the structure of writing proofs

[snow valley]

I'm sure it's a good book but I lack the appreciation maybe

But at the same time seems like there's so many options for learning about proofs

[fresh skiff]

There are.

There are plenty of books. Or you can directly jump into Abbott's book (understanding analysis) he doesn't assume much of proof writing from the reader.

[molten mason]

If you've already done a semester of undergrad Algebra and also Linear Algebra, then Lang's Algebra is fine. The controversy comes from those that are weak. If you plan to go to graduate school you'll have to go through it eventually.

[molten mason]

His Introduction to Algebra is basically an undergraduate version, it's written to prepare you for his graduate text Algebra

If you feel you might need a refresher or to learn how to read the way Lang writes, you might want to skim through that book first.

[lone orchid]

can anyone suggest me a good math book, that i can read before college starts?

just for general interest

[primal summit]

This is very unspecific

What kind of math?

At what level?

And for what purpose?

[drowsy nacelle]

Ah I see

Yea I’ll take a look at both

[lone orchid]

pre univesity...just for general interest

i have done basic calculus,algebra...high school stuff

i was wasting time after exams..so better utilise it it a better way

[wet sentinel]

is there a good youtube playlist that covers all of calc I and II

[fluid violet]

Rautenberg

[fluid violet]

I'd maybe look at khan academy

[hollow shore]

https://www.youtube.com/@HoustonMathPrep

[torn blade]

any good books / problem sheets on proof based maths, naive set theory, logic, elementary number theory (like primes, divisibility, modular arithmetic etc)

basically like an intro to uni maths course

[trail hemlock]

jay cummings has a book called “proofs” which has absolutely 0 prerequisites

[trail hemlock]

https://www.youtube.com/playlist?list=PLfbradAXv9x5az4F6TML1Foe7oGOP7bQv

i like this one

for calc 1

[gray gazelle]

sounds like the Foundations course at the university I'm learning from, but honestly, for the latter you'd probably be fine with reading the first couple of chapters in a number theory book, or a few chapters from a DM book.

do you want a gentle or rigorous introduction?

wait... i know what uni you're going to

LMAO the odds

congrats on that, that's a good one for math

[gray gazelle]

from our mutuals

if you need more advice, you can DM me, because I've taken several courses at your university

it's a bit complicated but ik how to help

[snow valley]

Honestly I only want to learn proofs so I can understand how contour integration works but the complex analysis books, I have no idea what's going on

[near quail]

Do you have any calculus book recommendations for self-study? I'm only using Khan Academy and YouTube resources, but I don't get a deep understanding

@wet furnace

[wet furnace]

khan academy, paul's online math notes, and stewart's calculus book if you're asking me

feel free to disagree I leave this channel muted cause I don't want to take part in recommending books at all

[near quail]

By the way I have downloaded Paul's calculus notes and book. It's full of theory which I really like for understanding math... AGAIN THANKS

[gray gazelle]

Paul notes made me cry

https://www.korpisworld.com/Mathematics/Calculus Maximus/Calculus Maximus Splash.htm

[hexed jolt]

You can check out the first couple of chapters of Discrete Math with applications by Susanna Epp. She explains proof writing in a beginner friendly manner.

[torn blade]

hahahaha nice

[still adder]

I haven't read lang, but tbh Hoffman and Kunze is very "dry" in that it's all theory and no applications. Mostly meant as a textbook guide to university courses, which was how I was introduced to it. I'd recommend wetting your appetite first with some applications of LA

[junior isle]

I agree with your bio

[junior isle]

I was referring more to how the theory is presented

[gray jungle]

is it? i feel like they give quite a bit of motivation for all concepts they build

[still adder]

not exactly math per se, but Grothendieck's autobiography or Hadamard's An Essay on the Psychology of Invention in the Mathematical Field

[gray jungle]

given the motivation is purely theoretic in nature

its good buildup

[gray gazelle]

Yall who have Chris mcmullen ebooks

[still adder]

well yea, purely theoretical motivations. Very complete presentation of LA as a theory tho, very good as a reference guide.

[junior isle]

That's nice to hear

[gray jungle]

H&K builds things the most naturally out of all books i have seen

discusses its way towards a definition/theorem

so by the time you see it makes sense

[still adder]

I agree, though it was also the case that the book and the course it appeared in for me was so theoretical, that the physics profs would apparently complain about how students from our course could not diagonalise a 2 by 2 matrix

[near quail]

I will see thiss stuff

Thanks for the valuable information

[still adder]

It's great to know that matrices are just the computational equivalent of linear transformations in finite dimensional vector spaces tho

[fresh skiff]

Is it suitable to use munkers (general top) with abbott (I am doing derivatives)?

[still adder]

u mean munkres topology or munkres analysis (on manifolds)?

[fresh skiff]

Munkers general top

[still adder]

if you only stick to the point-set stuff, sure

[elder stratus]

probably best to use it after, but with is fine as well

[fresh skiff]

ah yes, not algebraic top

[fresh skiff]

oh, maybe untill i cover abbott I spend some time on chapter 1 studying sets and axiom of choice stuff

[elder stratus]

it’s best to study topology after learning about the topology on the real numbers and continuous functions

those will provide the intuition behind the unmotivated topological definitions

[fresh skiff]

I guess I have studied them (except connected sets)

[elder stratus]

then go for it

[strange sentinel]

I’m not convinced this is true

[still adder]

connectedness is probably the most important topological notion for the real line tbh

[elder stratus]

munkres covers the connectedness of intervals etc in detail

so it’s fine

[elder stratus]

…the entire reason topology was invented was to put these concepts in a generalized framework

[fresh skiff]

Thank you guys I will try to read if i found it difficult then I will stop

[elder stratus]

good luck !!

[fresh skiff]

untill study some more amount of analysis'

Thank You!!

[still adder]

have fun

[strange sentinel]

Right, and now the field is much more than that

[spark oracle]

Hello!!!!

[molten mason]

Professor Leonard and Brian McLogan have some good playlists

[upbeat rover]

https://math.stackexchange.com/questions/4932312/what-book-should-i-study-linear-algebra-textbook-for-first-course-lang-axler-o

Is there any comparison LADR versus FIS

[loud cradle]

they've both been discussed quite a bit in this channel, you can probably find some comparisons by searching
here is an old pinned msg that may be of interest: #book-recommendations message

[upbeat rover]

Thanks so much

[loud cradle]

np, you might also check in #linear-algebra

[gray gazelle]

Do you have a physical copy of Lovász’s Combinatorial problems and exercises, @remote sparrow?

[left pasture]

any good books for college statistics ??

for beginners

like total beginner I don't even know what a statistic is

[foggy quest]

The best I've read is https://mtaylor.web.unc.edu/notes/linear-algebra-notes/

[upbeat rover]

Thanks

[fresh skiff]

Do I need some good knowledge of set theory for measure theory?

I am not familiar with Zorn's lemma, Axiom of choice, etc

[strange sentinel]

You said you'd done real analysis right? You're probably fine for measure theory

[fresh skiff]

Not done, but I said I have covered more than half of abbott (I will start last section of chapter 5, derivatives soon)

[strange sentinel]

Hmm, I might consider finishing a first exposure to analysis before moving onto measure theory

[fresh skiff]

Surely I will do this
Sequence of series of functions, and integration
I will cover these two then will more to measure maybe.

[strange sentinel]

I think that's a good plan, yeah

[fresh skiff]

Thank you

[remote sparrow]

no

[gray gazelle]

I have heard of the book before, and there are about over hundreds of combinatorics problems.

All in this one book.

[strange sentinel]

There are many books in which you can find hundreds of exercises

[shadow river]

you'd need a basic knowledge, in terms of choice/zorn's lemma you should at least understand what they're saying, why they're equivalent, and to be comfortable using them

nothing deep, but both are used in analysis and measure theory

[fresh skiff]

Could you please suggest some book or resources from where I learn these things

[shadow river]

Enderton's Elements of Set Theory, Naive Set Theory by Halmos, both are good (Enderton is much more in depth, has lots of exercises). They basically cover all the set theory you'd ever need (unless you decide to take more advanced studies).

[fresh skiff]

Thank You!

[torn blade]

ok not necessarily looking for a book here (but i dont mind if it is) but whats the best way to learn computational/first course linear algebra? most of the pinned tweet stuff is more theory

i dont want it to be completely theoretical but i also want the computations to be explained and intuitively understand why they work

[remote sparrow]

#book-recommendations message

[trim kayak]

Anyone use SpringerLink for books? I've browsed the site and found several books I want to read. I'm not even sure which ones to start with. What algebra, geometry, trig, and stats books would you recommend from that site?

[remote sparrow]

i don't think springer generally caters to that audience

[trim kayak]

I found random books on those topics. Just don't know which is best.

[narrow relic]

I've never seen this, thanks for the link.

[fleet mountain]

does anyone have any book reccomendations for AP stats self study?

[strange sentinel]

The standard AP prep books are Barron's and Princeton Review

[narrow relic]

There's a good book by Poole, Introduction to Linear Algebra that I got a lot out of.

[lusty escarp]

Just pick up anyone of the measure theory books and see how far you can go. Try first with axler maybe.

[fresh skiff]

Ok. I will try this too.
Maybe I pick axler with Schilling or maybe wheeden

[abstract copper]

I'm using Axler. The set theory needed will be introduced. The prereq is just analysis

[fresh skiff]

So Abbott is enough for Axler? (Up to chapter 7 of Abbott)

[abstract copper]

Yep

[modern ruin]

tbh you should just try reading it and find out

[fresh skiff]

Agreed. Thank you guys
Idk why I am very much obsessed with measure theory right now

[abstract copper]

It's a really interesting subject!

[fresh skiff]

Ah it will be fun.

[remote sparrow]

it is enough for the first five chapters of axler

axler spends a section covering metric spaces in the sixth chapter

although it's more intended as review

[trail hemlock]

ur using abbott?

i thought u were on rudin

[fresh skiff]

Oh. Well I found some supplements for Axler too by Axler itself, it contains some real analysis

[fresh skiff]

Yes lol.
I am using Abbott for self-study.
I only use Rudin for HW problems (whenever I solve HW problems -- which are assigned from Rudin, I read rudin. Otherwise (mostly) Abbott)

[trail hemlock]

the amukh method

[fresh skiff]

Oh fr? Wow. I guess it's another coincidence lol
Amukh and I are almost near each other in Abbott also the method is same

[trail hemlock]

the similarities end there though, as amukh is decidedly 4 feet shorter than you

[lusty escarp]

What is amukh method?

[trail hemlock]

abbott in reading group

[lusty escarp]

Can you explain more?

[trail hemlock]

the reading group for analysis follows rudin

amukh is using abbott and doing all the problems out of rudin

[lusty escarp]

Can you share link for that group?

[trail hemlock]

ask zorn or darq

they manage it

[lusty escarp]

Ok

[fresh skiff]

Amukh is the name of a person (our friend on discord). We are talking about the strategy for study, which amukh is using.

[near junco]

Hello. can u send me the link for invitation pls

[fresh skiff]

Sorry, ask zorn or darq. They are the instructors

[near junco]

can u dm them pls

i dont know who are u talking 'bout

[dapper root]

What is amukh method

Specifically

[last bloom]

Could you recommend a textbook centred on math to self-study cryptology?

[golden salmon]

Just dropping by to simp for my favourite real analysis book, which is also free https://www.jirka.org/ra/

[fierce hedge]

@remote sparrow is there an errata for the algebra book by Robert ash? I couldn't find anything

[trim kayak]

Anyone use SpringerLink for books? I've browsed the site and found several books I want to read. I'm not even sure which ones to start with. What algebra, geometry, trig, and stats books would you recommend from that site?

[next storm]

How is Rudin’s so far?

[next storm]

Lovely book

[violet fiber]

Have you guys used AoPS's Calculus Book if so how is it because I'm planning to use it to self study calc and would using it be a good idea or not?

[timber bronze]

yes

good idea

best idea

[violet fiber]

alr thx

[fresh skiff]

It depends.
It is first course in analysis for me and I already read 3 chapters of Abbott before starting rudin.

[next storm]

Which has the best problems?

[fresh skiff]

I guess yes
Well I get 5 problems from each chapter as HW. And honestly it isn't that much easy for me to prove. I still remember the proof I did and was very happy ( Every compact metric space has a countable basis )

[remote sparrow]

i'm not aware

also robert ash died in a car accident some years ago

[fierce hedge]

I knew he died around 2015 but damn didn't knew he got hit by car

[remote sparrow]

https://www.amazon.com/review/R2IADID8E966E8

[proud goblet]

Do you guys think using the math major series for abstract algebra will be enough to serve as an introduction

Or is there maybe a better series out there that covers more content

I also saw the ones from Harvard which also follow the Artin book

[strange sentinel]

It's a closed reading group

As far as I know

[strange sentinel]

It's a well written book

[strange sentinel]

I think you'll learn more by reading a book

[proud goblet]

So do yo think it’s better to not use lectures

Cuz UO till this point I’ve been supplementing lectures with problems sets and it got me up to ODE’s

It helps me to see and hear the work being done

[strange sentinel]

I think your main resource should be a book and you can augment that with stuff like notes or lectures

[proud goblet]

Okay well then in lieu of that do you have a recommendation for a quality abstract algebra book

[strange sentinel]

Depends on your mathematical maturity

How much proof based math have you done

[proud goblet]

A sizable amount
I did linear algebra abstractly and I did an intro to proofs thing too

I can handle a heavy hitter

[strange sentinel]

You could consider Dummit and Foote or Aluffi then I think

Yeah I think probably one of those

[proud goblet]

Is there any specific difference between the two?

[strange sentinel]

The category stuff is the big one

I also think DF is more dry, but that's very much a me thing

[strange sentinel]

Aluffi does a lot of stuff from a category theory perspective, DF doesn't really have that

[proud goblet]

So what kind of approach do they take?

Or does it take

Whatever

I just want to make sure what I’m getting into is going to be the most beneficial for me

[strange sentinel]

Either will be good for you

[proud goblet]

Alright I’ll look into both of them and see which one better fits my needs

Thanks 🫡

[drowsy nacelle]

anyone know if the 2012 version of differential forms and connections by darling is a new edition or just a reprint

[shadow linden]

Does anyone have any advice for what happens if reading a math book is "too hard?"

I'm struggling with Vick's homology theory, published by springer

[willow merlin]

best book for harmonic analysis

aka harm anal

[barren heart]

lol

[violet fiber]

Thx

[strange sentinel]

Depends

This can happen for a couple reasons

One can be a weak foundation/understanding of prerequisites or less mathematical maturity than the text expects, in which case you go back to previous material or maybe drop the book for a bit while you get more maturity respectively, but there also just exist books that are hard

I’d also recommend making use of either the channels in this server, MSE, Reddit, or knowledgeable people you can ask IRL even for books you aren’t necessarily struggling with too much but especially for hard books

[next storm]

What are coverings used for? I've heard of Vitali's covering lemma but that's Topology.

Although I guess Analysis is a subset of Topology.

[willow merlin]

Which books explain integrating factor for dummies?

[gray gazelle]

Hello, what are some good books for learning linear algebra?

[willow merlin]

Strang, David C Lay, Hoffman Kunze, ladr, are some of the most common

Anton aswell

[drowsy nacelle]

for ODEs?

which ones did u try and not like

cause i would say pretty much anywhere like khanacademy or pauls math notes or something has an explanation and examples

bunch of youtube vids too

[gray gazelle]

Yall should I grind khan academy website as a workbook for calculus or which workbook do yall recommend

[gray gazelle]

is there a basic algebra titled book that isnt for early grad

[willow merlin]

im new to the topic so I havent tried none ode book

[tight spade]

Yo

[strange sentinel]

By basic algebra do you mean groups/rings/fields

[gray gazelle]

https://mathematicalolympiads.wordpress.com/wp-content/uploads/2012/08/putnam-and-beyond.pdf

[strange sentinel]

If so, you could check out Fraleigh, Pinter, Dummit and Foote, or Aluffi

[gray gazelle]

Good book?

[strange sentinel]

Putnam and Beyond is fine

[gray gazelle]

Im trying to study for the putnam which Ill take in like a year and a half

are there any other books that are better?

[strange sentinel]

I think there are definitively better ways to spend your time, but I don't think I know of a better book than the one you posted for that

[gray gazelle]

well Im not going to sit down everyday and study just for that test lol, but I think if I study for the putnam it'll also help with other math

[modern ruin]

it won't

[trail hemlock]

there are also problem-solutionbooks titled The William Lowell Putnam Mathematical Competition: Problems and Solutions that you can check out

just mentioning, most peple here really dislike comp math

[modern ruin]

I don't dislike it

[gray gazelle]

why?

[modern ruin]

it just won't help you more than just being generally interested

in math

[gray gazelle]

I see

[modern ruin]

like if competition math is your thing then go for it

becuase studying for competitions actually does help you with competitions

[trail hemlock]

comp math was my intro to pure math tbf

and i was never good enough to make it past national oly

[willow merlin]

but they train number theory

[dim sierra]

How often does springer have a sale for hardcover books? Do yall think they will have an insane sale this winter like they had in 2023?

[trail hemlock]

oh this is not a book but a great resource regardless
https://artofproblemsolving.com/community/c3249_putnam

[strange sentinel]

Elementary stuff mostly, no?

[trail hemlock]

extremley so

most of the time its memorizing theorems and knowing when to apply them

[strange sentinel]

You won't care about elementary number theory pretty much at all after your first course in it

[trail hemlock]

this may be a hot take, but some competitive NT problems are pretty interesting

[gray gazelle]

NT?

[strange sentinel]

Oh totally, they can have some pretty neat solutions

But I was specifically responding to "it will help me with other math"

[modern ruin]

try aluffi if you're doing algebra as a passion thing @gray gazelle, i like the presentation, and if you feel like you're drowning in it then try judson (or whatever other recommendation that's not aluffi or D&F)

[trail hemlock]

yeah comp math is in its own bubble lmfao

[gray gazelle]

alr thanks

[modern ruin]

if you like competition math putnam and beyond is a good book yes

[remote sparrow]

at least twice a year it seems

one in the middle of the year and then a holiday sale

[dim sierra]

i c

does ams ever have sales?

[foggy quest]

https://mtaylor.web.unc.edu/notes/linear-algebra-notes/

[remote sparrow]

not sure

some i've seen require you to be a member

[daring lake]

Any book recommendations for non linear dynamics?

[willow merlin]

elementary spectral theory book

[mossy portal]

Mine too

[remote sparrow]

use strogatz for a nonrigorous treatment. hirsch, smale, and devaney; perko; hubbard and west; guckenheimer are rigorous

[daring lake]

Thank you 👍

[trail hemlock]

🤓

[strange tree]

isnt math in general some kind of " knowing when to apply them", like know when to apply something is quite hard. You could argue that it is memorizing tricks rather than theorems, I do think you memorize more theorems/results in real(UG-G) math than in comp maths lol

[trail hemlock]

the difference being comp math never makes u prove theorems

[strange tree]

quite false :P

[trail hemlock]

im not saying comp math is easy

[strange tree]

yup

[trail hemlock]

its just different

[strange tree]

you havent said such thing

but you can choose to prove or not a theorem they are presenting (a book)

its not like you start memorizing every theorem you see lol

I found abstract algebra kinda related to comp NT btw, it was easier for me to learn it (comparing to my classmates)

Yes, in graduate school you wont use elementary theorems but its not like you are doing physics or whatever

[trail hemlock]

in my experience with comp math at least, it was more memorzing tricks and results than proving them

for example constantly spamming cauchy schwarz

[strange tree]

from 2013 to 2019 there were no inequalities at IMO

Ofc there are examples that you are just spamming things, like doing geometry with complex numbers or bary coordinates

[strange tree]

Im pretty sure the book presented the proof of cauchy schwarz. Tbf I never liked inequalities so I just learned like am-gm but I proved them lol, cauchy induction

Im just saying there is an intersection between oly and real math

not that oly is a subset of real math

[trail hemlock]

i cant speak to IMO, but at least at USAJMO, in any prep or exam, there was no emphasis

however i agree that there is a definate intersection of comp and real math

and the inequality book i read, The Cauchy-Schwarz Master Class, also presented the proof of its theorems

[heady ember]

Hi blackmoustache

[strange tree]

then you could have proved it 👀

Ig USA its pretty different from my country tho

Like USAMO problems usually require knowledge + problem solving

[trail hemlock]

hi wheat

[trail hemlock]

true. i came across a problem that could only trivially be solved using graph theory

ugg i cant find it

sometihng about blackboards

[strange tree]

maybe Im miss remembering but richard borcherds said he dont read every theorem's proof

he uses examples in those theorems to figure it out what the theorem is saying

[strange tree]

yeah, USA is able to require their contestants that knowledge

[trail hemlock]

wish rudin would give examples for me to use 😭

[strange tree]

hamiltonian and eulerian path and stuff

[trail hemlock]

there was an extremley convoluted algebraic solution, but the graph theoretic approach was more fitting

since the point was to draw points on a blackboard

[strange tree]

"prototypical example for this section 🤓 👆 "

[trail hemlock]

rudin trying to include motivation in his book (impossible)

[strange tree]

oly algebra can be really sad

[trail hemlock]

all i need is my pal desmos graphing calculator 🙏

[trail hemlock]

ehh i found it kinda fun

since it was basic algebra with problm solving

[strange tree]

I didnt >:D

NT and Combi were beautiful for me

[trail hemlock]

those were OK for me

[strange tree]

I just liked FE cause I could played with it

[trail hemlock]

anything except geometry i was good at

[strange tree]

I spent a lot of time in geometry, I HATE GEOMETRY

but its my best subject...

[trail hemlock]

im so bad at geo

anyway i think we are getting off topic

since this is #book-recommendations

[strange tree]

yeah sorry

Im just going to delete everything and go to sleep

2am

have a good night :D

[trail hemlock]

nah dont delete too much hastle plus ill look like im talking to myself 😭

[trail hemlock]

yeah u 2!

[magic leaf]

what are some good historical fiction books?

[loud cradle]

i, claudius

[hexed stone]

1984

[dusk flare]

Has anyone read any of these psych/thinking (like they supposedly make you think better) books?

-Read people like a book- Patrick King
-Farsighted -Steven Johnson
-Anti-fragile - Nassim Nicholas Talib
-33 strategies of war- Robert Greene
-Taming your gremlin - Rick Carson
-The inner game of tennis -Timothy Gallwey
-Die with zero -Bill Perkins

If so can you recommend / denounce any? I want to read some but I feel like reading all of them is too much, especially the 5th and 6th one cause they seem very similar

[rigid flint]

Anyone have any introductory books to complex analysis/contour integration?

[remote sparrow]

#book-recommendations message

[foggy quest]

A good one here: https://mtaylor.web.unc.edu/notes/complex-analysis-course/.

[fading flint]

I've been struggling to find a good cheap calculus book

the thing is that I live in Brazil so a lot of books that are supposed to be cheap get pretty expensive

[trail hemlock]

lots of good books are on archive for freee

[orchid otter]

https://www.thriftbooks.com/w/linear-algebra_georgi-e-shilov/363407/item/6434642/?mkwid=|dc&pcrid=76897273066017&pkw=&pmt=be&slid=&product=6434642&plc=&pgrid=1230353808544789&ptaid=pla-4580496735976160&utm_source=bing&utm_medium=cpc&utm_campaign=Shopping+-+High+Vol+Scarce+-+%2410+-+%2450&utm_term=&utm_content=|dc|pcrid|76897273066017|pkw||pmt|be|product|6434642|slid||pgrid|1230353808544789|ptaid|pla-4580496735976160|&msclkid=040ed6c6f9a91165abe7b0a9cc53998f#idiq=6434642&edition=3580964 best linear algebra book ive ever read

[fading flint]

Imma search more though

physical copies hit more

[willow merlin]

why not buy used

I am from argentina and I buy used books for 10$ , if that is too expensive why not read the pdf?

[fading flint]

I dont have any problems with used books

just the shipping that makes a 10dollar book turn into a 100 one

[willow merlin]

but you looking for books in portuguese or in english

[fading flint]

I've been in english

There's this language barrier

but I think that I will just surrender to pdfs

Do you think that stewart's book is a good start?

[willow merlin]

I mean is a longass book stewart and it has great exercises but lowkey I still prefer spivak though its harder

I have similar problem, usually the books that get translated to my language are not the best but I still read regardless if its a good book or not and then compare what I saw in these books with the material on the pdfs in english

[fading flint]

The problem is that regardless of the language, mathbooks are really expensive here

for some reason

[haughty walrus]

The fourth one, that's a good book

[fading flint]

I had a bunch though ,but grandma threw them away

[willow merlin]

I thought the same but the prices on the internet are different than prices of used books in real person at least here, I used to buy a lot of books in fb marketplace but stopped doing that since is expensive and ended up going for local used books fairs

still if that is still too expensive, maybe printing in black and white from the pdf can help

you can also get your copies of the pdf ringed together

[fading flint]

Even being expensive I think that Im gonna get the money for 1 really good book

[willow merlin]

which is?

are you trying to learn precalc, calculus or real analysis?

[fading flint]

calculus

I've learned precalc in pdf

[willow merlin]

what about thomas calculus

[ruby lodge]

Guys do you have any good rigorous books on vector calculus that prove everything?

I can't find a rigorous proof of green's theorem without having to study the whole field of differential geometry (which i can't)

[trail hemlock]

baby spivak

[fading flint]

the thing with thomas is that I struggle proving things

[ruby lodge]

There are many good books about proof writing

Maybe you should start with that

[fading flint]

maybe I should put more effort on that

[willow merlin]

lang calculus of several variables has a green chapter with proof iirc

[ruby lodge]

How To Prove It: A Structured Approach is really good

[fading flint]

thanks

[ruby lodge]

i'm looking at it right now, but it just proves it for very simple domains

[trail hemlock]

id like to add jay cummings has an excellent proof writing book

[ruby lodge]

Agree

[charred vigil]

someone can recomend me a book with basic to complex mathematic problems?

[trail hemlock]

what topic in math?

and what level

[charred vigil]

secundary level

[trail hemlock]

like middle school?

[charred vigil]

yeah

[charred vigil]

it doesnt care

i just want to know more

[ruby lodge]

why don't you try looking at some olympiad level problems?

there are many, ranging in difficulty

a good website is art of problem solving

[trail hemlock]

https://www.amazon.com/After-School-Maths-100-Challenging-Problems-ebook/dp/B07QFWSTDD
this is a good one

by middle school i mean 6th to 8th graders, who are younger than 14 btw

[charred vigil]

thanks,

[trail hemlock]

just to clarify. for more advanced problems, consider
https://www.amazon.com/Problems-Algebra-Training-Team-Enrichment/dp/187642012X

[charred vigil]

and in what level of english they are, because im from a hispanic country

[trail hemlock]

these books are written exclusively in english as per my knowledge

[charred vigil]

ok

thanks

[trail hemlock]

whatever country you are from, i am sure you can find a book publishing a lot of olympiad level questions from whateber national exam there is

in your native language

[charred vigil]

ok, thanks

[strange sentinel]

Spivak is good but it's not for everyone

Specifically, most people don't want/need an intro to calc that hard

[lapis barn]

Greetings, i have a few questions

(i) for people who have read spivak's calculus, what are the prerequisites of the book beside basic proof writing skills? i know it covers/reviews many of the topics, but still would be nice to know. (please mention the exact topics rather than just "basic algebra" or "basic trig", which isnt really helpful)

(ii) any good book for latex? something not too big or too small, it should preferably discuss text layout/fonts and graphics in depth.

[ruby lodge]

(i) You basically have to be good at everything precalculus: polynomial equations/inequalities, algebraic manipulations skills, properties of real numbers, functions (for example, can you solve x^3 + x^2 + x + 1 > 0?. Can you show that if a^2 + b^2 = 0 then a = b = 0?. Is f(x) = x^2 + x an injective function? Is it surjective?), trigonometry (what is sin(pi/6)? Can you solve sin (2x) = 1/2? Can you solve sin x + cos x = 0? And sinx cosx > 0? what is sin(x + pi/3)?)

In other words, you have to be able to solve every question (or almost every question) in a precalculus book

[lapis barn]

havent done functions yet sadly, other questions, i can.

[ruby lodge]

I suggest you to learn about them before trying to attack spivak

[lapis barn]

alright, if i can solve every question of paul's online notes (the precalculus section), would that be sufficient?

[ruby lodge]

In my opinion, you should choose a random precalc book and spend some time on it before moving to precalc

[lapis barn]

https://tutorial.math.lamar.edu/ this one, it has a bunch of problems and basic explainations

[lapis barn]

well, i need to catch up to basic calculus in a 4 months. i kind of janked out on math while programming

[ruby lodge]

it doesn't look bad

[slender cargo]

I know it doesn't sound very helpful but going through a precalculus book quickly is enough, with emphasis on trigonometry and geometry. The first four chapters of Spivak's Calculus will cover basic properties of numbers and review functions and geometry with more depth.

The calculus content does not start until chapter 5.

[ruby lodge]

TopDreg i agree, but many exercises in the first 5 chapters require a lot of ingenuity on handling real numbers

[lapis barn]

so spivak covers all the needed about numbers, functions, graphing

[lapis barn]

i did the first two chapters, and i could do most problems with enough messing around

but i had difficulty in the third

[slender cargo]

That's fine. There's a separate answer book. I think it's better to go through the precalculus content quickly and then take your time on the first four chapters of Spivak

Ch. 4 on geometry is not very well fleshed out from what I saw, hence why I suggested spending some more time on trigonometry and geometry

[lapis barn]

this was months ago, i might pick it up now

[lapis barn]

what exaclty do you need

in geometry

[slender cargo]

Just some basic intuition

Don't be too worried about it

If you're reviewing precalculus, then just do a quick skim over

Spivak has a full solutions book which you can reference if you get stuck on a problem.

[lapis barn]

yeah i guess i will just watch some videos on the precalculus topics, and use paul notes for problems

no recommendations on latex?

[slender cargo]

latex?

Like on how to write up LaTex?

[lapis barn]

yeah, i need atleast basic layouting skills and how to do graphics and stuff

[slender cargo]

Can't help you there

Not so Short Introduction to LaTex is recommended often

[lapis barn]

https://tobi.oetiker.ch/lshort/lshort.pdf this one?

[slender cargo]

Yep, that's the one that everyone suggests

[lapis barn]

thanks, will go through it

lets hope my professor is kind because i slaked off the last few months

[remote sparrow]

https://tobi.oetiker.ch/lshort/lshort.pdf

https://tikz.dev/

https://ctan.org/pkg/pgf?lang=en

same thing but the manual is in pdf form

[tight spade]

Hey

I am an 8th grader and I want to expand my math knowledge (self study)in long holidays to be able to self study physics further

So any tips

?

[narrow prairie]

learn calculus

[gray gazelle]

calculus

linear algebra

most useful fields imo

geometry too

group theory shit

stick to linear algebra/calculus for the most part though

u want to eventually develop ur calculus knowledge into multivar

statistics/probability would be pretty useful too for quite a few fields in physics

in calculus u also wanna get real good at ur ODEs and PDEs

like real real good

[tight spade]

So can U like arrange them

@gray gazelle ..

[gray gazelle]

Most important: Calculus (Multivariable, ODE, PDE), Linear Algebra
Good to have: Statistics, Geometry (Euclidean and Non-Euclidean), Set Theory.

Start with Euclidean Geometry and Linear Algebra, then move onto basic calculus (Differentiation, Integration) and work your way through calculus until you hit ODE, PDE, multivariable, then you can pick up your Non-Euclidean, stats, set theory

[tough knoll]

Bara I think you first have to do precalculus like basic math curriculum basically stay in school

Maybe get into high school first before trying it at math self study and I'm not discouraging or anything

I don't really know what you have learned by now of course

@tight spade read Harry Potter or smth for now

[strange sentinel]

Try to study high school math (algebra 1, algebra 2, precalc mostly), single variable calculus (calc 1 and 2), linear algebra (proof based or computational), and multivariate calculus (calc 3)

Differential equations are also good

[molten mason]

Lang's Basic Mathematics is perfect for you then.

Should take you maybe 1-2 weeks to go through it, you'll figure out your weak spots. Then you csn focus on your weak spots for another week or two before going to Spivak

[tight spade]

Look I have a book for college algebra which I started with , which I think is the equivalent of algebra 1 & 2

[gray gazelle]

i mean if u can understand it completely then go read it

[tight spade]

You know I like learning and I don't do anything in long holidays so I kinda want to invest my time learning

[tight spade]

Yeah I can

[strange sentinel]

Lang shill...

[strange sentinel]

Then yeah, I'd finish that first

You'll need at least algebra to do any physics

[molten mason]

College algebra is probably 80% identical to pre-calc curriculum

[tough knoll]

@tight spade I second Lang's basic math,also try this https://tutorial.math.lamar.edu/Classes/Alg/Alg.aspx
Also known as Paul's online math notes,but it's meant more like a revision than to learn for the first time

[tight spade]

@molten mason look I did some research and pre calc curriculum is college algebra and trigonometry together so I think I will learn each one separately then jump into calc

@tough knoll oh thanks I have heard about this site

[molten mason]

Yeah whichever works

[molten mason]

https://www.mecmath.net/trig/

This is a good pdf for trig

[tight spade]

Oh thanks

[trim kayak]

Hey Salagos

[tribal crow]

Hey Salagos

[willow merlin]

hey salago

[slender cargo]

Hey Salagos

[trail hemlock]

Hey Salagos

[strange sentinel]

Hey Salagos

[left cloud]

Hey Salagos

[hybrid brook]

also before jumping straight to these books i suggest getting introduced with proofs first

coz many of the high schools things are v non rigorous in my expereince

so unless u correct those it will be hard to for u write a proper proof which is what u do in olys

[strange tree]

El impa tiene muchos libros no-caros si vives en rio

[empty trellis]

https://www.twitch.tv/freedom4butterball

[tender river]

is that a book review stream?

[charred vigil]

I will take that in consideration, thanks

[agile grove]

good book for differential geometry?

[trail hemlock]

higher why the reactions

[tribal crow]

because I'm always interested in seeing what people recommend for DG, so I can add more pdfs to my folder

[sage python]

For curves/surfaces, the default is Do Carmo. He also has a Riemannian book but friends of mine who used it didn't like it

Petersen I've heard is good, as well as GHL, and Loring Tu

[gray jungle]

andrew pressley is goated too when it comes to curves and surfaces

[agile grove]

thanks

[foggy quest]

There are https://mtaylor.web.unc.edu/notes/differential-geometry-riemann-surfaces-cr-manifolds-index-theory/. Also the 3 Partial Differential Equations books by M. Taylor apply differential geometry to PDE.

[unborn jackal]

im almost done with linear algebra and was wondering what i could study after this? (i did single and multivar calc, discrete math, lin alg so far)

i was thinking about going for abstract algebra or diff eqs

[dense pumice]

Both could be very useful

[unborn jackal]

both sound interesting in their own way

[dense pumice]

In particular for abstract algebra, you'd probably want to look at group theory and/or ring theory

[unborn jackal]

oh yea if id choose abs algebra then my plan would be to just go through dummit & foote

or any other textbook

[dense pumice]

I've heard that one is dense, though I could be misremembering

You could also start learning real analysis

[abstract copper]

Second analysis

[unborn jackal]

ill start uni next year and thus will be doing real ana there

thus selfstudying it to study it in 5months doesnt really make sense in my opinion

[abstract copper]

A preparation for analysis goes a long way

[dense pumice]

Hmm, when you learned linear algebra did you do it more practically or abstractly?

[unborn jackal]

used hoffman kunze

thus no practice at all

or nearly no practice

but i liked learning it that way more

i also tried using strang parallel to it to learn how to apply the stuff i learned but i didnt like that book

[dense pumice]

Aight cool, that looks to cover most of the abstract stuff you'll need later on

[unborn jackal]

what do you mean by this

and is dummit foote the go to book for abstract algebra?

[dense pumice]

How confident are you with doing proofs?

[unborn jackal]

i think good enough/good

i dont know enough about proofs to be able to say anything about my ablilities

but the proofs ive written for textbook questions were similar to the ones that can be found in solutions

thus probably as good as they can be

[abstract copper]

Some find analysis really difficult because of the proof writing. I guess since you used Hoffman Kunze, it would probably be easier for you

[unborn jackal]

ah ok good

when i learned calc/analysis, i didnt learn it in a theoretical way

i used stewart

[abstract copper]

It also depends on what you're planning to do in Math

If you think Algebra is useful to what you're doing then go for it

Algebra review here

[unborn jackal]

oh thank you

will read that

[abstract copper]

(sry for the ping btw)

[sage python]

All good

Just

Sleep with one eye open

[abstract copper]

You just lost the game

[sage python]

You are manually holding up your jaw

[fiery steppe]

guys anyone wanna learn git, go open source and collaborate with others, you can do that with me
here is my github profile, do check guys

https://github.com/Orcus-IRL

[gray gazelle]

not the right channel ig

[molten mason]

Always room for more

[tribal crow]

[trail hemlock]

what are the prereqs for DG

perhaps i will learn DG in a few years

[modern ruin]

i like dc riemannian geo

it's fine (tm)

[mossy flume]

I'd say a course in real analysis (perhaps with some multivariable flavor), some basic point set topology, and some abstract algebra

[trail hemlock]

ok ill get on abstrac algebra

im very excited to learn abs alg

will begin next school year

[remote sparrow]

it varies depending on the book

if it's just curves and surfaces, maybe real analysis and linear algebra at most

[foggy quest]

main prereq for basic differential geometry is multivariable analysis and linear algebra, like chapter 1 and 2 of https://mtaylor.web.unc.edu/wp-content/uploads/sites/16915/2018/04/analmv.pdf.

[trail hemlock]

yes i will use tao 2 for multivar anal since rudin sucks

[normal crystal]

are you that Professor? His relative? or just appreciate his work🤔

I doubt I would've seen his notes without you recommending them before, so thanks either way

[grizzled drum]

im trying to teach myself the stats110 course but unit 5 is too fast-paced

[fresh skiff]

Well today I found Schroeder's book on analysis contains Measure theory and one chapter on DG too
Well that's interesting.

[trail hemlock]

schroeder? i barely know 'er

[fresh skiff]

Yes, Grass has studied it, he probably knows more about it

[tribal crow]

yes, Schroder covers a lot of material

[ashen compass]

ballsack shaver

[tribal crow]

he even does some applications to physics at the end, iirc

[tough zealot]

based and brazilian pilled

[modern ruin]

i like ur discord banner

[tough zealot]

thanks

[trail hemlock]

HIGHER IS SO SMART