book-recommendations

[dusk wind]

curious about how the other books look now

like ideally it'd be great to have certain topics in your pocket

[trail hemlock]

i have no idea, i just own the calc one . its really great, lots of "hand-holding"

[dusk wind]

I think these might be better than openstax actually

very clear with no clickbait

[trail hemlock]

lmao clickbait

[dusk wind]

yea a lot of books have unnecessary distractional material+colors (click my link/donate) etc

(I'm going to use this crappy format and you're going to enjoy it)

[trail hemlock]

lmaoo

[dusk wind]

don't worry about this we'll learn it in chapter 10

chapter 10

[trail hemlock]

you should remember this form chapter 4, so we will be brief

[remote sparrow]

https://www.brownmath.com/twt/index.htm

someone mentioned this a few months ago

seems neat

[trail hemlock]

yo thats so cool

reinvent the wheel 🙏

[dusk wind]

hmm apparently Feynman recommends the practical man series

[dusk wind]

algebra for the practical man quality scan

this is way more to the point than a lot of books and even khan academy

[hard viper]

I am... a practical man

[trail hemlock]

yeah i love this style of books

develop intuition not just present facts to take for granted

[steel cloud]

Recommend book for learn group actions

And is there any active reading group for algebra?

[dusk wind]

As typical with such sequences, College Algebra, Algebra and Trigonometry & Precalculus are essentially the same book with slightly different beginning and endings. So there's no point to owning all of them.

It seems College Algebra contains a strict subset of the chapters of Algebra and Trigonometry, & Precalculus is the same as Algebra-Trigonometry except that it omits the first two chapters ("Prerequisites" & "Equations and Inequalities"), it has slightly different coverage of trigonometry (removed section) and it adds a new chapter called "Introduction to Calculus".

For self-study purposes, Algebra and Trigonometry seems to be the most desirable to have, since the material in the "Introduction to Calculus" chapter from Precalculus can be found in any calculus textbook."```

[dusk wind]

https://www.nytimes.com/2023/12/05/us/math-scores-pandemic-pisa.html

apparently poor students had a good chance of outperforming more well off students

too much technology/progression making math+reading irrelevant lol

[scenic chasm]

Any recommendations for book on stochastic processes and stochastic calculus?

[rich sun]

TwT

[sick river]

it's a bit of a tome but cinlar's probability and stochastics is a great book imo

also you can pick it up hardcover for $20 rn during the springer sale

[scenic chasm]

I’m in Malaysia but thanks

[sick schooner]

Cengage calculas

[gray gazelle]

Any good book recs for lie algebra?

[remote sparrow]

there were some books and sites mentioned earlier if you scroll up a bit

precalculus books are also algebra and trig books in disguise

[mossy flume]

Beyond any sort of algebra text?

Like do you know group actions are and the basics and such?

Or do you just need an intro algebra text

[sleek ice]

Looking for several types of books:

• books for generally learning all important math (ranging over algebra, calculus, but also stuff like axiomatic approaches to natural, integer, rational, real numbers)
• 3x+1 (most up2date stuff if possible)
• mathematical stuff that is relevant to computer science

[crimson leaf]

I'm pretty sure this person is just asking for an intro algebra book. They were previously asking for reviews of undergrad books and asking for field theory and module books

[vital bane]

there's a bunch

artin, D&F, herstein, gallian

[crimson leaf]

Algebra and calculus pick what you like doesn't really matter what you read though Khan academy should be fine or just see what books colleges use. Then you should pick a book that covers proofs, Lay's analysis with an introduction to proof might be good for you.

As for collatz conjecture the up to date stuff is very far from any of this and I would generally discourage someone new to math to pursue the problem due to it's difficulty.

You could pick up some books on stuff like discrete math or a combinatorics book I'm partial to the one by Guichard.

[vital bane]

first 5 chapters of tao's analysis 1 is also good for the axiomatic approach to rationals and reals

[crimson leaf]

That's true Tao is also good if you don't know anything yet lol

[sleek ice]

1. Regarding algebra and calculus: I have no colleagues as I don't study math and am just interested in math. Any books in particular you can recommend?
2. Since I'm just interested, I don't mind stumbling upon a problem that is considered very difficult. I'm not interested in solving it (since I don't think a "just having fun learning new stuff" mathematician, if I can even call myself mathematician, will have the knowledge nor intuition to solve it). I'm just interested in seeing how the problem has been approached. Again: just fun learning new stuff.
3. What do you mean by "this" (is very far from any of this)? So there aren't any books covering the up2date stuff?
4. Discrete math and combinatorics sounds interesting. Any books in particular?

[sleek ice]

[vital bane]

i wouldnt worry about the collatz conjecture for now lol

just focus on algebra and calculus

[crimson leaf]

1. I said colleges like look at syllabuses (syllabi?) that colleges use. Then use that book

2/3.I mean that the current approaches to the collatz problem are extremely advanced. You can look at Terence Taos paper ( https://terrytao.wordpress.com/2019/09/10/almost-all-collatz-orbits-attain-almost-bounded-values/)

4. The one I mentioned is a gentle introduction to combinatorics. As for discrete math Rosen has a good book for beginners.

[vital bane]

damn im surprised there are even approaches to collatz conjecture

[crimson leaf]

Afaik this is the best so far and from what I've heard it's still pretty far off

This is way over my head though

[sleek ice]

Oh, there are lists of books that colleges use? Interesting 😄

[remote sparrow]

You might find Number Systems and the Foundations of Analysis by Elliott Mendelson interesting. It shows all the gory details of constructing the naturals, integers, rationals, reals, and complex numbers.

[sleek ice]

Yoooooo, exactly my stuff

[lean pagoda]

Numbers by Ebbinghaus et al is a similar survey of the number systems and all that jazz, though it's written more like a handbook

[sleek ice]

The Guichard one doesn't seem to sell on Amazon, is that right?

[dusk wind]

maybe aops vol 1/2

[crimson leaf]

It's free online by the author

[sleek ice]

yeah i saw that, kinda just prefer books since it's easier for me to read

but fair enough, will note that down somewhere

[tame tree]

@remote sparrow hubbard is so good

[remote sparrow]

I'm glad another recommendation went well for you

[tame tree]

sour drop = book king

[remote sparrow]

https://tenor.com/view/hata-no-kokoro-kokoro-koko-fumofumo-fumo-gif-13950252188036957509

[sudden kindle]

Thoughts on Fulton Harris?

@flat lantern any thoughts?

[broken meadow]

i had lectures following fulton harris

order of ideas was chill

[remote sparrow]

Anyone familiar with standalone Galois theory textbooks?

https://maa.org/press/maa-reviews/galois-theory-through-exercises

https://maa.org/press/maa-reviews/galois-theory-4

examples

[modern needle]

Brzeziński is good. Also I've used Leinster's Galois Theory and chapter from Aluffi. Leinster has many workshop references: "you will do this in workshops; this is workshop 3.1416 question", but overall theme is still clear — Leinster calculates a lot of examples by himself. Aluffi firstly build algebraic closure and then proof similar theorems with this knowledge

I would combine Brzeziński, Leinster — practice/lectures

[remote sparrow]

https://www.thepsmiths.com/p/review-galois-theory-by-david-cox

Footnote 1:

I once had a professor who frequently asserted in class that things were obvious when they were extremely non-obvious to me, but in his case I think he really was a genius and he genuinely didn’t understand why something had to be explained further. I turned this situation to my advantage by answering a question on this final exam with: “it’s obvious”, and got nearly full credit.

[dusk wind]

Lol where have I read this before

[dusk wind]

https://amazon.com/Geometry-Its-Applications-Textbooks-Mathematics/dp/0367187981 this seems useable, its previous edition sucked

[steep root]

need me a book on applied combinatorics 🙏

[pliant wadi]

Any good alternative to Munkres' Analysis on manifolds? Or some interesting book to supplement it as a side reading?

[remote sparrow]

https://link.springer.com/book/10.1007/978-1-4419-7332-0

https://link.springer.com/book/10.1007/978-3-662-48993-2

https://matrixeditions.com/5thUnifiedApproach.html

[dusk wind]

https://archive.org/details/algebraforuseofc00todhuoft/mode/2up No clickbait in this period

[vital bane]

Multivariable Mathematics by Ted Shiffrin

[earnest wolf]

soft question: is there a list of all channels in this server? 🙃

cause when I joined I didn't have #book-recommendations for some reason 🤔 So now I'm curious if there are any other

[remote sparrow]

rare slayyla in #book-recommendations

[tender river]

what's the secret club

[vital bane]

it's a foot fetish channel

[smoky zephyr]

there’s a few channels that fall under that category

and you literally have access to one of them…

[left cloud]

[undone rapids]

hey guys, can someone give me a great precalculus book for self studying?

[vital bane]

khan academy is what is usually suggested for precalculus

Also

wow man stein and shakarchi's analysis series seems awesome

[undone rapids]

really?

[vital bane]

oh I wasn't talking specifically to you, it was more of a comment I wanted to share with the whole channel yk

but ye

those 4 books seem really cool

[undone rapids]

ok

[fading hatch]

give me book recommendation on engineering maths please

applied mathematics?

[vital bane]

depends on what you mean by "engineering maths" and "applied maths"

engineering uses lots of different fields of math

are you looking for a mathematical methods book meant for engineers?

[fading hatch]

yes exactly neamesis

[vital bane]

if so "Mathematical Methods for Physics and Engineering" by Riely, Hobson and Bence is a really cool book that's used by a lot of physics undergrads

it would be super useful for engineering undergrads as well

[fading hatch]

i have a book

• advanced engineering maths by kreyzig
  have u heard about it

@vital bane

[vital bane]

I have heard of it but I dont know much about it

[undone rapids]

ok, but what about book?

[vital bane]

not sure

someone else might know

[quick hornet]

just use openstax

at a high school level, textbook quality isnt a big deal

openstax is good, free, and has lots of exercises

[vital bane]

this is true openstax have good books

[quick hornet]

https://openstax.org/details/books/precalculus-2e

[undone rapids]

thanks

[haughty dagger]

can someone suggest some good book for differential and integral calculus from the very basics to advanced please?

[tame tree]

spivak

[steel cloud]

Little bit

[mossy flume]

define a little bit

[steel cloud]

Like just defination 🥲

[mossy flume]

Like what text did you learn group actions out of

ok so just definition

then really any abstract algebra text will cover group actions

I like Artin

work through all the group theory stuff (not just actions) in there

[steel cloud]

Now I doing group from Artin

[mossy flume]

yea go through that

[steel cloud]

Okay

[mossy flume]

and then if you still want to do more group theory (and not look at other things like ring and field theory)

[steel cloud]

Then?

[mossy flume]

sorry Discord crashed on my laptop lol

then if you want to do more

you can look at second courses in group theory

of which there are many books

For the group theory I was doing in my REU I liked Gorenstein's text and Issac's text

[steel cloud]

Gorenstein Homological algebra?

[mossy flume]

no uhhhh

finite groups

But I'd recommend those two texts after going through all the introductory group theory in Artin (or a similar text)

[dapper root]

Doesn’t that book use xf to mean f(x) lol

[mossy flume]

such is the price to pay sometimes

[steel cloud]

Yeah 🥲

[mossy flume]

ok but in terms of commutative diagrams xf is better

[steel cloud]

Issac which one?

[mossy flume]

Finite Group Theory iirc

[steel cloud]

Which topics I should cover?

[mossy flume]

I mean Artin gets decently deep

[steel cloud]

A graduate course Issac Martin review?

[steel cloud]

Okay

[mossy flume]

It's just called "Finite Group Theory"

[steel cloud]

I think there is another book of Issac Martin

[mossy flume]

Oh no no

Issac Issacs lol

https://bookstore.ams.org/gsm-92

Oh his middle name is Martin

did not know that

[steel cloud]

Thanks

[fierce hedge]

If you just want group theory, "An Introduction to the Theory of Groups" by Rotman is also good

[steel cloud]

Okay and for semi-groups?

[mossy flume]

I mean in what context are you trying to learn about these things

[steel cloud]

May be I like to do this

[mossy flume]

That's not what I mean

Like are you trying to just learn algebra, or is there a particular area of math you're trying to learn about?

Just trying to understand the focus on group actions and semi groups

[steel cloud]

Can I DM you?

[crimson leaf]

Realistically you should probably just read artin first

[steel cloud]

Just trying learn algebra not particular

[crimson leaf]

Get your feet wet before trying to collect 20 different books on groups

[mossy flume]

^^^^

Just work through Artin

Don't focus on groups

[steel cloud]

Means?

[mossy flume]

Means like don't try to go down this rabbit hole of only group theory

Just work through Artin

All of it, not just groups

Rings, fields, etc

[steel cloud]

Yeah I will

[mossy flume]

And then after with a strong foundation maybe look at second courses

[steel cloud]

What's second course?

[mossy flume]

Who knows maybe later down the line you'd rather learn like ring theory, or Galois Theory, maybe group theory, or a different area of math

[crimson leaf]

You could spend a lifetime reading about groups there's so much literature on the topic

[steel cloud]

I completed rings and fields but not from Artin

[mossy flume]

oh what why didn't you say that

[crimson leaf]

What book did you use?

[steel cloud]

Gallian, Herstein, Dummit

[mossy flume]

Wait but you only know the definition of a group action?

Have you learned things like orbit-stabilizer, burnsides lemma?

[steel cloud]

From Gallian , little bit knows about orbit-stabilizer like I did Gallian first then I did rings from Herstein and Dummit

I did not try group theory from Dummit

I think groups actions is not covered in Gallian

[mossy flume]

Hm ok I still think work through Artin

skip over whatever you already know

and then you'll have a strong foundation to go into more specific areas

[steel cloud]

Okay

[lime sapphire]

what you've chosen isn't bad at all

the main idea is to get started

go at your own pace

stay consistent

there's no pressure of being able to do a certain level of math so fast from anyobe except for yourself

[lime sapphire]

a lot of people get lost in finding "the best resource"

phys without calc is mostly there to test your problem solvibg which you can strengthen through your math

Great honestly

no worries

[molten mason]

Basic Mathematics is essentially a pre-calc book and would be a great step before Friedberg

[slender cargo]

When you go down the math rabbit hole you'll eventually have to decide if you want simply enough math to learn physics, or to go into proofs, which leads to a much deeper study of math (and can help with understanding more advanced physics). Lang's Basic Math gets you more so started on proofs compared to other pre-calc books, so I hear.

[crimson leaf]

If you're algebra 2 you'll probably be comfortable going straight to precalc

[slender cargo]

I personally would wait to learn Calculus before opening up a physics book.

Spivak's Calculus is the most well known Calculus book that takes a proof-oriented approach, proving all of the theorems and getting you to become more proficient at proofs yourself. If you would rather go at it faster and not deal with proofs at the time, then I think Stewart is the most well known, although there's probably less expensive alternatives. And if you do study from a book like Stewart, there are dedicated books that will get you up to speed on the proof side of things if you later want to go that route.

Newton's Laws deal with concepts that come from Calculus, so yeah. If you want to go at the subject honestly, you need to know Calculus first.

At a minimum you would study Physics and Calculus side-by-side.

[dusk wind]

I did Physics without Calculus but it certainly helps

Physics is also much more enjoyable than any other topic in math

[vital bane]

calculus originated with newton's laws lol

newton invented calculus! (of course Leibniz also did at the same time which is crazy)

[median saffron]

Nope not electromagnetism

That shit sucks

[dusk wind]

eh I didnt mind it too much

[vital bane]

[dusk wind]

[distant bronze]

I’m taking precalc this year and I want to take calc bc next which is basically calc 1 and 2 I’m pretty sure, what would be good books for self study? Wanted to get one so I’d have something to do over winter break

[vital bane]

calculus books?

[magic hollow]

Calc in 15 mins a day is decent for knowing a good chunk of calc AB within a few hours

[tacit heron]

https://drive.google.com/uc?id=1bYj4MVTmxnwT1vk7G7GOYxBviDThwOOw&authuser=0

[stiff tulip]

any reviews on Stochastic Differential Equations by bernt oskendal

[mossy crow]

Can anyone recommend me some good books for learning different methods for solving integrals?

[vital bane]

"Inside Interesting Integrals" by Paul J nahin

[mossy crow]

I'll check it out

[golden dagger]

isnt that pirating or am i dum

[lime vessel]

They're publishing them for free

[golden dagger]

ok

thanks

[dusk wind]

openstax sucks don't use them

[quick hornet]

as opposed to all those high-quality precalculus textbooks out there like...

like i am not a particular fan of openstax either but its not like precalculus demands a high standard of pedagogical rigour lmao

[dusk wind]

there are critical errors in their books, it is not worth it

[quick hornet]

like?

[dusk wind]

like missing information or not fully explained

[quick hornet]

i wanted examples

[dusk wind]

You can look at reviews or read the books yourself

[quick hornet]

i feel like youre consistently more concerned with being "right" than being helpful

whenever you participate in this channel

[dusk wind]

oh I'm helping you plenty

but you also have the capability to read or elicit trust

[quick hornet]

you provided neither a single example nor an alternate recommendation despite being asked for both multiple times

[dusk wind]

this is an example

their books are public, you can check for more info

[quick hornet]

i wanted a concrete example of a "critical error" in their precalculus book

[dusk wind]

for recommendations, don't use content mills for books

[quick hornet]

that is also not an alternate recommendation lmao

[dusk wind]

the thing is there are other projects like openstax (which also suck)

[quick hornet]

i do not care

[dusk wind]

better to just use some random assigned text for your course as its safer

[quick hornet]

if you think their precalculus book is significantly worse than other options, either provide an other option or point out something specific that you think the precalculus book does poorly

[dusk wind]

Ok so I had the misfortune of having been assigned these books before

[quick hornet]

otherwise your standpoint is impossible to discuss or take away anything concrete from

[dusk wind]

And you are right that any book is fine, but I have recommended other precalc texts before, just pick any open source or cheap book from your fav professor

[pliant wadi]

Thanks! The suggestion helped.

[modern ruin]

sorry like what do precalculus books even contain? i think when i took precalc i didn’t use a book because it was just a sludge fest full of random algebra topics

[distant bronze]

Yep calculus books

[vital bane]

spivak's "Calculus" is good if you want a hardcore calc book

if you dont like that then you can use Thomas' calculus

[distant bronze]

alr I’ll check them out, also what would be the best place to look for them?

[vital bane]

I dont condone piracy 🫡 But just google it and you'll find a pdf of the books lol

[distant bronze]

Ah lol

Definitely not gona do that them and I am very honest🙂 👍

[distant bronze]

So for him I noticed that here are like 15 editions, does it matter which one I use?

[marble solar]

You can find old copies of Thomas' Calculus for very cheap

I wouldn't even care too much about the edition. Any of them will do

Although early editions are really cool for historical reasons

[vital bane]

what do you mean?

[marble solar]

Prior to Thomas' Calculus, Calculus was taught something along the lines of: Analytic Geometry, Calc 1, Calc 2, Calc 3. This required approximately 4 semesters worth of math classes. Often times Green, Gauss' and Stokes' theorems were upper division material

The genius in Thomas' Calculus was finding a way to shove the analytic geometry curriculum into the Calc 1, 2, and 3 material

There are other androgogical differences too, but it is very fascinating

[vital bane]

oh wow nice!

prior to thomas calculus as in? like before the 40s and 50s?

[marble solar]

Yep!

In fact, Calc 3 was an upper division class at many institutions in the 40s and before

[vital bane]

damn, now 1st and 2nd years take it

[marble solar]

Granted, it probably had more to it than your standard lower division calc 3 today

[vital bane]

I wonder what upper division course will become a lower division course in the next 50 years

[vast jackal]

hi i think i will go down with serge lang's basic mathematics first

[marble solar]

It's more likely to do with technology that gets moved down. Like computational modelling, using MatLab to do some basic Calculus/DiffyQ/Linear Algebra thing

[vast jackal]

i need a new book

whether if the topics are on a one book im good

or like many different

since my goal is to learn calc

[marble solar]

Where are you currently at in your math journey?

[vast jackal]

integer part

[marble solar]

Do you know algebra 2, trig, and pre-calculus?

[vast jackal]

still not

im currently gr 8 (just turned 14 on oct)

[marble solar]

I wouldn't worry so much. Just pick a book that covers basic algebra and continue from there. Your teachers should be able to guide you

[vast jackal]

i want to go to my dream uni lol so that's why im studying my ass off

[gray jungle]

Category theory for middle school , dont let anyone tell you otherwise

[marble solar]

It's hard for people on discord to guide you because we don't know your strengths & weaknesses, nor what curriculum you're learning. Talk to some of the teachers at your school and they'll be able to tell you the best approach

[grave egret]

💯

[marble solar]

That's an awesome goal to have! Do you want a career in STEM?

[vast jackal]

ofc

[vast jackal]

they will just tell us the topic we need

[marble solar]

If that's the case, then try to talk to more senior students. They might be able to give you better advice

But in general, Algebra 1 & 2, Geometry, then Trigonometry is a good path for you to follow

[vast jackal]

most students in my country are low at the math skills

[grave egret]

I did algebra 1->geo-> alg2/trig

[vast jackal]

im interested of Spivak Calc

any rigorous book?

you'd recommend

[marble solar]

I wouldn't worry about the rigor. Just learn how to solve some problems!

[grave egret]

^

rigor doesnt reslly matter that much atm for you

Youre a kid

[vast jackal]

nah you need a rigor one since Spivak needs some certain level of understanding in theorems and proofs..

[marble solar]

So I used Spivak when I was a student, and I've TA'd that class many times

What I can tell you is that the students that know how to solve the problems do the best in that class

You can learn how to prove basic things in Geometry

[vast jackal]

TA'd?

[marble solar]

I helped the professors teach the class. Grading assignments, hosting office hours, helping to write exams, etc.

[vast jackal]

should i learn trig first or geo?

[marble solar]

Definitely geometry first

[vast jackal]

i did do that in my gr 6

may i ask a question? what did you take in your undergrad?

[marble solar]

I studied mathematics at UCLA

Now I'm a PhD Student

[dusk wind]

Leithold, Thomas, Antons

[vast jackal]

thats cool

[dusk wind]

An actual PhD imagine

[vast jackal]

i mean yeah awesome

[marble solar]

In math at least. Anyways, let's not flood the book recommendation channel

[vast jackal]

thanks for the advice

i will do Aops

[dusk wind]

tbh you can skip geometry for trig

aops is really good much better than khan academy

[marble solar]

The biggest thing you learn in geometry are the basic proof structure, and working in a confined list of axioms/postulates & theorems

If Klaus' main interest is learning on how to prove things, a good place to start is Geometry

[dusk wind]

it might prove to be more interesting later, after they do more algebra

[vast jackal]

@dusk wind do you have a pdf of the 2nd edition introduction to algebra?

[dusk wind]

I don't believe so, but its certainly possible to find, otherwise Vol.1-2 should be good enough

[vital bane]

I thought you had a PhD lol

[vital bane]

We need to introduce arithmetic to children via category theory

[jagged panther]

what are some good books on graph theory?

[terse mason]

yo thinking of getting this for PreCalculus self study https://www.amazon.com/Precalculus-Mathematics-Calculus-James-Stewart/dp/0357753631/ref=sr_1_1?keywords=Precalculus%3A+Mathematics+for+Calculus&qid=1703356612&sr=8-1

a good choice ? (Precalculus: Mathematics for Calculus 8th edition)

[dusk wind]

judging by the reviews it doesnt seem good

wow that price is outrageous for just precalculus

[terse mason]

ok what is a good book for PreCalculus then ?

keeping in mind I'm self studying

[dusk wind]

maybe try aops or an open source text from a university http://wallace.ccfaculty.org/book/book.html alternatives https://www.opentextbookstore.com/precalc Trig https://mecmath.net/trig or https://math.oit.edu/~watermang/math_100/100book.pdf https://math.libretexts.org/Courses/Kansas_State_University/Your_Guide_to_Intermediate_Algebra (no trig, functions only)

You can either do something with Algebra 2/Trig or a book that does all in one, with an answer key but not really necessary

[terse mason]

http://wallace.ccfaculty.org/book/book.html this link seems dead

[dusk wind]

unsecure? maybe search the link it should pop up

opens for me 🤔

some of these professors also go above and beyond in the material and have videos + answer key

none of that password bs

[terse mason]

yeah tried it on my phone and it worked perfectly fine

[dusk wind]

okay, let me know which one works best for you

[terse mason]

honestly this one looks the most appropriate https://www.opentextbookstore.com/precalc

I'm working my way up to this https://ocw.mit.edu/courses/6-042j-mathematics-for-computer-science-fall-2010/

but never touched Calculus

[dusk wind]

you never know, some writings styles might not mesh well with your learning

Just make sure your Algebra fundamentals are solid and it'll be a breeze

you might also want to study some logic on the side too booleans and such

[terse mason]

yeah I'II cover that too

[dusk wind]

people rave about this book but there are probably easier ones https://www.people.vcu.edu/~rhammack/BookOfProof/

[terse mason]

thanks !

[dense loom]

Hello, I'm looking for one or some books that covers the proof of U_{p^α} is cyclic for α>0 (p is an odd prime).
I already have a book from Ireland (it's the name of the author) written in the 80's and another from Vinogradov (1954) but I got stuck in the proof of the result in both books. I need to see more proofs, any of them, of this result.
Thanks a lot in advance

[gray jungle]

I want to shed light on a lovely book i found on distribution theory :

"Distributions, Partial Differential Equations, and Harmonic Analysis" by Dorina Mitrea

• The book is very detailed and covers all the important topics in just the right amount of conciseness ,while give all the machinery with plenty of detailed examples.
• Throws the more theoretical aspects like the Topology of D(Omega) , D_K and D*(Omega) to the appendix to give more time to more fundamental ideas.
• Appendix is comprehensive and fills the gaps needed for the subject beautifully.
• Long list of exercises after each chapter with selected solutions/hints at the end of the book.
• Builds the subject in a really simple way without glossing over the important details.

This is in comparison with other books i have read on the subject by authors including : Rudin , Folland , François Trèves and Gerd Grubb. They all seem to either cover too little or too much of the subject while missing the essence of distribution theory and why its developed in the first place.

[fading hatch]

i got my book list ready to read from a friend recommendation

1. book of proof
2. elementary linear algebra - aton
3. Steward Calculus - Early Transcendentals
4. Walter Strauss - Differential Equations

what do u guys think of it?

[rare estuary]

Sounds pretty good to me

I like Anton for computational linear algebra.

[gray gazelle]

I don't understand math in english.

[marsh ingot]

You should try to read more books of things you already know to get used

Because math in english is like 95% common

[gray gazelle]

I've gotten everything explained to me in danish my entire life, it's like learning everything from scratch when I read about it in english.

[trail hemlock]

💀

[gray jungle]

bit unrelated to language but i should say that relearning things you already learned is a good thing

but being able to learn math in english is important imo , you lose access to so many beautiful books

[gray gazelle]

It's painful.

Aristotle: ''You cannot learn without pain''

[gray gazelle]

Got like any introductory books to calculus, like for beginners.

[trail hemlock]

.

[gray gazelle]

thanks.

[trail hemlock]

in all seriousness, all of these are good books for intro to calc
https://www.amazon.com/shop/themathsorcerer/list/SKD9TCJQOZAI?ref_=aip_sf_list_spv_s_ofs_mixed_d

Also good references for calc books:
https://archive.org/details/calulusforthepra000526mbp
https://archive.org/details/TarasovCalculus
https://schtschenok.github.io/calculus-made-easy/ (dark mode 😩 )

[gray gazelle]

thanks bro

[gray gazelle]

Any book that teaches me how to solve world-problems correctly?

[scarlet steeple]

I don't know any danish but It is closely related to english so you're quite lucky

[frosty ermine]

Hey what's a good differential geometry book to start out with?

[haughty dagger]

can someone suggest some good book for differential and integral calculus from the very basics to advanced please?

[molten mason]

I have his 4th edition calculus book and loved it. I didn't realize he also had a linear algebra book, might need to cop it

[molten mason]

Pretty much any calculus book, all the modern ones are basically the same. Spivak and Apostol are more rigorous

[trail hemlock]

there are:
https://archive.org/details/piskunov-differential-and-integral-calculus-volume-1-mir
and
https://archive.org/details/piskunov-differential-and-integral-calculus-volume-2-mir
which are free 🥳
assuming you mean advanced as rigerous, there is also "Honors Calculus Book by C. R. MacCluer" which assumes prior calc experience, but takes an interesting approach to continuity

[vital bane]

depends on what you mean by differential geometry

do you mean differential geometry of curves and surfaces? if you mean that then "Elementary Differential Geometry" by Andrew Presley is good, or Do Carmo's "Differential Geometry of Curves and Surfaces" as well

But if you mean Differential geometry of manifolds

Then Spivak's "Comprehensive Introduction to Differential Geometry" seems really good you could check that out

[frosty ermine]

I think I'm particularly interested in the manifold stuff.

[vital bane]

And Lee's "Introduction to smooth manifolds" is another famous option

[vital bane]

the first volume is basically almost entirely differential topology and some algebraic topology

[trail hemlock]

i dont think there is a specific book for "word problems" but i assume word problems require problem solving skills, so:

Problem solving through problems, by Loren Larson.
Problem-Solving Strategies, by Arthur Engel.
The Art and Craft of Problem Solving, by Paul Zeitz.
How to Solve It, by George Polya.

are all good books to develop problem solving skills. i think the first two are for higher levels of competition

[unique pumice]

One of the books I admired was “one million digits of pi”. This book was awesome, highly recommend. I now know 1 million digits of pi and feel special. “SPOILER ALERT” The book starts off with 3.14, and the moment I layed eyes on that number, I was hooked in. I really recommend this book

[haughty dagger]

is thomas' calculus a good book for a beginner?

[dusk wind]

'Any calculus book' they all teach the same things & you can sample them

[dusk wind]

that's because math isn't english 🤣

Hold up bro is writing us in english this might be a paradox

[trail hemlock]

yeah i read the book, but honestly there was no character development at all. the ending was a jumbled mess and nothing ever seemed to resolve 😦

[trail hemlock]

prob means someone explaining something in eng, or maybe the terms?? idk

[dusk wind]

Could be another case of 100 pages

US has a monopoly on a lot of math research, that + other reasons most math texts have no choice but to be in eng at some point

not wanting to read or understand it is pure laziness

from what they wrote their english seems fine also

[trail hemlock]

yeah that makes sense

i get not understanding a foreign languahe, but maybe either the math is too difficult, or you are using the wrong book

like that one scene in the incredibles, math is math

[dusk wind]

I mean hell if Asian countries are writing curriculum in English you can't avoid it

[dusk wind]

Syndrome is woke tbh

[trail hemlock]

lmaoo

[trail hemlock]

english 🔛 🔝

and by extension, america (the inventors of english)

[dusk wind]

Leithold's books seem pretty good

[gray gazelle]

^

[maiden halo]

should've been obvious that's what he meant

[gray gazelle]

can someone recommend a book teach Some logic (at least a course in mathematical logic through Godel's theorem )

[gray gazelle]

Thank you 🙂

[remote sparrow]

A Friendly Introduction to Mathematical Logic by Leary and Kristiansen

it doesn't cover propositional logic, but you can probably read chapter 1 of mendelson or the first couple chapters of goldrei for that

https://www.logicmatters.net/tyl/

more recommendations can be found here

[dusk wind]

Get a book on FOL

[remote sparrow]

i just gave a book covering first-order logic

[lyric gate]

I second learning formal logic & proofs then pick up Apostol

[balmy crown]

I'm curious, does that book go more in depth in logic than the Book Of Proof?

[remote sparrow]

the book is free online if you want to see for yourself

there is also a review on the blog i linked and one by maa

[remote sparrow]

Book of Proof doesn't at all go into territory that would be considered mathematical logic

[heady ember]

Are there any (freely avaliable) good lecture series following Jacobson, which you guys would rec? Normally I just read my books, but I'm thinking of doing a bit of experimentation and see what works for me.

[fierce hedge]

Are you seriously gonna start with Jacobson grass?

[remote sparrow]

jacobson is a firmly graduate text that begins with monoids rather than groups

[heady ember]

Yeah, probably gonna read chapter 1 (taking a break rn) before getting back on lin alg and anal

[fierce hedge]

That's not a big issue but Jacobson is dense, probably slightly more than Rudin also for an abstract algebra book

Not a word is wasted on chit chat

[heady ember]

Eh, isn't the exposition pretty good?

Just that he doesn't ramble on?

[fierce hedge]

It's good but again, a bit dense for a beginner

[heady ember]

Yeah I know its a bit denser than say dnf

[fierce hedge]

Lmaoo, dnf is very chatty

[heady ember]

Yeah

[fierce hedge]

Jacobson is almost the opposite end

It's too efficient for a beginner is what I'd say

[heady ember]

DnF is as dry as a brick from what some have said

[heady ember]

Well, guess I'll find out

[remote sparrow]

@heady ember if you find jacobson too much for a first pass, you can use pinter or judson

[heady ember]

[livid bobcat]

Is there a book that I can use to complete calculus for my ap exam in 3 months?
cuz I searched up the courses in my country and its gonna take around 8 months to complete the entire calculus

and the other books are quite bulky and will take a lot of time

[daring lake]

You do not have to do entire books. Once you complete a topic, try solving problems. You will probably solutions for easier ones without any working, skip those. Do some moderate - difficult ones. Once you feel satisfied in the concept, go to next one. Write down important formulae and derivations which you can use for revision.

Since I do not know the syllabus, I can only provide tips on how to use a calc book.

3 months should be very plenty if you can spend like ~2 hours a day.

[wheat wind]

Hello. I'm looking for a guide about inference in first order logic, but I haven't find a good source which I can study. Anyone know anything like this?

[rapid wave]

Hi, I want to start studying complex analysis and I am looking for a good textbook one of you might recommend.

I have heard my fair share of classes, such as calculus, multivariable calculus, linear algebra and algebraic topology.

I have two main interests:
-I want to have a good, rigorous introduction into to the fundamental topics, such as differentiation, integration, the residue theorem and more.

-Another motivation of mine to start with complex analysis is qanting to understand modular forms. Therefore it would be nice if the textbook had a part on that or would deal with it.

So far I have found two recommendations:
Complex analysis by Ahlfors and complex analysis by Busam and Freitag. The latter seems to deal with modular forms from what I can gather.

One additional question I have is:
What is the difference between the following two books?

https://doi.org/10.1007/978-3-540-93983-2

https://doi.org/10.1007/3-540-30823-7

[weary violet]

RD SHARMA IS THE BEST!!!!

[novel hound]

The 2005 one is the first edition, the 2009 is the second, as it says on the image of the book cover on those links.

The preface for the 2nd edition doesn't go into details of the changes. Just says that the book has been updated to match the German 4th edition. There is no translation of the German preface.

[novel hound]

Actually, just realized that the first edition is also based on the German 4th edition, but prior to it's printing. While the English second edition is post the printing of the German 4th...

[gilded veldt]

i need book recommendations for jee advanced maths

[marsh ingot]

Advanced math in what?

[mossy flume]

JEE is a set of entrance exams in India

[marsh ingot]

Ohh I didnt know about them

[jaunty socket]

Guys, what do you prefer algebra or geometry?

[marsh ingot]

No

[graceful moon]

Really? Everything related to maths on the internet usually has someone saying it’s much easier than JEE

[marsh ingot]

Geometry tbh

[manic tendon]

Recommend me a book in Lattice Algebra

[marsh ingot]

Im from Europe and I didnt interact with ppl about math until i joined the server

🥲

[jaunty socket]

I'm new here too

I joined bc I like math

So.. hello everyone!

I would like to get to know you guys and make new friends! 🙂

[dusk wind]

It sucks to find old editions of a book more than a newer one

[marsh ingot]

Why you want older ones? New ones correct some errors

[marsh ingot]

Hello ^^

[dusk wind]

you get lost in the sea of editions/ different versions

[marsh ingot]

I just pick the first one I see I didnt wait to check the edition lol

[dusk wind]

like this physics book by halliday for example has like 3 different names

[hybrid sparrow]

This channel is only for on-topic discussion. Please take casual conversation to #discussion or #chill.

[marsh ingot]

Ohhh I see

[finite gale]

Bot really said no

[marsh ingot]

[marsh ingot]

Btw there is smth called algebraic geometry

[stuck zephyr]

lmfao

[smoky zephyr]

[dusk wind]

do physics actually

[dusk wind]

looks like Fundamentals of Physics is the one to go for

[earnest wolf]

analysis xD

we dont, we learn real analysis first 😆😆 (in eu at least)

[smoky zephyr]

very weird thing to quantify

[coral sedge]

Hi

What is the best book for starting in:

• Real Analysis
• Graph Theory

[hearty steppe]

Anyone familiar with this text https://geometricalgebra.org

[modern ruin]

to me algebra is just a tool

that you can use to study geometry

oh boy i can’t wait to enter higher standards of mathematics

[willow adder]

b

[torn crypt]

@fickle whale

[torn crypt]

Algebra, since in many cases syntax <-> semantics

But I like studying algebra via geometry via algebra…

[willow adder]

geltroll

[fickle whale]

@slim nacelle do you have a rep theory recommendation that is on the springer sale rn

[fickle whale]

I'm actually not familiar with this but I want to be

[zealous light]

Dude are you in one?

[fickle whale]

It's got one of the few good expositions on conformal geometric algebra, if a bit dated and using the direct space rep

[modern ruin]

okay if i’m gonna be serious about it then i’ll say that algebra means something a bit different than just “equations”

[zealous light]

No

[modern ruin]

it’s more about “structures” abstractly, and studying functions between those things, so not just the number line, but maybe you only care about part of it, like the integers, or complex numbers, or quaternions, or a whole bunch of other, wackier things, like the space of “loops on a shape”, and we want to say some things that are true about all of them at once, like how you can add them together, or sometimes you can multiply them and get nice properties

[zealous light]

Structures abstractly

[modern ruin]

well they can sometimes, but that’s sort of missing the point

[zealous light]

No that’s still missing the point

[modern ruin]

you don’t always want to even if you could

[heady ember]

Look up the definition of a monoid, group, ring, or field for some examples.

[zealous light]

Equations don’t really give you a lot of information

[left cloud]

describe borel sigma algebras with equations

[sage python]

prod_{Borel sets} etc

[zealous light]

Okay that’s an even more insane description than I was going to go with to explain why equations aren’t always useful

[zealous light]

Clearly it’s just the sets of countable unions and intersections of open sets (every measure theory student has thought this at some point)

[sage python]

Lol

[zealous light]

Dami’s about to come in like “I’ve never done that”

[sage python]

My measure theory class actually proved that the Borel hierarchy terminates in omega_1 steps

[modern ruin]

well, some structures are just too complicated for equations, in the sense that you are better off spending your time trying to just do things with them rather than thinking about them with equations. Also, you can’t actually define the integers with nice equations even

[zealous light]

Yeah, if we have a definition of something without a concrete way to construct it, it’s too much of a headache to try to construct it in such a way

[sage python]

So yes I've never done that but that's because I learned that fact pretty soon after learning what a Borel set was

Could be axioms

[modern ruin]

we just use axioms, things that we assume about them

and then we work based off those

we build new statements about them that must be true given the original assumptions we made about them

then, if you can show that a particular structure satisfies those axioms, then you can also conclude all the other statements we’ve built up

how everyday are we talking

you count every day

[torn crypt]

Omega based

[modern ruin]

that uses an incredibly complex structure

the naturals are INCREDIBLY HARD to talk about if you are only allowed to use equations to describe them

[torn crypt]

Military targeting systems

[sage python]

One step of that proof never made sense to us tho

[modern ruin]

and studying the naturals requires the use of models (and monoids)

[lapis sundial]

Most maths is not going to be too applicable to everyday life in the way you seem to have in mind, but then that extends to most/all academic pursuits lol

[modern ruin]

which are incredibly abstract

[sage python]

Something something universal set in the plane with respect to a property

And somehow its intersection with the diagonal is... something

[lapis sundial]

Poggies

[sage python]

Okay let me actually try to remember how it went

[modern ruin]

sorry sharp you can skin me alive later i don’t know how to describe model theory to someone

[torn crypt]

How could they define universal laws

[heady ember]

Wdym by "define universal laws"

[sage python]

Something about how, if P is some property, a universal subset A of the plane with respect to that property is a subset
(a) which satisfies it
(b) for which every subset of R satisfying it is a horizontal slice of A

I think

[heady ember]

[modern ruin]

i think i know what you’re saying, and sort of the answer is yes

well how could you possibly know the laws which define the universe

[zealous light]

Complex numbers are used extensively wherever electrical signals are used (this is not what you meant by complex, but it still goes)
It can be achieved in a 2d number system, but the structure of the complex numbers make it much easier

[heady ember]

We are doing math, not physics so why would the relevant mathematical constructs be the laws of the universe

[modern ruin]

i mean all we can do is say “if these things are true, then this other thing is true”

[gusty smelt]

cause i made it.

[torn crypt]

If X < R is P, then there’s some x in R such that A_x = X?

[sage python]

Something like that yeah Sharp

[modern ruin]

how could you possibly know that

[torn crypt]

Sounds very generic

[sage python]

And then the idea was, if you give me some countable ordinal, call it... idk tau or some shit

[modern ruin]

how do you know that those don’t break somewhere else in the universe and you just didn’t see it?

[sage python]

Then you wanna show there's a universal set with respect to the property of being F_{sigma delta... (tau many things here)}

And somehow that guy's intersection with the diagonal will give you something new

[torn crypt]

Therefore not of countable depth

[modern ruin]

how do you know? the other day i saw the laws of the universe being broken, all the particles were having a little dance party

[sage python]

Not that it's not of countable depth but

You haven't yet "used up" the hierarchy

[torn crypt]

More like, we always have something at least rank tau+1

[sage python]

Like if it stops at tau, not it odesn't you can go to tau + 1

[zealous light]

There has been no observed evidence of antimatter, and that is part of what some scientists use to explain discrepancies in gravity

[sage python]

Yeah

[modern ruin]

the real answer is that we don’t know, and physics isn’t math!

we just sort of assume that these things are true

and we try really hard to get it right

[sage python]

And then omega_1 should suffice because we're taking countable unions and shit

qed

[torn crypt]

The countable limit ordinal steps obviously add something from below because union of everything below wtv

[sage python]

Lemme find it actually

[torn crypt]

Or at least do limit+1

Making that universal set sounds like the hard part

[zealous light]

He’s getting there

[sage python]

Well okay so

The part that none of us could ever end up figuring out was

[zealous light]

Yes, basically

[modern ruin]

i mean what do you mean? there are a whole bunch of philosophies surrounding the existence or non existence of mathematical things

[sage python]

If the property P is "membership in a given Borel class"

[heady ember]

So what if they're not "present" in this world

They're interesting in their own right

[sage python]

And A is a universal P-set

Then diagonal intersect A satisfies P

[heady ember]

[modern ruin]

[torn crypt]

Why would it

[sage python]

While complement of diagonal intersect P doesn't

This is what we have yet to figure out

[heady ember]

Math \neq irl.

[modern ruin]

the integers obviously exist

[heady ember]

You can construct all sorts of groups assuming ZFC

[zealous light]

You’re trying to conflate abstract mathematical ideas with reality, which leads to things that don’t make sense

[heady ember]

By assumption, the naturals exist

[zealous light]

Mathematicians study abstraction because it helps understand less abstract objects

[torn crypt]

Ok try rotating around 0 to make the diagonal horizontal? Does that rotation preserve borel hierarchy?

[modern ruin]

integers are when you count things

but they’re an example of a structure called a ring

so rings exist

you can see one

it’s the integers

idk we weren’t having an argument

i was trying to tell you what algebra was

yeah

but studying the ring axioms gives us useful things about the integers

so we study the ring axioms

and then we can count better

this is what algebra does for us

this is a lot!

it’s a really big step in mathematical maturity

[torn crypt]

If this works, then rotating slicing (via translating) and un-transforming would get you as desired?

[modern ruin]

sounds good

linear algebra studies vector space axioms

[zinc sundial]

that's just 6 nouns in a row you can't fool me

[torn crypt]

@sage python does intersecting with the diagonal get you the next step up, or what gets you the tau+1 rank set?

[zealous light]

Reacting with a 🤡 emoji requires a well written response as to why you reacted in such a way or swift moderation action will occur

[modern ruin]

lol

they’re joking of course

i do find it funny that you clown reacted though

sharp is always saying clownable things around here

[lucid shoal]

Does anyone have book recommendations? Always looking.

Like for real ALWAYS-.

[sage python]

@torn crypt here's the screenshot of the notes from that bit

[torn crypt]

“I don’t know why this is the case” lmfao

[sage python]

Oh wait hold up one sec

Let's move this elsewhere since this is no longer book talk

[hardy kindle]

Calculus for the practical man by tompsan dont know ehich copy but its on amazon and some dude on youtube has it in shorts. One of the first ones

[vapid skiff]

i'm a highschooler considering reading baby rudin
is it most likely going to be too advanced for me or should i be good

[crude sage]

@sage python Sorry about the ping. In your pinned algebra book review, you mention D&F can theoretically be done without "serious" linear algebra. Does this include anything other than the coverage of a typical intro LA course (up to and including diagonalisation)? If that's too vague, I specifically mean all the LA in chapters 1-4 of Artin

[modern ruin]

@sage python i’m not sorry about this ping i just wanted to ping you, but you should answer that question it’s a pretty good one

[sage python]

Oh yeah I'm sure you're fine in that regard

Like... for getting started in D&F you mostly need to know the linear algebra needed to work with matrix groups

So knowing about orthogonal maps, determinants, etc

[crude sage]

Coolio, thank you 😄

[daring lake]

I dont think rudin is good for first read, esp. at high school

You can try a proofs book first to get an idea how things work. Something like Jay cummings proofs book is very gentle. If you want to jump to analysis, Tao or Bartle & Sherbert is better for first read

[dim sierra]

im in high school as well and its safe to say i dont think rudin would have been good for me as a first read

id recommend u read abbots understanding analysis. its very friendly, also you should supplement ur reading with lectures by francis su (can be found on yt). these lectures follow rudin but abbotts book also does the topics in a similar order to rudin just in a more friendly and less terse manner

[daring lake]

Its terse. In HS we spend time in computations and formulae, so something very rigorous might be difficult. Though yes, if they can understand rudin's method of writing proofs then yeah, not a issue. I personally really like his writing style.

Funnily enough, I think Rudin's Real and complex analysis (RCA) is less terse than PMA

[dim sierra]

what do you like about his writing style

[daring lake]

I am having a much nicer time with RCA

[dim sierra]

just trying to understand what people mean when they say this

[daring lake]

very slick. most authors over explain imo. But rudin just writes enough, that it makes me think for a while and when it finally clicks, i understand the elegance in his proof. Also amazing problem set at end of every chapter

Yes, both PMA & RCA

[dim sierra]

what are some books you think “over explain”

[daring lake]

idk, Tao, it felt like reading a novel ngl

[stiff tulip]

What do people think about Zorich's analysis

[dim sierra]

I haven’t read it but I’ve heard it’s incredibly detailed and rigorous

[stiff tulip]

I liked it

We used it in my analysis class

[daring lake]

Rudin completes his proofs. its not left as an 'Exercise to the reader' which is very huge

[stiff tulip]

and when i got a new prof, who was pretty dog shit and absent all the time spring quarter, Zorich's had the best explanation of smooth manifolds

[daring lake]

do not go to google and do not accidentally type book name + pdf

i got hardcopies though

[dusk wind]

@gray gazelle of those books you read how did the old ones fare against current versions?

[trail hemlock]

idk if this helps, but when i finished singie variable calc, I started with "Real Analysis: A Long-Form Mathematics Textbook" by Jay Cummings. Baby rudin is very advanced, so I would say go through real analysis at a snails pace because since ur still in high school, your maturity would be a little low (maturity = experience)

[dusk wind]

If possible try to get really solid in Algebra then branch out into stats, there's no rush to learn calculus but the more subjects you learn the easier it'll be especially if your Algebra is good

[vapid skiff]

this is helpful ty

[trail hemlock]

but calculus is so ✨ cool ✨

[dusk wind]

There are some really great Calculus books that take an algebraic approach and can serve as an excellent introduction

[trail hemlock]

honestly to learn intutively and rigerously, i think the Aops Calc book is really good: they force you to prove and derive stuff before presenting shortcuts (which are also derived).

idk tho maybe thats all calc books and im tweakin

[dusk wind]

A few days ago we literally hunted down some of these books and it turns out some of these older ones are kinda good for that with a low page count/more clarity. Like Calculus for the practical man or https://schtschenok.github.io/calculus-made-easy/ orr https://archive.org/details/calculus7ofsingl0000leit/mode/2up

[trail hemlock]

aye good shit

💀

[dusk wind]

I noticed theres a lot of clickbait in some of the new books released now

Also other unnecessary nonsense like teacher solution manuals/downloads etc

Old books didn't really have any DLC so you got the full product

that wasnt always the case though

[magic hollow]

I’m doing the class

[dusk wind]

in university the student is punished for lack of efficiency, but little actually occurs to the actual department

[magic hollow]

They don’t follow the book at all

[trail hemlock]

luckyyyyy

[magic hollow]

They ignore all of the rigorous stuff

[trail hemlock]

😦

what

[dusk wind]

Yeah this is what modern gaming looks like

[trail hemlock]

when they derived the definition of the definate integral

shi was revolutionary

for me

[dusk wind]

skip this you dont need it

[magic hollow]

They used some random area accumulation thing in class

Idk if they did that in the book

u sub as of last class

[trail hemlock]

yeah u sub is straight algebra

u-substitution

yuhh

[magic hollow]

We skipped epsilon delta stuff

[trail hemlock]

:((

what

when the book deals with delta epsilon i think i had a stroke

but its ok my boy blackpenredpen got me

[magic hollow]

Same

[trail hemlock]

damn

smart

im ngl

this aint no book discussion

[magic hollow]

Learning it rn

Know most of calc 1

Precalc I guess

Aops

School won’t let me

Yes

[trail hemlock]

they have online classes

yuhh

[magic hollow]

And In person

[trail hemlock]

lots and lots of money

sadly

[magic hollow]

Sad

But probably worth it if you can’t learn anywhere else

[trail hemlock]

to be honest, its not worth it for me. i learned more algebra from a book than than class ever taught me

shi was 100% useless

[magic hollow]

I don’t have motivation

So I need classes

[trail hemlock]

💀 me neither. but my pen and book are infront of my keyboard, so i cant play games

[magic hollow]

I just end up on discord

[trail hemlock]

bro 💀 same

wait

thats me

right now

fuck

[magic hollow]

Yeah

[trail hemlock]

its ok im on the same page for 2 days

shi noit making sense

[magic hollow]

What are you learning

[dusk wind]

imagine being able to eat while attempting to learn math

[trail hemlock]

no cuz ill destroy my paper

[magic hollow]

I can

[dusk wind]

either math or food

you cant have both

[trail hemlock]

analysis rn..

shi not making sense

[dusk wind]

being stuck on the same page is good its progress

[magic hollow]

Are you going to join zorn’s class?

[trail hemlock]

yes i hope so

cuz im lost like atlantis rn

[dusk wind]

LOL

[magic hollow]

Same but I’m trying to audit and not actually take it

[trail hemlock]

🤣

lol

[dusk wind]

that movie was animated so well

[trail hemlock]

ok wait

i think im making progress

[magic hollow]

Nice

[dusk wind]

great

[trail hemlock]

🥳

revolutionary

[dusk wind]

now you made it past 1.5 pages

[trail hemlock]

yuhh

[dusk wind]

now you have to steal all of newtons ideas

[trail hemlock]

did 50 pages (its been 3 weeks 💀 )

[dusk wind]

and run him for his lunch money

[trail hemlock]

LOL

[magic hollow]

How many hours of khan academy should I do tomorrow

[trail hemlock]

i can intuitively prove stuff, but i never understand how to make it rigerous, all my calc experience is competitive calculus so i never needed rigor just intuition

[magic hollow]

Same

[trail hemlock]

khan academy fake. lock urself inside attic, dont leave until you have singlehandedly rediscovbered all of single variable calculus

[magic hollow]

Besides for a little bit of stuff

[trail hemlock]

bro the proof long form textbook saved me

[magic hollow]

How will I know if I’m missing something

[trail hemlock]

i can prove shit now

[dusk wind]

"I discovered it first"

[trail hemlock]

shi is a superpower

got me feelin al types of ways

[magic hollow]

I can’t prove anything

[trail hemlock]

good point. u gott start at the star of math and work ur way INTO calc

[magic hollow]

Can you send example of a proof

[trail hemlock]

ay a cristmas party

look on here tho

https://proofwiki.org/wiki/Main_Page

[magic hollow]

What if in this new math calc doesn’t exist

[trail hemlock]

u did smth wrong then

ok wait dont lock urself in attic

cuz how are u gon get food?

maybe pantry or supermarket are beter options

[remote sparrow]

it's not "too advanced" in terms of the formal math, but it's probably too difficult to learn from

[magic hollow]

What if this math only contains positive integers and addition

How should I know if I missed something

[trail hemlock]

cuz u gotta tune the negative haters out

good thinking

[magic hollow]

A student in my math class argued against the use of negative numbers for about 30 mins one day

[trail hemlock]

💀

[magic hollow]

Teacher kinda agreed

[trail hemlock]

💀

noo

[magic hollow]

It’s painful being in that class

[trail hemlock]

fr my math class is pure brainrot

[magic hollow]

And the student is the type to brag about his grades

When he gets 0.5/4

On tests

[trail hemlock]

lmaooo

my school hates me tho

cuz i self studied the ap exam

and they still made me take the clas

😦

[magic hollow]

F

My school might let me skip Ap calc

[trail hemlock]

luckyy

[magic hollow]

50 50

[trail hemlock]

i gotta sit in that brainrot class and listen to the teacher yap all day

[magic hollow]

What grade are you in?

[trail hemlock]

10th

[magic hollow]

My school usually doesn’t let people take any calc until 11th

I am in the worst school

For those who are kinda decent at math

The only good this is the graduation rate

[trail hemlock]

im actually terrible at math 💀

wrote polygamous instead of polynomial by accident

[magic hollow]

Wait this is book recommendations

I thought this was the chill chat

Mods don’t ban me

[trail hemlock]

we were discussing a novel we read

pls trust

[magic hollow]

An autobiography

Of our lives

[trail hemlock]

for calc, i "legally purchased" Honors Calculus by C. R. MacCluer cuz its very very terse

[magic hollow]

F

[trail hemlock]

oh my school has one of those "advanced placements" thing so we can take classes sooner

[magic hollow]

My schools stats are in chill

[trail hemlock]

thats actually dumb

yoo its the next day for me

[magic hollow]

You’re from the future

[trail hemlock]

yeah

[trail hemlock]

relax the mods are gonna attack us if we keep chatting in #book-recommendations

nah idk if they are but they prob are

seems to be ig

[remote sparrow]

if not out of concern for moderator action, then at least as a courtesy to people who are here to discuss books

[remote sparrow]

there aren't that many results for zorich, so you can probably browse through hits for "zorich" in discord search

[trail hemlock]

aye mb mb

[wise falcon]

what the square root of x

[trail hemlock]

like 3.6

[cold elbow]

book recommendations became discussion-3

[gray gazelle]

can someone recommend me good lecture resource for learning hyperbolic trigonometry

[thin meadow]

Where can I find the answers to the book "Number systems and the foundations of analysis"?

[gray gazelle]

just google the question

it should lead to the relevant math stack exchange post

[blazing badge]

IS RD SHARMA GOOD FOR CLASS 8?

[native cradle]

examplar or agrwaal is better IMO

when I was in 8th I used RS agrawaal, less problems, higher quality

[dusk wind]

seems good for precalc https://archive.org/details/beforecalculusfu1989leit

[manic cairn]

this opinion makes me sad.

i am tired of the 10 billion full-color books in their 10 billionth edition.

i honestly think that the ap test prep books (at least for the stem subjects) are more informative, cheaper, and less busy than reading most textbooks meant to be teaching those subjects. that’s not even mentioning the fact that 30% of those books are just mock exams!

openstax is amazing, but i don’t think it means we should be trying to write better textbooks for hs

[finite gale]

I think you might as well just say that the ap math curriculum just sucks

[dapper root]

Hi tubu

[finite gale]

Hi chmuwu

[dapper root]

Did u eat

And drink

[dusk wind]

openstax sucks actually

better off using a regular faculty book

[remote sparrow]

This book is somewhat obscure, so I doubt any solutions exist on the web.

https://www.youtube.com/watch?v=UiKgy9rLviA

[manic cairn]

amazing is too strong of a superlative in general, but compared to the books i had to use in school, they are much better.

[remote sparrow]

there's this guy working through this book; you might be able to ask him for help on a few problems

[dusk wind]

considering they are glaring with errors your mileage may vary

a lot of their content is also borrowed/remixed too

so not really any different from those other books you mention

[manic cairn]

i think the princeton review test prep books are the best for learning the subject because they are forced to both

1. contain all the requisite material
2. contain nothing else other than mock exams and exercises

other books are marketed to everybody, and thus to nobody

at least, compared to school textbooks

[quick hornet]

it's easy to vaguely say "it should matter", but the reality is that, as it currently exists, it doesnt

all pre-uni math textbooks have largely the same contents presented similarly

exercise volume and quality is the most important thing, but because most are just teaching to some sort of standardized test, their exercise quality ends up being very similar

i.e. problems like that on said test

[dusk wind]

in general aops or any text written for your uni should be good enough

[trail hemlock]

https://github.com/luifrancgom/number_systems

Notes, exercises and solutions from the book Number Systems and the Foundations of Analysis (2001) by Elliot Mendelson
mabe this?

[remote sparrow]

@mystic orbit turn this into a quote 👆

[trail hemlock]

#discussion 🤓 ☝️

[mystic orbit]

say less

[trail hemlock]

#chill 🤓 ☝️

thoughts on this book, for anyone who has read it?
https://ia800908.us.archive.org/2/items/ElsgoltsDifferentialEquationsAndTheCalculusOfVariations/Elsgolts-Differential-Equations-and-the-Calculus-of-Variations.pdf

Differential Equations and the Calculus of Variations by Lev Elsgots

[remote sparrow]

https://maa.org/press/maa-reviews/a-course-in-point-set-topology

[molten mason]

I was literally staring at that book 5 minutes ago on the Springer website lmao

Only 142 pages is what made me question if I should get it or not

[remote sparrow]

https://www.youtube.com/watch?v=CIQN7H6Km34

[long steppe]

Hi

I recently started getting into competitive math

any reccommendations

thx

[trail hemlock]

https://artofproblemsolving.com/wiki/index.php/How_should_I_prepare%3F

[molten mason]

I was initially confused on why Christopher Walken was talking lmao

I was looking at topology books on the Springer website and I saw Jänich as well. I think that video sold me to pick Jänich instead lol

Thanks for sharing! Was informative

[tawny copper]

https://discord.gg/3sbwZdh

[tender river]

👋

[modern ruin]

ok

[sage python]

What happened here

[lusty elk]

I have a physical copy of that book. It's nice, the author states that it's based on lectures that he'd delivered in the physics dept. but it is still fairly rigorous imo (has theorems and proofs, but plenty of examples and some nice vector field diagrams as well). The exercise problems are mostly computational however.

[trail hemlock]

gotcha, tysm!

will prob go with something a bit more modern and rigorous, prolly use this to supplement.

[manic cairn]

do you speak english fluently? this comes across like liam neeson on the phone in taken

[gray gazelle]

guys

if i get james stewart which edition is the minimum for it to be good?

[fringe torrent]

Hi guys i need a good ressources of algebraic structure please

With a lot of exercices

[long sigil]

Does anyone have any good books on Cryptography for beginners to recommend?

I'm currently getting started with Duncan Bell's Fundamentals of Cryptography and Serious Cryptography by Jean-Philippe, but I'm not sure if these are the best for beginners like myself. 🙂

Hopefully this is not off-topic, as if I'm not mistaken, Cryptogaphy has gone from being a purely Mathematical realm to being a cyborg hybrid of computing and higher mathematics.

[long sigil]

BTW, is there a good place to ask for PDF recommendations

[dusk wind]

there are plenty of good intro books on cryptography, just pick your favorite I.E finish reading those books

[trail hemlock]

🏴‍☠️🏴‍☠️

my fav

[long sigil]

Afriad of 🦠

[dusk wind]

sounds like a genetic issue

[long sigil]

I just found a good one (Introduction to Mathematical Cryptography, 2nd ed).

But I'm worried because VirusTotal claims that there's a virus hiding inside.

[dusk wind]

uhh

this isn't virus support

[long sigil]

Yeah, I know
Just asking if you have any resources for that book

[dusk wind]

yea

google.com

[long sigil]

Already tried, all had 🦠

It's fine, as long as it's a book you'd recommend

I'll find a way around it LOLOL

[trail hemlock]

idk if i can recommend🏴‍☠️🏴‍☠️ sites on here

[dusk wind]

ability incoherence

forget reading 100 pages

[long sigil]

Just saying that it's OK if you can't recommend 🏴‍☠️

[dusk wind]

read the first sentence

[long sigil]

What about the book itself, do you think Introduction to Mathematical Cryptography, 2nd ed is good?

[dusk wind]

idfk

[long sigil]

.

[dusk wind]

theres too many of those books to count

[long sigil]

I see

[dusk wind]

anything you can learn from is good

so just use google

[long sigil]

I'm just worried I will end up working with holes in my knowledge. I already made that mistake once before, I don't want to do it again.

[dusk wind]

that wouldn't be the books fault but your own

[long sigil]

nvm, it's ok

[dusk wind]

get a good book

[long sigil]

That's the issue, I'm not sure which is good for a beginner. I know there some excellent phd-level books out there, but that won't really help me.

It's OK, let's just stop here, I get your message

[dusk wind]

besides that field is very broad so you most likely won't learn everything from just 1 resource

[maiden halo]

I think any "semi recent" one should be fine

[molten mason]

I have a calculus book from 1993 and it's roughly identical to another one I have from 2020.

Any edition is fine, not much has changed.

[mystic orbit]

nothings

byee

we'll miss you 👋

[dusk wind]

@gray gazelle Do what this guy says and get a book from the 90s, no clickbait and probably better than Stewarts

[vast jackal]

internet archive

[long sigil]

Thanks, I'll get on it!

[vast jackal]

almost all of the books are in there i don't know for the new ones yet

[gray gazelle]

rlly? I was considering thomas finney

[vast jackal]

do ones from Mir publishers

they have lots of good books

[dusk wind]

try this https://www.amazon.com/Calculus-7-Single-Variable/dp/0673469697

[maiden halo]

found this discussion of Thomas & Finney. I'm sure you can google for many others: https://www.physicsforums.com/threads/thomas-calculus-3rd-edition-vs-9th-edition.811522/

[dusk wind]

thanks to that forum I found some interesting physics books

[vast jackal]

get a rigorous one or an old book mostly all of the discussed topic is just the same as the old one and much better

[long sigil]

Hmm, which would you recommend?

[long sigil]

I mean, if Introduction to Mathematical Cryptography is a bad start, what would you recommend then? I'm definitely open to suggestions!

[vast jackal]

I'm not quite into computers these days since I'm still a high school student but you can do some computer science courses like the Cs50 im quite a fan since i know programming kek

the edx

[long sigil]

Hmm... they start with cryptography?

[vast jackal]

cryptography books are a bit bad since i think you only learn some concept stuff try to experience them

[dusk wind]

depending on their interest they could just write their own stuff

[vast jackal]

cryptography usually needed some programming skills so it's a good start to familliarize yourself with programming also

[dusk wind]

its more historical anyway

[vast jackal]

its freaking fun

[vast jackal]

yeap

[dusk wind]

in that sense every book would be different and like... you'd probably learn more from something on the history channel

[long sigil]

I already know Python, and I'm currently working with Rust. What I need is a book that teaches me Cryptography

[dusk wind]

lmao

[dusk wind]

this doesnt make any sense

[vast jackal]

@long sigil even if you searched in google most resource today is courses idk why

but doing it is much better than jsut reading it