#book-recommendations | Mathematics | Page 218

molten wave Dec 26, 2020, 10:25 PM

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that's what "mathematical maturity" is

marble solar Dec 26, 2020, 10:49 PM

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I think Rudin is really meant for someone who is in on the game

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They're like a set of rough lecture notes for profs and TAs to fill in details

gray gazelle Dec 26, 2020, 10:50 PM

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I see, I haven't been in the mathematical world in a few years, my intuition was never trained towards proof rather just applying.

marble solar Dec 26, 2020, 10:50 PM

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There are other books that are geared towards getting you up to speed

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Some people enjoy the challenge of trying to fill in the puzzle

gray gazelle Dec 26, 2020, 10:50 PM

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so I need to develop a better intuition

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I'm guessing tao is a better and easier appraoch for me probably

sage python Dec 26, 2020, 10:50 PM

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Tao's probably a bit too drawn out tbh

marble solar Dec 26, 2020, 10:50 PM

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Alternatives are like Pugh's mathematical analysis, apostol's mathematical analysis

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Or sloth king's igor

sage python Dec 26, 2020, 10:51 PM

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Idk Apostol, Pugh is good though his chapter 2 is awkward af

marble solar Dec 26, 2020, 10:51 PM

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Apostol's text is basically Rudin with details added

sage python Dec 26, 2020, 10:51 PM

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Though afterwards it seems to pick up quite a bit

marble solar Dec 26, 2020, 10:51 PM

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There's a lot of stuff in there on fourier series, boundary value problems, bounded variation

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It's a solid text

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I found a first edition for pretty cheap

sage python Dec 26, 2020, 10:53 PM

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Here they use Apostol for calculus actually instead of Spivak

marble solar Dec 26, 2020, 10:53 PM

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Apostol's a more difficult read, with some more focused problems

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His volume 2 for multivariable calculus is absolutely beautiful

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Also, doing integration first is something I'd like to try

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I learned differentiation and integration at the same time

sage python Dec 26, 2020, 10:54 PM

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Integration first hmm

marble solar Dec 26, 2020, 10:54 PM

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That's what volume 1 does

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Apostol's a solid author, doesn't have a bad book in his name

sage python Dec 26, 2020, 10:55 PM

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So I guess it's one of those things where, there might be a nicer logic flow? Like you start with series and then you say integration is kinda your generalization of series

gray gazelle Dec 26, 2020, 10:55 PM

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Now I'm so confused which book to start with 😛

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😦

marble solar Dec 26, 2020, 10:55 PM

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Prior to Thomas' calculus, books were split down the middle where they did integration first

sage python Dec 26, 2020, 10:55 PM

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But I guess "a priori" there are two sorta different tracks that are kinda independent and it's probably more efficient to do differentiation first

marble solar Dec 26, 2020, 10:55 PM

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or differentiation first

sage python Dec 26, 2020, 10:56 PM

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Because then you get FTC and can compute things more easily

marble solar Dec 26, 2020, 10:56 PM

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Thomas' calculus was able to shave a semester or two off of doing calculus, since there was a semester of analytic geometry

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Thomas was able to incorporate that and shove calc 3 in lower division

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I think books/courses have over committed to doing differentiation first

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There should be more of a mixture in my opinion

sage python Dec 26, 2020, 10:57 PM

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What's the advantage either way?

marble solar Dec 26, 2020, 10:57 PM

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The advantage is integration theory/integrals are harder than differentiation

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So if you do it first you can spend more time on it

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Throughout the term

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This is especially true in multivariable

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Almost no one struggles with partial differentiation

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But setting up double and triple integrals is tricky

sudden kindle Dec 26, 2020, 10:58 PM

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My intro analysis course did integration first

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We followed apostol's Calculus vol 1

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And prof notes

sage python Dec 26, 2020, 10:59 PM

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I mean if you decide in advance how much time you'll likely spend on each topic then that resolves it right?

marble solar Dec 26, 2020, 10:59 PM

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The way people learn isn't linearly in a nice theoretic way - you should spread out the topics throughout the term

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Another advantage is front-loading a course puts the hard things first, where other classes are doing easier stuff

sage python Dec 26, 2020, 10:59 PM

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You can't really really fine tune it obv because a class might eat something up or get stalled

marble solar Dec 26, 2020, 10:59 PM

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So they have more time to think through the harder things

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So that when you get to the final/end of the course, you can go back over the simpler things you skipped

sage python Dec 26, 2020, 11:00 PM

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But you can say alright I'm spending no more than, say, 3-4 weeks on differentiation

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Actually in my undergrad we had quarters instead of semesters so it was like

marble solar Dec 26, 2020, 11:00 PM

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Yeah, quarter systems are literal garbage

sage python Dec 26, 2020, 11:00 PM

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First quarter ends with differentiation

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Second begins with integration

marble solar Dec 26, 2020, 11:01 PM

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All the literature/education research shows decreased learning

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and retention

sage python Dec 26, 2020, 11:01 PM

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Do we know why quarters do that?

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I actually hard prefer quarters lol

marble solar Dec 26, 2020, 11:01 PM

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Yeah, we have a basic theory for why that is

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The idea is that to really learn something you have to forget it

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And relearn it multiple times

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You have to pick it up, put it down, pick it up again

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This is why you take a break from something for like a week or two, come back to it

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And you're better

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On the quarter system there isn't enough time to do enough cycles of this

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To have long term learning - however there are advantages to the quarter system

sage python Dec 26, 2020, 11:02 PM

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I mean in semesters is there much of that going on anyway?

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People just move on to the next topic

marble solar Dec 26, 2020, 11:02 PM

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Faster paced, you get better at solving problems faster

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If the course is well balanced, there should be plenty of that

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That's mainly from the education POV, at the grad level this seems to not have as much as an impact

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In fact, at a research level, quarters are better

sage python Dec 26, 2020, 11:03 PM

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Like from TAing calc here in Madison.. now the structure is a bit weird thanks to covid but

marble solar Dec 26, 2020, 11:04 PM

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Since you have the basics better, you can focus on getting exposure to advanced topics

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And rotate through those faster

sage python Dec 26, 2020, 11:04 PM

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In ordinary semesters I feel like there wasn't that much review going on except midterm and final

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Obv the nature of calc is such that later topics review older ones

marble solar Dec 26, 2020, 11:04 PM

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It's on the students to plan out their study for the semester. For me, there's a huge difference between semesters and quarters

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Since I have ADHD, it gives me ample time to plan out my course study

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On Quarter system it was literal hell

sage python Dec 26, 2020, 11:05 PM

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So I guess on my end, I feel like the good thing about quarter system was that you could sorta do more on the whole, and you never really felt comfortable getting too far behind if that makes sense

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Like in grad school I've definitely been feeling like, oh things are going along suuuuuper slowly

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So I never feel pressure to get on my feet and actually do things

marble solar Dec 26, 2020, 11:06 PM

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Yeah, there are advantages to the quarter system - especially at the grad/research level

sage python Dec 26, 2020, 11:06 PM

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Until wait now I just missed 5 weeks of class and have to catch up

marble solar Dec 26, 2020, 11:06 PM

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But at the Undergrad level, semesters edge out quarter for education reasons + professional reasons

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e.g. graduating in may gives better employment opportunities/internships

sage python Dec 26, 2020, 11:06 PM

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And I just wing it for the sake of tests and psets and not really learn things well

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While in undergrad if I missed 3 days I already feel like I'm fucked

gray gazelle Dec 26, 2020, 11:07 PM

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So should I do Pugh or Apostol?

sage python Dec 26, 2020, 11:07 PM

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And that's enough of an ass kicking to get on top of my shit

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The disadvantage of quarter system at Chicago in particular (or maybe it's secretly an advantage idk) is that classes differed on whether they had 2 midterms/semester or just 1, and when

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So basically half the quarter was midterm season lol

marble solar Dec 26, 2020, 11:08 PM

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Yeah, that was the other thing for me

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Constant exam stress just burned me out

sage python Dec 26, 2020, 11:09 PM

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Now I haven't had many tests in grad school

marble solar Dec 26, 2020, 11:09 PM

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Whereas on semester I could mitigate it

sage python Dec 26, 2020, 11:09 PM

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So I can't really say whether having a single week or two with 4 exams would've been better

marble solar Dec 26, 2020, 11:09 PM

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I'm also a fan of dead week

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e.g. no classes/assignments the week before finals

sage python Dec 26, 2020, 11:09 PM

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We have two days lol

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Thursday and Friday of 10th week officially no required classes or assignments

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Though I think profs who wanted it had their workarounds lol

marble solar Dec 26, 2020, 11:10 PM

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"Review session"

sage python Dec 26, 2020, 11:11 PM

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Well so, many profs held honest to God review sessions

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But that's a good thing lol

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Helps study for the final

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But for example you could just give a handout before reading period and say "You're responsible for this material on the final, I'm hosting a bonus session during our normal class time if you want to go over it"

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Make the assignment due Wednesday (resp Tuesday) but you'll accept late submissions until Friday (resp Thursday)

marble solar Dec 26, 2020, 11:13 PM

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In all likelihood I'll end up at a quarter school

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Unless Austin or Berkeley somehow accepts me lol

sage python Dec 26, 2020, 11:13 PM

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Austin and Berkeley are for nerds tbh

blissful pike Dec 26, 2020, 11:13 PM

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Can anyone recommend a good proof based ODE textbook

marble solar Dec 26, 2020, 11:13 PM

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Boyce and DiPrima?

sage python Dec 26, 2020, 11:13 PM

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But yeah I mean in grad school obv things are different, you don't have as many exams and classes are kinda easier

blissful pike Dec 26, 2020, 11:14 PM

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Just finished abstract algebra

marble solar Dec 26, 2020, 11:14 PM

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I might actually have to learn algebraic topology properly : (

sage python Dec 26, 2020, 11:14 PM

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And grading is usually ez

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Zoph: Check out Perko, ODEs and Dynamical Systems

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I haven't read much of it but in analysis when we were doing some stuff a friend discovered it since it aligned with what we were doing reasonably well

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Moonbears: I've been trying to learn some homology with a friend recently actually

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We're working through Bredon

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Chapter 4

marble solar Dec 26, 2020, 11:16 PM

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Yeah, I have to learn homology and cohomology I guess

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I tried reading the primer on mapping class group

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I get like 70% of it, but there's this 30% that just references facts in alg. top.

blissful pike Dec 26, 2020, 11:16 PM

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@sage python link me plz

sage python Dec 26, 2020, 11:16 PM

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Bredon kinda has the correct logic flow for homology I feel

marble solar Dec 26, 2020, 11:16 PM

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What'd you think of hatcher?

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I like fulton, but is is a little underwhelming

sage python Dec 26, 2020, 11:17 PM

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Hatcher had the stuff there and I recall his explanation of things in homology to be at least locally decent?

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I missed a lot of lectures in my Hatcher class and mostly just winged the psets tbh

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But idk Hatcher's run through stuff seems like it is perhaps more... "motivated"/historical

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But less nicely organized

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Bredon's flow is basically

marble solar Dec 26, 2020, 11:18 PM

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Hatcher seems to be great for passing qualifying exams

sage python Dec 26, 2020, 11:18 PM

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Okay this is singular homology. Yay. Okay let's compute H_0. Now let's compute H_1

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Uhhhhh we can't really compute anything else in full generality

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Alright let's talk about the axioms of homology then

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And now let's use the axioms to compute the homology of any CW complex

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Boom

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Now let's talk about other cool things

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It's very clean like you know where it's going

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Hatcher iirc kinda presents things like

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This is simplicial homology of a delta complex. But wait is it a property of the space? What if we retriangulate or do this or that?

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Okay you know what simplicial homology needs patch notes

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Time for singular homology

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And oh hey cellular homology is a thing too that's cool!

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And now at the end let's present some formal stuff 🙂

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Which is like sure but kinda awk to me

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The nice thing about Hatcher for quals is examples

ripe granite Dec 26, 2020, 11:23 PM

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My first intro to cohomolgy was cech cohomology

sage python Dec 26, 2020, 11:23 PM

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Lmao

ripe granite Dec 26, 2020, 11:23 PM

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from Rick Miranda's Algebraic curves and riemann surfaces

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it was pretty well motivated

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from the whole mittag-leffler problem/riemann roch point of view

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and my second cohomology theory was de rham

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which is super easy to motivate

dapper root Dec 27, 2020, 12:52 AM

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My firsts cohomology theory was sheaf cohomology

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FeelsSpecialMan

steel viper Dec 27, 2020, 2:20 AM

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alex why...

dapper root Dec 27, 2020, 2:22 AM

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Cuz I am based

marble solar Dec 27, 2020, 2:55 AM

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That's a good book brofibration

ripe granite Dec 27, 2020, 3:39 AM

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it's alright

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I am a fan of it now

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wasn't a fan of it when I first read it opencry

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the exercises were either too easy or fucking impossible

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I've heard donaldson's book on it is good

ripe granite Dec 27, 2020, 3:46 AM

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ripe granite wasn't a fan of it when I first read it <:opencry:586078614865444865>

this should be taken with a grain of salt as I did not even know what a manifold was when I read it

sage python Dec 27, 2020, 4:17 AM

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Yeah Donaldson is supposed to be nice

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Apparently Miranda's more AGish, Donaldson is more topology/GGT, and Forster is more sheafsy

drifting elm Dec 27, 2020, 4:44 AM

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what do you think of this? https://www.amazon.com/Linear-Algebra-Signal-Processing-Wavelets/dp/3030029395/

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I have two DSP books already

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nothing on wavelets or linear algebra

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I have shannon's papers which are obviously the foundation

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sometimes I feel like the math in shannon is over my head

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not sure what I need to be more prepared for the DSP books

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is it all just calc II? or does it require more ODE or PDE?

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I also have these two https://www.amazon.com/Network-Analysis-Mac-Van-Valkenburg/dp/0136110959/

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https://www.amazon.com/Analog-Filter-Design-Van-Valkenburg/dp/0030592461/

gray gazelle Dec 27, 2020, 4:58 AM

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is there a concise reference of category diagrams and how to go about reading them? ie something with "here are all the possible arrows you may see", "here are common patterns to look for", etc.

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like most books have them introduced gradually in the text

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i want a quick reference

drifting elm Dec 27, 2020, 5:08 AM

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does this help?@gray gazelle

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📎 catarrows.jpg

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https://math.jhu.edu/~eriehl/context.pdf

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there is a glossary of terms and notation with page numbers

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everything is there for a beginner level

gray gazelle Dec 27, 2020, 5:13 AM

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not really

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some books use different flavours of arrows to denote onto and other things

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and ideally what im looking for would have stuff like a quick list of common diagram patterns

warped sun Dec 27, 2020, 6:07 AM

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Does anyone know a good resource for learning about the theory of modular forms?

sudden kindle Dec 27, 2020, 6:10 AM

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Diamond and Shurman?

warped sun Dec 27, 2020, 6:13 AM

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Thanks

hidden herald Dec 27, 2020, 7:29 AM

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oh, category theory in context?

gray gazelle Dec 27, 2020, 8:57 AM

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Hi

lucid lantern Dec 27, 2020, 9:02 AM

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@gray gazelle maybe Basic Category from Leinster would help ? He gives a list of common limits in the book. I guess you're looking for pullback diagrams, equalizers, etc.

gray gazelle Dec 27, 2020, 1:30 PM

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Which is a good boor for linear algebra for beginners -insel or hoffman or axler?

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All three are good, though I would prefer axler

karmic thorn Dec 27, 2020, 2:05 PM

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For beginners to pure maths, Insel might be the better one. If you have some mathematical maturity, Axler is good.

static crest Dec 27, 2020, 2:32 PM

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axler lin alg

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pepega

smoky surge Dec 27, 2020, 3:34 PM

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Hahhaha I liked axler LA

static crest Dec 27, 2020, 3:34 PM

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axler is fine

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it's just his crusade against determinants

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is excessively stupid

smoky surge Dec 27, 2020, 3:35 PM

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Yea lmao

gray gazelle Dec 27, 2020, 3:36 PM

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@lucid lantern looks a bit more in the ballpark, what I'd kind of like is if something like that had an appendix that just quickly summarizes the diagrams in one spot

warped cedar Dec 27, 2020, 3:53 PM

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If you wanna reach a higher level of math maturity you're gonna need to start reading lol

gray gazelle Dec 27, 2020, 3:58 PM

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everybody wants to be a mathematician; ain't nobody want to read no heavy ass math books

static crest Dec 27, 2020, 3:59 PM

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I want to read heavy ass math books

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I wish I could read more

warped cedar Dec 27, 2020, 4:00 PM

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I read heavy ass math books doe Sadge

gray gazelle Dec 27, 2020, 4:03 PM

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that was a reference to a ronnie coleman quote

golden bear Dec 27, 2020, 7:11 PM

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Thoughts on Introduction Modern Algebra by Neal Mccoy

warped cedar Dec 27, 2020, 8:14 PM

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Never read the book so I cant give you my opinion but If you are looking for a good Algebra book Id recommend Abstract Algebra by Dummit and Foote

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it really is a classic and im sure others would recommend it aswell

gray gazelle Dec 27, 2020, 8:15 PM

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i've heard good things about jacobson's books

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catThink

soft terrace Dec 27, 2020, 8:45 PM

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i have nathan jacobsons algebra 2

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its very nice

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algebra 2 is grad algebra 1 book is undergrad

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anyone know any good grad level books on "distance geometry"?

gray gazelle Dec 27, 2020, 9:57 PM

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wait @molten wave why is this channel called #book-recommendations and not #discussion-books? my ocd is bothering me here

molten wave Dec 27, 2020, 9:58 PM

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ch-discussion-ill

hollow peak Dec 27, 2020, 10:08 PM

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I looked at d&f, jacobson, artin and knapp for abstract algebra before knapp was really able to grab my attention and I'm finding it good so far

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is there any real difference beyond basic presentation in them though?

hearty steppe Dec 27, 2020, 10:11 PM

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Artin is probably the hardest to read out of all of them maybe

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Haven’t actually read D&F since most people tell me to stay away from it since I’m a newb

waxen elbow Dec 27, 2020, 10:11 PM

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hey, any book for calc 1-2-3 ? it’s for my brother, he got pre calc / trig and no proof writing

broken meadow Dec 27, 2020, 10:11 PM

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stewart or thomas

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or similar

waxen elbow Dec 27, 2020, 10:12 PM

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are they heavy ones ? i think he wants something pretty straightforward

broken meadow Dec 27, 2020, 10:12 PM

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no

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they're written for highschoolers basically

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well

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ok no i won't say that

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but

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they don't require proofs so like

hollow peak Dec 27, 2020, 10:12 PM

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stewart is the most common one I've seen used for calc 1

broken meadow Dec 27, 2020, 10:12 PM

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🤷‍♀️

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yea

waxen elbow Dec 27, 2020, 10:13 PM

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do you think it’s worth for a math major ? since he will do R analysis after calc3, idk if he needs something with proof

broken meadow Dec 27, 2020, 10:13 PM

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hmm

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well

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i think itll be fine

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if its that much of a concern

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use spivak

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after

hollow peak Dec 27, 2020, 10:14 PM

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if it's an intro analysis course they'll take it slow

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he'll be fine for proofs probably

broken meadow Dec 27, 2020, 10:14 PM

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yea

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do advise him to take other courses while doing calc stuff

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like if ur school has an intro proofs class

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do that

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and uh like

waxen elbow Dec 27, 2020, 10:15 PM

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yup i think he got lin algebra, so ye

broken meadow Dec 27, 2020, 10:15 PM

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around the time they take calc 3 u wanna do linear algebrw

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yea

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good

waxen elbow Dec 27, 2020, 10:15 PM

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i did lin algebra with calc 2 : (

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thank you ! i’ll advise him stewart/thomas and spivak to go deeper then

broken meadow Dec 27, 2020, 10:17 PM

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nioce

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yeah it's fine tbh

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probably better to do linear algebra before calc 3

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unlike my school 🤢

waxen elbow Dec 27, 2020, 10:23 PM

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i really think that going calc1-3 without lin algebra feels weird

dapper root Dec 27, 2020, 10:25 PM

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FWIW this might be a hot take but I think even for a math major just doing a computational not-proof based calc class is fine

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You just get familiar with operations and how they work then in your intro analysis you make it rigorous. Just knowing what to expect makes that process a lot easier IMO

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Like... you know what the answer should be because you already know how to integrate things, you know how to take derivatives, you’ve seen infinite series and such

broken meadow Dec 27, 2020, 10:34 PM

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i see

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i mean i have no room to like complain about this stuff

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whats done for me is done

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i went through calc 1-2 in highschool which was complete garbage and my calc 3 class has proofs for the theorems/some statements that are accessible at that level (which we were also not tested on)

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and only now am i going to go to linear algebra to do proofs and stuff and then i think next year ill be doing analysis

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i think itll be totally fine

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i don't think that's a hot take at all

static crest Dec 27, 2020, 10:43 PM

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hearty steppe Haven’t actually read D&F since most people tell me to stay away from it since I...

isn't d&f literally kinda made for noobs, it has excessive detail and proofs understandable for even high schoolers

static crest Dec 27, 2020, 11:27 PM

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it's good for self learning imo

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if you have an instructor, then I'd say it's not the best

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or if you're already good at abstract algebra and wanna go fast fast fast through a tb

sturdy sail Dec 28, 2020, 1:28 AM

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Yeah d&f definetely feels slow

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would you recommend serge lang tho?

hollow peak Dec 28, 2020, 1:45 AM

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lang is a graduate reference

barren briar Dec 28, 2020, 1:49 AM

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he has a book called undergrduate algebra

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its literally the graduate book but with less content and more explanation

sturdy sail Dec 28, 2020, 1:58 AM

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barren briar its literally the graduate book but with less content and more explanation

This is the one I'm referring to

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I have this one downloaded and I'll try to give it a try along with d&f

barren briar Dec 28, 2020, 2:00 AM

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That's what I did to learn group theory, now I'm doing ring theory

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if it helps I found these problem sets:
http://math.columbia.edu/~kyler/MA1.html
http://www.math.columbia.edu/~khovanov/ma2_fall/
also there's a book named Algebra: Chapter 0 that takes a more categorical view if youre into that. There's also "Abstract Algebra: Theory and Applications" which gives nice exposition

sturdy sail Dec 28, 2020, 2:04 AM

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These problem sets look useful

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but I think I'll just stick with one or two books at a time

gray gazelle Dec 28, 2020, 2:05 AM

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guys anyone on number theory and cryptography

sturdy sail Dec 28, 2020, 2:05 AM

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because working with lots of references when you are studying a subject for the first time may be kind of a pain

drifting elm Dec 28, 2020, 5:16 AM

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@gray gazelle I know a tiny bit

gray gazelle Dec 28, 2020, 5:17 AM

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drifting elm <@456226577798135808> I know a tiny bit

Cool

gray gazelle Dec 28, 2020, 5:17 AM

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drifting elm <@456226577798135808> I know a tiny bit

Help me

drifting elm Dec 28, 2020, 5:17 AM

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what exactly

gray gazelle Dec 28, 2020, 5:17 AM

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well on resourses

drifting elm Dec 28, 2020, 5:17 AM

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are you a student or?

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what is your area

gray gazelle Dec 28, 2020, 5:18 AM

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student

drifting elm Dec 28, 2020, 5:18 AM

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cs?

gray gazelle Dec 28, 2020, 5:18 AM

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nope

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maths

drifting elm Dec 28, 2020, 5:18 AM

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ok

gray gazelle Dec 28, 2020, 5:18 AM

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yea u?

drifting elm Dec 28, 2020, 5:18 AM

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me cs

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you want pure maths? number theory?

gray gazelle Dec 28, 2020, 5:18 AM

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cool

drifting elm Dec 28, 2020, 5:18 AM

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or do you want ECC

hasty turret Dec 28, 2020, 5:18 AM

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Well, You should know the Euler theorem

drifting elm Dec 28, 2020, 5:18 AM

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group theory?

hasty turret Dec 28, 2020, 5:18 AM

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Because RSA

gray gazelle Dec 28, 2020, 5:18 AM

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well all u have

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and does anyone teach?

drifting elm Dec 28, 2020, 5:19 AM

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you need to specialize in one area at a time

gray gazelle Dec 28, 2020, 5:19 AM

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yeaa

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number theory

drifting elm Dec 28, 2020, 5:19 AM

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pick something that is fun for you

gray gazelle Dec 28, 2020, 5:19 AM

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as of now

drifting elm Dec 28, 2020, 5:19 AM

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ok NT

gray gazelle Dec 28, 2020, 5:19 AM

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ye

drifting elm Dec 28, 2020, 5:19 AM

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so you start with any book that says introduction or elementary number theory

gray gazelle Dec 28, 2020, 5:19 AM

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i finished that

drifting elm Dec 28, 2020, 5:20 AM

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I started reading introduction to elementary number theory by calvin long

gray gazelle Dec 28, 2020, 5:20 AM

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cool

drifting elm Dec 28, 2020, 5:20 AM

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oh ok

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I have more

gray gazelle Dec 28, 2020, 5:20 AM

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ye

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ok

drifting elm Dec 28, 2020, 5:20 AM

#

let me grab my books

gray gazelle Dec 28, 2020, 5:20 AM

#

cool

#

do u teach?

drifting elm Dec 28, 2020, 5:21 AM

#

not really

#

I don't have enough experience to teach

junior wadi Dec 28, 2020, 5:21 AM

#

i've been having fun with linear alg for the past few days

gray gazelle Dec 28, 2020, 5:21 AM

#

well not realy teach

#

like just go over topics

junior wadi Dec 28, 2020, 5:21 AM

#

reading the book: Linear Alg Done Right by axler

drifting elm Dec 28, 2020, 5:21 AM

#

I have theory of numbers by niven and zuckerman

#

that might be too low level for you

gray gazelle Dec 28, 2020, 5:22 AM

#

oh

drifting elm Dec 28, 2020, 5:22 AM

#

topics in number theory volumes 1 and 2 by leveque

gray gazelle Dec 28, 2020, 5:22 AM

#

ok

drifting elm Dec 28, 2020, 5:23 AM

#

this book is just packed with impressive facts in NT

#

it goes fast

gray gazelle Dec 28, 2020, 5:23 AM

#

ok

#

cool

drifting elm Dec 28, 2020, 5:23 AM

#

higher level NT stuff

gray gazelle Dec 28, 2020, 5:23 AM

#

soo can u just go over the topics

#

like i am a quick learne

drifting elm Dec 28, 2020, 5:23 AM

#

you really got stop and prove these things as you go

#

each page is an hour of practice and cross reference other books

gray gazelle Dec 28, 2020, 5:24 AM

#

oh ok

#

cool

drifting elm Dec 28, 2020, 5:24 AM

#

I went to fast and none of it was any benefit to me

gray gazelle Dec 28, 2020, 5:24 AM

#

oh

drifting elm Dec 28, 2020, 5:24 AM

#

then when I tried to go read it a second time whoa

gray gazelle Dec 28, 2020, 5:25 AM

#

cool

drifting elm Dec 28, 2020, 5:25 AM

#

it was just a massive knowledge dump

gray gazelle Dec 28, 2020, 5:25 AM

#

yea

drifting elm Dec 28, 2020, 5:26 AM

#

also you may be interested in rheimann zeta functions with complex numbers

#

if you study primes

gray gazelle Dec 28, 2020, 5:26 AM

#

yea

drifting elm Dec 28, 2020, 5:26 AM

#

that connects to complex and imaginary numbers

gray gazelle Dec 28, 2020, 5:26 AM

#

yea

#

gotcha

hearty pollen Dec 28, 2020, 5:27 AM

#

I'm reading elementary number theory by David M burton

#

quite comprehensive

drifting elm Dec 28, 2020, 5:27 AM

#

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

Asymptotic analysis

In mathematical analysis, asymptotic analysis, also known as asymptotics, is a method of describing limiting behavior.
As an illustration, suppose that we are interested in the properties of a function f(n) as n becomes very large. If f(n) = n2 + 3n, then as n becomes very large, the term 3n becomes insignificant compared to n2. The function ...

gray gazelle Dec 28, 2020, 5:28 AM

#

cool

drifting elm Dec 28, 2020, 5:28 AM

#

NT works with inf series or diophantine equations

gray gazelle Dec 28, 2020, 5:28 AM

#

yea

drifting elm Dec 28, 2020, 5:28 AM

#

I always brute force first

hearty pollen Dec 28, 2020, 5:28 AM

#

@gray gazelle how old are you?

#

I have a recommendation

gray gazelle Dec 28, 2020, 5:29 AM

#

17

gray gazelle Dec 28, 2020, 5:29 AM

#

hearty pollen <@456226577798135808> how old are you?

whats it?

hearty pollen Dec 28, 2020, 5:29 AM

#

oh nice

#

are you familiar with python?

#

I have a book with a basic introduction for cryptography in python

gray gazelle Dec 28, 2020, 5:30 AM

#

not realy

#

well i could learn

#

i know java

hearty pollen Dec 28, 2020, 5:31 AM

#

https://www.tutorialspoint.com/cryptography_with_python/cryptography_with_python_tutorial.pdf

#

python isn't really hard

#

if you know java

drifting elm Dec 28, 2020, 5:31 AM

#

either one works

#

there are java libs

gray gazelle Dec 28, 2020, 5:32 AM

#

cool

drifting elm Dec 28, 2020, 5:32 AM

#

I also use mathematic but I do java and python

hearty pollen Dec 28, 2020, 5:32 AM

#

the only problem with python is it compiles really slowly

#

so beware of that

#

not like really slowly though

gray gazelle Dec 28, 2020, 5:32 AM

#

oh ok

drifting elm Dec 28, 2020, 5:32 AM

#

there are ways around that also

hearty pollen Dec 28, 2020, 5:33 AM

#

yeah, you can pick a different version of python

gray gazelle Dec 28, 2020, 5:33 AM

#

hm

hearty pollen Dec 28, 2020, 5:33 AM

#

but even if an older version has a faster compiler, there are still consequences based on that

#

I use python 3

drifting elm Dec 28, 2020, 5:34 AM

#

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

Cython

Cython is a programming language that aims to be a superset of the Python programming language, designed to give C-like performance with code that is written mostly in Python with optional additional C-inspired syntax.Cython is a compiled language that is typically used to generate CPython extension modules. Annotated Python-like code is compile...

#

this is built on top of python 2.7

#

old python fast python ironically🙃

drifting elm Dec 28, 2020, 5:57 AM

#

not related but anyway this is cool https://www.amazon.com/Random-Processes-M-Rosenblatt/dp/1461298539/

#

the second edition is 1974. they added a chapter on martingales

#

the other one was printed by oxford 1962

gentle pine Dec 28, 2020, 10:47 AM

#

Has anyone read "Discrete Mathematics with Application" by Susanna S. Epp ? I just got the book and was wandering if I should start reading it, because in the introdution part she says a good algebra foundation is the base. I don't think I have that foundation in Algebra, but I also bought "Algebra10e for College Students" by Kaufmann/Schwitters.
If somebody has read "Discrete Mathematics with Application", do you think the algebra foundation is actually required in order to understand the concepts provided in the book?

prisma snow Dec 28, 2020, 10:51 AM

#

You can always try it and see if you can follow

gentle pine Dec 28, 2020, 10:52 AM

#

prisma snow You can always try it and see if you can follow

You are right but I feel like I would waste my time if I found it out after some weeks

prisma snow Dec 28, 2020, 10:53 AM

#

Not really. You will still have learned the parts that you could follow. And then you can continue where you left off after learning more algebra. Or you can learn what you need as you go through the book

gentle pine Dec 28, 2020, 10:54 AM

#

Yeah you're right. Are you supposed to learn everything which is covered in these kinds of books or is it more like "I learn what I like" ?

prisma snow Dec 28, 2020, 10:57 AM

#

That's entirely up to you

calm crane Dec 28, 2020, 11:19 AM

#

gray gazelle not realy

if you're interested in like crypto crypto checkout cryptohack
i suggest using python and sage

gray gazelle Dec 28, 2020, 12:28 PM

#

calm crane if you're interested in like crypto crypto checkout cryptohack i suggest using p...

cool

drifting elm Dec 28, 2020, 2:47 PM

#

gentle pine Has anyone read "Discrete Mathematics with Application" by Susanna S. Epp ? I ju...

"The screenshot demonstrates one of the many mistakes left in the Kindle version of this book.
Especially for the price paid for it, this is unacceptable. And there is no acceptable reason why the hardcopy of this textbook should have any corrections that the digital copy does not.
Universities/Professors, stop using and requiring this dumpster fire of a textbook.
Students, do yourself the favor and just rent the hardcopy of this book (but only if you must; otherwise, avoid it altogether). "

#

amazon review

#

why not start with Discrete Mathematics and Its Applications
by Kenneth H. Rosen

#

that gets mentioned here constantly

#

also, algebra might be a little misleading

#

probably more like boolean algebra, abstract algebra, number theory

gray gazelle Dec 28, 2020, 2:58 PM

#

drifting elm "The screenshot demonstrates one of the many mistakes left in the Kindle version...

whats it about

drifting elm Dec 28, 2020, 2:58 PM

#

discrete mathematics

gray gazelle Dec 28, 2020, 2:58 PM

#

yea i got that

drifting elm Dec 28, 2020, 2:59 PM

#

https://www.amazon.com/Discrete-Mathematics-Applications-Susanna-Epp/dp/0495391328

gray gazelle Dec 28, 2020, 2:59 PM

#

oh ok

drifting elm Dec 28, 2020, 2:59 PM

#

you want to know what else is in the book?

gray gazelle Dec 28, 2020, 3:00 PM

#

yup

drifting elm Dec 28, 2020, 3:00 PM

#

boolean algebra, combinations and permutations, abstract algebra, number theory

#

discrete sometimes includes graph theory set theory group theory

gentle pine Dec 28, 2020, 3:00 PM

#

drifting elm boolean algebra, combinations and permutations, abstract algebra, number theory

I got the book today an so far it is pretty good and well written

gray gazelle Dec 28, 2020, 3:00 PM

#

wow

drifting elm Dec 28, 2020, 3:00 PM

#

yeah some 5 star reviews also

#

thonk

gray gazelle Dec 28, 2020, 3:01 PM

#

whats the cost?

drifting elm Dec 28, 2020, 3:01 PM

#

$33 used

gray gazelle Dec 28, 2020, 3:01 PM

#

ok

gentle pine Dec 28, 2020, 3:01 PM

#

drifting elm $33 used

watch out!

#

no

#

I got scammed after I bought the used one!

gray gazelle Dec 28, 2020, 3:01 PM

#

why?

#

how

gentle pine Dec 28, 2020, 3:02 PM

#

idk, you'll get the paperbook v.4

gray gazelle Dec 28, 2020, 3:02 PM

#

oh

gentle pine Dec 28, 2020, 3:02 PM

#

📎 20201228_160252.jpg

gray gazelle Dec 28, 2020, 3:02 PM

#

wow

#

looks cool

gentle pine Dec 28, 2020, 3:03 PM

#

but that's not the one I ordered

#

😦

gray gazelle Dec 28, 2020, 3:03 PM

#

oh

drifting elm Dec 28, 2020, 3:03 PM

#

https://www.amazon.com/Discrete-Mathematics-Its-Applications-Seventh/dp/0073383090

gray gazelle Dec 28, 2020, 3:03 PM

#

damn

drifting elm Dec 28, 2020, 3:03 PM

#

this one is $40 legit

gray gazelle Dec 28, 2020, 3:03 PM

#

hm

drifting elm Dec 28, 2020, 3:03 PM

#

hardcover

gray gazelle Dec 28, 2020, 3:04 PM

#

wow

drifting elm Dec 28, 2020, 3:04 PM

#

honestly though, I get this stuff in different books

#

group theory books for group theory

gray gazelle Dec 28, 2020, 3:04 PM

#

same

drifting elm Dec 28, 2020, 3:04 PM

#

boolean algebra for boolean algebra

gray gazelle Dec 28, 2020, 3:04 PM

#

even i would do that

calm crane Dec 28, 2020, 3:04 PM

#

eh

gray gazelle Dec 28, 2020, 3:05 PM

#

like yea i am buying a mobile

#

xD

#

so that i can read

calm crane Dec 28, 2020, 3:05 PM

#

get an abstract algebra book

#

you will see group theory and possibly boolean algebra

drifting elm Dec 28, 2020, 3:05 PM

#

yeah abstract algebra is pretty much just group theory

calm crane Dec 28, 2020, 3:05 PM

#

uh

#

NO

#

huhh

#

uhhh

#

uh

#

what

#

no

#

wht

drifting elm Dec 28, 2020, 3:05 PM

#

people get mad

gray gazelle Dec 28, 2020, 3:05 PM

#

calm crane uh

chill

drifting elm Dec 28, 2020, 3:05 PM

#

but other people agree

calm crane Dec 28, 2020, 3:05 PM

#

yes

#

im ok

#

but

#

no

drifting elm Dec 28, 2020, 3:05 PM

#

depends on your stance

calm crane Dec 28, 2020, 3:05 PM

#

group theory is a tiny part of algebra pls

prisma snow Dec 28, 2020, 3:06 PM

#

But rings are just groups too really, so just agree, ari

calm crane Dec 28, 2020, 3:06 PM

#

wtf

#

no

drifting elm Dec 28, 2020, 3:06 PM

#

every abstract algebra book has group theory

calm crane Dec 28, 2020, 3:06 PM

#

rings are super different

#

no shit

#

doesnt mean group theory = abstract algebra

gray gazelle Dec 28, 2020, 3:06 PM

#

hehehe

#

nice fight

prisma snow Dec 28, 2020, 3:06 PM

#

Wow, ari doesn't thing rings are groups under +

calm crane Dec 28, 2020, 3:06 PM

#

uh

#

no

prisma snow Dec 28, 2020, 3:06 PM

#

(I'm trolling, the rest prob not)

gray gazelle Dec 28, 2020, 3:06 PM

#

wait abstract algebra has more

calm crane Dec 28, 2020, 3:06 PM

#

rings are super different from groups

#

groups are a tiny tiny part of algebra

drifting elm Dec 28, 2020, 3:07 PM

#

I can agree

gray gazelle Dec 28, 2020, 3:07 PM

#

i cant say tiny but yea its a part

gentle pine Dec 28, 2020, 3:07 PM

#

guys we are on a mathematics discord. Try to prove stuff
😄

calm crane Dec 28, 2020, 3:07 PM

#

..

#

...

drifting elm Dec 28, 2020, 3:07 PM

#

but at some level you will be introduced to them at the same time

calm crane Dec 28, 2020, 3:07 PM

#

no shit?

gray gazelle Dec 28, 2020, 3:07 PM

#

huh

drifting elm Dec 28, 2020, 3:07 PM

#

you win

#

🥰

gray gazelle Dec 28, 2020, 3:08 PM

#

wow

drifting elm Dec 28, 2020, 3:08 PM

#

catLove

gray gazelle Dec 28, 2020, 3:08 PM

#

https://tenor.com/view/oscars-standing-ovation-clap-clapping-applause-gif-12604309

Tenor

drifting elm Dec 28, 2020, 3:09 PM

#

this conversation does not commute

gray gazelle Dec 28, 2020, 3:10 PM

#

nvm

#

back to the point

calm crane Dec 28, 2020, 3:10 PM

#

i suggest jacobson basic algebra heh

gray gazelle Dec 28, 2020, 3:10 PM

#

to be frank i like only reference books

#

i preffer videos

#

or lectures

calm crane Dec 28, 2020, 3:11 PM

#

ah

gray gazelle Dec 28, 2020, 3:11 PM

#

ye

gentle pine Dec 28, 2020, 3:11 PM

#

if you guys are not native English speakers -> do you learn all math in English or our mother tongue ?

calm crane Dec 28, 2020, 3:11 PM

#

technically lang/bourbaki is good reference book

hasty turret Dec 28, 2020, 3:11 PM

#

gentle pine if you guys are not native English speakers -> do you learn all math in English ...

English

calm crane Dec 28, 2020, 3:11 PM

#

english cuz idk chinese maf books lol

#

but i tkhink im non native english and chinese lol

drifting elm Dec 28, 2020, 3:11 PM

#

math is a language

calm crane Dec 28, 2020, 3:11 PM

#

my standard vry low one

#

...

gray gazelle Dec 28, 2020, 3:11 PM

#

gentle pine if you guys are not native English speakers -> do you learn all math in English ...

mother tongue

stray veldt Dec 28, 2020, 3:11 PM

#

gentle pine if you guys are not native English speakers -> do you learn all math in English ...

both

gentle pine Dec 28, 2020, 3:12 PM

#

stray veldt both

Germania, I see

drifting elm Dec 28, 2020, 3:12 PM

#

german math books when I feel like going on a quest for something good

stray veldt Dec 28, 2020, 3:12 PM

#

indeed

gray gazelle Dec 28, 2020, 3:12 PM

#

wow

drifting elm Dec 28, 2020, 3:12 PM

#

some old stuff

#

you have to work for it

stray veldt Dec 28, 2020, 3:12 PM

#

but the situation is a bit different, since there are actually good german math books that are sometimes not even translated

drifting elm Dec 28, 2020, 3:12 PM

#

exactly!

gray gazelle Dec 28, 2020, 3:12 PM

#

oh

drifting elm Dec 28, 2020, 3:12 PM

#

and some old ones also

stray veldt Dec 28, 2020, 3:13 PM

#

also in my professional life i probably talk english 50% of the time and german 50% of the time

gray gazelle Dec 28, 2020, 3:13 PM

#

galois ur in germany

#

?

drifting elm Dec 28, 2020, 3:13 PM

#

nope

#

american

gray gazelle Dec 28, 2020, 3:13 PM

#

oh ok

stray veldt Dec 28, 2020, 3:13 PM

#

so it makes sense to at least be familiar with both languages when it comes to mathematical terms

drifting elm Dec 28, 2020, 3:13 PM

#

but the german books are amazing

gray gazelle Dec 28, 2020, 3:13 PM

#

i am moving to cz soon

drifting elm Dec 28, 2020, 3:13 PM

#

the older ones

gentle pine Dec 28, 2020, 3:13 PM

#

stray veldt but the situation is a bit different, since there are actually good german math ...

can you recommend a book for general mathematics for beginners in german?

drifting elm Dec 28, 2020, 3:13 PM

#

foundations of analysis

#

in german

stray veldt Dec 28, 2020, 3:13 PM

#

what do you consider "general mathematics"

gray gazelle Dec 28, 2020, 3:13 PM

#

good question

gentle pine Dec 28, 2020, 3:14 PM

#

stray veldt what do you consider "general mathematics"

idk actually know what I mean by that. I just started learning math on my own and have almost no knowledge so idk

stray veldt Dec 28, 2020, 3:14 PM

#

well

#

elementare zahlentheorie by steuding then

gray gazelle Dec 28, 2020, 3:14 PM

#

gentle pine idk actually know what I mean by that. I just started learning math on my own an...

oh

gentle pine Dec 28, 2020, 3:15 PM

#

stray veldt elementare zahlentheorie by steuding then

thanks

gray gazelle Dec 28, 2020, 3:15 PM

#

do u know number theory

drifting elm Dec 28, 2020, 3:15 PM

#

Grundlagen der Analysis by landau

gray gazelle Dec 28, 2020, 3:15 PM

#

or prime number theory

stray veldt Dec 28, 2020, 3:15 PM

#

it's an introductory number theory book

gray gazelle Dec 28, 2020, 3:15 PM

#

cool

stray veldt Dec 28, 2020, 3:15 PM

#

my (harder) analysis suggestion is amann escher

gray gazelle Dec 28, 2020, 3:15 PM

#

number theory is the best

stray veldt Dec 28, 2020, 3:16 PM

#

other than that ehrhard behrends wrote some nice books

gray gazelle Dec 28, 2020, 3:16 PM

#

u dont really need to have any past edu for that

#

well

stray veldt Dec 28, 2020, 3:17 PM

#

that book by steuding is pretty cool in that it starts with highschool knowledge and then builds some algebra and analysis

#

there is a sequel i think in english

#

sequel in the sense that it is written for undergrads in math

fathom monolith Dec 28, 2020, 6:14 PM

#

I had 0 knowledge going into college (took 7 years off after high school) and after 3 months of khan academy I was unstoppable in calc 1 and have been very successful ever since. I think khan academy is THE best source to learn pre college math

#

oh this conversation is long dead nvm

warped cedar Dec 28, 2020, 6:16 PM

#

khan academy is really good for precollege i agree

wide turtle Dec 28, 2020, 6:26 PM

#

I'm looking for a set of books in advanced real analysis and introductory functional analysis to self-teach. I've narrowed it down to Tao's measure theory and "an epsilon of room", in combination with either Stein-Shakarchi's Princeton Lectures 3&4 or Rudin 2&3. Anybody who has read both Stein and Rudin who could give a comparison of the two? Any other recommendations?

sturdy sail Dec 28, 2020, 7:22 PM

#

gentle pine if you guys are not native English speakers -> do you learn all math in English ...

both really

#

There's a lot of good content both in english and portuguese

static crest Dec 28, 2020, 8:01 PM

#

I'm not native english, but I only learn math in english

#

(however, I've been in Canada since I've been 3, so I'm kinda almost native, even if not technically)

valid moth Dec 28, 2020, 8:11 PM

#

static crest (however, I've been in Canada since I've been 3, so I'm kinda almost native, eve...

bruh

#

i learned english when i was 5 and i count it as native

#

just say native

#

sully

static crest Dec 28, 2020, 8:21 PM

#

but I'm not native

#

english isn't even in my top 2

timber mesa Dec 28, 2020, 10:10 PM

#

gentle pine if you guys are not native English speakers -> do you learn all math in English ...

translating back and forth is sometimes a great exercise for learning since it involves active thinking and requires a decent conceptual understanding. I usually read math stuff in English and write in my language (Spanish)

frozen shuttle Dec 29, 2020, 1:24 AM

#

Started to take OCW 18.06 (the linear algebra course with strang), but after doing some research I stumbled upon the current 18.06 outline here https://github.com/mitmath/1806/blob/master/summaries.md which mentioned the more modern version version of the course uses julia and doesn't focus on echelon forms or hand calculation as much which I think is great because they always felt boring and somewhat pointless to me.

WARNING: we are not following the book and OCW directly. Rather you are getting an updated course that throws away echelon forms (practically never used), and favors the singular value decomposition (dished out slowly over the whole semester), linear transformations, and matrix calculus. We will do less hand computation, but there will still be some. Eigenvalues are losing their place in line, but still key.

Does anyone have a resource that would follow a similar approach rather than standard approach? The new 18.06 course doesn't seem to have lectures published online yet.

GitHub

mitmath/1806

18.06 course at MIT. Contribute to mitmath/1806 development by creating an account on GitHub.

fathom monolith Dec 29, 2020, 2:37 AM

#

my first lin alg course was an any% speed run of row echelon -> determinant. If you couldnt do it fast then you just couldn't answer the questions on the test in the allotted time

quick hornet Dec 29, 2020, 2:40 AM

#

ditching echelon forms is interesitng since they're very very useful to know about for proving things

#

though admittedly only really in the case of specific spaces (particularly "nice" finite dimensional ones)

#

a focus on SVD makes sense from a practical-application perspective though

frozen shuttle Dec 29, 2020, 2:47 AM

#

interesting. yeah guess I was kind of curious on the approach. From the rest of the summary page seems like the course was reworked cater better to appliactions in data science/machine learning.

#

Im pretty sure strang's course was always trying to be more practical rather than theoretical though so it makes sense. Was planning on reading through linear algebra done right after strang for some more theory, but trying to build intuition and get started with computer graphics atm.

#

is there a good resource for learning SVD and whatever else that course was focusing onseparately if I do the normal strang course because the lectures are recorded?

gray gazelle Dec 29, 2020, 2:50 AM

#

somehow i still don't really understand SVD, which is sad

frozen shuttle Dec 29, 2020, 2:50 AM

#

never heard of it before that, but Im just a run of the mill software engineer at amazon trying to take up math/cg as a hobby.

gray gazelle Dec 29, 2020, 2:51 AM

#

nice, i am also a software engineer

gray gazelle Dec 29, 2020, 4:21 AM

#

I will have the course of Analysis II: contains differentiation, integration, and all that for Analysis II.
Me need book which is abstract.. (Rudin feels too much like introductory analysis)

#

pong

drifting elm Dec 29, 2020, 4:25 AM

#

I found the meta programming in julia. it reminds me of lisp.

#

just installed julia. thanks for the tip.

silver herald Dec 29, 2020, 4:27 AM

#

Julia is freakin' awesome

drifting elm Dec 29, 2020, 4:30 AM

#

no visuals though?

gray gazelle Dec 29, 2020, 4:40 AM

#

Visuals?

drifting elm Dec 29, 2020, 4:50 AM

#

text only no color graphics library that I could find.

#

https://www.wolfram.com/mathematica/newin7/content/VectorAndFieldVisualization/PlotFieldVectorsIn3D.html

worldly prawn Dec 29, 2020, 7:33 AM

#

Hi guys. I wonder, is there any good standard reference on combinatorics that covers pretty much every famous combinatorial identities for an example the Hockey-Stick identity etc? I need it in order to give citation to this well known combinatorial result in a final year project I am writing

hidden herald Dec 29, 2020, 7:45 AM

#

worldly prawn Hi guys. I wonder, is there any good standard reference on combinatorics that co...

Hmm, I think if it's so well known, that anyone (say before first year in uni) can figure what it is when looking at it, you probably can leave it out.

worldly prawn Dec 29, 2020, 7:46 AM

#

I thought so too but my advisor insists me on giving a citation.

hidden herald Dec 29, 2020, 7:47 AM

#

Eh, might as well prove it, combinatoric proof is just, say, 2 lines?

dense wasp Dec 29, 2020, 1:37 PM

#

Hey Guys, about to enter my last year of undergrad. Any recommendations on a solid linear algebra book at this stage to solidify what I should know and expand into some topics more deeply? Having a hard time picking as most of all my previous algebra courses have been done using professors notes ect so don't really have anything to reference what book I should get.

hybrid dawn Dec 29, 2020, 2:25 PM

#

You can always check the pinned posts in this channel :)

timber mesa Dec 29, 2020, 4:56 PM

#

gray gazelle I will have the course of Analysis II: contains differentiation, integration, an...

is Spivak or Apostol not a good fit? They prove all result but still have some computations

timber mesa Dec 29, 2020, 4:56 PM

#

hybrid dawn You can always check the pinned posts in this channel :)

or rather #books-old

timber mesa Dec 29, 2020, 4:57 PM

#

dense wasp Hey Guys, about to enter my last year of undergrad. Any recommendations on a sol...

Hoffman & Kunze if by "linear algebra" you mean a math major's linear algebra.

flint forge Dec 29, 2020, 6:32 PM

#

Linear algebra done wrong is also a good option

static crest Dec 29, 2020, 6:33 PM

#

do they overuse determinants

azure orchid Dec 29, 2020, 6:57 PM

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Hello everyone!
Does anyone have a recommended book to introduce the topic of probability? Specifically, I'm looking for something written by someone who had an enormous impact on the field of probability during their lifetime. For example, the book that comes to mind for me to look at is The Art Of Probability By Richard W. Hamming, given his incredible other writing and enormous impact on mathematics. However, that book doesn't appear to be for people with no prior experience in probability and, therefore, I'm looking here.

soft terrace Dec 29, 2020, 7:02 PM

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do you already know probability?

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you need probability befor stats if you are doing calc based

azure orchid Dec 29, 2020, 7:03 PM

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I've actually made an error and called probability statistics @soft terrace I'll correct the original message. I am looking for an introduction to probability.

soft terrace Dec 29, 2020, 7:06 PM

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open textbook library has a pdf of a book called "introduction to probability" that looks pretty nice. I don't know about being written by someone with a huge impact or not though

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if your doing it by yourself you might want more than one book in case one of them explains something a way that doesnt agree with you

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https://open.umn.edu/opentextbooks/textbooks/21

Open Textbook Library

Introduction to Probability - Open Textbook Library

Probability theory began in seventeenth century France when the two great French mathematicians, Blaise Pascal and Pierre de Fermat, corresponded over two problems from games of chance. Problems like those Pascal and Fermat solved continuedto influence such early researchers as Huygens, Bernoulli, and DeMoivre in establishing a mathematical theo...

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i wouldnt worry too much about the impact of the author if the book is written well but thats imo

azure orchid Dec 29, 2020, 7:09 PM

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I definitely agree it isn't hugely important, though just googling his name J. Laurie Snell does actually seem to have been at least somewhat influential.

soft terrace Dec 29, 2020, 7:09 PM

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what is "influential" is largely in the eye of the beholder

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imo it should be whether or not their work is interesting to you

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whether its written by a big name or not the introductory books are mostly going to be the same material

hearty steppe Dec 29, 2020, 7:16 PM

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Snell is supposed to be good from what I heard

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But I mean I feel like introductory probability isn’t difficult but more or less a little tricky

soft terrace Dec 29, 2020, 7:16 PM

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getting used to random variables is half the battle

hearty steppe Dec 29, 2020, 7:17 PM

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You shouldn’t be spending as much time looking for an intro probability book than you would for math proof writing and intro analysis

azure orchid Dec 29, 2020, 7:23 PM

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soft terrace whether its written by a big name or not the introductory books are mostly going...

This is just a quick justification for why I'm asking about influence. I realize it seems pretty nonsensical to ask about given that if someone's work is good, it doesn't matter if no one knows about their work: I'm interested in influence because I think influence has to do a lot with skill. I don't necessarily mean the author is well known, just that several other people have adopted the methods they've pioneered in their field.

I need one of these things to judge if I should start reading the book because I'm asking people I don't know for advice when I have no experience in the field I'm asking about. This isn't me insulting you; I will now read this book on your recommendation and am sure you're knowledgeable; I'm just describing why I'm asking about influence. Really I should use the word impact.

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(Side note, I'm really sorry for being hyper-verbose. I'm really really sleepy.)

prisma snow Dec 29, 2020, 7:25 PM

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But someone's ability to do groundbreaking research has almost no impact on their ability to write an intro book

azure orchid Dec 29, 2020, 7:26 PM

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I don't agree with that, I think knowing how to do great work is a skill and being able to do that work will be reflected in all of their writing.

azure orchid Dec 29, 2020, 7:30 PM

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hearty steppe You shouldn’t be spending as much time looking for an intro probability book tha...

It actually is probably better for me to ask for a book based on my goals rather than the topic 😅.
I'm looking to read "The Elements of Statistical Learning" and it recommends that, before reading it, you take an introductory level statistics course:
"We expect that the reader will have had at least one elementary course in statistics, covering basic topics including linear regression."

I have never taken one so I'm asking for recommendations based on needing that. (I realize I asked about probability, I made a mistake while doing that though I imagine s00mb is totally correct and I should have an understanding of probability going into learning about stats and would also appreciate a recommendation about that, which you have already given.)

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Really sorry that this question has become this overly complicated. I am super running on low sleep 😓.

karmic thorn Dec 29, 2020, 8:00 PM

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azure orchid I don't agree with that, I think knowing how to do great work is a skill and bei...

The great work will be reflected, true, but whether that work is reasonably clear or accessible to the audience is not always true. Being an expert and being a communicator are not necessarily the same thing.

azure orchid Dec 29, 2020, 8:02 PM

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karmic thorn The great work will be reflected, true, but whether that work is reasonably clea...

I grant that to be true, but I don't grant that all influential people are bad writers and so I have a preference for books written by people who are influential.

timber mesa Dec 29, 2020, 9:10 PM

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azure orchid **Hello everyone!** Does anyone have a recommended book to introduce the topic o...

Kai Lai Chung's "Elementary Probability Theory" might fit all your criteria: it's introductory, very complete and the author was central in the early development of the theory of Markov chains as well as the study of Brownian motion (https://en.wikipedia.org/wiki/Chung_Kai-lai#Biography). Accordingly, the last edition includes a chapter on stochastic processes and another on applications to mathematical finance.

drifting elm Dec 29, 2020, 9:13 PM

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azure orchid It actually is probably better for me to ask for a book based on my goals rather...

https://www.amazon.com/Fundamentals-Statistics-5th-Michael-Sullivan/dp/0134508300/

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read the part about linear regression

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read about conditional probability

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https://stats.libretexts.org/Bookshelves/Introductory_Statistics/Book%3A_Introductory_Statistics_(Shafer_and_Zhang)/02%3A_Descriptive_Statistics/2.05%3A_The_Empirical_Rule_and_Chebyshev's_Theorem

Statistics LibreTexts

2.5: The Empirical Rule and Chebyshev's Theorem

The Empirical Rule is an approximation that applies only to data sets with a bell-shaped relative frequency histogram. It estimates the proportion of the measurements that lie within one, two, and …

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chebyshev is a huge influential name in mathematics

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you could argue that hamming and shannon were the founders of information theory

azure orchid Dec 29, 2020, 9:16 PM

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timber mesa Kai Lai Chung's "Elementary Probability Theory" might fit all your criteria: it'...

Thank you so much 😃
This is absolutely wonderful.

drifting elm Dec 29, 2020, 9:16 PM

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but that overlaps into probability

azure orchid Dec 29, 2020, 9:16 PM

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drifting elm https://www.amazon.com/Fundamentals-Statistics-5th-Michael-Sullivan/dp/013450830...

Do you recommend I read this instead of Kai Lai Chung's "Elementary Probability Theory?" (This also looks amazing.)

drifting elm Dec 29, 2020, 9:17 PM

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all these books are almost the same

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like 2+2=4 in every book on addition

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but I am skeptical about reading hamming if you don't care about combinatorics and information theory

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I am a huge fan of shannon but that is more for different areas of math not exactly related to statistics

azure orchid Dec 29, 2020, 9:20 PM

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I'm avoiding Hamming's book on probability because it's clearly not at the level of reading I'm at. If you're talking about Hamming more generally, than the only other text I'm reading by him at the moment is "The Art of Doing Science and Engineering: Learning to learn."

drifting elm Dec 29, 2020, 9:20 PM

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https://halshs.archives-ouvertes.fr/halshs-01389403/document

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this gives some history of claude shannon

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it argues that he was big in the foundations of probability

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but this is really coming from an information theory context

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I don't think you will see any mention at all in an intro to statistics course today

azure orchid Dec 29, 2020, 9:22 PM

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I mostly know about Shannon through reading about him in "The Art of Doing Science and Engineering: Learning to learn." I will almost certainly read more about him and I appreciate you linking me writing about his work 🙂

drifting elm Dec 29, 2020, 9:23 PM

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he did so much for math and you don't hear the name talked about very much

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aliasing is something I study a lot

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it comes up in analog to digital converters

azure orchid Dec 29, 2020, 9:24 PM

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He also did a bunch for computing. He was really amazing.

drifting elm Dec 29, 2020, 9:24 PM

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yes

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and physics of fiber optic communication

azure orchid Dec 29, 2020, 9:24 PM

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So amazing.

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Just unbelievably talented. Really really glad he was brought up in the book.

drifting elm Dec 29, 2020, 9:26 PM

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he invented math that made fiber optics possible before fiber optics were invented. before digital audio was invented. the math preceded all digital communication and information theory that we use today.

azure orchid Dec 29, 2020, 9:27 PM

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😮

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He did even more than what I knew about holy poop

azure orchid Dec 29, 2020, 9:37 PM

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timber mesa Kai Lai Chung's "Elementary Probability Theory" might fit all your criteria: it'...

What is the lastest edition?

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(Like, is it the fourth edition?)

timber mesa Dec 29, 2020, 9:37 PM

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yeah the fourth edition

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the title should be "Elementary Probability Theory: With Stochastic Processes and an Introduction to Mathematical Finance", the finance bit was included in the latest edition iirc

azure orchid Dec 29, 2020, 9:38 PM

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Is it this: https://www.amazon.ca/Elementary-Probability-Theory-Introduction-Mathematical/dp/038795578X/ref=cm_cr_arp_d_product_top?ie=UTF8

timber mesa Dec 29, 2020, 10:00 PM

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yes

azure orchid Dec 29, 2020, 10:01 PM

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Thank you!

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Ok, I think I'm going to run with this book. I appreciate your time 🙂

glass inlet Dec 29, 2020, 10:18 PM

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Is the above book the recommended book for probability? I took a course in College, but I forgot most of it after years of not practicing. Now I am trying to learn probability and get a deeper understanding as I begin machine learning and statistics.

warped cedar Dec 29, 2020, 10:20 PM

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honestly if you really wanna learn some probability you can start with khan academy

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probablility and statistics for engineers and scientists by walpole, myers, myers, ye

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is a cool book

glass inlet Dec 29, 2020, 10:22 PM

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Ok, thanks very much! I prefer books over video lectures so I will look into that book instead

timber mesa Dec 30, 2020, 12:00 AM

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There's a ton of books for probability, Clue was asking specifically for a introductory book written by someone influential in probability theory and I thought Chung's was a good fit.

smoky surge Dec 30, 2020, 2:21 AM

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Intro to probability imo tends to be a bit dry

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Just feels like learning a lot about a whole bunch of distributions which kinda all feel similar in purpose

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Feel like the fun stuff is applying probability

fossil island Dec 30, 2020, 2:32 AM

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Applied math???

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Probably is a pure math subject, only.

smoky surge Dec 30, 2020, 2:35 AM

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hmmm

warped cedar Dec 30, 2020, 2:36 AM

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its true

smoky surge Dec 30, 2020, 2:40 AM

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catGun

gray gazelle Dec 30, 2020, 3:47 AM

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can i jump right into Algebra by artin or should i cover some LA first (strang)

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for self study

static crest Dec 30, 2020, 3:47 AM

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should do lin alg first

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you dont exactly need lin alg to do much of groups or rings or stuff

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but it's more of a mathematical maturity kinda thing

hearty steppe Dec 30, 2020, 3:49 AM

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A lot of formalities covered in a pure LA book is exactly what you want before actually going into Abstract Algebra, I think that’s the main point a lot of people here are trying to make

gray gazelle Dec 30, 2020, 3:49 AM

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alright seems reasonable

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thanks

static crest Dec 30, 2020, 3:50 AM

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also abstract algebra can often be a bit too abstract at points, lin alg (and vector spaces) are much easier to think about

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and a bunch of major theorems in other places in abstract algebra

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have nice analogues

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to lin alg theorems

gray gazelle Dec 30, 2020, 3:51 AM

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LA just a special case of AA

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hmmm

heavy barn Dec 30, 2020, 3:51 AM

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AA is just a special case of math hmmm

gray gazelle Dec 30, 2020, 3:52 AM

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math is just a special case of philosophy hmmm

static crest Dec 30, 2020, 3:53 AM

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all of the universe is a special case of physics hmmm

gray gazelle Dec 30, 2020, 3:53 AM

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Chemistry hmmm

heavy barn Dec 30, 2020, 3:55 AM

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hmmm is just a special case of hmmm

static crest Dec 30, 2020, 3:56 AM

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catThhhh is a special case of catThimc is a special case of catThink is a special case of hmmm

gray gazelle Dec 30, 2020, 3:56 AM

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thonkeyes is a special case of thonk

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hmmm

hasty turret Dec 30, 2020, 3:57 AM

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🌕 -> thonkzoom -> thonk -> thonkeyes ->🌕

haughty bough Dec 30, 2020, 3:58 AM

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Mildly related to the probability recommendation. Since I was interested in combinatorics and some TCS, I found a probability course that involved applications of concentration inequalities and other prob ideas to theory and the probabilistic method quite nice. Are there any books that have this kind of a flavour? The only one I can seem to recall is Mitzenmacher and Upfal.

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Oh yes, I've heard of that. There must also be other combinatorics books that have a good chunk on the probabilistic method, like Jukna's Extremal Combinatorics.

soft terrace Dec 30, 2020, 4:20 AM

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Anyone know some good up to date books on classical differential geometry and riemann geometry respectively? I've got some old books and the notation is dated; it's starting to drive me nuts.

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whats the first name

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oh was that mine or different

gray gazelle Dec 30, 2020, 4:25 AM

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john m lee

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presumably

soft terrace Dec 30, 2020, 4:25 AM

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ok sounds good

gray gazelle Dec 30, 2020, 4:25 AM

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he has a trilogy on manifolds

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good books

soft terrace Dec 30, 2020, 4:26 AM

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i see them

drifting elm Dec 30, 2020, 4:26 AM

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📎 PMAmemekermit.jpg

soft terrace Dec 30, 2020, 4:28 AM

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is there any difference really between a riemann geometry book and manifold one? i know what a manifold is i was just wondering if there is any notable difference

gray gazelle Dec 30, 2020, 4:29 AM

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riemannian geometry imposes a metric

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on a smooth manfold

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and discusses the consequences of that

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by metric i mean something that allows you to measure geometric quantities like length, volume, angle of tangent vectors, and so on

soft terrace Dec 30, 2020, 4:30 AM

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im not digging how lee is leaving most of the theorem proofs as exercises

gray gazelle Dec 30, 2020, 4:30 AM

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pensivebread

soft terrace Dec 30, 2020, 4:31 AM

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lee isnt being friendly lol

gray gazelle Dec 30, 2020, 4:31 AM

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i like lee more than do carmo

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but do carmo has much lighter prereqs imo

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oh yeah, s00mb, you could check out do carmo's book as well

soft terrace Dec 30, 2020, 4:32 AM

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like every theorem and lemma in this book is followed by "exercise. prove the lemma.

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yeah i'll try that

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its nice if u want a challenge not so nice if u want to see a proof on the spot

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when you are self studying it is very inconvenient having all the main theorems as exercises

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do carmo looks much nicer

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i like having examples from the main theorems because it clarifies things that might be vague

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i do not go to college so i have no one except this discord to clarify things

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when everything is "proof this" with no example i dont like it

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yeah

gray gazelle Dec 30, 2020, 4:37 AM

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i don't recall do carmo leaving theorems and stuff to the exercises

soft terrace Dec 30, 2020, 4:37 AM

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im looking at it now he doesnt

gray gazelle Dec 30, 2020, 4:37 AM

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i know he's talking about lee

soft terrace Dec 30, 2020, 4:38 AM

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im not saying i cant do lee but when im reading for review i dont want to have to go back and prove everything to get a small piece of information i want

gray gazelle Dec 30, 2020, 4:38 AM

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i used do carmo for a semester and found it to be good, also it's short compared to the monster that is lee

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do carmo jumps right into the meat of rg but lee spends a ton of time building up the basic stuff

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well

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lee assumes you read ISM so he can afford to spend a lot of time building up basic stuff

soft terrace Dec 30, 2020, 4:39 AM

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lee is nicely written

gray gazelle Dec 30, 2020, 4:39 AM

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like chapter 2 in lee's IRM is fucking packed

soft terrace Dec 30, 2020, 4:39 AM

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honestly id prefer lee if it had examples

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what dont u thonk me

gray gazelle Dec 30, 2020, 4:39 AM

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lee has examples thonk

soft terrace Dec 30, 2020, 4:39 AM

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yeah but not enough proofs

gray gazelle Dec 30, 2020, 4:40 AM

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understandable

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do carmo is kind of sneaky with his prereqs

soft terrace Dec 30, 2020, 4:40 AM

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how so

gray gazelle Dec 30, 2020, 4:40 AM

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first half of the book requires very little

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then in the second half words like covering spaces and equicontinuous and whatnot start popping up here and there

soft terrace Dec 30, 2020, 4:41 AM

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thats just undergrad analysis though isnt it

gray gazelle Dec 30, 2020, 4:41 AM

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ya

soft terrace Dec 30, 2020, 4:41 AM

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i dont imagine too many ppl taking riemann geometry would skip that

gray gazelle Dec 30, 2020, 4:41 AM

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well let me see what do carmo says at the start of his book

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lol

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nice one

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i'm taking analysis next semester and i've already finished a full riemannian geometry class

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opencry

soft terrace Dec 30, 2020, 4:41 AM

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no analysis at all?

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really?

gray gazelle Dec 30, 2020, 4:42 AM

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well i've never had a trouble with knowing analysis, and i picked up a fair amount of analysis during my """"""functional analysis"""""" course

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look

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it's complicated opencry

soft terrace Dec 30, 2020, 4:43 AM

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how did u take functional without real lol

gray gazelle Dec 30, 2020, 4:43 AM

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""""""functional analysis""""""

soft terrace Dec 30, 2020, 4:43 AM

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functional is what metric spaces and what not

gray gazelle Dec 30, 2020, 4:43 AM

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oh like metric spaces

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uuuuuh

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let's say i learned whatever analysis i know now by either my topology class or by googling random shit

soft terrace Dec 30, 2020, 4:44 AM

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so u never proved basic calculus? oh u missed out 😉

gray gazelle Dec 30, 2020, 4:44 AM

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do carmo

📎 unknown.png

soft terrace Dec 30, 2020, 4:44 AM

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lol riemann geometry before analysis analysis is going to be easy

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my prof in undergrad college made me take real analysis before doing classical differential geometry

gray gazelle Dec 30, 2020, 4:45 AM

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this is the first year calc course called "analysis 1"

📎 unknown.png

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so

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maybe i lied

soft terrace Dec 30, 2020, 4:45 AM

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oh u took it?

gray gazelle Dec 30, 2020, 4:45 AM

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ya

soft terrace Dec 30, 2020, 4:45 AM

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yeah thats what i meant

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equicontinuity is undergrad analysis

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i still remember my professor getting upset at someone for confusing it

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he wasnt really stuck up

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just reallllly nerdy

gray gazelle Dec 30, 2020, 4:49 AM

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yohan read all 595 pages of lee's ism before irm opencry

soft terrace Dec 30, 2020, 4:49 AM

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like he wasnt mad he was just so smart that he couldnt figure out that other people couldnt understand certain things

gray gazelle Dec 30, 2020, 4:50 AM

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probably not a good idea tbh

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i am pretty sure IRM assumes you read ISM

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LIKE

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fully

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caps

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well "fully" as in "the meat of it" since ISM is a gargantuan book

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This book is designed as a textbook for a graduate course on Riemannian
geometry for students who are familiar with the basic theory of smooth manifolds.

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idk

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probably?

soft terrace Dec 30, 2020, 4:53 AM

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yes it is

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classical differential geometry is the undergrad prereq

gray gazelle Dec 30, 2020, 4:53 AM

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i wish my RG course had classic dg as a prereq

soft terrace Dec 30, 2020, 4:53 AM

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well i guess u can skip that but it makes more sense if u do it

gray gazelle Dec 30, 2020, 4:54 AM

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lee opencry

soft terrace Dec 30, 2020, 4:55 AM

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if lee leaves all the proofs as exercises for DG id get a supplement that shows proofs

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well not mine mine is like 1950s and builds it up from cartan theorems lol

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yeah its a dover book republish

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i love it to death but the way it builds it up is NOT the way you would normally do it

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yeah i dont think cartan matrices are used in modern dg

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did you do lie groups in riemann geometry tterra?

gray gazelle Dec 30, 2020, 4:57 AM

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sadly, no

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i've been reading up on them myself the past while though

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working on the exercises in chapter 3 of lee's irm catThink

soft terrace Dec 30, 2020, 4:58 AM

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if you want something interesting to take a peek at look at my old book "differential geometry" by guggenheimer

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i think it uses lie derivatives to prove stuff at some point

gray gazelle Dec 30, 2020, 4:59 AM

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holy fuck the amazon preview for the kindle version is ugly af

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let me libgen it

soft terrace Dec 30, 2020, 4:59 AM

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its an old ugly book

gray gazelle Dec 30, 2020, 4:59 AM

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lie derivatives catThink

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fun stuff

soft terrace Dec 30, 2020, 4:59 AM

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lie algebras lie derivatives moving frames cartan matrices

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its got a lot of old stuff thats still interesting but isnt covered in newer books

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well cyall tommorow

smoky surge Dec 30, 2020, 5:41 AM

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I like truth derivatives better

sage python Dec 30, 2020, 5:50 AM

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H e l g a s o n

knotty venture Dec 30, 2020, 6:27 PM

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Anyone has this book by any chance

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📎 51HbsXNcpaL.png

pearl imp Dec 30, 2020, 7:11 PM

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I'm starting probability and have chosen "A First Course in Probability by Ross" as my book to self-study.

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I am past half of Calc II.

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What do you think?

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Maybe other choices better for this?

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Thanks

gray gazelle Dec 30, 2020, 7:36 PM

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Idk where that is in the US curriculum, but have you done measure theory?

marble solar Dec 30, 2020, 7:37 PM

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It's unlikely

gray gazelle Dec 30, 2020, 7:38 PM

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Hmm okay, I‘d usually recommend doing these two side-by-side

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Or probability theory after measure theory

grave egret Dec 30, 2020, 7:46 PM

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I think they were trying trying learn statistics. And instead found a probability theory book.

pearl imp Dec 30, 2020, 7:47 PM

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no, I want to learn probability first

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then maybe do some statistics

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I don't even know what measure theory is 😅

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I'm not advanced

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Like mid of a full computational calc book (Thomas/Larson/Stewart)

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Wanted to take a probability book along calc

gray gazelle Dec 30, 2020, 7:49 PM

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elementary probability theory chung ThinkingFren

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I think that‘s a good book but I have only skimmed the contents a bit

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It‘s entirely self contained

sturdy sail Dec 30, 2020, 7:57 PM

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There's this MIT open course https://youtube.com/playlist?list=PLUl4u3cNGP61MdtwGTqZA0MreSaDybji8

YouTube

6.041 Probabilistic Systems Analysis and Applied Probability

Videos from 6.041 Probabilistic Systems Analysis and Applied Probability, Fall 2010

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Where they use this book as a reference

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📎 Screenshot_20201230-165451.png

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And yeah, it's a great book to learn basic probability.

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And is really basic.

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You only need like real one variable and multivariate calculus to go through it.

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It doesn't talk too much about the modern way we study probability theory, which is by using a tool called measure theory.

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You usually learn about measure theory after a first course in real analysis.

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So if you still haven't

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This book is a great and the lectures by MIT are a great reference for studying the subject.

pearl imp Dec 30, 2020, 8:01 PM

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thanks will definitely check

sturdy sail Dec 30, 2020, 8:01 PM

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If you want a more advanced book you can check this

📎 Screenshot_20201230-165932.png

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"A course in Probability Theory by Kai Lai Chung"

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I still haven't read it mostly because I don't have too much appreciation of Probability Theory.

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https://youtube.com/playlist?list=PLo4jXE-LdDTS5BYqea-LcHdtjKwVcepP7

YouTube

Master Program: Probability Theory (2020)

Claudio Landim These lectures cover a one semester course in probability theory. Comments, corrections and exercises can be found in my webpage http://w3.imp...

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This book is used as a reference for this course.

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So again, if you are more of a lecture kind of person instead going through books this is a really set of lectures.

pearl imp Dec 30, 2020, 8:03 PM

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this too advanced for my level 😅

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the first one with the lectures was about right

sturdy sail Dec 30, 2020, 8:04 PM

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pearl imp this too advanced for my level 😅

That's ok, take your time. But if you feel interested to learn more, then these are really good references.

pearl imp Dec 30, 2020, 8:05 PM

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will definitely do, thanks a lot

sturdy sail Dec 30, 2020, 8:05 PM

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There's also lots of problem solving videos between each one of the lectures.

📎 Screenshot_20201230-170331.png

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Don't forget to check them.

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WanWan

pearl imp Dec 30, 2020, 8:06 PM

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hype

dawn tapir Dec 30, 2020, 11:19 PM

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Hey everyone. I'm a highschooler who's been self-studying Spivak's Calculus on and off for a while now. I've decided that I want up to resume my studies, but I'm not sure if I should continue with Spivak or if I should pick up a different book like Abbott's Understanding Analysis. I've taken calculus in school, and I've developed experience reading and writing proofs through books in other areas. I guess, since I haven't worked through Spivak in a bit, I've become kind of demotivated to read it. The exposition is great and the problems are difficult and interesting, but I've started to get excited about reading other books. I'm wondering if I should stick with Spivak. On one hand, I think I have sufficient mathematical maturity to move onto a real real analysis book. In fact, I've already read most of Tao's Analysis I. I've just forgotten a lot. Also, I'm kind of burned out with Spivak. On the other hand, I think I might benefit from working through it. What do you guys think I should do?

marble solar Dec 30, 2020, 11:22 PM

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How's your multivariate calculus?

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I'd suggest apostol volume 2 if it's lacking

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Linear algebra is also good to pick up

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Hoffman and kunze is the best

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Spivak's calculus on Manifolds is the natural next step after multivariate, linear, and spivak's calculus

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@dawn tapir

dawn tapir Dec 31, 2020, 12:11 AM

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@marble solar I took a multivariable calculus course this summer using Stewart, which was pretty computational

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I’m taking Linear Algebra right now.

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I’ll probably go through a book like Axler or Hoffman and Kunze eventually too

marble solar Dec 31, 2020, 12:23 AM

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Spivak's calculus on Manifolds is an excellent book

dawn tapir Dec 31, 2020, 12:23 AM

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Yeah that's what I've heard

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I'll definitely read that one eventually

marble solar Dec 31, 2020, 12:25 AM

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I think it's a good book to continue with

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It introduces a lot of the beginnings of all the subjects you'll learn about

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And shows how they're related

dawn tapir Dec 31, 2020, 12:26 AM

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I'll probably stick with it

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I guess I'm just kind of burned out since I've been working through it for a while

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And there are a lot of other subjects that I'm excited about

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I really want to learn more about algebra and linear algebra too

static crest Dec 31, 2020, 12:33 AM

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you're in high school still, and spivak isn't an easy book, you have a ton of time to learn everything

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if you're burning out and not progressing through spivak that well

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then take a break for a few months

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do lin alg in the meanwhile and then come back to spivak later

dawn tapir Dec 31, 2020, 12:39 AM

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That's true

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I might do that. I'll give Spivak another try, and I'll focus on Linear Algebra if I feel like I need a break

drifting elm Dec 31, 2020, 4:36 AM

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marble solar Spivak's calculus on Manifolds is an excellent book

last night I was checking prices for spivak calculus. the manifolds book is way cheap the calc book is $100+

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supply and demand I guess

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I really have to think about dropping $100 on a book though

obsidian valley Dec 31, 2020, 4:37 AM

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calc book is also like 500 pages

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lol

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i have the manifolds one besides me it is tiny

drifting elm Dec 31, 2020, 4:38 AM

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I heard the spivak book is out of print super collectible is that true?

obsidian valley Dec 31, 2020, 4:38 AM

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what book?

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manifolds is very in print and so is calculus

drifting elm Dec 31, 2020, 4:38 AM

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spivak calculus

obsidian valley Dec 31, 2020, 4:38 AM

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i mean i got a brand new copy of calculus here

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👀

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regret buying it tbh

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lol

drifting elm Dec 31, 2020, 4:39 AM

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haha

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my school uses the ron larson book

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I hate it

gray gazelle Dec 31, 2020, 4:39 AM

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spivak hmmm

drifting elm Dec 31, 2020, 4:39 AM

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but I had the ron larson videos and they were excellent

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ron larson teaches calc 1 like an analysis class on video

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you can only get it streaming from great courses plus

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the book is really a mess with all the hot hints and colored word balloons in the margins

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pointless math history in a calc 1 book everywhere

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pictures of dead people

marble solar Dec 31, 2020, 4:50 AM

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That's because that's what sells

warped cedar Dec 31, 2020, 4:50 AM

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schools always buy dumb ass books filled with bloat

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its easy to sell bulk

drifting elm Dec 31, 2020, 5:32 AM

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have you seen this book IRL? https://www.ebay.com/itm/Calculus-of-a-Single-Variable-11th-Edition-for-the-AP-by-Edwards-and-Larson/393000401296

eBay

Calculus of a Single Variable (11th Edition for the AP) by Edwards ...

Calculus of a Single Variable (11th Edition for the AP) by Edwards and Larson. With Calc chat and Calc View. Condition is "Like New". Shipped with USPS Media Mail.

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it is thick

warped cedar Dec 31, 2020, 5:41 AM

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Yes I have

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When I was in highschool we had a version of this

drifting elm Dec 31, 2020, 5:41 AM

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there is the AP edition for HS right?

warped cedar Dec 31, 2020, 5:41 AM

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I think I used the 6th edition

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yes there is

drifting elm Dec 31, 2020, 5:42 AM

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there is also the precalc by larson

warped cedar Dec 31, 2020, 5:42 AM

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the book covers AP

drifting elm Dec 31, 2020, 5:42 AM

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the precalc book is really good

warped cedar Dec 31, 2020, 5:42 AM

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I never read a textbook before calculus so idk

drifting elm Dec 31, 2020, 5:42 AM

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the precalc book teaches calc start to finish

warped cedar Dec 31, 2020, 5:42 AM

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Nice

drifting elm Dec 31, 2020, 5:42 AM

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the calc book skips steps in the examples

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then fills the book with exercises but no answers

warped cedar Dec 31, 2020, 5:43 AM

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yeah I used the 6th edition shit came out in 1998

drifting elm Dec 31, 2020, 5:43 AM

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but they still haven't even shown any step by step of a really hard problem

warped cedar Dec 31, 2020, 5:43 AM

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before i was born

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They dont do really hard problems in calc1

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lol

drifting elm Dec 31, 2020, 5:44 AM

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right but the examples don't show anything at all

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it was like here is the question here is the answer

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now do these 30 problems

warped cedar Dec 31, 2020, 5:44 AM

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Highschool textbooks always suck

drifting elm Dec 31, 2020, 5:45 AM

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I compare the ron larson calc to ron larson precalc and I don't understand how one of them is so great while the other is so shit

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and his videos are amazing

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basically teaching it like rudin

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theorems on screen, proofs on screen

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super hard examples

warped cedar Dec 31, 2020, 5:46 AM

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I never had a proof based calculus class in highschool

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or any proof based class at all

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I wont could geometry proofs

drifting elm Dec 31, 2020, 5:47 AM

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all the proofs were introduced as soon as the theorems were introduced

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some of them he didn't show proofs of the theorems but proofs of the problems at least

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he did prove some of the theorems though

storm sleet Dec 31, 2020, 7:23 AM

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Any good suggestion for Model theory books?

obsidian valley Dec 31, 2020, 7:37 AM

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I think I've heard Chang & Kiesler suggested

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I found this one the other day https://web.stanford.edu/group/cslipublications/cslipublications/Online/doets-basic-model-theory.pdf

gray gazelle Dec 31, 2020, 7:47 AM

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Marker

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Actually what kind are you looking for? Intro?

storm sleet Dec 31, 2020, 7:48 AM

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Intro and maybe something I can work towards

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I have a bit of background (not a ton) in logic if that helps

sage python Dec 31, 2020, 7:49 AM

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My undergrad logic class uses Chang and Kiesler I think

storm sleet Dec 31, 2020, 7:49 AM

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Y'all are blessed for having logic classes smh

gray gazelle Dec 31, 2020, 7:50 AM

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Something more advanced: Topological Model Theory by Flum, Ziegler, First Order Categorical Logic by Makkai, Reyes, if you know your set theory then Forcing, Arithmetic, Division Rings by Hirschfeld and Wheeler

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Topological model theory will use some (weak) second order however

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https://projecteuclid.org/DPubS?service=UI&version=1.0&verb=Display&handle=euclid.pl/1235417263#toc this book is also pretty good, it‘s about infinitary languages

Table of Contents

Project Euclid - mathematics and statistics online

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Note that the notation is a bit non standard in all of these but ig that‘s common in model theory

storm sleet Dec 31, 2020, 7:53 AM

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Non-standard notation isn't too much of a bother for me

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Only one that irked me was in my copy of mendelson where they use the subset symbol as implication

gray gazelle Dec 31, 2020, 7:54 AM

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That‘s.. suboptimal

storm sleet Dec 31, 2020, 7:54 AM

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Tbf it was a first edition that I got for $8

gray gazelle Dec 31, 2020, 7:55 AM

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I think that notation is also used in the principia

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So ig it‘s standard from a certain point of view