book-recommendations

[karmic thorn]

[stray veldt]

also its decent exercises

prove that Tx and Ty imply Tz or wtv

[karmic thorn]

[gray gazelle]

[stray veldt]

those names though

[iron granite]

Imagine if there was just a Mike b/w all these names.

Would be hilarious.

[quick hornet]

the naming is really dumb

i will forever be mad that "regular" and "normal" are not equivalent

they sound like words that should be equivalent

and the definitions seem really similar

but nope

[stray veldt]

i like how they were like "damn we forget something"

and now there is T2.5

also T2 and completely T2, wtf??

[quick hornet]

well completely t2 i get

since it only barely feels like a separation axiom

[iron granite]

Do all Topology books adopt the Naive Theory of sets?

[stray veldt]

well, point-set topology basically only talks about sets, so

[iron granite]

And how can you have an incomplete metric space?

[stray veldt]

Q with standard metric

3, 3.1, 3.14, 3.141, ... is cauchy but doesn't converge, bcs pi is not in Q

[quick hornet]

wdym

3 + 14/99

[iron granite]

He got you there.

[stray veldt]

ignore nami, he is a known shitposter

[iron granite]

Ah, so basically, for distance we need the reals

[quick hornet]

no?

[iron granite]

Suppose the distance is pie, but since Q doesn't have pie, it isn't possible.

Something like that?

[stray veldt]

distances between rationals will be rational

[quick hornet]

review the definition of "complete"

it doesnt rely on a metric at all

(intrinsically)

(it does in defining cauchy ofc)

[stray veldt]

i just remembered i have a related meme, mods dont ban me

[gray gazelle]

lmao

[iron granite]

Stupid question but, do Abstract Algebra and Topology ever intersect?

[stray veldt]

yes

algebraic topology is a rich field (of current research)

[iron granite]

k, thanks for the answer.

[novel obsidian]

algebraic topology channel when?

[supple folio]

hello, does anyone here knows where to read some parts of From five fingers to infinity : a journey through the history of mathematics by Frank Swertz?

[livid ermine]

normal hausdorff
completely normal hausdorff
perfectly normal hausdorff

sus

[graceful egret]

has anyone read discrete mathematics with applications by susanna epp? i've heard great things about it but it's pretty lengthy

ima give it a try but ive never dedicated myself to 993 entire ass pages

[iron granite]

It's nice.

You obviously don't have to read it all.

Some stuff I feel is just for CS people.

[craggy sapphire]

Good books to learn basic high school geometry? A book that explains things well, is easy to grasp for a noob and has good practice problems? Please don't recommend me euclid's elements man

[sudden kindle]

everything's perfectly normasl

nothing sus here

[karmic thorn]

Not particularly basic but maybe first few chapters from Coxeter's Introduction to Geometry?

[iron granite]

I've heard good things about Kiselev's books, check him out if you want to.

[strange vine]

does anyone know any books about the philosophy of statistics (e.g. bayesian epistemology)?

and which covers different interpretations like bayesian, frequentist and information-theoretic probability

[craggy sapphire]

looks good thanks

[wintry lotus]

Hi! Just wondering if Stein and Shakarchi's book on Fourier Analysis is a good book for the topic?

[broken meadow]

it is very elementary

i would recommend it if you're like

new to analysis

[wintry lotus]

Also, if anyone's studied it before, how much can I aim to cover in a month, assuming no prior background in Fourier Analysis? Just trying to plan something for the month of December, want to learn Fourier Analysis. I was thinking about first 4 chapters?

[broken meadow]

according to daminark and some older ppl you wanna learn some more math and do a different book if u wanna do fourier analysis a lot more solidly

yeah

up to ch4 sounds doable in a month

[wintry lotus]

I have done courses on Measure Theory, Real Analysis, Complex Analysis, Functional Analysis, so I'm certainly not new right? Not sure

[broken meadow]

oh dear

ok you might be able to do it in a week

[wintry lotus]

LMAO what

[broken meadow]

yeah totally just look at it

half of the time it's just basic integral estimates

[wintry lotus]

ok what's a better book then

[broken meadow]

no clue since im a baby

@sage python

[gusty smelt]

the correct answer is to learn fourier analysis on locally compact groups

[wintry lotus]

but idk any Fourier Analysis at all, yet :P

I wanna start from scratch

[broken meadow]

it wouldn't hurt to look at stein shakarchi for sure

i just think that you'd find it is very very easy

[wintry lotus]

Okay at least it'd be a good starting point

[broken meadow]

hopefully daminark will give you a secondary source

yeah

he might provide a book so that you could continue

[wintry lotus]

Yep! Cool

[gusty smelt]

i think their fourier analysis book doesnt have like, lebesgue integral

[broken meadow]

it doesn't

[gusty smelt]

so its a bit wierd

[broken meadow]

it assumes only riemann integration

[wintry lotus]

Eventually, I want to be able to read Koldobsky's book on Fourier Analysis in Convex Geometry

That's what I'm doing this

[wintry lotus]

That's true, because they teach Measure Theory in a later volume

[sudden kindle]

Might be good for me to look at it

I never really learned Fourier analysis

[gray gazelle]

riemann integration

[sage python]

Yeah Stein Fourier is prob on the easy side if you know measure theory

@frigid comet prob has better recommendations, one of my friends swears by Schlag for harmonic analysis and it's likely what I'll use

Grafakos is also supposed to be good

[remote ginkgo]

https://cdn.discordapp.com/attachments/755572912425009276/906295765574516786/IntroRealAnal.pdf

just pop open rudin

[sage python]

@remote ginkgo this covers very little Fourier analysis and Hausdorff later indicated having background in subjects like measure theory that go far beyond this document

[remote ginkgo]

hm

ya

i had some stuff in my to read list on the topic

[sage python]

It does seem good at a glance but yeah that's why the other recs were Stein+

[remote ginkgo]

i have a russian translated dover book

and ofc i have stein which i havent read yet

[frigid comet]

Yeah I'd say Grafakos classical fourier analysis is what you want.

[marble solar]

I think Stein's volume 4 is really good intro to harmonic

The first 3 or 4 chapters

[misty wyvern]

Stein also has a literal book on harmonic analysis.

[marble solar]

He has 3: Singular Integrals, Fourier Analysis on Euclidean Spaces, and his mammoth harmonic analysis

The thing is that volume 4 has a lot of the same sections contained in some of the books

But the exposition/arguments are cleaner, and they have exercises to solve

So I think as far as getting a grounding in the material, I think volume 4 does a better job

Than the other texts by stein, which are classics

[iron granite]

but he's a guy...

[dapper root]

だが男だ

[sage python]

I should say about Schlag's books that my friend, whose opinions I'd say tend to be good, has referred to it as the best textbook ever written

And tbh I will likely use that when it's time for me to learn the stuff

I'm gonna make @orchid agate read it

Oh wrong one

@ionic wren

Since you like automorphic forms you wanna learn some Fourier analysis eventually

[ionic wren]

sick

ill have time to read stuff once my exams are over

[sage python]

Lol F. Had any time to do some fun math?

[gray gazelle]

excuse me, could anyone recommend me some good AA book other than Herstein?

hardcore one*

[sage python]

If you want hardcore try Lang

More realistically, Jacobson

[gray gazelle]

thanks dami

cool recommendation you got there

[ionic wren]

nah not really, i had been practicing for exams

i did 124/62 (each exam had 2 parts to it) exams in practice for maths

i hope i did well

[reef wolf]

any good book for 3d coordinate geometry

[gray gazelle]

Hungerford homie

Besides the classic d&f but its not h4rdc0r3

[prisma snow]

Rotman

[gray gazelle]

no

[frosty girder]

i liked artin for as much as i did it
pretty nice it is

[cobalt arch]

Knapp is really good too

Or if you are really hardcore Lang with the supplementary notes by Bergman

[iron granite]

what is the most comprehensive group theory book?

[gray gazelle]

Rotman

[iron granite]

Full name?

[karmic thorn]

Advanced Group Theory by Joseph Rotman, I think

[iron granite]

k thanks

uhh there's no such book?

I cant find it

[gray gazelle]

The advanced one is advanced modern algebra

The group is introduction to the theory of groups

[iron granite]

okay

thank

[wintry lotus]

Great, thanks!

[solemn panther]

I found it, Plane Trignometry is very good, it gives a conceptual understanding of every concept along with practise problems.

[iron granite]

Have any of you read Measures, Integrals and Martingales?

[cunning notch]

The Art of the Deal

[raven patio]

Not many math books are there tho

[cunning notch]

The Bible

[raven patio]

[stray veldt]

i have a good recommendation for the history of mathematics: https://link.springer.com/book/10.1007/978-1-4939-3264-1

@karmic thorn because you might care

[iron granite]

Asking again;

Have any of you read Measures, Integrals and Martingales?

[misty wyvern]

why, is that your book?

Well I'm looking at the TOC and it actually looks really good. I know Schilling's book on BM so I like his writing style.

[karmic thorn]

Thanks!!

[misty wyvern]

If you want to learn measures this way I'd say it looks good.

[karmic thorn]

They forgot to list my birth smh

[iron granite]

Heard good things about it and wanted to know whether it lived up to it's rep

[remote ginkgo]

I love you

[iron granite]

https://www.youtube.com/watch?v=dW8Cy6WrO94&list=PL55C7C83781CF4316 @karmic thorn

Don't know how useful this is to you but I found this guy decent.

It's an entire playlist.

[karmic thorn]

Wildberger

I just hope he didn't mix finitist takes here as well

[iron granite]

yeah he says that there is a hole at the bottom of analysis (paraphrasing) but im too analysis illiterate to understand.

[karmic thorn]

[iron granite]

btw what is a finitist?

[karmic thorn]

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

[iron granite]

seems stupid

considering how far we've come using the notion of infinity

[karmic thorn]

I don't know much

Maybe there's some genuine work being done with that perspective

[iron granite]

I'll just wait for the Veritasium video.

[misty wyvern]

Veritasium is the worst

[iron granite]

I thought his godel video was really good

[misty wyvern]

His best video is the day he didn't upload one

[iron granite]

damn, did he do something? what's this hatred? lol

[misty wyvern]

He is the reason why every math grad student gets 10000 crank emails about solving the collatz

[iron granite]

Not much of a reason to hate him

What is he supposed to do? Not make a video on an interesting problem and earn mone?

[misty wyvern]

yes

[iron granite]

Maybe I'll empathize when I'm a grad student.

[misty wyvern]

I'm just memeing, most pop sci folk aren't bad, just cringe

[iron granite]

What are they supposed to do except be pop tho

you can't expect most folk to be able to understand technicalities

although I guess Vsauce did do this better.

[sage python]

So idk about Veritasium, we'v definitely had debates about Numberphile though that was less about popularizing and more about the fact that the thing he was trying to popularize was the zeta function

But he was playing games with divergent series in order to do so, at which point you've pretty much tossed out the irl content/what's interesting about it

[foggy relic]

Veritasium is interesting imo

like he combines math and history

i especially liked his vid on equations of higher degrees

we all know 3b1b is the best mathtuber

[sage python]

Eventually the Numberphile discussion did go the crankery direction. Like okay he's wrong, and in an irreparable way, but he's making people interested in math and that's good, right? To which a number of people responded "He probably created more cranks than he did people who would engage in math in a quality manner". Which is an empirical question rather than pure reason so obv it couldn't be resolved

I think Vsauce's video on Banach-Tarski is the best pop math video there is. 3b1b feels slightly less pop math and more, introducing cool math to people who were probably interested in math already.

[karmic thorn]

I agree with the take on 3b1b

[grim pivot]

Like you said, popularizing an idea/subject often requires exposing people to the cool parts and and far-reaches of that subject. This will get a lot of people thinking and will naturally increase the number of newbies who think they’ve solved something amazing. It’s honestly just part of getting people interested in a topic

[misty wyvern]

Thanks primarily to pop sci I had no interest in hard sciences until I accidentally studied it rigorously.

[grim pivot]

3b1b does a good job at not luring people into thinking they can solve something amazing with just a little thought, but that laid back-ness also is less likely to get new people super interested in a subject

[sage python]

So the thing that I am more inclined to believe based on my experience is that "X video introduced more people to math" being correlated with "X video leads to more math crankery" is less that the individuals who end up getting into math through these videos have a newbie/crank stage and is more a general statement about accessibility

[misty wyvern]

I don't care about more or fewer people getting into math, I do care about people butchering my work aieeeeeeeeeeEEEE

[sage python]

I think there are a wide variety of reactions one can have to a piece of content like this. Tbh I'd wager most people who would find the video interesting are already vaguely into math anyway. If those people play around with it further I doubt they become "permanent cranks", feels like they have enough mathematical common sense that eventually someone can get it through to them that shit's harder than they think. In which case either they continue to learn or the momentum is stuffed out

Others will watch it and be like oh that's cute

And not continue

Then you have the people who had little interest in math before but actually get into it somewhat seriously because of this video. My guess is that this group is much smaller, and it's not clear to me what the distribution is of cranks vs people who actually run with the math in a positive way

So that's where it's like 🤷

[gray gazelle]

its an old playlist

I dont think he does

[karmic thorn]

Aah, I see

I've just grown more reluctant to actually watch his videos to learn stuff

Because as a novice I can never tell if he just mixes his own agenda and affects my own understanding that way

[gray gazelle]

thats fair, but I know some of those vids use stillwell's book

[karmic thorn]

Ahh

[brittle latch]

thoughts on Proofs from THE BOOK

just checked it out of the library and im excited

[quick hornet]

@sage python youre giving a pretty generous treatment to a video with a title that says math has a "fundamental flaw" or some shit

like maybe the content is fine but you know how many people dont read articles past the headline

[sage python]

I'm talking about Numberphile mostly

I have no idea who Veritasium is

[foggy relic]

this dude https://en.wikipedia.org/wiki/Derek_Muller

and this is one of his best vids imo https://www.youtube.com/watch?v=cUzklzVXJwo

[quick hornet]

how not to read a room

[brittle latch]

vid was interesting but god that title makes me squirm

[stray veldt]

another interesting book: https://press.princeton.edu/books/hardcover/9780691199221/do-not-erase

[stray veldt]

you're more like a sibling to me

[remote ginkgo]

The love is platonic, not fraternal

[remote ginkgo]

Ok now it's fraternal.

[dapper zenith]

should i know something before reading concrete maths by knuth i am finding it quite difficult after 1st chapter

[misty wyvern]

Just keep bashing your head against it, it's dense but I don't think it has a high barrier to entry.

[iron granite]

I have it

It's good so far though Ive only read 4 chapters

[glad prairie]

"is popmath GOOD or BAD?" volume 837272737743

[cursive orbit]

Lol

Popmath titles are bad

[gray gazelle]

Anyone knows a book that develops synthetic geometry for the plane rigorously and like talks about linear spaces, ordered geometry and neutral geometry, and euclidean and hyperbolic? preferably without using real numbers for axioms

[gray gazelle]

Robin Hartshorne's Geometry: Euclid and Beyond seems interesting so far

[marble solar]

GOAD

[glad prairie]

Greatest Of All Dime

[gray gazelle]

people in this server are so unserious

[gray jungle]

is there any good concise books on probability
and what are the standards for proba in general?

[marble solar]

Rick Durrett's text on probability looks good

[gray gazelle]

Resnick, A probability path is nice imo

[gray gazelle]

I liked Shiryaev's approach

[gray jungle]

what about YA rozanov probability theory a concise course ?

[gray gazelle]

of course

[broken meadow]

people in this server are so unserious

[gray gazelle]

ikr right

[buoyant eagle]

Never seen “A Comprehensive Introduction to Differential Geometry” recommended alongside “Goodnight Moon” and “Green Eggs and Ham” before

But apparently Spivak wrote a children’s book?

[gray jungle]

what do you guys think of Basic probability theory by robert B ash

[subtle siren]

What level are you talking about?

[subtle siren]

The most standard, though I think more for applied math than for those who like Analysis-Probability

[subtle siren]

Amazon says it is concise, which might be what you want.

[subtle siren]

No clue on this. Though TBH I am not sure why you are looking for books that old. Personally I am more of a published-later-is-better than earlier is better. i.e. if possible I rather not read Feller+Billingsley

Actually as a segue, I'd like to know people here's opinions on more modern alternatives to Feller/Billingsley

[gray jungle]

this is the content of rozanov

tho i might go with rober b ash book
im looking for intro proba that bridges into more advanced concepts eventually

[subtle siren]

TBH I would recommend a book on intro and then a specific book on advanced things, but up to you. I'm not sure on those

[gray jungle]

what would you recommend

[gray gazelle]

can someone recommend valuable resources for Combinatorics?

[karmic thorn]

Do you have something more specific in mind?

[subtle siren]

Durrett for the intro, you'd need something more specific for the advanced stuff

Wait apparently Durrett is into grad, for my own digital library of undergrad probability I have Blitzstein Hwang and Wagaman Dobrow, though I have not actually read them in detail, but they seemed undergrad-ish to me

For harder stuff you would probably need to ask for specifically. I have seen Schilling's Measures/Martingales book for that sort of thing

This is I think a standard for undergrad prob
https://www.amazon.com/First-Course-Probability-10th/dp/0134753119
(replaced 9th ed with 10th ed)

Other than the less-than-stellar amazon reviews, also
https://news.ycombinator.com/item?id=18429429

and
https://www.reddit.com/r/statistics/comments/is3o5t/q_looking_for_good_intro_to_probability_books/

TBH I realised my uni provided me with the lecture notes and stuff, so I can't quite comment on just using one book. Also I suppose it should be good to try various books

[gray gazelle]

I wanna recap what I have been learned during high school.

[karmic thorn]

Oh, then probably the concerned parts in any discrete math or introductory combinatorics book

You can look up Art of Problem Solving and the likes for slightly more challenging problems (mostly with solutions) as well

[gray gazelle]

I can see books like this one: https://www.amazon.com/dp/1441927239

and this: https://www-math.mit.edu/~rstan/ec/

[gray gazelle]

I think this is well suited for me

[gray gazelle]

it's very basic to be honest

[gray jungle]

i don't want to spend more than whats needed on non-measure theory proba its just required so im gonna use romanovs concise book for intro proba (and suppliment when needed) and then use other books to bridge for measure theory and advanced concepts
thanks for the help

[karmic thorn]

Oh, yeah, if you consider AoPS to be basic then undergraduate textbooks on combinatorics would be much more handy

I shill Miklos Bona's A Walk Through Combinatorics

[bitter raptor]

i swear manan has read every book

[gray gazelle]

I wanna recap Olympiad-level Combinatorics

[subtle siren]

"every" is actually just Vakil, I'm pretty sure

[karmic thorn]

*ToC and Preface of every book ;)

[karmic thorn]

I suppose undergraduate texts like Bona are near that level, even a bit beyond

[gray gazelle]

great, I'll have a look

[karmic thorn]

[gray gazelle]

got it, thanks

[steel temple]

any good books for an intro to combinatorics?

[gray gazelle]

Serre - a course in arithmetic

[gray gazelle]

I started Graduate Lang and I didnt expect it to be so dense

but the examples are cool af

[dark orbit]

i think it's assumed by the time you're reading lang that you actually enjoy this for some reason

[gray gazelle]

[sudden kindle]

Lang

Big book

[uncut zealot]

My school's library only has Munkres first edition, which only has 8 chapters. Is it worth looking elsewhere for a copy of the 2nd edition?

[karmic thorn]

Chapter 9 onwards is the bit on algebraic topology right? And I guess that's not particularly recommended either

[karmic thorn]

A Walk Through Combinatorics, Miklos Bona

[quick crypt]

Principles and Techniques of Combinatorics

[marble solar]

It's actually pretty good

In that it does a lot of details slowly

[karmic thorn]

Ah, I see

[grim lion]

Hi, does anyone have a recommendation for a good book that explains precalc
(high school level) well? Not just examples, but steps and repeatable processes, as well as explanations why? I know the info can be found online for free, but the problem with that is the info is not organized cohesively or in order. I'd like a book where everything I need to learn the concepts is in one place

Something I can use to kind of teach myself precalc because I feel my class explanations aren't very helpful to me, with easily understandable resources (also please ping if you have a suggestion, thank you for your time!)

[karmic thorn]

Have you tried Khan Academy?

The organisation and content are both very clean and standard.

[grim lion]

Yes, but I feel that it is helpful to a point- it teaches things the basics, which are too simple compared to what my teacher wants us to know- he assigns homework that uses the same concept in more difficult and in depth ways to test understanding, rather than steps

and doesn't really explain the reasoning

Thank you though

[karmic thorn]

I see. There's a precalculus textbook by OpenStax I think, you could check it out (it's available for free online); another common recommendation given here is Serge Lang's Basic Mathematics-bear in mind this doesn't adhere to standard curriculum in a lot of places and emphasises mathematical rigour much more than usual.

[grim lion]

Okay, I will have to check those out, thank you so much! They sound promising :)

[karmic thorn]

Goodluck

[craggy radish]

Any suggestions for a linear algebra book?

As complement to linear algebra 2 im taking rn

[sage python]

@craggy radish proof based? What topics are you covering?

[craggy radish]

So far we covered vector spaces, linear transformations, and change of basis.

And its a mix of proofs and computation

[sharp latch]

People's opinions on Linalg textbooks vary wildly so I'd wait to hear from other people than just me. But my take is: Friedberg is pretty based if the course has a lot of proofs, otherwise pretty much any linalg textbook will do

[craggy radish]

I did some googling and people are mainly saying Linear Algebra Done Right by Axler and Strang's "Linear Algebra and its applications"

[craggy radish]

Ill take a look at this as well

[sharp latch]

Yeah I personally didn't like axler but havent checked out strang before

[slow matrix]

how is it compared to brown's topology and groupoid? since both seems aimed at pointset topology and a bit algebraic too in the latter half

I'm thinking of printing one of these, munkres seems to be more standard, while brown has better pdf source

[glad grail]

Like are there any online resources I can use to practice uni level problems? books are very expensive and I can't keep on buying so many because of the variety of stuff included in electrical Engineering

[versed bough]

does anyone wanna rate my essay

[karmic thorn]

You'll have to scavenge good resources but you should be able to find lots of lecture notes, problem sets, etc. on MIT OCW.

[glad grail]

I heard david tong's notes contain good problems, any similar math notes

[karmic thorn]

MIT OCW has a ton of stuff, but usually "(topic name) lecture notes" will show up a lot of results on Google.

[gray gazelle]

finance math book recommendations?

[oak pecan]

what level? Shreve vol 2 is probably the standard thing to start with for a math major

[iron granite]

uhh is Complex Variables by Kasana a bad book? @karmic thorn

[karmic thorn]

I've never heard of it, I have no opinions

[iron granite]

the emojis had me scared

it had almost 4.4 on Amazon so I thought that I might as well buy it...

[karmic thorn]

[frosty girder]

dont judge books by their amazon rating

[iron granite]

I know, I judge them by their prices first because most math books are fucking expensive.

[slow matrix]

I judge them by their page count since I simply print them.

[gray gazelle]

You can't judge a cover of a book by its look.

[sharp latch]

But you CAN cover a compact book by a finite subcover

[dark orbit]

frankly this raises the spectre of a non-compact book and I'm not especially thrilled to imagine what that might look like

[karmic thorn]

Ultra's puns are always on point.

[drifting wigeon]

lmao

[slender dragon]

Do you know some Inquiry Base Learning books on Mathematics?

An example of book is like Linear Algebra Problem Book of Paul Halmos

[gray gazelle]

Hello!!!🤗 So... I'm studying Newton-Cotes Formulas, Guassian Quadrature, ... , (a lot of fancy names😅) so any books you guys would recomend? My teacher is just using his powerpoint to explain and... that sucks so much ;-;

[limpid gazelle]

What do you guys suggest to read for dynamics? I want to read both continuous and discrete dynamics and a gentle introduction is probably better

[dapper root]

Calling in @gray gazelle and @glad prairie

[limpid gazelle]

Lmao

[atomic hound]

So, what would be a good and rigoruous book on calculus 1?

[gray gazelle]

well you could try calculus james stewart don't know if it's the best book ;-;

[atomic hound]

Man, james stewart seems very good,but i wanna a rigoruous one,you know?

[limpid gazelle]

Oh haha those two are the two books I have in mind actually

Alright I'm going to checkout both I guess

[gray gazelle]

no idea sorry mate

[atomic hound]

Alright,thanks for trying!

[timber mesa]

Robinson's Dynamical Systems: Stability, Symbolic Dynamics, and Chaos is very complete but at the same time fairly gentle. Another is Katok-Hassenblatt's A first course in dynamics (not to be confused with their larger and far more advanced dynamics book) which is more of an overview that doesn't go too in depth

there's also Hirsch-Smale-Devaney which is basically an ODE book that also contains a chapter on discrete dynamics

[limpid gazelle]

The larger book is called "Introduction to the Modern Theory of Dynamical Systems" right

[timber mesa]

yep

my rec would be Robinson, as I said it's fairly gentle and contains detailed proofs of most things

yet it covers many topics in both discrete and continuous systems

[limpid gazelle]

Alright cool

I just found out about sharkovskii theorem yesterday which got me really excited

And Hirsch-Smale-Devaney's book is "Differential Equations, Dynamical Systems, and an Introduction to Chaos"?

[low turtle]

Does anyone know of any upper level undergrad or intro grad level books that use pictures? iirc ive seen a few before but I can't remember what they are, id really like to look through and read parts of them though. Currently wrapping up my first semester of analysis and modern alg, I definitely like modern algebra better thus far, which I wasnt expecting

[fluid bay]

spivak calculus is the usual recommendation for this

[fluid bay]

a lot of geometry/topology books have some kind of pictures. Like Lee's introduction to smooth manifolds or Hatcher's algebraic topology

[timber mesa]

yep that one

[timber mesa]

yeah it's a pretty intriguing result, chap 3 in Robinson has a section dedicated to it

[karmic thorn]

There's a combinatorics book whose title is something like "An Inquiry Based Approach to Enumerative Combinatorics", you could check it out.

[gray gazelle]

Spivak

Don't pick up something trashy like Stewart or Thomas.

[gray gazelle]

[analog pollen]

spivak calculus

[analog pollen]

those books aren't that trash lol, depends on the context

[iron granite]

thomas isnt trashy

its decent

[analog pollen]

stewart is also decent

worked fine for me

[surreal phoenix]

I love looking at its price, especially

[analog pollen]

i got it pretty cheap so i don't have that bias

[gray gazelle]

Stewart is made for edgy High schoolers xd

[quick hornet]

edgy high schoolers
username: Ted Kaczynski

[analog pollen]

lmao

[quick hornet]

those in glass houses...

[gray gazelle]

Lmao

[surreal phoenix]

I need to look up that name brb

[quick hornet]

unabomber

[surreal phoenix]

Oh, right.. Him

[gray gazelle]

I am not dead yet

Still fighting the rise of industrial society

[iron granite]

hmm

on discord

[gray gazelle]

via Netflix

[gray gazelle]

Yeah I hear this sentiment all the time online. 'Only way to learn calculus is by Apostol or Spivak.'

[analog pollen]

Wut

[gray gazelle]

'Only through the degeneracy of the multitudes do we use of Stewart or Thomas etc.'

[analog pollen]

I don’t see anything wrong with those 2 books lol

It worked fine for me

I see why ppl like spivak or apostol more but depends on preference

[karmic thorn]

They just have different audiences

Most people who learn calculus aren't math majors

And Spivak is not exactly the best fit for them

[surreal phoenix]

I mean, would you recommend spivak to anyone who's not doing analysis in the future? I feel like there's a lot in there people just don't need to know

[analog pollen]

Agree

[gray gazelle]

Good complex analysis specialist idk whats the deal

[gray gazelle]

Rudin

[atomic hound]

Oh yeah i gonna ccheck out.

[atomic hound]

Lol,really?

[atomic hound]

Rudin,huh?

[slow matrix]

people are calling on which and which book is best read, and here I am just innocently looking which book has best pdf source to print to decorate my room.

[gray gazelle]

Spivak/Apostol if youre in math major, Stewart if not

major.....

[atomic hound]

i am computer science major,but i wanna be rigouous about math so i´ll take it.

thanks Guys for the recommendations

[gentle wharf]

hello anybody here who can recommend me a book for complex numbers

for a undergraguate level

[tropic gulch]

who all gonna write pre rmo?

i want some good reference books for it

[iron granite]

any problem books in Abstract Algebra?

[crude sable]

dummit foote

[gray gazelle]

herstein

lang

jacobson

and hungerford

[iron granite]

okay

Will learning logic of compound and quantified statements help in analysis?

[distant bobcat]

any recs for abstract algebra?

[broken meadow]

scrll up

[manic cape]

idk there are plenty of good books on that

on different parts of the subject

[livid ermine]

[iron granite]

DONT LOOK UP THE NAME OF THE AUTHOR OF CAT IN A HAT

[frosty girder]

Artin and knapp and gallian

[frosty girder]

i almost forget that there exists a pinned message here

This one

[iron granite]

Has anyone read Induction by Adreescu Titu?

[gray gazelle]

Could someone suggest a problem book which deals with functions and relations? undergrad level

[brittle latch]

and an entire channel full of recommendations

[gray gazelle]

Bourbaki

[frosty girder]

[cedar ridge]

apostol?

nvm George B. Thomas, not Tom Apostol

what books can be considered "a rigorous course in epsilon-delta (real) analysis"

[frosty girder]

baby rudin, apostols book (which im doing currently), Taos books, bartle, abbott (recommended for new people a lot, seems pretty good)

[stray veldt]

amann escher

[karmic thorn]

[frosty girder]

[frosty girder]

what happened to ur notes manan

[gray gazelle]

Spivak might be a good fit

[iron granite]

The Foundations Of Mathematics by Kenneth Kunen is really readable.

[gray gazelle]

Another one which someone here recommended was Calculus: A rigorous course by Velleman

[karmic thorn]

I'll get back to them tomorrow

[frosty girder]

:nice:

[stray veldt]

manan textbook author arc?

[karmic thorn]

I'm reading notes, not writing yet

I did start a blog but Just never got back to it after a post

Might consider dumping some logic as I learn it over there

[cedar ridge]

abbott or taos better 🧐

[gray gazelle]

Abbott

[iron granite]

Manan, coaching center arc when?

I want to see degredation.

[cedar ridge]

whys that 🧐

[gray gazelle]

I have heard things about Tao like lacking quality amount of problems, unclear exposition, etc

[cedar ridge]

ty🙇‍♂️ ill look into it

[gray gazelle]

👍

[karmic thorn]

Never

[iron granite]

but what about mone?

you just need to sell your soul /s

[gray gazelle]

Mooching off of some poor mother selling her jewellery to get money to educate her kid in some fancy ass coaching isn't very satisfying I suppose

[frosty girder]

i would say abbott

[frosty girder]

put it so that someone like me can understand as well

[livid ermine]

If I were you I would skip calculus and real analysis, and go straight to topology. And then differential geometry.

[prisma snow]

And if I were you, I would be a clown

[frosty girder]

⭐

[karmic thorn]

Nothing changed

[frosty girder]

oh fuck this star

its getting annoying

[prisma snow]

You've done this like 5 times today...

[frosty girder]

more actually

idk why but the star is the top emoji whenever i type sta

im not doing it on purpose

And im used to just typing sta and pressing enter so i cant even stop it

[prisma snow]

just type stare and don't be so lazy, jfc

[frosty girder]

I want to be quick

[prisma snow]

Is having to edit every message quicker?

[frosty girder]

no

but i cant understand why this fucking star is in the top

[prisma snow]

It's the closest match

[frosty girder]

it used to be the stare emoji

whatever

😔

[gray gazelle]

just make a keyboard shortcut to type :stare: when you press it

simple

[marble solar]

Is it any good?

[atomic hound]

Wait this seems conterintuitive.

@livid ermine and why go straight to topology?

You got me curious.

[atomic hound]

Very random

[prisma snow]

Don't listen to them

That's why i called them a clown

That's terrible advice

[livid ermine]

more compact and efficient. if you know diff geo well you know calculus, but if you know calculus you don't know diff geo. takes less time to learn 1 subject than to learn 3

[prisma snow]

That's actually false

Since you are not taking into account how much longer it would take to learn it without knowing any prereqs

[analog pollen]

is "An introduction to Manifolds" by Tu good?

[atomic hound]

That is why i should go to topoly?

[atomic hound]

What?

[atomic hound]

Yeah, it sounds like one.

[atomic hound]

Oh yeah, i think you are smart person.

[prisma snow]

I agree

[analog pollen]

bump

[timber mesa]

yeah, literally every topology or diffgeo book assumes you're already proficient with calculus and some analysis, and most people don't grasp these things instantly.

[timber mesa]

spivak is the usual rec for "rigorous calculus"/real analysis

[sand crescent]

what do people feel about algebraic number theory by neukirch?

[frosty girder]

thats a nice idea

[atomic hound]

Thanks, bro. And thanks to everyone here the recommended the book.

[gray gazelle]

Dunno. Haven't tried it.

[marble solar]

Based

[sudden kindle]

Fuv

[sage python]

I like it!

[dapper root]

I like it!

[broken meadow]

Good morning!

[gray gazelle]

good afternoon

[gray gazelle]

good evening

[regal wasp]

IMO yes but in general the subject is a bit dry to me so Idk if I’m evaluating it correctly

[atomic hound]

Good morning. Northing is more good than start the day with math.

For me,it is 8:30pm

[broken meadow]

it's 6:30pm for me lol

i said good morning as a joke for something else haha

[grim pivot]

How’s the Atlantic Ocean?

[atomic hound]

I don't live that close on the coast.

[atomic hound]

[atomic hound]

Man, where do you live?

If you dont mind

[broken meadow]

Florida

[smoky zephyr]

est zone gang

[atomic hound]

What?

[atomic hound]

Humm,miami.

[smoky zephyr]

at least part of florida is est then, didn’t known that

[broken meadow]

i don't live that far south

pretty sure most of florida if not all of it is est

[grim pivot]

This server is slowly just turning into 5 discussion channels

[rain birch]

I wanted to recommend "Mathematics for the Nonmathematician" by Morris Kline.

[sand crescent]

arigato, I'll give it a read

[cedar ridge]

cant remember the name of the book but anyone know of a undergrad prob book that uses/based on real analysis?

[iron granite]

any rigorous books on counting?

[dark orbit]

i hear this teaches you how to count pretty rigorously

less jokingly, can you be more specific?

seems like a general discrete math introductory text if it's just general counting, no?

[iron granite]

like you define permutation using 3 cycles and translocations etc

[quick hornet]

im not sure if id consider an algebraic approach to combinatorics "more rigorous"

[iron granite]

certainly it's interestin

[quick hornet]

the point is to offer an alternate perspective thats sometimes useful for reasoning

not necessarily a "rigorous" one

since if you want to make that approach fully rigorous, you have to introduce a shitton of group action stuff to justify everything to the point where it just gets tedious

[iron granite]

hmm

then can you recommend a book on counting with a general approach

[karmic thorn]

A book on combinatorics?

[frosty girder]

Bona's "A walk through Combinatorics"

[crystal lion]

Bona is the new Rudin

[gray gazelle]

Pughs book is massive damn

[analog pollen]

ok ill see thanks!

[halcyon garden]

What would you consider to be a good book that's pretty damn representative of undergraduate math. Like what book would you recommend a person who is confused between a physics and math major and has done proof based linear algebra, analysis and elementary differential geometry to gauge their interests in a better way.

Right, that makes sense. What book would you recommend ? Something that doesnt require too much math maturity

I see, thank you

[regal wasp]

Linear algebra + diff geo + analysis+physics sounds like a natural precursor to differential manifolds if you know topology as well

[analog pollen]

Maybe nakahara’s “geomtery, topology and physics” might be fun

See if u like it

[sage kelp]

Has anyone heard about Krantz's book on Real Analysis?

[marble solar]

I think Krantz has

[remote ginkgo]

Have you seen the book on analytic combinatorics

[remote ginkgo]

I've been recommended this book before for topics in geometry

[cedar ridge]

one of my lecturers mentioned being very engaged by "an axiomatic approach to linear algebra" during his undergrad. what does this mean and what books teach this way

[frosty girder]

any non engineer oriented book will teach this i suppose

like Axlers book, or insel and spencers book

etc etc

[cedar ridge]

so LA w/out determinants?

or just learning about vector spaces/inner products

[frosty girder]

No not that

LA without determinants doesnt mean axiomatic on itself

it just means learning LA properly

defining and proving stuff

[frosty girder]

learning and using what u learn to prove other stuff, yeah

[cedar ridge]

dont quite get it

[frosty girder]

it just means to do LA rigorously

[cedar ridge]

ok

[sterile cedar]

i dont think learning LA without determinatns makes it rigourous or proper

[gray gazelle]

Advanced linear algebra by Bruce cooperstein.

It weird I never see this book mentioned here.

[frosty girder]

Axler btfo

[fresh nest]

You all fucking suck

[surreal phoenix]

[frosty girder]

no u

[sterile cedar]

module theory makes LA rigorous, not the removal of determinants, axler can go btfo

[frosty girder]

[gray gazelle]

first order logic makes LA rigorous

removing determinants has nothing to do with rigor btw. both approaches should be correct.

[analog pollen]

nice its a great book for physics students

doesn't assume knowledge in analysis/topology and diff geo

[iron granite]

Pugh has sinned for he uses the epsilon of belonging rather than the epsilon of curvature.

[gray gazelle]

$\varepsilon \epsilon \mathbb R^+$

[hasty eagle]

Carla_

[crude sable]

$\epsilon$ supremacist

[hasty eagle]

Ryuzaki

[polar mango]

hey does anyone know any good books for clac 1

calc

[gray gazelle]

a lot of people here suggest spivak's calc

[gray gazelle]

[polar mango]

ok

[atomic hound]

Who ping?

I am curious.

[analog pollen]

Depends, rigourous or less formal?

[polar mango]

For now a less formal

But in the future I would like for formal so I need a strong foundation

[analog pollen]

Spivak then

You a math major?

[polar mango]

No I’m in engineering

[analog pollen]

Ah

[polar mango]

Mechanical to be exact

[analog pollen]

*stewart calculus

@polar mango

[polar mango]

Ok

Which edition should I get

@analog pollen

Or does it not matter

[analog pollen]

Idk they are all the same

[polar mango]

Ok thanks

[analog pollen]

Cheapest is best ig

[polar mango]

Alr

[analog pollen]

Or just download a pdf

[polar mango]

Are there any free ones

[analog pollen]

Just look up on google or something

Stewart calculus pdf

[polar mango]

Ok

[analog pollen]

Or hol up

[polar mango]

?

[analog pollen]

Ill send it

Wait

[polar mango]

Ok

[analog pollen]

@polar mango

[polar mango]

Tysm

[modern stone]

I’ve pinged. I answered to your question about calc 1 recommandations but I’ve seen that I’ve just repeated what other said

[smoky zephyr]

interesting how it introduces differential equations before partial derivatives @analog pollen

[analog pollen]

Yes?

Pretty standard approach lmao

[smoky zephyr]

i actually didn’t know that

[analog pollen]

No need for partial derivatives when only covering seperation of variables and linear eqs

[smoky zephyr]

what i’m using only introduces differential equations after calculus 3

but that makes sense

[analog pollen]

Ye it just introduces basic methods cuz they overlap well in a mechanics class ig

[smoky zephyr]

yeah that makes sense

[craggy sapphire]

Is it just me or is most uni level maths books just a constant stream of theorem, proof, lemma, corollary? with no other explanations... what's up with that?

[gray gazelle]

I'd assume that the explanations come from the college courses these books are supposed to be studied with

but that just depends on the book

there are great ones out there, with great explanations

[craggy sapphire]

I see

[gray gazelle]

are you looking for something specific? Cause overall I do agree with you, at least YouTube exists 😩

[pale scarab]

I mean the D&F is a standard algebra book and it has a ton of exposition. There are plenty of books like you describe but the point is to fill in the details yourself. Then use the exercises to motivate the importance of the theorems which are often used to solve the problems.

Tao is another standard analysis book which has a lot of exposition. I honestly like a little of both which is why using multiple texts is important especially for self study where you don't have your professor to help you

[serene falcon]

which book would be better for a senior in high school doing an independent study in PDEs: PDEs by strauss or elementary applied PDEs by haberman?

[tulip blade]

You need to tell us about your math background. For all we know you can be a senior in high school that is familiar with measure theory or a senior in high school that only has knowledge through basic calculus.

[serene falcon]

by the time my senior year starts, i'll have taken classes in calc 1-3, linear algebra, and ODEs @tulip blade

i've heard really good things about both books, so i don't know which one to invest in

[remote ginkgo]

Look at the table of contents of each, skim through a 'legitimate' pdf of each to see which one you like the language of more

You can always read the other one on your own time

[late spear]

Hello, does anyone have a recommendation for an excellent linear algebra textbook?

[remote ginkgo]

Georgi Shilov

[craggy sapphire]

prerequistes for spivak calc?

[quick hornet]

high school algebra (and trig)

also spivak teaches basic proof techniques but some students will benefit from seeing a proper exposure to proofs first

so not necessary but, if you struggle, might be good to look into

[craggy sapphire]

Thank you

[gray gazelle]

Hi guys! Can anyone suggest me a book for geometry with tough proofs

[quick hornet]

hartshorne

[gray gazelle]

Oh any other?

Like the one which is easily available as pdf yk

[quick hornet]

vakil

[analog pollen]

l*bgen

[quick hornet]

http://math.stanford.edu/~vakil/216blog/FOAGnov1817public.pdf

☦️

[gray gazelle]

Like is there a geometry book where the are more questions than theory?

[karmic thorn]

Maybe a problems book

[analog pollen]

Schaums outline of geometry has alot of problems/worked out solutions ig (haven’t read it tho)

[atomic nova]

h. m. schey div grad curl and all that

[crude sable]

pretty sure you are not allowed to share pirated digital copy of books

[gray gazelle]

[paper stratus]

A lot of university professors like to throw around the phrase "mathematical maturity". If you could recommend 1 or 2 books you found helpful in building that "maturity", what would they be?

[quick hornet]

its more like... a skill you develop over your studies

so the best book to read will be a (proof-based) book of the appropriate level

[quick hornet]

also, yeah, echoing this

[paper stratus]

lmao yeah i'm about to take a part2 , grad level, class in which I kinda blew off the part1,ugrad level, class. It is proof based though but I'll probably have a lot of catching up to do before the semester starts

[remote ginkgo]

Baby rudin

And papa rudin

And lang and hartshorne

[gray gazelle]

this book is good for building mathematical maturity

[smoky zephyr]

what comes after 8

[modern stone]

Does religion mean something different in this context?

[quick hornet]

its just a turn of phrase

not a literal religion

[sudden kindle]

Opinions on Rick Miranda Algebraic Curves and Riemann Surfaces?

[subtle siren]

Did you really just Hartshorne Vakil someone who's new

[sudden kindle]

I will never read Hartshorne

[dapper root]

Coward

It comes for everyone

At some point

[sudden kindle]

No

I will forever read other books

There are a million other good AG books anyway

[solemn rover]

Hartshorne isn't that bad lol

[crimson pagoda]

Gabe's algebraic geometry book

[foggy relic]

what type of geometry

[quick hornet]

i answered the question as given

also yeah, hartshorne is tough but not terrifying

like, there a bigger gap between rudin and other analysis books than there is between hartshorne and other AG books imo

[dapper root]

I don’t know how it is in ANT or arithmetic geometry, but if you go into algebraic geometry hartshorne is unavoidable

You don’t have to use the book but at a certain point it’s assumed you’re familiar with everything in it and all the results in the exercises

It’s perfectly reasonable for someone to say “it’s in Hartshorne” as a reference for a result and then it ends there

[remote ginkgo]

||I found rudin to be the only one i could understand||

[wise umbra]

The book by Liu is really great

And half of the books is not in the exercices like in Hartshorne

[gray gazelle]

Stop gaslighting !!!!11!!!11!!1!111

[tacit abyss]

Always nice to see when opening a book

It's Lang analysis II and looked quite good?

[gray gazelle]

Jej I dont doubt nobody cared to proof read a lot of Lang books

[iron granite]

rudin is what nightmares are made of...

[surreal phoenix]

Rudin is the nightmare

[remote ginkgo]

Sweet dreams are made of lebesgue

Who am i to disagree

[crude sable]

i remember hating rudin's book

[surreal phoenix]

And then what happened

Did you revisit the beast's den after a first course in analysis?

[crude sable]

yeah

now I know why it's so highly regarded

[atomic stag]

I'm looking for a good video on topic

continuity and differentiability of a function

I'm currently in grade 12 India

any video in either English or Hindi would be fine

[frosty girder]

you can try checking out Khan academy

[gray gazelle]

Hi, where can I find (not too easy) exercises on relations, functions and sets (egg. prove an equivalence relation, prove two sets are equal....)? thanks

[tacit abyss]

would you recommend it? Was planning on reading over it next summer to solidify some things

not sure if I've looked at rudin, apostol was pretty good

[obtuse hull]

Recommend me any book that's either related to math/physics that you liked (Currently doing physics MSc). Could be literature as well.

Just recommend me anything you liked

[analog pollen]

Schwartz qft or nakahara

[obtuse hull]

I may read nakahara actually, qft is next sememster so gonna wait for that 😛

[analog pollen]

Nice

I love nakahara

Even touches on bosonic string theory at the end 🤤

[gray gazelle]

Why not? I havent read it myself. I only said that cause Lang wrote well... a lot, so editors might have just gave up at one point

[topaz kayak]

Chéri by Colette

[dark orbit]

got Conway I. excited for Conway I

Functions of One Complex Variable

bit off more than I could chew on the last book, realized I need a better understanding of some thms in complex analysis

if anyone has supplemental recs let me know. i know Conway's exercises aren't amazing

[brittle latch]

just found Sierpinski's book full of problems in number theory in my library, im excited

i only knew him as the triangle dude until i walked down a certain bookcase in the library :D

[gray gazelle]

niceee he has a lot of cool books I think Ive used the one you mentioned it had cool problems and I managed to find solutions online too

[brittle latch]

edition i found has soln's in the back

most of the thing is solutions actually but it's like 250 problems

[gray gazelle]

[brittle latch]

wonder how many of them i can do without any kind of actual study in number theory lol

[gray gazelle]

He wrote pretty good NT books as well, might help solve those

[brittle latch]

also checked out a copy of this

||was the shortest thing i could find||

[gray gazelle]

Is this the actual book cover?

[gray gazelle]

That's Hahn-banach in analysis II, nice

[misty eagle]

anyone knows any books that sort of develop the concepts needed for a maths sophomore by problems? like it does teach you the definitions but the theorems would simply be problems themselves

[tacit abyss]

cant find an ebook unfortunately so would have to let it out which'd be a bit awkward, might have to find another book

but it looked pretty good

[gray gazelle]

Awkward?

[gray gazelle]

Try Knapp

There are many good analysis books, see Munkres as well

[analog pollen]

L*bgen

[gray gazelle]

I recommend percy jackson battle of the labyrinth

[brittle latch]

I hear Dr. Seuss is also at the forefront of his study

[quick hornet]

i mean, he's a doctor

seems pretty qualified

[modern stone]

Is khan academy and other online resources enough to (self) learn single and multi variable calc?

[manic fox]

dude im feeling some analysis vibes but idk what to do. The usual real analysis intro course feels boring and i dont feel like trodding thru it 😔

[lapis sundial]

rudin

[manic fox]

i prescribe death

[frosty girder]

use apostols book

[surreal phoenix]

Yeah, it's enough

Professor Leonard doe

[toxic basalt]

Does anyone know any good books for 8th grade math high level?

[stray veldt]

try looking at khan academy

[tacit abyss]

not on there that I could find

[tacit abyss]

wouldnt be able to let it over the summer because i might be going to a different uni for my masters so would have to do it during term

[grand thistle]

do you guys think this linear algebra textbook is a good one

for someone who's just starting linear algebra with only knowledge up to like precalc

so far its been pretty intuitive and the explanations are good

and easy

to understand

[modern stone]

What’s with him?

[surreal phoenix]

Self studied calc 1, 2 and 3 by watching his videos, he uploads full lectures

Would recommend checking him out alongside Khan

[blissful badge]

anyone here know some good source for hard problems in calculus

I just cleared my high school and my counsellings are about to end, I feel like my brain is slowing down

I feel the need for solving some challenging problems and I really like calculus and PnC

[karmic thorn]

Spivak's Calculus is nice

For combinatorics, you can look up Art of Problem Solving website

[blissful badge]

ok 👍 😄

[gray gazelle]

what's a good self-contained intro to measure theory book?

[blissful badge]

https://pdfcookie.com/download/spivak-calculus-3rd-edition-nlz13pw5we25

this one?

[rocky jay]

Hello could anyone tell me a good source for matrices?
I have to start it from scratch.
Thank you.

[remote ginkgo]

Shilov linear algebra

[gray gazelle]

Greub linear algebra

[analog pollen]

Gilbert strang has nice lectures abt it

[rocky jay]

Yes, been planning to watch him.

[gray gazelle]

https://www.youtube.com/watch?v=kYB8IZa5AuE&

[gray gazelle]

??????

[prisma snow]

You need to know intro real analysis already, but if you do, Folland

[gray gazelle]

hm okay thanks

[karmic thorn]

Is anyone familiar with a (preferably short) introduction to universal algebra and lattice theory?

[gray gazelle]

Guys, who has the pdf for it?

I have the book itself but not the instructor's manual.

I'd really appreciate it. Please PM. :)

[prisma snow]

But are you an instructor? 👀

Also, you should probably say who the author is too

[gray gazelle]

Mathematics A Discrete Introduction by Edward A. Scheinerman

You know, I'm something of an instructor myself.

[gray gazelle]

you heard of me?

[gray gazelle]

yo wuzgud

[sudden kindle]

Anyone have a good reference to learn about theta functions and the solution to the jacobi inversion problem?

Specifically interested in genus 2

[sudden kindle]

I'm liking Mumford's Tata Lectures on Theta I so far

[dapper root]

Hahahaha tata like boobs

[primal mica]

Any good book gift recommendations for someone who is interested in higher-dimensional geometry? They've got a background in proofs (basic set and number theory stuff) and the general calculus track, but it doesn't necessarily have to be immediately approachable.

[grand breach]

hi,is there any good number theory book u guys can rec for me :>

not too academic ;-;

[pale scarab]

I really liked the first chapter from Artins algebra

[whole rain]

there's a pinned list of recommendations

[gray gazelle]

it's basic

[gray gazelle]

I to continue my linear algebra studies, so I need a book to study. I have went through intro analysis by bartle and Vector Calculus, Linear Algebra, and Differential Forms by Hubbard. @gray gazelle i know you have a great deal of experience, I want to eventually start smooth manifolds by lee, is the LA from Hubbard I learned ok enough for lee. If not what book would you recommend?

[teal junco]

I dunno about you but if you want to understand Gödels incompleteness theorem then i would recommend this book

[modern stone]

I think that’s a bit of an overkill lol

https://cdn.discordapp.com/attachments/719360951752851519/847253833175400478/Hofstadter_Douglas_R._Nagel_Ernest_Newman_James_Roy_-_Godels_proof-New_York_University_Press_2002.pdf

I think this is a gentler introduction

[dapper root]

umm

don't use principia mathematica

[teal junco]

Why not

if you understand Gödels numbers it should be a piece of cake

[quick hornet]

principia predates incompleteness

which is disqualifying on its own

but also, principia is really fucking hard for no reason

theres a reason no one uses russellian ramified type theory today

[teal junco]

Hmmm ok

[sage python]

"Differential Topology" by Guillemin and Pollack

[gray gazelle]

Who are you ? 👀

[livid ermine]

People say that baby rudin ch 9 and 10 are bad

What is a good replacement for those?

[gray gazelle]

yall should read "the very hungry caterpillar"

great read 👍

[remote nova]

The equivalent chapters of Munkres's "Analysis on Manifolds" or all of Spivak's "Calculus on Manifolds"

[gray gazelle]

Linear algebra book after Hubbard vector calculus, linear algebra and differential form book.

[gray gazelle]

Axler maybe

[tulip blade]

Linear algebra by friedberg et al

[visual echo]

Hey guys my sister has dyscalculia! She wants to learn math! Anyone got a good book that explains tough concepts in a ELI5 manner…? She wants my help but I’m not the best at explaining stuff

She was not taught math beyond 6 grade because of an exemption

She wants to give competitive exams now

Just ping me if you respond

[brittle latch]

i just borrowed sierpinski's book of problems from the library and it's been rly fun

[brittle breach]

I think you would want to aim for more conceptual math books,
"HOW TO PROVE IT by Velleman ", comes to mind for proofs and logic
others here might be able to recommend books on other topics

[gray gazelle]

uhh did you read what he wrote? "She was not taught math beyond 6 grade", this is a bad recommendation imo

[brittle breach]

maybe , but is the only conceptual book I can think for high school

[visual echo]

Yea she doesn’t know much at all

If anyone has any recommendations please tell me :)

[gray gazelle]

I'd recommend khan academy I guess

Worth giving it a try I think

[visual echo]

I recommended that only to her, besides that she wanted some other books

[brittle breach]

I heard persons with dyscalculia tend to do better at advance math than earlier math, hence the recommendation

[visual echo]

Also in case someone comes across this in the future, Math Doesn’t Suck by Danica McKeller is a good book acc to some sources

[visual echo]

I completely understand! Thanks I’ll be sure to recommend that to her too

:)

[brittle breach]

you might want to see what kind of books those in math-competition likes

[gray gazelle]

Its a very good book but assumes high school math

[visual echo]

Nah she asked me for help, so I’m gonna teach her in a way that she can understand. Atleast enough that she can get through daily life.

She is even doing CS as a part of her course so the preliminary knowledge for that is there too

[rapid hearth]

i'm into books like Mathematical Circles By Dmitri Fomin , any book similar to this?

[sudden kindle]

I highly recommend anything written by David Mumford

[gray gazelle]

could someone suggest me a problem book on mathematical induction?

[gray gazelle]

book of proof has a bunch of exercises on it.

[gray gazelle]

thank you!

[sleek sand]

Anyone have a good book for high school comp math that covers most topics

[molten linden]

what's a good book for a very basic and introductory course for discrete maths

or any books that build from the basics really

plz ping when answer

[gray gazelle]

Rosen is pretty much the standard introductory Discrete Mathematics textbook.

A little more challenging and rigorous cousin of Rosen is Knuth et al's Concrete Mathematics

[molten linden]

oh that's the textbook our teacher recommended

[mystic orbit]

I'm trying to pick a proof writing book and by far the most recommended ones are velleman's "how to prove it" and "Mathematical Proofs: A Transition to Advanced Mathematics"

can you guys help me pick?

[stray veldt]

the latter is even longer than the former

that is impressive

i dislike velleman but reading a 600+ page book for intro to proofs seems way, way overkill

i guess you really only need the first 10 chapters, but still

[quick hornet]

"Mathematical Proofs: A Transition to Advanced Mathematics"
2 pages on proofs
700 pages on how to write a research grant application

if any textbook publishers wanna take my idea, im open for negotiations

[mystic orbit]

uhm

[mystic orbit]

can you elaborate?

[stray veldt]

nami is shitposting

[quick hornet]

yeah im joking, ignore me

[mystic orbit]

oh

[stray veldt]

(i should write a chapter on relations at some point i think...)

im advocating for reading neither but if you choose, skip the later chapters

[mystic orbit]

neither?

why?

[stray veldt]

i guess "Mathematical Proofs: A Transition to Advanced Mathematics" could serve as an introduction to wtv topics the last chapters are about

maybe its good, but still 200-300 pages for intro proofs is a lot

well, if you want to learn mathematics you can do "intro proofs" in a week or so (assuming a decent highschool education) and then read an actual (easy) math book

i am advertising my intro to mathematics (#proofs-and-logic message) which will in theory suffice to then just read an (easy) analysis or linear algebra textbook

[mystic orbit]

I haven't finished highschool though

is that fine?

[stray veldt]

you mostly need to be ok with algebra

symbolic manipulation

if you pick velleman, skip the last chapter unless you are really interested

and be aware that some of the later exercises are horrible

i have no opinion on the other book other than that it is very long but in your case it might be good maybe

[mystic orbit]

ok thanks

[karmic thorn]

Your book could be a best-seller for a suitable choice of the word relation

[sage kelp]

Point-set topology book? Something lighter than Munkres?

[stray veldt]

topology without tears?

[modern stone]

How is Book of Proof by Hammack compared to Velleman?

[timber mesa]

Hammack is clearer and provides more motivation tbh

then again I've only read some of Hammack and skimmed through Velleman

so take what I say with a grain of salt

[sage kelp]

Thanks, I will check it out

[sage kelp]

I worked on Velleman and found it quite useful

[modest chasm]

does anyone know if Computing Through Combinatorial Topology is a good book?

[smoky zephyr]

does anyone know a pdf or book for a good intro to proofs?

i’ve looked stuff up but i don’t know if the stuff i’ve found is good enough, too long or too short or something else

[solemn rover]

have you checked out "How to Prove it" by Velleman

[smoky zephyr]

wow i actually looked this up earlier lol

yeah i’ve seen it

thanks

this will work

[late plinth]

has anyone read Grimaldi Combo/Discrete

need good book for applied combo to study over break

[opal magnet]

Just wanted to add on that I tried self learning from Top Without Tears and was extremely confused until I learned about metric space topology first

So if you haven't yet I'd suggest reading briefly about metric spaces for motivation, before diving into the more general point-set theory

[gray gazelle]

steven roman has a book on it.

wait not a book but a youtube series on the book.

[sage kelp]

Yeah, I see that the bok doesn't start with metric spaces. Any recommendation for metric spaceS?

[brittle breach]

baby rudin

[karmic thorn]

Chapter 2 from Amann-Escher's Analysis 1.

Even 3 or beyond, I guess 3 talks about continuity.

[fluid bay]

carother's real analysis has everything you need to know about metric spaces

[gray gazelle]

https://www.youtube.com/channel/UCalphvDmYSEzHchGFW8BxGg

is that his channel?

[fervent lava]

I have one it a decent 139 pages by Paolo Aluffi. It called Introduction to Advanced Mathematics Course notes.

[iron granite]

send notes

[fervent lava]

huh? like send it here. I don't think that allowed here since I got it off zlibrary.

[iron granite]

okay

[iron granite]

Is someone here an instructor and eligible to get solution manuals off of springer and other websites?...

[tender vault]

anyone have a recommendation for a tensor analysis book THAT IS NOT BORISENKO AND TARAPOV that covers introductory tensor analysis without requiring topology? i just need more practice problems on covariant derivatives, tensor algebra, etc

Borisenko and Tarapov is the Dover text on tensor calculus

[gray gazelle]

open up a riemannian geometry book and pretend everything is an inner product space

[craggy sapphire]

idk why i haven't learned number theory yet, but i would like to learn about it. need some easy books to get me started please

[tender vault]

thanks i'll look into it! i'd never heard of it before so im glad someone could find me a helpful book

[gray gazelle]

well obviously Serre - A first course in arithmetic. The name says it all

[craggy sapphire]

book too advanced for me. i just want something high school level

[gray gazelle]

I see

i didnt notice that first