book-recommendations

[sturdy shore]

depends on ur lvl

[blazing jetty]

I’m bad at it

[blazing jetty]

basic level I would say

[remote ginkgo]

u may want kenneth rosen discrete mathematics

[sturdy shore]

what you are looking for doesn't seem to be set theory

[blazing jetty]

Yeah, I’m going to see it

[blazing jetty]

that was the name of the unit…

idk

[sturdy shore]

if you really want something just on sets, probably halmos

[blazing jetty]

yeah that one

[sturdy shore]

so you are already using halmos?

[blazing jetty]

bro i don’t even know what’s that

all i know there is something named paul halmos

imma check it

i have to do an essay in only one day

[sturdy shore]

yes it is the book naive set theory by paul halmos

[blazing jetty]

nice, math is interesting

[sturdy shore]

...one day? on set theory?

gl

[blazing jetty]

no, the college essay

i’m lazy, that’s why

[lethal fox]

hi, i am looking for books or lectures on graph drawing using force-directed algorithms. Can someone help me out?

[acoustic ridge]

Could anyone recommend me a book with tons of geometry problems in it?

[gray gazelle]

Nathan Altshiller-Court - College Geometry should keep you busy for a while (i assume you mean hs geometry)

[karmic thorn]

What kind of geometry?

[lament bear]

Guys, can you recommend a book on discrete mathematics? I need to review core concepts and prepare myself for entrance exam by getting good at solving problems, so solutions for said problems are a must. If there would be a transition or short introduction into graph theory, that would be a plus.

(pls don't recommened Concrete Mathematics, I watched it and I need something more elementary, isn't really relevant to my goals)

[heady ember]

Are you sure you want discrete math? From my experience with like 30 pages of Rosen, its super boring

If you want challenging highschool problems you can try Cambridge's STEP papers (its Cambridge's entrance exam for math)

They're avaliable onliine for free

[signal ferry]

Hello does anyone know some book for linear algebra, something that focuses on proofs but isn't Linear Algebra Done Right cause I found it really difficult to understand motivations for lots of concepts?

[heady ember]

Look in pinned

[signal ferry]

What's pinned, is it a function a tab in this discord?

[signal ferry]

Found the function

[half hinge]

Hello i am second year electrical engineering but love math. Currently we are doing functions with multiple variables, and integrals of the same as well as multiple integrals and similar

Is there some good book or resource where I can read more formally about this topics because at university is too shallow and I would love to know a bit better

[karmic thorn]

I like Don Shimamoto's Multivariable Calculus. The approach adopted is more mathematical, maybe someone can drop better recommendations from a physics/engineering perspective.

[vast obsidian]

I forgot what linear algebra book I was recommended yesterday

Shilov good for beginner?

Friedberg? Lang?

[willow pecan]

Friedberg maybe

[crimson leaf]

Friedberg and Shilov are good

[vast obsidian]

@willow pecan@crimson leafthanks

[remote sparrow]

#book-recommendations message

[heady ember]

Look in pineed for good ol' Dami's review

[royal gale]

THANK U VERY MUCH ❤️

Thank u too my friend

[finite thorn]

Got this book in my uni library, is it good?

[turbid wolf]

Does anyone know any cheap pre calculus books I could buy on Amazon?

[remote ginkgo]

yeah its fine

[tardy walrus]

Yes

Though there is a fourth edition

[sturdy shore]

I thought 4th ed was considered inferior

[eternal dove]

Is Bonjorno a good book?

[sick river]

not really a book recc but where would one find open problems sorted by field ideally, to work on?

[heady ember]

Well, Cambridge provides the example sheets to nearly all, if not all, their classes at https://www.maths.cam.ac.uk/undergrad/examplesheets

[sick river]

i dont think those are open problems

[willow pecan]

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

[quick hornet]

to work on
please do not find a problem from a list of unsolved problems and attempt to work on it

this has literally never been productive

even in famous cases like that one "teacher writes unsolved problem on whiteboard, student unknowingly solves it thinking it's a homework problem" story, it was presented in the context of a class built around problems like that

[heady ember]

Oh that's what you meant by "open problems"

[sick river]

just looking for a problem i can use to get some exposure to the research process

[quick hornet]

famous unsolved problems are quite unusual examples of the "research process" since they have many many years (in some cases, literal centuries) of hyper-specific work that you need to catch up on

and oftentimes the proposed approaches are highly esoteric

e.g. the program to solve the riemann hypothesis through the geometry of the field of one element

most problems that a researcher tackles do not have nearly the same amount of existing work done on them

in fact, most papers are "we make some minor modifications that allow us to apply technique from [paper x] to [situation y], and describe our results" or something along those lines

that is to say, the flow for MOST problems is:

researcher identifies problem, researcher tries a few techniques, researcher solves problem

whereas the flow for famous unsovled problems is:

researcher identifies problem, a dozen researchers attempt to solve the problem, five different ambitious programs break out attempting to solve the problem, hundreds of researchers now need to catch up on hundreds of papers in order to even understand what needs to be done in order to solve the problem, repeat from step 2

its just a totally different "texture" to the process, and actual research doesnt consist of "attempting to solve the problem" so much as "attempting to slowly develop the theory of a program that some are hopeful will eventually lead to a set of techniques that can approach the problem, but first many holes in this program need to be filled in, and you need to identify that hole and chip away at it"

[sick river]

i see, so i'm not going to find anything realistic online, so i should probably just ask some faculty for a problem, thank you

[quick hornet]

right

i dont mean to be discouraging

its just a bad place to find problems that are actually reflective of the research process

asking faculty is a much much better idea

[blazing canopy]

Any recommendations for a mathematically-oriented, graduate or professional level signal processing text?

[zealous light]

@timber copper would you have any idea?

[timber copper]

probably something on algebraic signal processing

lemme check

[timber copper]

through a cursory glance at the contents: mallat's A wavelet tour of signal processing might be of use and the books given on this site: https://fourierandwavelets.org/

[blazing canopy]

Thanks, I'll check it out. I'm mostly just trying to build out my personal library of references for when I need to look something up for whatever I'm working on

[timber copper]

Bremaud's Mathematical Principles of Signal Processing also looks good at least from a functional analysis standpoint (This is probably the kind of rigor you're looking for)

[blazing canopy]

I looked at the table of contents and I feel that this is too steeped in Fourier analysis, rather than exploring concepts such as complexity, rigorous numerical error bounds, algorithm analysis, and so forth

In my view signal processing is not Fourier analysis, but developing algorithms that rely on that

[timber copper]

Yeah, generally agreed

I'm assuming you've already looked at oppenheim?

[blazing canopy]

it's on my list of possibilities

[timber copper]

if you're interested in discrete methods and the analysis of like the fft and fft variants and stuff like that, his book on discrete-time signal processing goes into that

[blazing canopy]

My main worry was just that that book looks extremely encyclopedic which is a little bit the opposite of what I need, but maybe it's OK

[stray veldt]

no

gathmann's notes

[acoustic crater]

does anyone know any book(s) that's good for people new to calculus?

[alpine orchid]

My lecturer recommended us to use Thomas calculus

[acoustic crater]

is there a specific edition?

[heady ember]

Pauls' Online Math Notes is available online for free by the author

[gray gazelle]

any book for dynamics available online pdf

[remote ginkgo]

strogatz for intro, kuznetsov for bifurcation theory

[acoustic ridge]

2D geometry

[remote sparrow]

#book-recommendations message

[karmic thorn]

I'm aware of Coxeter's Introduction to Geometry

[acoustic ridge]

I will try that out for sure.

[tame sphinx]

what's a good book for linear algebra? one that's proper posh, like with proofs and more theory involved?

[willow pecan]

"posh" lol

Friedberg

[tame sphinx]

I'll look into it when I get time

[modern quarry]

Hello, any book recommendations on the subject of "Philosophy of Math"

[lean pagoda]

Haven't read the book myself, but I've heard good things about the book Lectures on the Philosophy of Mathematics by Joel David Hamkins

[remote sparrow]

https://www.logicmatters.net/2020/11/16/philosophy-of-mathematics-a-reading-list/
https://math.stackexchange.com/questions/30572/good-books-on-philosophy-of-mathematics
https://plato.stanford.edu/entries/philosophy-mathematics/ (scroll down to the bibliography)

i also own and have read some of hamkins' Lectures on the Philosophy of Mathematics, it was pretty neat

https://www.reddit.com/r/philosophy/wiki/readinglist

oh just found this

it has a section on philosophy of math

[heady ember]

Idk

[glacial crypt]

Can I get a recommendation on a good introductory complex analysis textbook? (Assume that real analysis has been taken)

[gray gazelle]

Ahlfors is the usual recommendation. Gamelin and Stein&Shakarchi are also good.

[heady ember]

Look in pinned

[sturdy shore]

this also has lectures on yt by hamkins himself, which are really good

[placid pollen]

I want to check Nehari Conformal Mappings myself but I've already had some complex variable theory.
I wouldn't recommend Ahlfors because I in general hate the style where the author is talkative enough to skip a bold "Definition" statement, that's more of a thing for a classroom than a book. Not to say that makes it bad, just that it evokes bad memories from other authors or old textbooks which do this a lot.
Gamelin or Stein like @gray gazelle said seem more my taste but I haven't seriously sat through them.
Cartan is interesting to check.
If you took real analysis as in measure theory then check Rudin.

[glacial crypt]

Have not done measure theory. Thank you for the recommendations yeah

[gray gazelle]

Is Apostol Calculus good for first time learning Calculus?

[gray jungle]

Is kosaku yosida functional analysis book any good for someone interested in getting into operator theory?

[grand thistle]

yeah it's pretty good

but it's different in the way it covers integration before differentiation

[gray gazelle]

Which one do you think is better, Apostol or Spivak?

[grand thistle]

they're both good

spivak should be closer to a more conventional analysis text without the topology

[cobalt arch]

any axiomatic books?

[gray gazelle]

thanks

[heady ember]

Be more specfic

Axiomatic can refer to linear algebra (where vector spaces are defined axiomatically), AA, set theory, etc

[acoustic ridge]

I want to practice math problems. Can anyone suggest me a book to practice math?

[karmic thorn]

Math problems?

Which topics, specifically?

[acoustic ridge]

Algebra, equations, geometry, combinatorics, number theory etc

[cobalt arch]

I want a book that treats algebra, analysis, geometry, combinatorics, etc. axiomatically meaning it starts with some axioms and proves every other result based on these axioms

[remote sparrow]

if you know calculus and how to read and write proofs, A Walk Through Combinatorics by Miklos Bona is a neat combinatorics book. The problems are pretty hard, but I think all of the exercises have solutions in the book, minus the supplementary exercises, which are extra problems that aren't supposed to have solutions. Elementary Number Theory by Underwood Dudley (a lot of stuff is left as exercises or done in problems) or Elementary Number Theory by David Burton (more traditional exposition) are good for number theory.

[remote sparrow]

well, even going axiomatically, there are different approaches. you can give an axiomatic description of the real numbers, for example, as the unique complete ordered field. or you can start from scratch with the peano axioms and work your way towards constructing the naturals, integers, rationals, and reals, proving that the reals are the unique complete ordered field in the process. i'm not sure if combinatorics has been treated in a bourbakian fashion, but i don't think it would be conducive to learning, and besides that, combinatorics as a field is very broad and diverse. if by geometry you mean euclidean geometry, i'm pretty sure nearly every book echoes euclid's axiomatic approach. as for algebra i can only think of a graduate text, namely lang. i didn't like very axiomatic books; i prefer to be engaged in dialogue with my books. that doesn't mean i have a problem with foundations, i love foundations. i think the construction of the number systems is pretty neat. but i prefer thinking backwards about foundations and axioms in a sense. i try to think about how axioms reflect my common sense, or don't, and transform my understanding accordingly.

[gentle arrow]

i need a DE book recommendation, preferably one that covers both ODEs/PDEs
it can be rigorous i dont mind

i didnt expect to see DEs this early in ap physics C

(i thought it would appear later in the year but turns out were doing air resistance earlier on)

[remote sparrow]

boyce/diprima with boundary value problems i guess

[cursive orbit]

the only des you need to know for physics c is how to solve separable ones

[gentle arrow]

im p sure theres maxwells equations

and id also just like to know more

[cursive orbit]

maxwell's equations in differential form is not a topic you need to know for physics c

you will only use maxwell's equations in integral form

[dapper root]

I don’t think think any book really covers ODEs and PDEs

They’re very different subjects, and also there’s no way you have to know how to solve PDEs for a physics class

[gentle arrow]

oh i thought they were similar

[remote sparrow]

well, not for the equivalent of an introductory calc-based electricity and magnetism class anyway

[remote sparrow]

the theory for each are different

[dapper root]

You can hope to solve a random ODE that got thrown at you, not the case for a PDE

[gray gazelle]

The solution is just a matrix exponential plus some other irrelevant stuff.

Throw it out. ODEs is now easy.

[cobalt arch]

So could you recommend some axiomatic books?

such a book for analysis is landaus' book but its exposition is rather old

even better if it is explicitly stated that a book follows an axiomatic treatment

[willow pecan]

All modern math is axiomatic

[remote sparrow]

landau's book is not an analysis book. it's a book constructing the number systems. similar books might be thurston's The Number System, Number Systems and the Foundations of Analysis by mendelson, Number Systems: An Introduction to Algebra and Analysis

[remote sparrow]

yeah but i interpreted it as wanting something bourbakian

just a list of axioms and moving on to definition, theorem, proof, with little to no discussion

or like euclid's elements lol

seems like a harmful way to teach math and get people to think about it but if they really want something bourbakian...

[cobalt arch]

Are bourbaki's books axiomatic?

Because I have some of them and they don't seem particularly axiomatic

For example the integration books start with some very weird definitions

[remote sparrow]

exactly what are you thinking of when you want an "axiomatic" book?

[cobalt arch]

The algebra one is more axiomatic since it starts with binary relations

[willow pecan]

You want books that start with the very basics of set theory and binary relations?

[cobalt arch]

I don't know how much more specific I can be

I want books that start from a given set of axioms and build theory upon these axioms

[sage python]

Forsaken the Bourbaki books have to be done in order

As far as I know

If you do things ground up basically the "topic order" is

Well it branches but basically the first thing you do is some basic set theory

[cobalt arch]

I see

[sage python]

Then you can define the natural numbers set theoretically, from there the integers, the rational numbers

[cobalt arch]

Another axiomatic book might be grothendiecks algebraic geometry

[sage python]

You can talk about some number theory and algebra at this stage. Define integers mod n and do modular arithmetic

You can also go the route of ordered fields and construct the real numbers

[cobalt arch]

or sierpinski's topology

[sage python]

I would say this is definitely some of the early things you wanna do in math

After that things branch out a fair bit, and tbh the path isn't super linear since there's a lot of interdependency

[remote sparrow]

does bourbaki do axiomatic set theory and mathematical logic? iirc they actually didn't want to do either of those

[sage python]

Idk exactly how much they do but there's not a ton of axiomatic set theory that underlies most of what people do

[willow pecan]

Books do not generally take the desired approach because math is not done this way

[sage python]

ZFC basically just tells you what sets you're able to build

And you can't exactly "keep defining terms ad nauseam" if you get what I mean, so probably Forsaken can just like

[remote sparrow]

choosing the minimal set of assumptions that underlies a given field of math has historically been done far later than doing nonrigorous or intuitive investigation first or making some rigorous headway before concerning ourselves with axioms

if you're really interested, just dive into any """non-axiomatic""" book and try making up the axioms yourself after learning all the significant claims

and as an exercise, derive what you "know" from those axioms

[sage python]

Read Halmos Naive Set Theory

And then jump into algebra and/or analysis

[cobalt arch]

It would be good if I could derive the axioms myself but I don't trust myself enough for such an endeavor. I might as well say nonsense because I don't understand the theory well enough.

I don't know if combinatorics has any axiomatic approach

The tools used are very disjointed

Another axiomatic book might be enderton's set theory

I want such books

For analysis, algebra and number theory

[sage python]

I mean deriving the axioms yourself doesn't make any real sense

Because you can build any set of axioms and the question is have you developed something people care about

As for combinatorics, that's not really a good example

[cobalt arch]

It sucks that the axiomatic approach isn't followed that much. It is the most straightforward way to understand a subject.

[sage python]

I think you have the wrong idea of what axiomatic means

Everything is axiomatic

Even combinatorics

You're studying sets

And counting

[cobalt arch]

I don't think I have the wrong idea

[sage python]

It doesn't have a clear boundary of course

[cobalt arch]

I said earlier and was very specific about what I think an axiomatic book is

[sage python]

So I can count lots of things and you might think they have little to do with each other

[cobalt arch]

Something that builds theory based on some given axioms and is self-contained

[sage python]

But every single combinatorics object can be traced back to set theory

[cobalt arch]

Yes

[sage python]

"self-contained"
Nothing's self contained unless you're making almost 0 progress

Like even if you're doing basic algebra/number theory, eventually you start using shit from analysis and geometry

[remote sparrow]

i mean the logical conclusion to all this axiom and rigor talk is to just redirect them to a metamath/reverse math database /s

[sage python]

And that's fine even from an "axiomatic" point of view. Because the real numbers are Dedekind cuts of rational numbers, rational numbers are equivalence classes of integers, integers are equivalence classes of natural numbers

[cobalt arch]

Metamath is cool but not very enlightening

[sage python]

And N is just {0, 1, 2, ...} where 0 is the empty set, 1 = {0}, 2 = {0,1},...

So yeah real numbers are now fair game

[placid pollen]

Doing applied calculus and then classical analysis will make you realize why there's a need for theory with axioms. You can't really prove some things without hand waving if you're not using good axioms, constructing the reals is a good exercise, doing some set theory. Some topology. To get a hands on feeling of what are axioms good for and how abstractions can be used go understand concrete situations.
It's basically the fact that they capture the structure of geometry with the least amount of assumptions, then a good chunk of theory ends up being provable and even many algorithms.
Math is almost about making a 1-1 relation of language on geometry

[remote sparrow]

yes, but what you said is that you did some concrete investigation before thinking about axioms

doing the actual concrete work is what motivates axioms and theory

and it is more interesting and fruitful to look at concrete, well-chosen examples and try to develop a theory based on patterns you see

then extend the theory further

then see how your abstractions are encapsulated in the specific

rinse and repeat

[cursive orbit]

any book recommendations on representation theory?

[icy knot]

Not necessarily what you want but there’s Classical Mechanics by Morin, Introduction to Electrodynamics by Griffiths, and Div, Grad, Curl, and All That by Schey.

Not asking for any recommendations but I just ordered 3 “recreational “ style books and was wondering if anyone has read them before? The Joy of X, Math without Numbers, and Aha! Gotcha by David Gardner (brain teaser/math puzzles).

[long path]

I need a book in first order differential equations

[remote sparrow]

Boyce/diprima with boundary value problems or tenenbaum and pollard

[foggy relic]

do you want anything in specific

or just the general theory

[long path]

Thanks!

[placid pollen]

I know Boyce/Diprima, how does Tenenbaum compare? Could use a refresh on ODEs

[remote sparrow]

It's very thorough and step-by-step, so that actually makes it really long. Makes a nice self-study book plus reference.

The application problems are neat

There was a cool discussion on how a certain electrical circuit can be used as an analog calculator for the mechanical spring differential equation

Speaking of which, i wish there were physical replicas of high end slide rules

What if i need to calculate something in the apocalypse and there's no batteries or electricity

😔

I think it proves existence and uniqueness of certain solutions in full using Picard's theorem

[cursive orbit]

the general theory

[foggy relic]

ah ok

then fulton-harris and etingof are god

good*

[remote ginkgo]

serre

for finite groups first

then fulton harris after

[devout sphinx]

Fulton and Harris

[narrow relic]

Has anyone read Goldberg's Methods of Real Analysis?

[nimble ether]

hey can any one recommend me a good book to get started with

I learnt math until 12th grade im in 12th grade

I want to learn further but I can't find good books

[narrow relic]

I recommend you look at this book: https://archive.org/details/modernintroducto00dolc

(The word "analysis" there is something for American high schools, it's not the "analysis most people in math refer to, so don't worry.)

[nimble ether]

why do you recommend this

[narrow relic]

Because I learned a bunch of stuff from it when I was at the same stage as you (12th grade).

[nimble ether]

how do you download the book

[narrow relic]

You have to make an account with the Internet Archive, then you can log in and read it

The Internet Archive is a library in the United States

[nimble ether]

dude the book is from 1970

[narrow relic]

I would love to link you to the edition I used in high school but unfortunately there isn't a digitized copy. The content is virtually unchanged though

[gray gazelle]

I wonder how many books got digitalized out of the ones we know exist

[narrow relic]

Yeah.

[nimble ether]

how am i supposed to finish this it have over 500 pages

[narrow relic]

You don't have to read the whole thing, I suggested you just take a look at it

[heady ember]

You can also just take it slow and read a couple pages a day if you like it

500 pages is quite typical for a math book I think

[narrow relic]

do you have any recommendations for a person (me) who feels pretty unmotivated to learn math better but who feels like he sort of wants to have it done?

[heady ember]

Find a topic you like/are interested in?

[nimble ether]

I am the same person

[narrow relic]

I have things I wish I knew but I feel like if I spend time on them it's literally such a waste. I spent a bunch of time on some silly analysis problem last night and I felt like I just wasted time

It would take me hundreds of hours to finish the 10 chapters of this book I know I should finish to know the material, mostly fiddling around on weirdly worded problems

[heady ember]

Doesn't matter, I think if you self-study math the point of it should be fun

As a whole

[narrow relic]

For some reason, it isn't fun for me anymore, I don't know what happened

[heady ember]

Hmm

Perhaps take a break from that particular topic

[narrow relic]

I think what happened is, I spent a few years trying to learn all this stuff, and it ended up sort of not gelling for me

[gray gazelle]

well, also not every book is as dense as others

[heady ember]

True

[gray gazelle]

those 500 pages might be a breeze but they might also be a nightmare

[heady ember]

Yeah

[narrow relic]

Like, I spent over a month on some linear algebra last year and I wasted so much time. I then spent about 5 months doing it an hour and a half a day this year and that ended up being mostly a waste of time too

I generated probably about 100 pages of notes but a lot of them are just figuring out stupid stuff that the book didn't define properly or correctly, etc

And I spent months learning analysis from a book that had some other wonky definitions so the end result is I never was able to finish learning what I wanted to because I kept having to redo the definitions over and over again

[nimble ether]

yo can you recommend me a book

[narrow relic]

So the end result is I'm really hesitant to sink any more time into those topics, even though I don't know them very well, even after all this work

[gray gazelle]

Taking notes about everything is not something I'd recommend to anyone

it's mostly just a waste of time

[narrow relic]

Unfortunately it was necessary because the definitions weren't clear

But that's because the book sucked, but I didn't know that

Doing the analysis stuff I didn't take almost any notes

[gray gazelle]

I'd just grab a piece of paper and figure it out tbh

[narrow relic]

Oh, I guess I did because I had to try to fix the definitions, right

[narrow relic]

Yeah, that's what I did

Maybe I'm just burnt-out? I don't know

[nimble ether]

I have been burnt out of learning for 6 years ever since I became schizo

[gray gazelle]

I get stuck on things many times, I don't even know what direction I should be following

[narrow relic]

I don't mean to be weird but how could you be schizo if you're still in high school?

[nimble ether]

I got diagnosed at 13

[narrow relic]

(I assume you don't mean literally schizo, you're using it figuratively)

[gray gazelle]

it's not like schizophrenia is restricted for adults

[narrow relic]

Oh I'm sorry, I didn't know you literally meant it

[nimble ether]

nah I mean literally

[gray gazelle]

that's what you guys mean by schizo I suppose, since it's not the only thing of this kind

[narrow relic]

People throw that word around a lot. My bad @nimble ether

@heady ember @gray gazelle How do you recommend getting re-motivated?

[gray gazelle]

go for walks, start again, be happy you're alive

[nimble ether]

having a structure and routine helps me

[narrow relic]

@nimble ether maybe check out this thread: http://giftedissues.davidsongifted.org/BB/ubbthreads.php/topics/157738/all/Precalculus_text_for_independe.html

Oh, I'm very motivated to do my own work (job stuff), and I'm sort of motivated to do math on the side, it's just whenever I get stuck now I suddenly think this is a total waste of time

[gray gazelle]

if you think it's a waste of time then it might just be a waste of time

[nimble ether]

dude can you recommend me a book

[narrow relic]

I sadly think it probably is. So I spent almost two hours trying to prove this stupid thing about decimal expansions of real numbers. It turned out you had to use a proof technique that wasn't introduced in the chapter, rather the author had been going on about another technique, so I sort of got tricked into trying to apply that one. But it didn't work.

[gray gazelle]

what kind of book

[narrow relic]

Most people say "it's good to struggle with problems" but all I learned is that the author sort of fooled me into focusing on something the wrong way, and also didn't word the question carefully enough. So I wasted my Friday evening on that

[nimble ether]

something that will continue off from year 12

[narrow relic]

@nimble ether The thread I linked you to is people talking about book recommendations for your situation

[gray gazelle]

you should try to follow what you're interested, of course there will be stones there on the road, but if something isn't fun and you don't find motivation for it then you should probably just stop

[nimble ether]

okay

[nimble ether]

but dude its in 2013

[narrow relic]

What about reading a math book but not doing any problems?

[narrow relic]

The math you are looking to learn has not really changed for over 100 years. You'll be fine.

[gray gazelle]

That's completely fine of course

[narrow relic]

Also, if you're in the U.S., you should know that things have gotten significantly dumber in the last decades.

Like, it's unbelievable. The reason I recommended you that book is it's the one my old high school was throwing away, and they were replacing it with garbage. So I got a copy for free and learned a ton of stuff

[gray gazelle]

no need to do exercises, what's more important is understanding the material

[narrow relic]

A lot of good math books were written in the U.S. in the 1960's during the Cold War with Russia

But as far as I can tell the curriculum has gone significantly downhill.

[narrow relic]

I have a question about that if I may

[gray gazelle]

if you're doing something less theoretical then you probably should do some exercises to understand the material though

[gray gazelle]

shoot

[narrow relic]

Nah, this is "real analysis"

[gray gazelle]

I mean like, you can't learn how to integrate without doing computations

[nimble ether]

@narrow relic with the 1970s book I have no idea where to start from

I have no idea what its saying

[narrow relic]

So, I've studied two books on analysis. One was Bartle and Sherbert, where I mostly learned how to manipulate inequalities, absolute values, etc. Doing problems helped I think with that. The second one was Goldberg's Methods of Real Analysis. You can't read that book without doing some of the problems since later sections rely on some of the problem results. Luckily I had a good syllabus to follow, and I did every problem on that syllabus.

[narrow relic]

Did you try starting at the beginning?

I mean like literally the first chapter, first page.

[nimble ether]

but dude its 500 pages

[narrow relic]

Are you trolling me or are you serious? I already said you don't have to read the entire book

[nimble ether]

oh yeah sorry

[narrow relic]

Just start on the first page and check it out, see how the first few pages go

The first chapter teaches you how to understand statements in mathematics, it's super useful and cool

@gray gazelle So my question is: at what point is it okay to stop doing the problems? Like, this Carothers book seems to say some of the problems are necessary, he even marks them like that

Like that stupid decimal problem I wasted 2 hours on

[gray gazelle]

like I obviously don't have all the answers but I'll tell you what I'm doing with the current book I'm reading

[narrow relic]

Great, that's what I'm looking for

[gray gazelle]

I'm reading about dimension theory, in topology. And what I do is I don't bother with the exercises.
They are theoretical, probably would be interesting, but it's not what I really care about
Sometimes they use the exercises in the proofs etc. though.
What I do is I just go back and solve the exercise whenever I need it

[narrow relic]

That's sweet. Can I ask are you in undergrad? Also are you doing this just for your own interest or does it connect to work, etc.?

[gray gazelle]

For my own interest. It'd be useful if I ever got to do some research in topology though

[narrow relic]

That's cool, maybe I should just do what you're doing. What's with the whole culture of doing all these exercises, is it just for grading people in school? Why does everyone on r/math on reddit insist on learning that way?

[gray gazelle]

It helps you to develop problem solving skills, or something

[narrow relic]

Oh like, in general?

[gray gazelle]

well, in the early stage most of this understanding of the subject you have will probably go to waste

so yeah I guess

[narrow relic]

I appreciate you sharing your thoughts

You may have found the secret to un-burning me out

I should just learn stuff and stop obsessing with doing all these problems ever-so-perfectly

I feel this horrible internal pressure to do it

[gray gazelle]

yeah. If you find something interesting then go and do it though.
It's supposed to be for fun, not some kind of chore

[narrow relic]

Cool, thank you! 😄 I appreciate you taking the time to discuss it

[nimble ether]

dude recommend me a book

[narrow relic]

Is the Dolciani book not working out?

[gray gazelle]

I only know books about subjects you do in university

[nimble ether]

I haven't tried it yet but maybe there are better books

[narrow relic]

OK

[nimble ether]

yeah thats fine

[gray gazelle]

About something basic, there is always Lang's Basic Mathematics

[nimble ether]

what

why basic

[nimble ether]

is there anything more advanced

[gray gazelle]

on what kind of subject

[rich sun]

What do you think basic math is?

[nimble ether]

something they teach for beginners

[gray gazelle]

here it means things they do in high school for example

[nimble ether]

I learnt all of highschool math

[gray gazelle]

so you just want to learn something new?

[nimble ether]

yeah

[gray gazelle]

https://www.amazon.com/Introduction-Revised-Expanded-Chapman-Mathematics/dp/0824779150/ref=sr_1_3?qid=1667043117&refinements=p_27%3AThomas+Jech&s=books&sr=1-3

it'll give you some set theory knowledge which is fundamental to reading and dealing with mathematics in general

you can start reading something more advanced after

[nimble ether]

why this though

[gray gazelle]

because everyone that wants to read about mathematics should know some set theory

[nimble ether]

dude I didn't learn this at school though maybe I don't need it

I learnt stuff like trignometry and geometry why would I need this

[rich sun]

you wanted to learn something new

[gray gazelle]

[nimble ether]

but dude this is too basic

[rich sun]

you think set theory is too basic?

[nimble ether]

its weird I have never heard of it before

[gray jungle]

If you want to start studying any form of serious mathematics you need to know set theory

[nimble ether]

okay

[nimble ether]

is this one book of set theory enough or do I need more after this and do I have to read the whole thing

also why don't they teach it at school

[rich sun]

It's just the beginning, I can recommend you some lecture notes for the first semester in my uni, but they're in German.

[gray jungle]

Depends on different schools and countries , its often seen in a probability chapter (very briefly) , but if you join any undergraduate math program you'll learn set theory right off the bat

[gray gazelle]

they do teach set theory in school, but only at a basic level

at least in my school

[nimble ether]

nah i am asking If I need to read more set theory books after this one

[gray gazelle]

you don't need to do anything

and if you're interested then you can read more set theory, it's all optional though

[rich sun]

I'm not familiar with the book, but reading the description

relations, functions, orderings, finite, countable, and uncountable sets, and cardinal and ordinal numbers
should be enough

[gray gazelle]

I recommended it because after reading it you'll have more options about what to read further

it doesn't have to be set theory

[nimble ether]

okay

[blazing forum]

Does anyone know any free resources to learn about the following calculus topics? My uni just gives lecture slides which barely have any words to explain whats going on. Thank you!

[gray gazelle]

All resources are free if you know where to look.

[orchid mortar]

standard for calc
https://tutorial.math.lamar.edu/classes/calci/calci.aspx

Also Strang's (free) book, but it's too big for me to even review at a glance

[hazy elk]

Is there any source of math "puzzles" which are easy to understand but lead to some interesting math ?

[eager shoal]

Chris McMullen has a book on puzzles

[hazy elk]

Sort of the kind of things that math circles would use?

Basically for freshmen to get exposed to some cool math

[eager shoal]

Oh

I know just what you are asking for

Intended for high school people who are highly proficient?

Or like college freshman?

[hazy elk]

College

University

[eager shoal]

What math are you taking rn

[hazy elk]

Uhh ok so I want to organize a thing for my juniors

[eager shoal]

If you want college freshman to look into some "new" math I'd look at discrete math. But for problems solving go to https://artofproblemsolving.com/store/list/all-products and the AMC tests

[hazy elk]

The main idea is for the puzzles to lead to a rabbit hole that would hopefully pique the interest of a few people.

It's not really olympiad stuff that I'm interested in

[eager shoal]

At that point I'd just go to youtube and watch videos from people like 3blue1brown

[vast obsidian]

good calculus book that is not stewart or apostol?

too hard, its mor eliek an analysis book

1200 pages in that book

calculus is not a 5 year course subject

who needs 1200 pages wtf

it's just filled with a million exercises and overexplained visuals

but yeah ur right prob

i guess calculus is not for me

[inner token]

can anyone provide feedback on this book or recommend another?

[vast obsidian]

Has terrible reviews, I'm going to check out serge lang and gilbert strang calc

you're thinking of calculus made easy

[inner token]

Thanks

[vast obsidian]

tell me

who hhas time for that

when self studying

8-10 weeks

?

XD

That can only be done by someone who already has done the topic

Not a first timer like me

[remote sparrow]

why not just follow some online lectures about the length of prof. leonard's videos (i.e. 1 hour plus videos) in tandem with a book?

then you won't have to struggle with a 1200 page book all by yourself

many mainstream textbooks are designed to be used in a classroom, and not as a sole resource (i.e. they're not designed for self-study when used only by themselves)

they're very detailed to account for stuff the lecturer might want to omit or to maintain longevity as a reference in case you forget stuff

sorry, but there is no royal road to science

i'm just quoting marx here, i guess i could have paraphrased it to math

but math is a formal science i guess

just saying there is no easy way to learn math or science

some things can make it easier but it won't be "easy"

and i encourage people to find stuff that works for them

but ultimately learning math and science is hard

i don't agree. studying the best way to study is a time investment that can pay off in less time struggling with material. obviously there's an equilibrium point between hesitating too much before doing any material vs. just blindly going into a subject without even reflecting on how you want to tackle it, but i wouldn't say it's "infinitely worse" to do some introspection on how you want to absorb the material and how you would ideally like it to be taught to you.

one thing you could do is just start self-studying from a mainstream book. if you find you don't like it, you can just change the book and review stuff you have learned so far to get familiar with the new book's overall approach.

[gray gazelle]

Wissenschaft

[vast obsidian]

because I don't want to need 2 years to finish calculus 1

[remote sparrow]

well no one who has used these books needed that much time even when self-studying.

[vast obsidian]

Speed I mean between 6-8 months is fine for me, i dont have to finish all calc 1 in 2 weeks

[vast obsidian]

So average person just do 20+ pages a day?

[remote sparrow]

you're thinking too simplistically. firstly, a good chunk of stewart's calculus is in the appendix, a couple hundred pages or so. the first chapter is mainly review of functions and stuff. also, the book has a lot of fluff that is generally omitted at most high schools and colleges. if you want you could go with stewart's essential calculus, which is much shorter.

[sturdy shore]

first of all, the calculus books that are over 1200 pages long are not just calc 1 books

[remote sparrow]

^^^

[sturdy shore]

theyd include 1-2-3 sequence

and yes, average person does that in 1 year

[remote sparrow]

besides that, refer to my advice on watching online lectures so you don't have to sit down and just read

[sturdy shore]

dedicated person can do in much less

[remote sparrow]

given 16 week semester system, you cover calc 1-2-3 in three semesters

people can do all this stuff in three 10-week quarters

up to you

you should still allot some break time for yourself not just so you don't burn out, but so your brain actually has time to massage and absorb the material

[vast obsidian]

even calc 3?????

[remote sparrow]

i mean yeah

[vast obsidian]

If I could do calc 1 in 16 weeks I would be in university rn

[willow pecan]

Yes this is the standard pace that universities cover the material at

[remote sparrow]

calc 3 isn't that intimidating

[willow pecan]

AP classes as well

[remote sparrow]

unless you're gonna go with hubbard and hubbard or something

which you mentioned you didn't really want a rigorous book

[vast obsidian]

How much time per day is assumed to in those universities?

[vast obsidian]

I do want a rigorous book but they have too hard problems, I don't know how to write proofs, like Spivak

[remote sparrow]

calculus sequence is 4 units, so two 1.5 hour lectures per week plus homework

[willow pecan]

4 hours of class per week and 8 hours of homework was what my undergrad did

I think

[remote sparrow]

i know people double units for hours but in practice it's not quite true for every college

3 units = two 1.25 hour lectures for example, not two 1.5 hour lectures

[vast obsidian]

if I was tao-level smart spivak is first book I would pick up, but since you're making calc sound so easy i might try stewart or apostol accompanied by video lectures parallelled with linear algebra if I get bored/unmotivated

[remote sparrow]

apostol and spivak are supposed to be around the same level

[vast obsidian]

really didn't know that I thought it was stewart but a bit more rigorous

[remote sparrow]

in any case learning to read and write proofs is not super hard, but arguably calculus is one of the worst settings to learn it for people who aren't confident in math skills

[vast obsidian]

so a proofless book like stewart is better for me?

and then do proofs after that?

[remote sparrow]

stewart has some proofs for completeness, but they can be safely skipped for now

an intro to proof book like hammack, velleman, hamkins, or chartrand are fine choices. or you could go with a discrete math book like rosen or epp.

if you wanna try doing rigorous calculus velleman's book on calculus might work

it's explicitly meant not to be an analysis text, but still emphasizes proofs

it only covers up to calc 2 though

[vast obsidian]

dont know what discrete math is

[remote sparrow]

they are there

[vast obsidian]

velleman sounds cool then

what is calc 3? what will i be missing?

[remote sparrow]

multivariable and vector calculus

[vast obsidian]

oh okay thanks

last question

who is spivak for? it's insanely difficult for a first-time calculus learner, and not really used for first course in analysis like Tao i.e.

[remote sparrow]

people that want to learn calculus and how to read and write proofs

[vast obsidian]

but it teaches you analysis not calculus? right?

[remote sparrow]

both actually

[vast obsidian]

and how can you learn to write proofs from a book that assumes you already know proofs

[remote sparrow]

it's missing some application problems like optimization and related rates though

[remote sparrow]

by imitating proofs you've seen in the book or playing around with them

talking to people who are experienced with them

[vast obsidian]

This is how I'd end up spending 2 years on a book 💀

[vast obsidian]

I tried but they just say I should already know proofs

[vast obsidian]

i see fair thank you

actual last question: why does no one talk about serge lang calculus?

HAHA why

[dapper root]

You can look it up

But he was an AIDS denialist, used his position to espouse propaganda that AIDS isn’t real

And I think he was a homophobe

[vast obsidian]

"his position" what position?

[dapper root]

Like

Being a professor at Yale

Having incredible clout in the math community

He got some math journal to publish an article basically saying AIDS doesn’t exist lol

[vast obsidian]

I think even if he was a janitor he would have had the same opinion, I doubt he used his position to espouse that propaganda, he would've done it no matter what position he was in

And also lol

[dapper root]

You miss the point lol

Some random guy nobody cares about saying AIDS isn’t real and a respected mathematician saying it have different scope

For example, some random guy can’t get a math journal to publish an article about it

[vast obsidian]

Yeah but it doesn't mean the guy with clout is more of a bad person than some random no one cares about

[dapper root]

I am just saying what he did lol

[sturdy shore]

you know that not everyone with opinions is required to be an activist about it

there are loads of math profs some probably with shit beliefs that don't use their reputation to spread their message

[vast obsidian]

Yeah but you're also imposing unnecessary "he is powerful man, that makes him extra bad" type thing

[vast obsidian]

And not everyone with an opinion is doing it either, just like you said literally next sentence

[sturdy shore]

okay? I am saying that unlike your claim, there is a difference between having an opinion and using your position of power to spread that opinion onto others

[gray jungle]

people can have terrible beliefs and not choose to be an activist about it , his choice and ability to publish about it makes his actions quite bad imo

[vast obsidian]

True, if you're a nobody you can be an activist however you want cause no one cares, but if you are known you should never be an activist of anything.
I guess that concludes this discussion

[gray jungle]

ye i'm not gonna have this argument

[vast obsidian]

back to books

https://tenor.com/view/books-gif-24517932

[quick hornet]

the criticism is more that he intentionally campaigned against granting academic positions & tenure to people researching fields he personally disagreed with

a lot of stories of him getting involved in faculty meetings to protest against immunology applicants and whatever

generally speaking this is considered a pretty dick move

[vast obsidian]

that is fucked ngl

[quick hornet]

its not just "influential person had minority opinion", its "influential person had minority opinion and tried to ruin careers over it"

(though afaik most people didnt take him seriously)

[vast obsidian]

well this is way worse than what we discussed imo, here I would agree w you

[quick hornet]

dont mean to restart the argument, just clarifying the position

[vast obsidian]

I still kind of hope to find someone here who've read his calculus book to give me a review

[quick hornet]

yeah fair, this has no effects on the quality of his book unless you want to avoid the dude on principle

(and like, the guy's dead so i dont really think it matters personally)

[vast obsidian]

I think Algebra is still pretty popular

But none of his other books seem so

Except maybe Basic Mathematics

[willow pecan]

Lang did this thing where he wrote one book a summer

Really a quantity over quality approach

And it shows

[vast obsidian]

If you've read Lang's Calc please contact me :) 👍

[vast obsidian]

lol

[gray jungle]

Re-asking this just in case someone knows

[grand thistle]

any concise introductions to game theory?

ive found "Game Theory for Applied Economists" by gibbons

anyone know if it's a good resource?

[hearty turret]

whats a good book for calculus practice problems?

[old elk]

You are an undergraduate student about to look at the topology course for the first time, you are going to buy a book, you don't know which is the best one

Which book would you recommend to this person?

[old elk]

what other would you recommend

[grand thistle]

uhh

lee's topological manifolds is good ive heard

[hazy elk]

Allen Hatcher's point set topology notes, (it's good to have done analysis before tho) you can also check out http://www.math.toronto.edu/ivan/mat327/

[crimson leaf]

People also like mendelson

[grand thistle]

though if you havent done analysis, it might be good to read through something like rudin chapter 2 first

[hazy elk]

Chapter 2 of Pugh *

[grand thistle]

😭 sometimes i regret doing rudin very much

[old elk]

I will buy mendelson's jeje

[sage python]

Chapter 2 of Pugh feels awkward to me

[hazy elk]

Oh, why?

[grand thistle]

this is simultaneously my favorite and least favorite page in all of rudin

[old elk]

the other week I was going to start reading this chapter
what a pity

[gray gazelle]

Hi, I want to study geometry and am looking for a proof-based textbook about Euclidean geometry. I would like it to be very comprehensive, preferably with some exercises. Does somebody have a suggestion?

[lusty elk]

You could check out Hartshorne's Geometry : Euclid and Beyond
https://www.maa.org/press/maa-reviews/geometry-euclid-and-beyond

[carmine summit]

u should read scythe

really good book

https://www.google.com.au/url?sa=t&rct=j&q=&esrc=s&source=web&cd=&ved=2ahUKEwixsYum3If7AhV76jgGHdU-BP0QFnoECBIQAQ&url=https%3A%2F%2Fwww.goodreads.com%2Fbook%2Fshow%2F28954189-scythe&usg=AOvVaw3S5gKug-vHsWeD7TgHRScn

[gray gazelle]

Thank you both very much. The the books looks precisely like that what I was excepting.

[gray gazelle]

Well this might be expensive

Especially if you're looking to buy a physical copy

[gray gazelle]

Hatcher wrote a whole list of topology books recommendations, considering their prices as well

https://pi.math.cornell.edu/~hatcher/Other/topologybooks.pdf

Reading Intuitive topology and Shape of a space is not necessary at all

The first one is informal treatment of some concepts from knot theory

And the second one is more about surfaces and it reads like a pop-science book

I know because I read both

Dugundji is something I personally read, and while it is kind of like a reference book, you can learn a lot from it, though I suppose it's not for a beginner

Jänich is probably a good book (never read it)

Also note that some courses offer only metric space topology

Metric spaces are not the only naturally occuring spaces out there - even in theory

Also this

Also don't neglect the books that your lecturer is recommending for the course

[kind sierra]

Hello everyone

Do you have Thomas Calculus notes? If you have can you share with me?

[grand thistle]

how many chapters of rudin RCA would be covered in say a 1 semester real analysis/measure theory course?

these are the contents

what specific chapters should i cover?

since both complex and real analysis is mixed in, id imagine there would be some chapters that are independent of each other and i could skip

[willow pecan]

1 to 8 I think

[grand thistle]

cool

[gray gazelle]

One more reason Rudin is a reference book and not something great to learn from.

[gray jungle]

Folland real analysis for MT>>

[gray gazelle]

measure theory?

hell no

that's a real analysis book

go read Schilling or something

[gray jungle]

Im mostly using folland for reference aside lecture notes and i felt like its pretty alright so far
What makes schilling better ?

[gray gazelle]

it's a measure theory book while Folland is not

even though there is a lot of measure theory in Folland

I guess, if it suits you then maybe you should ask your lecturer if it's a good complement for the course

since all courses are vaguely similar but different

maybe the course follows more as an extension of a real analysis course

[fickle whale]

does anyone know where I can get a copy of "on numbers and games" for less than $160

[left depot]

by Conway?

[fickle whale]

yes

[remote sparrow]

kiselev's two geometry volumes

[remote sparrow]

gibrary lenesis

physical copy you'll just have to look for used copies i guess

[fickle whale]

Physical is my unfortunate desire

[hardy bough]

What is this most rigorous mind blowing book I could get to confuse my friends with?

[gray gazelle]

Did Hatcher just throw shade at Munkres

[fluid bay]

munkres kinda overrated tbh

[crimson leaf]

You can get international editions pretty cheap I think I scored mine for $15

[blissful oyster]

I’m looking for a good introduction to the basics of differential geometry, are there any good book recommendations?

[remote sparrow]

tapp's Differential Geometry of Curves and Surfaces or do carmo's book of the same name

not the most general introduction, but it's a "basic" enough intro

[late kite]

Hello everyone. I am a Highschool Junior student and want to dip into the deep qorld of Math. I just dont know where to begin. Are there any good books/textbooks yall can recommend?

[blissful oyster]

Ok thank you.

[crimson leaf]

Have you done any calculus?

[remote sparrow]

try hammack's Book of Proof, which is free on his website or printable for very low cost. alternatives would be How to Prove It by velleman, Foundations of Mathematics by sibley, Mathematical Proofs: A Transition to Advanced Mathematics by chartrand, polimeni, and zhang, or Proof and the Art of Mathematics by hamkins

you can save calculus for later if you want

learning how to read and write proofs is far closer to what math majors actually do past calculus

[crimson leaf]

Yes, however, I was going to recommend Apostol or Spivak if they had not done calculus and felt good enough at algebra

[remote sparrow]

they'll need to look back at apostol or a mainstream book for applications like related rates and optimization if they go with spivak

anyway with the lack of any sort of proofs besides a very boring, uninspired class in geometry, learning how to do proofs will make spivak more fruitful

[gray gazelle]

Opinion on arnol'd ODEs??

[drifting elm]

conway?

[hallow oriole]

print and bind it yourself, maybe?

there are guides on the internet and it'll be much less than 160$

and not very time consuming

well

a little

but not that long

there's also this ebay link

https://www.ebay.com/p/1797612?thm=1500

but it could totally be a scame for all i know

[opal ridge]

What should I use for studying math 2

[remote sparrow]

what exactly is the content of "math 2?"

[opal ridge]

https://www.khanacademy.org/math/math2

khan says that is what math 2 is consist of

[remote sparrow]

oh, i did this in high school. i guess you could google a topic in brilliant and stuff. paul's online math notes covers some of the algebra and trig. i feel like khan academy is good enough for this kind of stuff though. i think i had to use a textbook/workbook for this stuff in high school. try to look for such a book.

[opal ridge]

kk thanks

[next storm]

Hey what is a good for for learning ZFC?

[remote sparrow]

enderton's elements of set theory

or introduction to set theory by hrbacek and jech

are good undergraduate treatments

[marble karma]

I want to study linear algebra any recommendations?

[blazing canopy]

Do you have familiarity with proofs or some other proof-based subject already? If so, I used Friedberg, Insel, and Spence's linear algebra text when I was first learning. But it is not suitable if you are not already familiar with proofs.

[sage python]

Someone should write a linear algebra book that's simultaneously an intro to proofs tbh

I guess Axler would almost be in that category if not for his determinant/char poly stuff lol

[hazy elk]

Do the first 4+ chapters of Axler and then migrate to Hoffmann kunze + learn the multilinear algebra for determinants from Sergei Wintzki's book

[marble karma]

I am fine with proofs

[hazy elk]

Hoffmann Kunze would be fine for you then

[marble karma]

Thanks

How long do you think it would take to work through Hoffman kunze?

[hazy elk]

The whole book..?

[marble karma]

Yes

[hazy elk]

Under 2 semesters worth of content I'd wager

Too much for a single semester but too little for 2

Don't be too concerned about finishing the book cover to cover, choose the interesting topics wisely

[marble karma]

Any video lecture or reference book to compliment it ?

[hazy elk]

That's a more efficient way of learning math

[marble karma]

Yes 👍

[hazy elk]

Not sure, but there are plenty of lecture series on yt, I bet NPTEL has atleast one proof based LA course.

[marble karma]

Ok thanks 😊🙏

[heady ember]

Agree with your recs

[gray gazelle]

Thank you

[cinder trellis]

Spivak’s Calculus helped me when I first learned proofs, especially since anyone can read it after or during calculus I-II

[rain birch]

Has anyone checked out the introductory elementary mathematics books by I.M. Gelfand?

[lapis steeple]

yo can anyone recommend some books for year 8 students?

[vital bane]

yes, your year 8 math book

[storm sigil]

does anyone know a good book about cyclic group theory?

[quick hornet]

what do you mean by that? there isnt that much interesting stuff to say about cyclic groups specifically

like okay that's a lie, there is plenty of interesting stuff to say

but that stuff is usually number-theoretic in nature rather than group-theoretic

and considered the subject of elementary number theory

@storm sigil

[storm sigil]

i just to explain about the rubiks cube

how does it work

[quick hornet]

the rubiks cube group isnt cyclic

it's not even abelian

[storm sigil]

soe of them are

[storm sigil]

really

[quick hornet]

yeah; FL and LF produce different cubes

(F means "turn the front face clockwise", L means "turn the left face clockwise")

[storm sigil]

tru

[quick hornet]

in any case, i am unfamiliar with any sources that deal specifically with the rubik's cube group

it's more of a computational novelty than something actually considered useful afaik

[storm sigil]

oh wow

[quick hornet]

google produces this document https://people.math.harvard.edu/~jjchen/docs/Group Theory and the Rubik's Cube.pdf which might be worth a skim

seems well written at first glance at least

[storm sigil]

thxx

but

the moves are consired in z mod 4

right?

[quick hornet]

in the sense that rotating a face (clockwise) 4 times is the same as rotating it 0 times, yes

this doesnt mean the group itself is Z/4Z

[storm sigil]

why

[quick hornet]

because there's more than 4 valid moves?

like if you only cosnider rotations of one FACE, then yeah

that group is Z/4Z

[storm sigil]

but if u consider one type of move its cyclic

[quick hornet]

but a rubiks cube has 6 different faces with multiple ways to rotate them

[hearty sluice]

and nami has 2 faces

[quick hornet]

and the interaction between these faces is more complex than just (Z/4Z)^6 or whatever

[storm sigil]

ik but it was just to explain rootations in one face

[quick hornet]

okay, then yeah; thats just Z/4Z

and there isnt a book dedicated to it because theres nothing interesting to say

if you want some fun facts, you can check https://groupprops.subwiki.org/wiki/Cyclic_group:Z4 i guess

[storm sigil]

kk thank uu

[quick hornet]

it has normal subgroup {0, 2} i guess lmao

which represents what happens if you consider 180 degree rotations instead of 90

[acoustic glade]

Any opinions on Maunder's Algebraic Topology and Wallace's An Introduction to Algebraic Topology as an intro algebraic topology book (aka the two Dover books on the topic)?

[remote sparrow]

never heard of those, but i'm assuming hatcher's book isn't good enough for you? btw no experience with this topic, but hatcher is a common rec, and i think it's pretty cheap as a hard copy, too. plus hatcher's book is officially available for free in ebook form.

[acoustic glade]

I've looked at Hatcher, it looks okay but maybe a bit too geometric for my taste (plus it's like double the price not accounting for shipping, I'm looking to get a physical copy this time around)

[red swan]

Hello, I have a presentation about the irrationality of zeta(3) due in a few weeks, and even though I get the very basic idea of how the proof works, I severely lack the calculus skills needed to understand the meat of the calculations, do you have any recommendations for resources pertaining to multi variable integration? (I am solely familiar with basic riemann integration techniques and theory)

[finite heath]

Can anyone give me a reference for the study of non-commutative rings? Specifically, I want a book that will give the definitions of Euclidean domains and PID's in the non-commutative case. And also prove that Euclidean 'rings' are Principal ideal 'rings'. Thank you 🙂

[sudden kindle]

What is the proof you are learning?

[remote ginkgo]

they are probably nicer reads than hatcher me and all my homies despise hatcher

[manic cairn]

Serge Lang's Undergraduate Analysis covers it, along with a bunch of other stuff, and a review of what you mentioned already learning.
After that, you can move on to Lang's Complex Analysis, which will bring up the necessary complex analysis to understand the zeta function.
Finally, if you're interested in multivariable calculus on shapes, I'd read Munkres' Topology and (afterwards) Lee's Introduction to Smooth Manifolds.

You can probable do the necessary portions of Undergraduate Analysis in a couple weeks (before your presentation), and you can spend the rest of the semester going through the complex analysis and topology, and the second semester and summer on the differential geometry of Lee.

[rich ridge]

What’s a good book for review on trigonometry and pre calculus and also what’s a good book for Calculus 1? Would prefer a textbook like format if possible

[remote sparrow]

stewart's calculus has diagnostic tests and an appendix that reviews some algebra and trig. stewart also has a precalculus textbook.

[marble solar]

:< bleck stewart

[rich ridge]

Appreciate it

[fluid bay]

i don't have a recommendation but I can think of a discord server where your question might get some answers

ill dm an invite to the server im thinking of

[red swan]

beukers (Apery's seems way harder)

[red swan]

thanks a lot!

[gray gazelle]

Don't read Munkres

I have enough people talking about the box topology and limit points

[rapid lily]

What is not good about Munkres? Or why would you not recommend it?

[gray gazelle]

https://pi.math.cornell.edu/~hatcher/Other/topologybooks.pdf

[red swan]

I was only planning on reading lang

I already have a topology course, even though it mildly sucks

[gray gazelle]

Go read something from this list if you plan on reading topology

[rapid lily]

I have the book by Willard but I have barely read it

[red swan]

I have this more general math book that has a good chapter on topology

it's short but it'll do for now

[gray gazelle]

It will

[red swan]

especially since my uni has turned this subject into a massive disappointment so far

but that's besides the point, I checked out the serg lang book, it seems pretty nice, thanks for recommending it!

[gray gazelle]

I read a really awful proof in Willard once so I'm not sure about its quality.

[rapid lily]

Oh

I need to study topology from some book but I haven't done it properly yet

I learned some for functional analysis but that is it

[gray gazelle]

Munkres mentions box topology and teaches to use limit points to check if a set is closed.
Box topology is a useless topic and the latter is just bad from educational standpoint.

I haven't read it myself but I see people repeating this all the time

It's annoying. Just grab a better less popular book

[red swan]

what's wrong with using limit points?

[gray gazelle]

It's a middle man

The concept itself is fine

[red swan]

I mean the way we've done it so far was really stupid, it just felt like a complicated way to say "the inequality in the set definition isnt strict so it's a closed set"

[gray gazelle]

It does sound stupid if true

[rapid lily]

I will look at Dugundji perhaps

It sounds reasonably comprehensive

[gray gazelle]

Dugundji is a bit old and is somewhat a reference book

You won't be taken by the hand in that book

Arguments there might be hard to grasp. But it will give you a lot of topology knowledge

[rapid lily]

Ok thanks. I would be happy with something like that

[gray gazelle]

Then do try

[fluid bay]

im so offended rn. the box topology just so happens to be my favorite topology

|| .... /s ||

[vital bane]

[pseudo coral]

im in middle school and i missed algebra is there any recommendations of algebra books for middle school

[gentle arrow]

algebra by serge lang

(use khan academy)

[golden bear]

@gentle arrow damn, that is hrush

[fierce hedge]

What would you recommend for a quick but decently broad intro to topology that builds towards AT. I know about Hatcher's notes, other than that what would be a proper book? say Gamelin and Green or something like that? There's also Topology - A categorical approach in the recommendations

[willow pecan]

How unhelpful

[peak ledge]

Anyone know any good books on math comp. geom?

Or something that has all the useful theorems one should know to start

[willow pecan]

comp = competitive or computational?

[peak ledge]

competitive

[willow pecan]

Art of problem solving probably

[peak ledge]

by Sandor lehoczky and richard ruszczyk?

[willow pecan]

Sounds right

[peak ledge]

ty

[smoky zephyr]

i hope this is just a bad joke

[normal reef]

I'm looking for a good biography on Euler, any suggestions?

[dense wren]

Anyone know Altman and Kleimans commutative algebra book? How is it compared to atiyah and Macdonald?

[worn bay]

Does anyone know good competitive math books in geometry and number theory?

[sleek canopy]

aops

there are sections on number theory and geometry in Problem Solving Strategies (engel)

aops has volume 1/2 which are good overall books for contest type problems, their number theory text is very elementary

[worn bay]

Thank you so much!

[gray gazelle]

I don't know

[placid pollen]

You're a man of integrity just like me

[heady ember]

I have heard Lee's Introduction To Topological Manifolds is a good intro to general topology. You can give it a go and see if you like it I guess? Not sure if it builds towards AT tho

[forest sleet]

you can start reading Hatcher's AT book after just some point-set from Munkres

probably not going to be easy

but that's kind of how learning AT for the first time goes

[warm glen]

do y'all recommend learning category theory from a book that teaches something categorically or should one learn from a dedicated cat theory book

[remote sparrow]

eugenia cheng recently released an introductory category theory book called the joy of cats

[warm glen]

i have pdfs of topology: a categorical approach and riehls cat theory book and im wondering which one i should learn from

ah yea i saw it recommended here i think not too long ago

[livid ermine]

its good

probably better than atiyah macdonald, for self-study

[junior mantle]

can someone recommend me a book on euclidean geometry, with lots of problems?

i need to revise the grade school stuff, more in-depth, ofc

[gray gazelle]

Max always used to recommend Hatcher's notes as an introduction to topology so that'd be my guess on what to read first

[gray gazelle]

Dieck also wrote a short introduction to topology with AT in mind, now that I recall

[gray gazelle]

I mean that's like a book about a different topic. But it might contain just enough.
Still, I don't like this recommendation

[heady ember]

Well I just said that because it doesn't hurt to take a look, perhaps there could be some content that's useful

[gray gazelle]

Almost sure there will be since in principle the prerequisites should be around the same

But it's kinda weird

If you're going to read Hatcher's AT you might as well read his notes on general topology

That'll be same style of writing, more or less, and clearly the intended way to go through all of this

That's what the notes are for, I think. To serve as a complement for his book

[junior mantle]

should i just read elements?

[gray gazelle]

Euclid's?

[junior mantle]

yea

[gray gazelle]

I'd rather go for something modern

[junior mantle]

can you give me an idea, please?

[gray gazelle]

There is lots of usage of language in that book that we no longer use in the same way, even in translations

For example 'Euclid's axioms'

[junior mantle]

we got introduced to birkhoff's system of axioms

but now we are revising the grade school kind of geometry more in-depth and i forgot everything about this kind of stuff

lol

[gray gazelle]

I don't know any books for Euclidean geometry, I'm just advising against reading Euclid's Elements

[junior mantle]

ok then

thanks for the advice

[gray gazelle]

@junior mantle

[junior mantle]

appreciate it, mates

[fierce hedge]

Are you referring to his book on Algebraic Topology or his (incomplete) notes on Topology?

[gray gazelle]

Notes on topology.
His AT book definitely assumes you have some knowledge, both from category and topology

Most of what's there I already had with Dugundji though I admit there were some details I didn't know so it proved useful

Something about perfect maps I think

Not sure why you're calling the notes incomplete?

[fierce hedge]

Oh, it's just mentioned in the notes - "Preliminary and Incomplete. Version of November 13, 2011".

Not sure in what sense it means incomplete

[fierce hedge]

It says - "I assume that the reader has some experience with point-set topology including the notion of compactness" which doesn't seem like much
In any case I'll just read the notes first

[gray gazelle]

No, definitely assumes much more than that

[fierce hedge]

oh, alright then

[remote sparrow]

maybe kiselev's two geometry volumes?

[junior mantle]

thanks, ill try

where did you find that?

[thorn cloak]

Anyone have a recommendation for a calculus 3 book? I’m going into calc 3 next sem so I’m not the most advanced at calc but I know the basics and stuff from 1/2

I guess just good multi var books

[sage kelp]

Any comments on the Feldman,Rechnitzer,Yeager Calculus books? Are they good or still a work in progress?

[remote sparrow]

you can use stewart's calculus textbook

it has a standalone multivariable calculus book

same with larson

although if you're gonna buy, it's much cheaper to just get the book that covers all of calculus 1-3

the calc 3 standalone volumes are basically the same price as the big books

and it also helps to buy older editions, which are also significantly cheaper with essentially identical content

[crimson leaf]

Good resources on Ramsey theory at the undergraduate level?

[kindred chasm]

Hey, has anyone read some of OpenIntro's open statistics textbooks? I've started reading 'Introduction to modern statistics' and then I was informed that they have another edition named 'Openintro Statistics' which I'm not sure whether I should switch to that book. My main goal is to understand the topics at their conceptual level as much as possible, and hoping it should cover most of the introductory college level stats topics or more.

[foggy relic]

Barton IV

Few others I’m not recalling at the top of my head

What do you want to know?

[crimson leaf]

Just general info we're going over it in class but I don't really like the source my professor is using

[dry elbow]

What is a good online book for university level calculus

[heady ember]

Depends on what kind of calculus book you want: Single-var? Multi-var? Computation based? (Slightly more) Proof-Based?

[gray gazelle]

I'm working through Apostol Calculus, you can get a PDF online.

[dry elbow]

Single variable

And yes

.ore proof based

More

[heady ember]

Then Spivak's Calculus

is a good choice

[pliant girder]

hello

i am new here any books recommendations

[vagrant sedge]

Hi. Do you guys know about the three volume set "Applied and Computational Complex Analysis" by Peter Henrici? Is it good? Is it still relevant?

[tawny copper]

A beautiful journey through olympiad geometry by Lozanovski

Or EGMO by Evan Chen

Does someone know any nice video lectures course on algebraic number theory?

Something like this https://www.youtube.com/watch?v=NQM0XNxSkus&ab_channel=GraduateMathematics

(This is an excerpt from an analytic NT course)

[junior mantle]

Thanks a ton

[tawny copper]

👍 That text is really nice, I'm enjoying it a lot

It is free on-line btw, the author has a webpage

[junior mantle]

Thank you my crocodile friend

Hope you dont bite my leg off

[gray gazelle]

Are there any nice proof-writing books?

[rich sun]

See introductory books in #books-old

[gray gazelle]

Alr ill check that out

[icy knot]

Most combinatorics texts should have a section on it.

[gray gazelle]

Thankfully crocodiles don't have such sharp teeth. They'll pull you into the water snd drown you by repeatedly spinning in water

[junior mantle]

welp their bite has 3,700 PSI

so my leg would be crunched

its like you biting a potate chip

[gray gazelle]

Ah

[icy knot]

What is another recommendation for Algebra text for someone who already has Pinter’s book? I currently have Jacobson’s book in my shopping cart.

[remote sparrow]

chartrand's Mathematical Proofs: A Transition to Advanced Mathematics, hammack's Book of Proof, hamkins' Proof and the Art of Mathematics, sibley's Foundations of Mathematics, or velleman's How to Prove It are good choices. alternatively you could pick up discrete math books, such as those by rosen or epp.

[warm glen]

artin, herstein, clark are all good

clark's book has barely any exposition though, it's more of a problem book than a textbook but that can be useful

[remote sparrow]

thomas judson's book is very cheap

[gray gazelle]

best linear algebra book for a first course?

please ping w response, thanks!

[remote sparrow]

#book-recommendations message

[gray gazelle]

what would you say about Axler for a first course?

[willow pecan]

No

[gray gazelle]

why not

too theoretical?

[willow pecan]

Yes

Also treats determinants poorly

[gray gazelle]

and what would be your own personal recommendation

[willow pecan]

For a first course?

Well the one I used was not very good so not that one

Lin Nagle and Shaff or whatever

[icy knot]

Thanks

[icy knot]

Thank you

[hearty steppe]

I got a fun paper recommendation https://www.researchgate.net/publication/363307637_Quantum-inspired_cognitive_agents

This is more in line with the direction of my compulsive behavior dynamics publication in terms of where the math is going

[gray gazelle]

Ive skimmed over all of them and it seems like Chartand's book takes the cake

[cedar ridge]

not a particularly interesting/enjoyable book but gives the basic proof methods

[gray gazelle]

I’ve already received some recommendations but can anyone share the “standard” for a first course in linear algebra

[remote sparrow]

there isn't any, really. linear algebra is such a broad and diverse field some books will omit some topics that others find important. but generally first courses in linear algebra are more concerned about computing matrices and verifying simple properties rather than proving any especially deep theorems. my college uses david lay's Linear Algebra and Its Applications. other schools might use gilbert strang's linear algebra book. there are many others i haven't mentioned.

[gray gazelle]

thank you, I’ll check out the one your uni uses

[icy knot]

Has anyone ever browsed Galois Theory by Edwards? I recently came across a YouTube video from a Math Major as to that being the best introduction to Abstract Algebra rather than the standard textbooks most university use. Then again my Calc/ODE professor recommends Saracino’s book.

[remote ginkgo]

lang

[remote sparrow]

you mean daniel rubin? he's a math professor at cornell

[icy knot]

Yea. I miss heard. I thought he was just a former grad student. Didn’t realize he teaches now.

[fierce hedge]

Same

[fierce hedge]

If you wanna go deep into the history and need to know how Galois actually thought about the mathematics then it's a great book. It's just not that great as a standard textbook and reference book. Say if you wanna jump into research quickly, you are better off textbooks like D&F, Herstein or Gallian

[icy knot]

Thanks. I realize that the justification for Algebra came about to be able to solve polynomial equations. What kind of equations? I was mainly looking for an algebra text that expounded upon that to go with my copy of Pinter’s book which is essentially a “problem” book. Basically, all the theory that you learn in a math degree is invaluable, but I want to be able to use it to solve real world problems. But that’s probably idealistic, plus undergrad math just gives you an overview of several topics. One thing I can definitely say is that as I am completing my last semester of undergrad, there has been struggle, a lot of struggle, but I’m a better thinker and problem solver having taken all these math courses. I’ve learned probably that pure math is probably outside of my realm also, lol.

[vast obsidian]

calculus books )

for self study

[lean pagoda]

any good texts on domain theory?

[remote sparrow]

zlibrary got taken down

[sleek canopy]

Recommendations for a Homological Algebra book and an Algebraic Topology book not named Hatcher?

[dapper root]

Rotman

And rotman

[worn bay]

the onion link is still usable

[hallow oriole]

it's gonna be back

• while there's no zlib im 99% -- still works

censored c discord rules but you can still get any book out there

[sleek canopy]

thanks chmonke

Ive heard good thing abt both

[zealous light]

[sleek canopy]

[brisk ice]

rip ||z-lib|| 🙏

[fierce hedge]

Was zlibrary better than library genesis?

[remote sparrow]

it had better UI and searching and stuff

it also had more books than libgen

[fierce hedge]

More books? Wasn't it just a mirror for libgen

[remote sparrow]

in some ways, but i definitely found books on zlibrary that weren't on libgen

[heady ember]

I would say perhaps take a brief look through the various book recs in pinned (i.e. Flip through a couple pages of each book) and see which you like best! Personally, I have been using Friedberg, Insel, Spence

[remote sparrow]

pinned books are mostly for second courses

[heady ember]

ehh Im not sure if there's a need for that distinction

In the sense that Friedberg, for instance, is pretty doable I think even for someone like me who hasn't done any linear alg before

[violet shuttle]

LADW, or LADR (Linear Algebra Done Wrong and Linear Algebra Done Right, respectively).

[loud cradle]

LADR is explicitly intended as a second course, it omits many first-course topics such as row reduction and other matrix manipulations

[violet shuttle]

wait what? oops

[sleek canopy]

"first" course in Linalg axler?

I used LADW in my first semester and went between Roman/Axler for the later linalg class

[manic cairn]

Lang Part 4 for the first one

[sleek canopy]

no.

[hollow shore]

is it just me or zlibrary is down?

[remote sparrow]

it was seized by the FBI

i mentioned it a little earlier in this channel today

[hollow shore]

ah shit that sucks

[remote sparrow]

something will pop up in the future hopefully

[smoky zephyr]

woah lol

[remote sparrow]

can't really keep these sorts of sites down forever

[smoky zephyr]

ugh wrong message reply

[remote sparrow]

in the meantime you can still use libgen

[hollow shore]

there are books in zlib which aren't there in libgen

[remote sparrow]

yeah i know

[fierce hedge]

What kind of books, like novels or even textbooks? Are these like user uploaded?

[hollow shore]

I generally download textbooks from there and there are few of em which are there in zlib but not in libgen

same goes for novels too

like I found The Penguin Book of Spanish Short Stories on zlib but it wasn't there in libgen

[heady ember]

Just use their tor domain

[hollow shore]

bruh zlib has limited downloads per ip