book-recommendations

[heady ember]

How many books are you downloading everyday

Their cap is 10 with an account

[obtuse ridge]

can anyone suggest me good book for olympiad prep (like IMO)

[hollow shore]

is signing in from tor browser safe? (I am sorry I am not very tech savvy)

[hollow shore]

a lot . I am somwhat of a book hoarder myself.

[heady ember]

[rapid lily]

It's not appropriate to be advising people to go to piracy websites

[hazy elk]

Are the fundamental groups/covering spaces parts from Munkres easy to read?

[left cloud]

not for me 😭

[left cloud]

it's more appropriate than advising people to spend 10 million dollars on books 💅

[gray gazelle]

FBI

[gilded coyote]

Books for quadratic equations ??

[gray gazelle]

I don't think they make books about those

If anyone wants a basic intro to topology then you can check out Topology of Metric Spaces by Kumaresan

Finally found a book that does topology on metric spaces alone

[orchid mortar]

There probably are free collections of notes which are free for academic use if you have strong concerns about piracy

[orchid mortar]

The government can still link you to TOR, but perhaps not your account. Not that it matters. You can see that the government is going after distribution rather than end-users (which could be politically unpopular https://en.wikipedia.org/wiki/2022_United_States_elections ) - I don't know of any legal action that chased end users which ended up well

[gray gazelle]

More than using firefox, chrome or IE but not absolutely.

[rapid lily]

The price of the books does not change whether it is legal or not to do that. I'm not trying to judge anyone, I'm simply stating that illegal activity such as piracy (no matter whether it is perceived to be significant or not) should not be promoted.

[hazy elk]

Legal != moral

Does anyone have a set of notes for fundamental groups and covering spaces?

[hearty steppe]

No munkres is not an easy read but to his credit I will definitely say it is one of many books where people with a rigorous background outside of mathematics might have a chance to understand at least the first two or three chapters and complete some of the exercises maybe.

Definitely not an easy book but it is not quite Rudin difficult

[icy knot]

Here’s what my school is using for Putnam:

The USSR Olympiad Problem Book

Problem Solving through Problems,, Putnam and Beyond, The Art and Craft of Problem Solving, Mathematical Olympiad Challenges, A Problem Seminar, Winning Solutions, and Problem Solving Strategies.

[obtuse ridge]

i actually meant High school level

like IMO or national selection round of IMO

[grave thorn]

hot take: the FBI was right

[icy knot]

Got it. There is a IMO book that the coach recommended, but I don’t have the sheet with me right now. Maybe a Martin Gardner book? I know Dover has some.

[vast obsidian]

I got suggested Friedberg, et. al Linear Algebra book but it says I need calculus

[obtuse ridge]

ohk thnx

[still umbra]

It's just the domains which were killed

z*ibrary is still accessible through tor

or just use *ibgen

[gray gazelle]

has anyone read Vector calculus, Linear algebra, and differential forms by Hubbard?

if so, thoughts?

[icy knot]

The IMO Compendium

[obtuse ridge]

thnx

[fierce hedge]

+1

[remote sparrow]

sure, they were legally in the right

pretty lukewarm take at best

[kindred wren]

you may try searching the keywords "algebra trigonometry" on libretext
you would get plenty of free ebooks. i rmb grabbing a random hard-copy book with a similar title a decade ago.
a random book will do. if not, change to another one.
https://math.libretexts.org/Bookshelves/Algebra/Book%3A_Algebra_and_Trigonometry_(OpenStax)

[tawny copper]

Where do you guys download pdfs from? The places I usually went to stopped working

[vast obsidian]

There exists no good calculus books?

[violet forum]

I'm a new student and very interested in mathematics. Unfortunately I'm still a high school student and I haven't studied much, I want to get my shit together in algebra and trig, and also learn things like calculus and complex analysis, where do I begin?

[willow pecan]

Khan academy is probably a good place

[tawny copper]

Try Peter Clark notes

For exercises and problems, there are many good places

[gray gazelle]

I can dm you

[tawny copper]

Please

[vast obsidian]

Yeah but KA, Paul's Notes, Clark Notes and MIT OCW are not books
Spivak is too hard
Stewart 1000+ pages
Apostol no one has done it apparently
Lang no one can give an opinion because they think he is evil
Kline ???
Thompson it covers 1/5th material of calculus 1

It's weird that such an important topic like calculus has so few good books (multivar calc and analysis has great books I've heard)

[willow pecan]

1. I was not responding to you

2. What is wrong with stewart being 1000+ pages

[vast obsidian]

Don't want to spend 2 years on calc 1

[willow pecan]

It does not take two years to get through stewart

[vast obsidian]

With the amount of exercises it has I don't believe you

[willow pecan]

No one does all the exercises

[tepid prairie]

I don't believe either.

[vast obsidian]

why would you not do all the exercises?

[willow pecan]

Because there's no point?

[tawny copper]

If Clark notes were sold in hardcover from Springer by 35 dollars, would you be happier?

[vast obsidian]

Yes

[tawny copper]

🤦‍♂️

[gray jungle]

Just skip calculus and learn real analysis , problem solved.

stewart is fine

[tepid prairie]

Nah. It's these modern books which are just mass produced trash. Just like Khan Academy.

[vast obsidian]

Problem is I need calculus for analysis no?

Imagine if I die soon and have never studied calculus, if there is a heaven I wouldn't be in there

[vast obsidian]

I don't know if I have some mental issue but I can't watch videos and is why I don't do KA
However books I can read and enjoy and struggle but I still try, videos I skip, fast forward, get bored, sleep

[gray jungle]

Some might argue otherwise ,but its generally a good idea to do calc-->analysis , and you dont really need a book for calculus honestly , mit ocw course is good enough imo

[tepid prairie]

If you've been watching Khan Academy style videos then it's easy to see why you can't watch them. If I knew what you was trying to learn specifically I might be able to give you something as a last try of video media.

[vast obsidian]

yeah but my disease dont allow for videos

[tepid prairie]

You might wish to find a Dover book on the related things then. Those books are very good typically. Very different to the usual rubbish.

[vast obsidian]

If I were to pick up Stewart, which one do I pick? Early Trancendentals? Calculus? Essential Calculus?

[vast obsidian]

Calculus, from the derivative to double integral

I have spent more time trying to find what to use to read calculus than I've studied the topic :)

[tepid prairie]

Actually have you seen Paul's online notes?

[vast obsidian]

No

[tepid prairie]

Google them. Definitely worth a look.

[vast obsidian]

I will thanks

I think I will go for Lang as well it seems the best in terms of book quality? 600 pages, not hard like spivak/apostol, more rigorous than stewart
It seems to be perfect middle

[gray gazelle]

Recommendations for books to learn (all) GSCE topics

[cursive orbit]

that sounds more like a you problem than a calculus problem

[vast obsidian]

no I will never admit that!!1 bad books everywhere 🤢

[cursive orbit]

just pick something and go through it

it's hard to go wrong when studying calculus

if it's too hard go to something easier

[vast obsidian]

@cursive orbitk man ill do Lang

[remote sparrow]

lang's book is specifically designed to appeal to intuitions and deemphasize rigor as he mentions in the book. he completely leaves out epsilon-delta arguments, which he believes most people at this stage are not prepared for, in the main body of the text and reserves it to the appendix, which he also believes should be omitted for ordinary circumstances. this is not wrong but it is also not a "halfway" book between spivak and stewart. that would be something like velleman's calculus book. and for any book, you should learn to exercise judgment as to how many and which problems you should do.

[vast obsidian]

any book, you should learn to exercise judgment as to how many and which problems you should do
I don't know how to even approach that, like, do you want me to go back in the book and be like "yeah this was useless shouldn't have done these 5 exercises wasted too much time on this chapter"?

How can I know how many exercises I need or not?

[orchid mortar]

Likely you can't a priori do that

But as you gain knowledge you might

Also the point of exercises is for doing

And you learn more by doing than by reading

Once you can dismiss an exercise (or groups of them) with proof sketches you are ready to move on

[vast obsidian]

Also someone said dover books are bad just before you

[gray jungle]

problem sets , such as on mit-ocw are helpful when you're starting out

[orchid mortar]

That is, assuming your sketches are good. You should still do some to get hands dirty

[vast obsidian]

This contradicts dismiss exercises, shouldnt I just do as many as possible then?

[vast obsidian]

thanks

[dapper root]

Dover books are lretty good I think

[orchid mortar]

Not a good plan. But you should do some exercises

[dapper root]

They’re cheap which is great, and they have quality titles

[vast obsidian]

is intuition over rigor bad?

[remote sparrow]

no, but you said lang was more rigorous than stewart

like a halfway book between spivak and stewart

[vast obsidian]

it's not?

[remote sparrow]

it's in the foreword

[vast obsidian]

Lang says it's not that rigorous in the foreword yes, but he doesn't say it's less rigorous than Stewart

I'm not sure you can call Stewart more rigorous than Lang's

[manic cairn]

Lang is a great calculus book, although the problems could be harder

it isn’t meant for rigor

but it’s written in an intuitive way, such that I would recommend it to talented middle school students

[vast obsidian]

But is intuition bad? Should I go for more rigorous stuff like Velleman that @remote sparrow recommended, or less rigorous like Stewart?

[remote sparrow]

just pick something you vibe with

[vast obsidian]

I would use both tbh

But Velleman uses set theory a lot, lang doesn't

[gray jungle]

A new contender appears : Calculus with analytic geometry by George Simmons seems to be Mit's choice

which should be a good companion considering you get problem sets and assigments from the book if you use ocw

[vast obsidian]

maybe I should just read all calculus books ever made at the same time

[granite tide]

hey guys can suggest to me a good book on Mathematical Logic ?

[rich sun]

Have you taken a look at #books-old ?

[vast obsidian]

"Calculus for the Practical Man (James Edgar Thompson)"

[sturdy shore]

what is your level

[granite tide]

Am an Undergraduate student. Actually am in 2nd year preparatory class to artificial intelligence speciality

[sturdy shore]

then I'd recommend leary & kristiensen for the easiest introduction

most logic books are hard to tackle as early undergrad, ^ is the easiest from the ones I've looked at

but there might be others

other options to look at might be goldrei, rautenberg

okay probably not rautenberg

[remote sparrow]

antonio montalban has videos to follow enderton, which is usually considered as one of the harder intro texts, but that could be eased with his videos

you can also peep peter smith's logic matters blog

he has some recommendations

also check the pinned message by @ diligentClerk in this channel

@granite tide

[sturdy shore]

didn't know of this, seems to cover up to 3/4s of chapter 2 (completeness)

Math 125 -- Introduction to Mathematical Logic -- is a U.C. Berkeley class geared towards 3rd and 4th year math students who already have some experience with abstract mathematics and proofs.

[manic cairn]

Mendelson is good

[sturdy shore]

which is fair for enderton if you are getting lecturer support

[manic cairn]

get a newer edition, my old one has less standard notation

and the new ones don’t

[sturdy shore]

without anyone helping you, enderton can be hard even for 3rd/4th year, the book is not friendly at all (in exposition)

[vast obsidian]

Why would you study logic?

[remote sparrow]

why would you study how to obtain true conclusions from premises? how to correctly reason about things? that's what logic is

[vast obsidian]

I mean like advanced logic

What more logic do you need besides what you learn in discrete math

[remote sparrow]

you don't need more logic for typical fields like algebra, analysis, topology, etc.

just as you don't need much more set theory beyond naive set theory

i mean you can just look at the wikipedia page for mathematical logic and see why people think it's worth studying

or why people study set theory rigorously and on an axiomatic basis beyond the set theory they pick up in other math classes

you can ask the people in #foundations for more detailed responses

recursion theory is very applicable to computers

[vast obsidian]

what about pure mathematics

[remote sparrow]

for cleaning up the foundations of math?

[vast obsidian]

I c

[remote sparrow]

proof theory

[vast obsidian]

I'm still procrastinating Calculus because I can't choose between Lang and Velleman :) @remote sparrow

This has been my routine for the past few weeks, with various combinations of books/material

[remote sparrow]

check pinned

[fickle bough]

Alright thank you

[heady ember]

Look at Clerk's recs in pineed

Also, if im not wrong you should have studied some basic axiomatic set theory before trying logic

I know a number of books require that as a prerequesite iirc

[sturdy shore]

no

only for graduate level would you need that

[fallow thunder]

your 'about me' is crazy lems

[sturdy shore]

yes

[fickle whale]

I mean it works, because invalid application of rules doesn't mean that your answer has to be wrong

[marsh bridge]

Hello everybody, any recommendations from some books on introduction to differential geometry and that is in a more fluid language?

[scarlet steeple]

has anyone read Elementary Introduction to Number Theory by Calvin T. Long (specifically the edition from 1965?)

[devout hollow]

I have read Introduction to Linear Algebra by Serge Lang. Currently, I am reading his Linear Algebra. And after this, I am planning to read LADR by Axler. But can anyone recommend to me a book that can serve as a bridge between linear algebra and multilinear algebra? Thank you.

[fierce hedge]

I have an upcoming (competitive) exam with some extra topics I rusty over. Can someone suggest some quick reading for - Geometry: Elementary geometric properties of common shapes and figures in 2 and 3 dimensional Euclidean spaces (e.g. triangles, circles, discs, spheres, etc.). Plane analytic geometry (= coordinate geometry) and trigonometry.

[granite tide]

thank you so much guys that was so kind ❤️

[remote sparrow]

why are you reading three linear algebra books

[trail socket]

does anybody know any good book about matrices in Z/Z2?

[grand thistle]

if i were you id just read lang then halmos

roman is also a good choice

[devout hollow]

I wanted to gain a really good foundation in the subject. Also, I am not in university yet; without good guidance, I thought it would benefit me more to master linear algebra and calculus, rather than go far in terms of content. And I just like to study linear algebra.

[devout hollow]

Does Halmos cover multilinear algebra? To my knowledge, I need some multilinear algebra for differential geometry; that is why I want to learn it. Nonetheless, I will check Halmos. Thank you for your suggestion.

[hazy elk]

Hoffmann Kunze has some multilinear stuff at an intro level... but idk It felt too slow/a bit unfocused. Maybe you can also try Sergei Wintzki's "linear algebra a basis free approach" does the Wedge and tensor product stuff nicely, but no excercises tho. Ive heard Roman has the multilinear stuff but I haven't read it, so can't comment on it.

[gray jungle]

If i remember correctly the standard is to learn multi-linear algebra while you learn manifolds or differential geometry , but if you insist then hoffman-kunze does do some intro multi-linear stuff on determinants. @devout hollow

[hazy elk]

I didn't really like the multilinear stuff from HK, maybe a personal preference tho.

[gray gazelle]

thoughts on Serge Lang's Introduction to Linear Algebra for a first course?

[peak anchor]

How can I understand what quantum computing is?

[tame rampart]

im trying to speedrun ib middle school maths, i wanna do all the maths from grade 8 to 10 any recconmendations for resources?

[tame rampart]

also wouldnt mind getting a resource to just see all the topics normally covered between grade 8 -10 ib

[grand thunder]

Elliptic curves, especially in diophantine equations (mainly in them) resource?

[gray gazelle]

books for combinatorial game theory?

[grand thistle]

people have recommended me silverman's rational points on elliptic curves

[grand thunder]

i see, thank you very much

ah, i see there is another book by the same author, The Arithmetic of Elliptic Curves

[vast obsidian]

Any good book for trigonometry? (no yt or khan academy pls)

[sturdy shore]

halmos covers a very small amount of multilinear algebra, just to introduce determinants as alternating multilinear forms

I believe the book by Kostrikin & Manin goes more into multilinear stuff, but the book assumes considerably more math background

also, my knowledge of diffgeo is very limited, but I believe any multilinear algebra you'd need would be covered in an introductory diffgeo book

so don't focus on it too much

[main void]

yeah if you want a more solid multilinear algebra background, Tu's book introduction to smooth manifolds starts of with that

it's a nice read anyways, less verbose (and less hard) than lee's book

[river tangle]

for which level?

[vast obsidian]

basic

I guess the only option is precalc books

[fickle whale]

I've heard unironic good things about wildberger's book

but I can't personally vouch

[prime oak]

opinions on munkres?

i know its a standard but ive also heard its not the best text

[manic cairn]

I love munkres

I think all of the proofs are generally put forward in an easy to understand manner

[gray gazelle]

Munkres is boring, but effective.

[left cloud]

it can be harddd to read but i think it's good if you can understand it 🙂

[manic cairn]

Depends on your background, it was fun for me not knowing any analysis when I first picked it up

[gray gazelle]

"Boring" as in it doesn't really do anything special.

There is nothing in Munkres that you can't find elsewhere. It doesn't do anything special compared to other books on the subject.

Nothing makes it stand out.

Yet for some reason it's as popular as it is.

[prime oak]

im just looking for something that'll give me the same adrenaline as rudin

[prime oak]

mm i see

[vast obsidian]

@prime oakwhat anime is your pic from

[static crest]

that's ai hayasaka

[prime oak]

yes, it is

[manic cairn]

This is true, but this doesn’t mean it’s bad; your definition also only makes it boring to people who already know topology.

[gray gazelle]

Ok.

Let me clarify that everything I wrote is my opinion. I'm not claiming to state absolute truths about the book.

Please stop pinging me.

I also didn't say it was bad. In fact, I said it was effective. It does its job well.

[gray gazelle]

This is true

Do you know any particularly fun general topology books?

But it also gives people 2 topics that I don't like: box topology, and checking that a set is closed by checking if it contains all of its limit points

I have been doing math for so long and I have literally never seen the box topology come up.

The second one is fine to me though.

It's something you can do but why would you

Just check the closure is equal to it

But that's just the same as checking that it contains all of its limit points .

I feel you, though. There are much simpler ways than using limit points, even if it may be an effective method from time to time.

What I mean is that people calculate set of limit points of something

Ah. Yes, that's silly.

And it's easier to calculate the closure

[sudden trellis]

what definition of closure are you using here? I ask because Munkres defines closure to be the intersection of all closed sets containing the set of interest, which feels hard to compute

[gray gazelle]

I've used "smallest closed set containing the thing" quite a bit. It's very nice.

[gray gazelle]

Fixed point theory by Dugundji and Granas

It's also basically immediate that that is the same thing as what you wrote.

[gray gazelle]

Set of all convergent sequences from that set

For instance

[grave thorn]

sequential space moment

[gray gazelle]

no no no NON O NO NO NO

In practice all spaces are sequential anyway

It's more of a Frechet-Urysohn space moment

Because sequential spaces are such that sequentially closed sets are closed.
And for Frechet-Urysohn it's an iff

[dapper root]

AG doesn’t exist

Anyway, for me usually the definition “points for which every nbd intersects S” has been the most useful

I like the “smallest closed set containing S” as a property of closure when using the closure, but to like compute what the closure is or to show something’s dense the one I said has been most useful

[cedar ridge]

Is the latter not good/useful? I recall it only rarely showed up in my real analysis (with elementary point set) course

[shell valve]

hello guys

[fierce hedge]

Two interesting books I recently found are - Topology through inquiry by Francis Su (that analysis guy at Harvard Mudd) and Elementary Topology _ Problem Textbook (one of the very few topology textbooks with solutions)

[lime sapphire]

tfw "Harvard Mudd"

[fluid bay]

if you want to learn regular trigonometry, wildberger's book is probably not for you

[quick hornet]

if you want to learn regular trigonometry, wildberger's book is probably not for you

[gray gazelle]

It doesn't for me

Fun fact: all sequential spaces are quotients of metric spaces

In fact this is an iff

[hard beacon]

can i get a ban?

[gray gazelle]

Is this a joke? Doesn’t this book use category theory?

[gray gazelle]

?

Question was about fun general topology books

Not introductions to the subject

Ah okay 👍

[brave valve]

Any cool books on introductory real analysis?

[heady ember]

Not sure what you mean by "cool", but Dami likes Schroder

[brave valve]

well cool means just a good book in your opinion and thanks

[tough zealot]

actually based
sequential spaces are so much more general

[gray gazelle]

I honestly need to get back into Competition Math at around the Putnam and International Math Olympiad level, does anyone have some resources that could be beneficial?

Kind of cringe question but popmath has peaked my interest in this area of study thanks to stuff like 3b1b and Quanta Magazine
It's unclear to me how I go about and study math it was 7+ years ago I last touched the subject I know basically nothing

What's a roadmap from basic math to i.e. Knot Theory?

Or maybe I'm too old and that's practically an impossible dream? im 25

[thin hollow]

oh lol

[gray jungle]

too old
im 25
No , you're fine

iirc you'll need some topology and group theory (and even algebraic topology but that's out my expertise)
so its quite a big investment to get there tbh and i would advice you to simply start by getting into formal mathematics in general first , you'd wanna start with the basics at khan academy followed by intro to proofs and linear algebra.

[gray gazelle]

I feel like it's a long process with 10+ years of study to reach that level, especially when self-studying. I am closer to the age of alzheimer's than I am to the prime years of my learning ability :<

[gray gazelle]

thanks!

[gray gazelle]

This is a long road.

Knot Theory is cutting edge modern mathematics and a very active research field in modern mathematics.

However, you can likely reach your goal as you are not old whatsoever.

First and foremost, you have to learn Linear Algebra, Introductory Calculus, and Proofs.

However, if you feel bored by these you can look into Group Theory as it has little formal prerequisites.

Following Calculus, I recommend picking up Mathematical Analysis by Rudin
Following Linear Algebra, I recommend Dummit & Foote or Artin for Abstract Algebra. The former is more complete, and the standard recommendation for graduate students.

Following Mathematical Analysis, begin working through Topology. You will start investigating manifolds.
Following Algebra, begin working through Algebraic Topology, you will begin investigating knots.

Following this, you can read further based on your developed interests as you actually do the math.

[gray gazelle]

You're not too old, but you might get discouraged easily along the way

[gray gazelle]

I tried to keep this as general as possible, but you will notice that this is not encyclopedic and it is impossible to make it so due to you likely developing some other interests as you actually interact with the math, so good luck discovering.

[gray gazelle]

Yeah I feel embarrassed because my interest comes from just glimpses of math from mainly pop-math and I have no idea what it really entails

But I am certain it's what I want to do

[gray gazelle]

Thank you very much

Math can be boring at times until you grind to something interesting

[thin hollow]

yeah

[gray gazelle]

You have to realize they pick out interesting stuff in those videos

[gray gazelle]

This is not true (i) I doubt it would take you 10 years to reach “Knot Theory” (this is atrociously general and could mean a lot of things, but I’ll assume introductory knots) as long as you consistently put in effort (ii) you are 25, you’re merely becoming a true adult right about now, and you have room to develop and grow, there are people who start later than you who have done meaningful research in mathematics (iii) just have fun if you don’t want to make it a career, mathematics is a great battle of effort, more so than general intelligence in my opinion. Point is, just enjoy the journey if you’re doing it for fun, and don’t feel stressed if you’re doing it seriously with intents of becoming an academic (most undergraduates begin pure math only 3-4 years earlier than your current age)

[thin hollow]

@gray gazelle have u gone through these books

[gray gazelle]

Which books?

[thin hollow]

the ones u listed

[gray gazelle]

Yes, the three that I’ve listed I’ve done atleast a few chapters in each.

[thin hollow]

which linear algebra book

are u using

[gray gazelle]

I’m done with Linear Algebra, but I’m doing a review reading group via Linear Algebra Done Wrong with my friend group.

[sterile zealot]

bro, which standard u guys talkin' 'bout?

[thin hollow]

1st grade

[hard beacon]

about that age real life hits hard ... but 1 hour a day get u there like fast ... and ther u r 30 nothing new under the sun 😄

like maybe u can do order better but math have no point other than teaching others ... math

https://www.sciencedaily.com/news/computers_math/mathematics/

... and at the end of that hour ... dont take all that 2 seriously ...

upjoke.com/mathematician-jokes

[remote ginkgo]

ur smokin crack

[hazy elk]

Discouraging people (with some bs reasons) should warrant some action

Sorry for the off topic message, just wanted to highlight it*

[hard beacon]

hmm ... ask ur professor what u can work in real life with ur graduate degree

im curious bout that answer

... like u can do an appeal 2 authority with 1 simple question ...

or try

[gray jungle]

This channel is not appropriate to have this discuss but either way , math have no point if you choose to be ignorant about it.

[hard beacon]

then where is that channel 2 discuss completeness ness of math?

[smoky zephyr]

completeness ness

[gray gazelle]

Likely, #proofs-and-logic or #foundations , however, what you are talking about has nothing to do with the completeness of math.

[gray gazelle]

data scientist, you can work in finance

[hard beacon]

im a noob forgive me

[gray gazelle]

In a rare case, I’ve seen a Math PhD end up as a Physics Professor somehow.

[hard beacon]

whats that?

[crimson leaf]

Sports Data Analytics for an MLB team

[gray gazelle]

sorry, maybe it's called data analyst

anyway, just another word for a statistician

[hard beacon]

ohh only computing is a science ?

[gray gazelle]

No, formal science is still classified as a science.

are you trolling? Am I supposed to report you to moderators?

[crimson leaf]

Data scientist is correct as well

[gray gazelle]

I don’t think they are trolling, but sub-highschool quality of discussion. Probably a middle schooler.

[hard beacon]

pls do it ...

[gray gazelle]

formal science?

[gray gazelle]

Mathematics is a formal science, no?

yes. But that's not science. In English we distinguish between science and other things

Science refers to Natural Science solely?

alternatively you can use the beautiful German word, Geisteswissenschaften

[willow pecan]

(this is no longer discussing book recommendations and should go in #math-discussion or #discussion or #serious-discussion )

[hard beacon]

so kill the messenger

[willow pecan]

?

[hard beacon]

is there a channel called philosophy of math ? anywhere

[fierce hedge]

I hope I am adding something useful to the discussion but anyway to answer your question. No, you don't need a graduate degree to work in real life.
Quite a significant proportion of people make liveable amounts of money. If I remember correctly even Elon doesn't have a graduate degree, neither does Bill Gates

[fierce hedge]

Try #math-discussion or #foundations

[hard beacon]

... do they hire street smarts?

[hard beacon]

meh the discussion evolved(kind of) here

[fierce hedge]

(better to move the conversation to somewhere else, this channel is really meant for book-recommendations)

[hard beacon]

why?

how can u reco mend a book without discussing about what is the difference between 2 or more of the same?

[dense seal]

please keep the discussion here topical

and not get sassy when people tell you to move elsewhere

[hard beacon]

are u off topic of this channel?

... like i reco mended a book 4 kids logic thats of topic of this ?

... like can u define a gnomon from mind? ... or is it just mandelbrot tis days?

[dapper root]

Get owned

[crimson leaf]

How good is abbot understanding analysis? A professor recommended it if I feel the need to learn analysis quickly for my research

[willow pecan]

Pretty good

[gray gazelle]

I see it recommended to people all the time

[calm patrol]

hey y'all. im looking to get more into controls and game theory (applied eng side of math). Ive done decent amoutns of pure math (topology, alg geomoetry/topology, diff top) and im curious if anyone has any good books
im looking to read up on stochastics, game theory + mathematical controls

[crimson leaf]

Should I read a different undergrad book afterwards or could I just move on to different things

[gray gazelle]

@willow pecan

[willow pecan]

Move on to different things probably

[timber copper]

@calm patrol you might wanna look up mean field games and papers by like tamer baser and stuff like that

[calm patrol]

field games?

[gray gazelle]

Do you think Abott can substitute something like Rudin? If I recall correctly, it does not cover the same content as Rudin?

This is not because of Mathematical Rigor or anything, I think Tao or Zorich is the better modern alternative for Analysis, because I feel that Abott does not cover as much content.

[willow pecan]

It doesn't, but there are other books that will fill in the gaps

[remote sparrow]

at my college, abbott covers the first semester of analysis. it doesn't cover stuff from the second semester of analysis, which is like metric spaces and stuff. many undergrad analysis books are designed for a full year course, but abbott is not one of those books.

[crimson leaf]

Metric spaces are in the extra topics chapter

[gray gazelle]

Can someone tell me the prequisites to Evans’ PDEs and other Advanced-PDEs books? Not sure what I’m missing.

[willow pecan]

Functional analysis, measure theory, multivariate analysis

[gray gazelle]

Hammack Book of Proof or
Velleman How to Prove it?

I feel like half the server has finisher these books so should be getting good recs here

[smoky zephyr]

i prefer book of proof

[willow pecan]

Surely not half of the server has finished these books

Half the server is in high school probably

[heady ember]

Probably more than half is in hs, if I were to take a guess

[hallow oriole]

they don't really try and achieve the same thing imo

having said that you should read book of proof

it's a top tier book

[fallow cypress]

Anyone a fan of Stein-Shakarchi?

Just curious of people's opinions

[willow pecan]

Generally well regarded

[remote sparrow]

it's a DIY project section.

[remote sparrow]

#book-recommendations message

[gray gazelle]

The Stein-Shankarchi Lecture Series is well regarded

They are not linear excluding the 4th book, so following a complete course in Mathematical Analysis at about the level of Rudin you can dive straight into:

Complex Analysis

Fourier Analysis

Measure Theory

However, it is important to note that these books are fairly difficult regarding exercises so you might need a supplement or two.

[smoky zephyr]

you type so formally lol

[forest sleet]

i'm not a fan of the first stein shakarchi since it doesn't use measure theory, but the complex analysis book is good for a first complex analysis course

[crimson leaf]

Could explain a bit more why the lack of measure matters, I'm curious

[forest sleet]

you just can't do things as generally without measure theory

or even state some results precisely in fourier analysis without measure theory

since it necessarily involves integrals

[willow pecan]

Is that important for a first pass though

I think that fourier analysis is a subject with such richness that developing intuition is far more important than stating results precisely the first time around

[fallow cypress]

Yeah I'm just learning about fourier series rn for a first semester real analysis class

I have no idea how measure theory works unfortunately 😢

maybe someday

[grave thorn]

measure theory is the most beautiful part of math

[broken meadow]

I think Stein shakarchi 1 is good actually its imo the right entry point for students learning real analysis for the first time

U can do the good measure theory stuff later

when you know

you learn measure theory

[forest sleet]

sure but I guess it's a bit inefficient

if you plan to take fourier twice

you could just take measure theory instead of intro fourier

[fallow cypress]

I don't think that's an option the way the classes at my school are set up

there's no measure theory class or fourier series class per se

there's just a sequence of analysis class which have topics interspersed between them

[heady ember]

One thing I have heard people say is the toy contours part is kinda annoying. But of course I can't speak for that myself

[remote sparrow]

there is no axiomatic set theory or mathematical logic class at my school

we have intro fourier analysis here but it rarely gets taught

same for complex analysis

[forest sleet]

😭

logic and fourier analysis are more niche but no complex analysis is 😭

[remote sparrow]

no complex analysis is an official course

it's just that i rarely see it offered in my schedule of classes

[hazy elk]

Relatable, my school doesn't offer many courses either so when they do get offered there's a lot of pressure (on me) to take them even if I'm not well prepared for it

[remote sparrow]

yeah, kinda blows that i'm kinda forced to take classes that i don't really wanna take as "electives" in order to graduate on time

[fluid bay]

I can relate but at the same time I’ve always been able to find something that looks interesting even if it’s not my first choice. I think that’s not such a bad thing because you end up being exposed to a lot of different things

If you’re into logic or something but at a school that will never offer a logic course that’s kind of a bummer tho

I’ve always wanted to take a proper course in homological algebra but it’s only offered like once a decade at my school

[dapper root]

Bruh

Ur school only have analysts in it or something?

[forest sleet]

or the algebraists all got tons of grant money and decided not to teach for 9 years

[fickle bough]

They started a witch hunt against logicians over there

[fickle bough]

when logicians are an empty set

[sage python]

I do kind of agree about Fourier that doing it pre-measure theory is a bit premature

Like it can be done but it's just clunky

[dapper root]

My class did Fourier in freshman year kekw

2nd qtr doing math

[sage python]

Honestly I do think measure theory can come a fair bit sooner than it does

[cedar ridge]

tao analysis ii has lebesgue measure at the end

after metric spaces/riemann integral iirc

[fluid bay]

yea there's a lot of analysis. There's also a lot of other stuff, but i don't think there is a lot of research that requires super heavy-duty algebra or cat theory for example

[remote sparrow]

cat theory

[forest sleet]

yeah my uni did measure theory (for R) right after 1st term real analysis

if you do riemann integral formally in many ways lebesgue is simpler

[fluid bay]

the AG people i know of do computational or classical kinds of stuff for example

[remote sparrow]

my school has a decent stats program (well, i guess because it makes money) and we actually are well-known for being a good place to get your math ed degree, so we have a bit of a reputation as a math teacher school

so there's much less emphasis on math relevant to research

[forest sleet]

you don't have to do measure theory in full generality the first time for sure

and just having dominated convergence theorem for all those contour integrals is so nice

and having defined almost everywhere and L^p spaces is quite useful

[fluid bay]

is rudin the canonical place to learn measure theory-based complex analysis, or are there other options?

[sage python]

Yeah exactly Washingberry

[forest sleet]

i'm not sure there is that much measure theory going on in normal complex analysis

by dominated convergence i just meant to interchange limit and integral

which is justified by dominated convergence but you definitely don't need measure theory to just use it

since everything is analytic or at worst continuous, (improper) riemann integration is fine

[sage python]

If you already know a decent amount of real analysis

Idk big Rudin super well for complex but try Narasimhan

[forest sleet]

actually you don't even need improper riemann integration, stuff like \int_\R e^{ix^2} isn't exactly integrable in any sense other than principal value limits anyway

[remote sparrow]

i heard narasimhan has topology as a prerequisite. if you did rudin narasimhan sounds like it could be good but if you did abbott you might not be ready

[fluid bay]

i took a course that followed conways text. it didn't really stick with me all that much tbh

[sage python]

Conway is very boring

[fallow cypress]

reading stein-shakarchi for fourier series and it's going p okay so far

I like it

almost at parseval's identity 🤩

[remote sparrow]

just curious, i've heard a lot of praise for stein and shakarchi's Fourier Analysis, but has anyone used tolstov's Fourier Series as a main text for fourier analysis instead?

[brittle breach]

the chapter on applications was nice

[brittle breach]

it is very good,
the style feels very naturally,

[remote sparrow]

if you have a good lecturer. for self-study there are reading groups and online lecture videos, notes, and other supplemental resources.

[gray gazelle]

what SAT prep do you recommend

princeton or official

or should i buy both

[fluid bay]

pretty sure there are people here who have done that

i think in some european undergrad programs that might even be the standard path in analysis

[fluid bay]

its been a long time, but what I remember being the most helpful was khan academy's sat prep. its also free

[gray gazelle]

i want book though

people spend hundreds of dollars on prep

if i don't spend hundreds of dollars does that mean I wont be able to get 1500 >

[remote sparrow]

i went to an sat prep school and i didn't get much out of it

studying at home with the workbooks was better

but tbf socioeconomic status highly correlates with sat performance since ppl are shelling out money for prep schools

so don't put too much weight on these scores

some colleges thankfully don't consider these tests anymore

[gray gazelle]

that's really really really bad

i was hoping SAT score could improve my application

ill just shell out a few hundred bucks + a hours and get 1560 on SAT because my GPA is shit like 3.8 unweighted

and i wont be able to get to T50

[remote sparrow]

just a long history of these tests being racist or used to gatekeep minorities and other sordid stuff too

[gray gazelle]

how do tests gatekeep minorities..

it's just a test

just take it

[crimson leaf]

I didn't study at all and still pulled out a 1280 not super impressive but good enough

[gray gazelle]

price is the same for everyone

[crimson leaf]

Right but people with less money can't afford test prep or the time to test prep really imagine you have to work a job as much as you can to support your family or you have many siblings to take care of

[gray gazelle]

same goes with GPA

now getting into good college will be hard for me

cuz i was depending on SAT to make up for bad grades

i am a A/B student (A/B students don't get into T50 colleges unless daddy donates building)

plus my school is mostly As so i am competing with a lot of very very good people

class average got an A in AP Physics and A in AP calculus

[crimson leaf]

I know someone who went to T30 with 3.8 unweighted

[remote sparrow]

^ yeah this rat race mentality is just so unhealthy, plus colleges are smart enough that they can recognize possible grade inflation, not saying that's necessarily the case for your school

3.8 sounds good

[gray gazelle]

what's grade inflation

[gray gazelle]

bro u have no idea what my school average is bro

so we have 4 categories of students

[crimson leaf]

I know people with lower than your gpa who go to GA Tech which is a T50

[gray gazelle]

• the uncaring (avg GPA of 3.0)
• the average (avg GPA of 3.75)
• the high achiever (avg GPA of 3.9)
• the natural smart (avg GPA of 4.2)
  note that the higher, the more Ap classes

and only avg-natural smart applies to good colleges

[remote sparrow]

sounds like grade inflation to me 😂 i mean c = 2.0 i.e. average supposedly right

[white laurel]

Can't see a flaw in that argument

[gray gazelle]

I have to get into T50

so gtg study for SAT

[crimson leaf]

I mean based on what you said Steve you either go to a super fancy high school or major grade inflation

[remote sparrow]

you'll be fine, trust me

[quick hornet]

any school where an A+ is not a 4.0 is inflating

[forest sleet]

isn't it sometimes 4.3

[remote sparrow]

4+ i comes from "weighted" classes like AP

[crimson leaf]

Yeah AP is like a 5.0 scale or some bs lol

[quick hornet]

correct, and that is (indistinguishable from) grade inflation.

[white laurel]

Damn these inflation rates are out of control

[gray gazelle]

Top 50 high school in California

[remote sparrow]

getting an A in an AP or IB is 5.0

[crimson leaf]

Honors was 4.5 max I think

[forest sleet]

I guess it depends how A+ is assigned

[gray gazelle]

only for some school

[white laurel]

No wonder why they talk so much about that on the news

[forest sleet]

oh I was thinking college

[gray gazelle]

A-, A, A+ are all the same

4.0

[remote sparrow]

i mean C was and is considered basically failing at my place even tho it should really just mean average

[forest sleet]

at least one uni I know of has any - is -.3 and any + is +.3

[crimson leaf]

My research advisor complains about this

[forest sleet]

and had some departments that curve some classes to C+ average

[crimson leaf]

"Why does America have C as average if a C is bad this makes no sense"

[remote sparrow]

zoe bee has a nice video on grades

[gray gazelle]

guys

[white laurel]

Oh i love Zoe bee

[gray gazelle]

only 2 people from my school got into UCSD last year though

[white laurel]

Sweetest person on YouTube

[gray gazelle]

wait y'all asians?

[quick hornet]

i have a dirty secret for you

if your university claims that an A+ is a 4.3

professional and graduate programs adjust that to 4.0

they do not care what your university claims your GPA is, they care what your grades are

[crimson leaf]

Why do schools have A- that also makes no sense to me

[quick hornet]

the 4.3/4.0 distinction is almost exclusively to make students feel better

it also matters for merit-based scholarships

and employers might be fooled by it

but thats about it

[remote sparrow]

stop lapping up this anti-affirmative action propaganda ong 😂 anyway i won't comment further than this here. im asian myself

[quick hornet]

no one takes it seriously

[crimson leaf]

Like oh you got a 92 in the course guess you get a 3.7

[gray gazelle]

explain how only to people got into UCSD

and like worse schools got more

[remote sparrow]

dude, asians make up a plurality of students at ucsd 🤣. they are the largest racial demographic there. your anecdotal evidence of only two asian people going there barely means anything. besides, it's not like your entire school only has asian students that are all trying to go to ucsd, maybe some wanna go to ucla or berkeley or stanford or ivy leagues or some other top tier school. and what about previous admission years? maybe in some of those years way more asians were admitted. like sure affirmative action is just a band-aid and actually something MORE fundamental than AA needs to be implemented to correct historical injustices but even without diving into all of that your argument is just so weak.

[zinc thistle]

why lmao

[gray gazelle]

otherwise i'd be below average

[gray gazelle]

i agree. we should implement AA to admit more asians, remember the Chinese Exclusion Act?

[zinc thistle]

uhh

what grade are you in?

[gray gazelle]

10th

[zinc thistle]

ok makes sense

[gray gazelle]

why

[zinc thistle]

cuz you care too much about it

[gray gazelle]

and juniors don't care?

wdym

[zinc thistle]

never said that

[cursive orbit]

???

this is the most 10th grader take i've ever heard

[gray gazelle]

bro

how

[hearty steppe]

Found something interesting on RG https://www.researchgate.net/publication/361257410_Iconic_Mathematics_Math_Designed_to_Suit_the_Mind

[cedar ridge]

Summary?

[zinc thistle]

summary is that you should read it

idk im too lazy too

[cursive orbit]

because it's simply wrong

[gray gazelle]

r u saying 10th graders are dumb?

[crimson leaf]

A large percentage of them lack any meaningful life experience or understanding of the world

[cursive orbit]

I'm saying 10th/11th graders usually have an extremely unrealistic view of the college admissions system

[gray gazelle]

what about 12th graders

@cursive orbit id literally jump and cry if i get into T50

[cursive orbit]

plenty of A/B students get into globally ranked T50 schools

chill out man

[gray gazelle]

what about you?

[cursive orbit]

I was an A/B student in HS

and I got into 3 such schools

[gray gazelle]

what were they?

[cursive orbit]

let's move to #chill

[vapid parcel]

Can someone recommend books for 10th grade advanced mathematics

[heady ember]

What do you mean by '10th grade advanced mathematics'?

[unborn quail]

What topics do you want in it?

[unborn quail]

Also, 10th grade in what country?

[vapid parcel]

Well I'm in Asia

[heady ember]

Still, what did you mean by '10th grade advanced mathematics'?

[grand thistle]

asia is literally a massive continent

doesn't really narrow it down

[vapid parcel]

Uhm like the tb in my school has pretty basic problems , i am having trouble solving advance problems in competitive exams

[heady ember]

What level of books are you searching for? I ask this because there are highschoolers here studying graduate math so yeah

[heady ember]

Ah I see

What kinds of basic problems

You should elaborate more so people can give you their recs

[vapid parcel]

Trignometery , geometry , algebra , polynomials

Co ordinate goemetry

Geometry*

[grand thistle]

if you're looking for a challenge, the aops books are good

[vapid parcel]

Art of problem solving ?

[gray jungle]

If you just want challenging problems , prolly any olympiad book.

If its to improve at your specific class then thats out my expertise and probably should ask your teacher for recs.

[grand thistle]

yaeh

[vapid parcel]

Oh ic , wat r some good olympiad books ?

[gray jungle]

Im only familiar with "The imo compendium"

[gray gazelle]

hey can I get some differential geometry book suggestions?

[grand thistle]

think bott tu and lee are common recommendations

[heady ember]

Oh and John (JohnDS) shared his diff geo notes here before

https://drive.google.com/drive/folders/13QqswmY7gHF39_YnmV6blcilm3ZZ_tSd?usp=sharing

[gray gazelle]

oh thank u so much

i rlly appreciate this srsly

[heady ember]

np! :D

You should thank John moreso than me lol

But it would be nice to have this link pinned for those who may be interested; either here or in #diff-geo-diff-top

[gray gazelle]

You didn't write anything about Velleman's book but all the other books

[fierce hedge]

Does anyone has a good pdf copy of Hoffman and Kunze Linear Algebra? Couldn't any good quality book on lib gen.

[crimson leaf]

If you google Hoffman and kunze pdf you should see a link from Peking university

[fierce hedge]

It is similar to what I found on lib gen. So, I am guessing this is the best pdf quality available

[finite heath]

Does anyone have a pdf of Introduction to Algebraic K-Theory by John Milnor?

[quick hornet]

pretty sure it's not legally available freely, and thus we ask you not to exchange pdfs of it on this server

[remote sparrow]

velleman has a good reputation, it's a very popular choice for schools to use

[vast obsidian]

Someone recommended me Friedberg Linear Algebra

This is not for highschool students

[fluid bay]

friedberg is more theoretical. if youre looking for something more concrete/computational, there's Gilbert Strang's book

[remote sparrow]

#book-recommendations message

do note meckes has calculus as a soft prerequisite, but calculus examples could be omitted

cohen's book has no calculus prerequisite, just basic high school algebra

hefferon and beezer mention calculus but again those examples could be omitted

[heady ember]

It's linear algebra... its a math university course so yeah. However, I think its certainly readable by highschool students, I'm reading through it myself right now.

[gray gazelle]

what would the prerequisites be for studying lebesgue integrals and measure theory?

[willow pecan]

Real analysis

Topology

[cinder trellis]

I’ve read friedberg as a high school student, it’s not that bad

[gray gazelle]

and what would the prereq be for Topology? Real analysis?

[willow pecan]

Topology doesn't really have prereqs, but knowing real analysis before hand can help with intuition and motivation

[gray gazelle]

gotcha

[cinder trellis]

Set theory helps with PST (point set topology)

[gray gazelle]

yeah i've done set theory

[cinder trellis]

Which is usually the type of topology you need for real analysis and its analogues

James Munkres has a good book for PST

[vast obsidian]

congrats ur smart?

[cinder trellis]

You said it wasn’t for high school students

🤷‍♂️

[crimson leaf]

Does anyone have linear algebra recommendations that discuss quadratic forms?

[willow pecan]

I think friedberg discusses them maybe?

In the chapter on inner product spaces

[crimson leaf]

You're correct it didn't pop up when I searched the pdf, weird. I also need a source that looks at them from an applied perspective maybe Lay would be good but I'm open to suggestions

[willow pecan]

What does an applied perspective entail

[crimson leaf]

Honestly I couldn't really tell you that's just what I think my presentation is supposed to be partly about is quadratic forms applications

And implementing them with code

[willow pecan]

Implementing them: compute x^TAx

You may be interested in the Minkowski metric

Which is an example of an important non-positive-definite quadratic form

Of course, if a quadratic form is positive definite then it is just some inner product in disguise

[fickle whale]

Do you guys know any cheap (<$25) but good differential geometry books

[remote sparrow]

https://www.amazon.com/Differential-Geometry-Curves-Surfaces-Mathematics/dp/0486806995/ref=pd_bxgy_sccl_1/145-1561213-0365747?pd_rd_w=7isBO&content-id=amzn1.sym.7757a8b5-874e-4a67-9d85-54ed32f01737&pf_rd_p=7757a8b5-874e-4a67-9d85-54ed32f01737&pf_rd_r=KA07BHW1206HZ3GMSBMQ&pd_rd_wg=8IWDs&pd_rd_r=40a42672-967c-48bc-922a-f2eea905d5e0&pd_rd_i=0486806995&psc=1

the only one i know of is this

[remote ginkgo]

do carmo bad, try kreyzsig

same material, but more, and better written, and also is a dover book so cheap

[remote ginkgo]

shilov

[weak violet]

what are some prereqs for algebraic topology?
for context im a high school student, ive selfstudied some real analysis some abstract algebra some topology havent done calc3 or complex analysis

[cedar ridge]

compared to vol1/2 of spivak?

[heady ember]

@fickle whale You might be interested in John's notes

[remote ginkgo]

completely different subject

[gray gazelle]

guys whats the most comprehensive precalc book that i should get?

especially for trig

[fierce hedge]

Definitely some basic group theory and some point set topology, you need to know quotient groups and topology at the very least. For topology, you can try Hatcher's freely available notes and usually the necessary group theory is there in most algebraic topology books. For AT books Hatcher is the most famous and standard textbook. You can try Gamelin and Greene for a book which goes slowly from topology to algebraic topology.

[gray gazelle]

probably Stewart precalc book

It’s very complete

[gray gazelle]

huh. Group theory wasn't in any books about AT I tried

also I'd argue module theory

for homology stuff

[hollow garnet]

i recommend brotherband

really good series

if u like viking

[sand ivy]

any book recommendations for teaching myself algebra2+

so anything alg2 or higher

^ or basic physics

[fierce hedge]

Either I got lucky or I have false memories

[gray gazelle]

maybe. But I also didn't try the standard choices for learning AT

[sage python]

Van Kampen?

[gray gazelle]

the necessary group theory is there in most algebraic topology books

we weren't arguing that there's no group theory in AT books, but if there is basic group theory in them

as a replacement for an actual abstract algebra book

[sage python]

Perhaps I should've been more specific, Van Kampen

The main actual thing beyond definitions you need is amalgamated free products

And those are very often covered

[gray gazelle]

I guess that's true, every book about AT I tried did have those, I was just thinking about something more basic

[sage python]

In hindsight that was too many question marks

It's morning and I'm a bit like uh fam?

[sage python]

Ah like you can't learn "What's a group homomorphism?" from it that's more fair

[fierce hedge]

usually the necessary group theory is there in most algebraic topology books
I just meant the part that is necessary/enough for studying AT

[gray gazelle]

yeah, me too

[remote ginkgo]

the 'group theory' you need is available in any good linear algebra book

in the section on quotient spaces

just replace R or C with Z

[fierce hedge]

we weren't arguing that there's no group theory in AT books, but if there is basic group theory in them
Ah, I got confused by that statement

Anyway, this is an interesting playlist I found on AT if someone is interested. So far I have watched first two videos and it felt nice.
https://www.youtube.com/playlist?list=PLuFcVFHMIfhJSSX-tlv8XxiAZSAbhv1DA

[vital bane]

yea his channel is pretty nice

[gray gazelle]

Who is studying engineering in here? Book recommendations for civil engineering first and second year please?

[icy knot]

Stewart or Larson’s calculus and any standard physics textbook. I can’t recommend a good book on statics or dynamics as I’m not in engineering.

[gray gazelle]

what's a complex analysis textbook with relatively few prerequisites? (and what are those prerequisites)?

something that could even be taken before real analysis

[heady ember]

Check pinned

[grand thistle]

probably gamelin or needham in this case

[heady ember]

Ah yeah was about to mention needham's visual complex analysis too

[gray gazelle]

thanks!

[willow pecan]

You should learn real analysis before complex analysis

[rose geyser]

you can learn anything anytime

sometimes, its nice to look further to get motivation at what you're currently doing

[cinder trellis]

Visual Complex Analysis by Tristan Needham is a good book with not a ton of prerequisites. In my experience, complex analysis isn’t as enlightening without having done real analysis. Maybe that’s just me though.

[remote ginkgo]

ahlfors

i did complex analysis before real

[gray gazelle]

any rudin like book for real analysis?

[willow pecan]

Rudin is a Rudin like book for real analysis

[gray gazelle]

I meant linear algebra

[willow pecan]

[gray gazelle]

lol was typing too slow

[willow pecan]

It depends on what you mean by rudin like

[gray gazelle]

Short and concise

But hard

If u get what I’m saying

[cinder trellis]

Linear algebra books are written a little differently than analysis in terms of “slick proofs”, but a tough book on linear algebra is Advanced Linear Algebra by Steven Roman

[gray gazelle]

that how I meant to describe it “slick proofs”

[cinder trellis]

Roman’s book requires some mathematical maturity that the average linear algebra student probably doesn’t have, though, so it’s not the best introduction to the subject by any means

Friedberg and Spence or Hoffman and Kunze have solid books on the subject that are rigorous enough

[sudden kindle]

Whats your favorite galois theory book for absolute beginners?

[cinder trellis]

It’s not a book, but Dummit and Foote has a good section on Galois Theory that is very comprehensive.

They also have plenty of examples which is super helpful in my opinion

[sudden kindle]

Yes I agree

Thats where learned

[cinder trellis]

A lot of people I know have mixed feelings about Dummit and Foote because of how it can be dry at times

I see it more as a really straightforward and comprehensive text than anything else, I’ve personally never had an issue with its “dryness”

[forest sleet]

It is very wordy

[cinder trellis]

That’s true, and unnecessarily so at times

[forest sleet]

It's the only algebra book I own though

[sudden kindle]

Same

The galois theory chapters are really well written imo

[cinder trellis]

Same! I have a PDF of Artin’s book on my computer but I’ve always just stuck with D&F

[subtle mango]

ive been wanting to read aluffi chapter 0

[cinder trellis]

I’ve never heard of this book before!

[subtle mango]

afaik its algebra through a categorical lens

[rough tulip]

does anyone have a recommendation for a book on algebraic curves?

[glossy bison]

Probably been asked a lot but how come there's no discrete math textbook recommended in the #books-old channel?

[cinder trellis]

Wow I’ve just taken a look at some of its contents, and it looks fantastic. I might actually get my hands on this…

[subtle mango]

same lol

i might pick it up over thanksgiving break or something

[willow pecan]

Discrete math is not really a subject

It's a bunch of subjects that math majors need to know that were taped together into a class

[glossy bison]

Oh, okay.

Odd that it's what they say all CS students need to learn then.

[forest sleet]

it covers several different topics

like you'd probably get different books for graph theory than for combinatorics

[gray gazelle]

I’m probably going to read up to Galois and switch to Lang for Homological Algebra tbh

[forest sleet]

but in a discrete math class it might cover an intro to both of those

[gray gazelle]

I’ve heard good things about this part

[foggy relic]

aluffi

[foggy relic]

beware of the bad exercises

just do lang

[subtle mango]

does lang do cat theory too

[lean pagoda]

Neither are a substitute for an actual category theory text, but both of them make use of categorical language if that's what you're asking

[vivid river]

Hey all. I was wondering if the Art of Problem Solving books are good for self-teaching math from the start?

[willow pecan]

They are good for practicing competition math

[vivid river]

does that include the non competition themed ones? For example they seem to have pre-algebra, for example which they say is a full course.

I am wondering if there's a difference

[hearty steppe]

Just found this. May be worth looking at @narrow oyster @remote ginkgo

https://www.biorxiv.org/content/10.1101/2022.11.05.515307v1.full

Here are a couple more
https://www.nature.com/articles/s41583-022-00642-0

https://www.sciencedirect.com/science/article/pii/S136466132200242X

[narrow oyster]

can you dm?

ill loose this

[hearty steppe]

you don't copy paste things into a task board or something 🤔

how you keep track of what you find?

[subtle mango]

ye thats what i was asking, thanks

[gray gazelle]

Personally I don't

But there's not much worth keeping track of that isn't already in my head or my bookmarks

[hearty steppe]

I have well over 500 archived publications in one of my trello boards

That is stuff I won't keep in my head for sure.

[gray gazelle]

What for though

[hearty steppe]

I am an independent researcher... well officially since the beginning of the year. Things have been panning out pretty well with my work.

Monetarily speaking... things are going the opposite direction xD

I also design fidgets

[gray gazelle]

Ah. I see, I see. It's a honourable work

[hearty steppe]

well I don't have much of a chance to do anything else besides be honorable and maybe a martyr for American financial despair at this point. I am destined to become a kind of poster child I guess.

I went to Math Discord University I tell them... if they ask.

[cinder trellis]

I would say their main sequence of books (prealgebra, algebra, geometry, algebra II, precalculus) are fine for what you're asking. Their other books (combinatorics, number theory) are fine for little kids but don't teach you serious stuff, there's much better literature on those subjects. Their calculus book is decent, but I would read Calculus by Michael Spivak or something better.

They also have contest books like Volume I and Volume II which are useless

[knotty prism]

percy jackson and the lightning theif

also another book i would recomend is

i was with your mama and had a good time

jk

dont take me seriously

[willow pecan]

[foggy relic]

yes

but you shouldnt consider that

why do you need categories

[gray gazelle]

what prerequisites, other than mathematical maturity, are there for PST? (point set topology)

and what literatures could you recommend for learning a first course

[gray gazelle]

it's not necessary, but good to know what ordinals are

to understand some of the examples of topological spaces

[gray gazelle]

Could you recommend a book for a beginner?

other than that, basic set theory will be enough

[grand thistle]

for linear algebra halmos is good

[gray gazelle]

Kelley probably

I like Dugundji myself

[gray gazelle]

for a first course right?

actually no. I see now that Kelley is pretty dated

I heard Munkres is good

[sage python]

Munkres is too long

Bredon Topology and Geometry chapter 1 is my pick

Or Lee Topological Manifolds

[gray gazelle]

I don't really like Munkres, I'd go for Dugundji if I were you

[sturdy shore]

one advantage of munkres is it has a very long/detailed introduction section

[remote sparrow]

Is gamelin paired with willard a good way to learn topology?

Munkres sounds nice but it costs a fair amount

Unless someone has had a good experience with buying an intl edition

Might add it to my cart then

[gray gazelle]

buying books

[fickle whale]

Say it to my face

[crimson leaf]

I have an international edition of Munkres think I got it for $15 or something

[gray gazelle]

If I wanted to respond to you, I'd do it in the channel you posted in.

[crimson leaf]

the quality of the book itself is nice it's not a low quality print

Better than some of my other books tbh

[fickle whale]

I'll have to keep an eye out for something similar

[gray gazelle]

buying books

[fickle whale]

I can't absorb the chakra from an e-book

[crimson leaf]

I do find physical books keep me less distracted

I can turn off both my monitors just have music or white noise playing through the headphones and focus on the book till exercises come

[gray gazelle]

I actually don't like physical books

starting from where you left reading just by opening an app

now that's technology

Bookmarks.

[crimson leaf]

The advantage of ebooks personally is ctrl f

[gray gazelle]

bookmarks, saves what you last read... there's more to it thought I can't put a finger on it

it's like it's better in every way possible

I'm talking about real, physical bookmarks.

Slips of paper you put in the pages of a book to save your page.

(Yes, digital bookmarks are easier to work with, they can't fall out, etc.. Just teasing.)

I can see

[gray gazelle]

I have no idea

You know, people should try books more often

see if it gives you a hard time

live to tell the tale or die trying

and then report to me, so I can recommend some topology books to people that aren't Dugundji

[remote sparrow]

Well you should never buy ebooks, yes

Buying physical is nice though

[sturdy shore]

I agree, it is sort of insane just how many textbooks exist for some subjects

and yet only 2-3 get recommended

but I understand why people aren't willing to try unknown textbooks

[tepid prairie]

There's many great forgotten textbooks.

[remote ginkgo]

no

it has like

nothing on it

as they say, 'lurk more'

i dont engage in illegal activity

[quick hornet]

sigh

please do not discuss piracy here

daddy discord doesnt like it

[north scroll]

I remember reading "Running With Scissors," because the cover art looked interesting

Worst mistake of my life

[fierce hedge]

How does this and Lee's book compare to Hatcher's notes?

[remote ginkgo]

way more in depth

also bent towards manifolds

[fierce hedge]

I didn't mean the whole book. I meant how good are they, just comparing the chapters dedicated to point set topology

[remote sparrow]

i guess i will buy an intl ed. of munkres along with gamelin

might try gamelin as a main text but keep munkres as a reference since it's so popular at least

same thing for stewart's calculus i guess

[fierce hedge]

Lemme know if you liked gamelin, I am also planning on buying it.

[sudden kayak]

book recos for statistical intuition especially on hypothesis testing

[ornate saddle]

I need some self-study book recommendations that approach PDEs in a concise and rigorous way for someone coming from a non-mathematical educational background, but can handle proofs to an extent. I know it is very specific.

[willow pecan]

Do you know what a banach space

If yes, Evans

If no, Strauss

[remote ginkgo]

if you are feeling like a liar

try olver

[willow pecan]

Alternatively, Brezis for no

[foggy relic]

i got munkres new for like $15

[vital bane]

banana space

[brittle latch]

why is artin held in such high regard? it seems to take a different path than other algebra books

[brittle latch]

where

[foggy relic]

Abebooks

[cinder trellis]

He just has a different lay out and approach compared to other algebra books

[vague smelt]

Got a really nice book today called a-z mathematics handbook second edition from my local library.

[tawny copper]

Thoughts on Tourlakis lectures on logic and set theory (both volumes)?

[remote sparrow]

http://jdh.hamkins.org/tourlakisbookreview/

[tawny copper]

Ty. I really like Joel btw

[hearty turret]

whats a good introductory book on mathematical proofs?

[remote sparrow]

#book-recommendations message

[devout hollow]

I am up to page 100 of Serge Lang Linear Algebra. So far, I proved almost every theorem before I looked at the proof. Also, I did like 90% of the exercises. Is this excessive? Or should I continue to do this as long as possible?

[sage python]

If you're satisfied with your pace then it's excellent practice

[devout hollow]

Yes, pace is one problem; It took me about a month for 100 pages. But then, I also have to put up with school at the same time.

[icy knot]

Mathematical Proofs by Chartrand, A Transition to Advanced Mathematics by Eggen and Smith, Proofs - Jay Cummings

[hearty turret]

oh ok

[icy knot]

Books are really expensive these days. I just bought Basic Algebra 1 by Jacobson (Abstract Algebra), Essential Math for Data Science by Nield (O'Reilly), and Foundations of Mathematical Economics by Carter (MIT Press).

[hearty turret]

i try to get most of the books on the internet as pdfs or borrow from my uni lib

what just happened lol

[hearty steppe]

Oh boy here’s another RG article I gotta work through. Gona save it for next week

https://www.researchgate.net/publication/363219137_Connecting_the_free_energy_principle_with_quantum_cognition

[violet forum]

Book recommendations for:

I'm a high schooler, just getting into Algebra 2.

I'm striking an interest in mathematics that is nothing but increasing, I want to start from the beginning, algebra and trigonometry and have a precise understanding of them before getting into calculus, linear algebra and number theory.

I want hard exercises too.

What kind of book suits me?

[orchid mortar]

Maybe any calculus book, and/or how to prove it

[violet forum]

I don't know much about trigonometry

I tried reading the openstax calculus book, I did do well at the limits, I do understand them decently although I get fucked at all of the exercises that have "sin(x)"

[orchid mortar]

I don't really have better advice than practise more

[violet forum]

My problem is, I want to understand all of these precisely.

Why it's that way, what's the proof, etc

How to prove it

I have no idea where to start

[orchid mortar]

Have you read "how to prove it"?

It's a book

[cursive orbit]

basic algebra should be p cheap

seeing as it's a dover

[left cloud]

you could look at books by Hung-Hsi Wu 🙂
he has some friendly but rigorous books on high school level math that i think would fit what you described

[violet forum]

thank you for the recommendation!

i'll check it out

i'm looking for something to master math from the bottom-up, to "understand" not just "know" how to solve problems, problem is, i cannot get there without an understanding of fundamentals.

[left cloud]

i think you’d like Wu a lot then ✨

[violet forum]

tyty!!!

[spring anchor]

mathematics undergrad

[heady elbow]

books to learn mechanics?

[remote ginkgo]

landau 1

[leaden sleet]

Can anyone recommend me book for calculus

Ping me if anyone can help

[hollow shore]

https://ocw.mit.edu/courses/18-01sc-single-variable-calculus-fall-2010/

[safe horizon]

I know vector calc and linear alg; is it fine for me to try to learn calc-based probability? or should I learn analysis before that?

[willow pecan]

You should learn analysis before

[safe horizon]

pain

I guess abbot or rudin is fine for it?

[willow pecan]

Yes

[icy knot]

Kleppner or Goldstein, Taylor

[finite thorn]

Any good books for probability?

[orchid mortar]

Many, what level are you looking at?

Without any prompt I'd just say Billingsley

[remote ginkgo]

nice choice

[finite thorn]

Well, in my country we don't get probability covered too deeply beyond the basics but I AM at university, so I can handle books that are about graduate level

just please don't be rigorous like rudin's real and complex analysis

[finite thorn]

probability and measure?

[orchid mortar]

How do you find Ross' First course?

[orchid mortar]

Yes

[finite thorn]

simple enough, might work

[finite thorn]

taking a look I see it assumes you know calc, which good thing I do. Does it require anything else?

[orchid mortar]

Mostly not other than being used to dense math I think

[finite thorn]

well yeah it sure as hell is dense

by page 30 you can already smell chalk

anyway, thanks

[hazy elk]

There's Blitzstein as an alternative to Ross

[nimble ivy]

can anybody recommend a math book for someone in his mid 13s
cz i'm tryna improve my math a bit

[lime folio]

Pearson IIT Foundation Mathematics Class 8 | Tenth Edition| Includes Active App -To gauge Self Preparation| By Pearson | Link: https://www.amazon.in/Pearson-Foundation-Mathematics-Active-Preparation/dp/935449823X || This is a really good book

[nimble ivy]

tysm

[lime folio]

welcome

[nimble ivy]

oh fuck

i dont think amazon delivers to my country

[lime folio]

what

lol. wait im gonna send you the link for flipkart

[nimble ivy]

ok ty

[lime folio]

https://www.flipkart.com/pearson-iit-foundation-mathematics-class-8/p/itm8bbfeccf745e7 here it is

you'll not regret with this

[nimble ivy]

tysm

[nimble ivy]

i hope so

[lime folio]

or do you want to read this in ebook format for free?

i mean just see how it is

[nimble ivy]

i mean yea i can check the first few pages out

if it helps i'll buy it

[lime folio]

ok wait i'll try if i can get the ebook

[nimble ivy]

ok ty

[lime folio]

here it is but its not the latest version it is the 9th edition and the link i sent u was of 10th edition so there wont be any significant changes in the books its very similar

[nimble ivy]

ok ty

[lime folio]

😃

[nimble ivy]

just read 2 pages

[lime folio]

i sent you the practice book's pdf. it only has questions but the link i sent you has theory and explanation for each question

[nimble ivy]

it's perfect already

[nimble ivy]

ye i can see that

it's better like this

tysm

[lime folio]

wait

i got the pdf of the actual book

the pdf of the actual book

gotta go

[acoustic ridge]

Can anyone suggest me the best book for learning 3D calculus, differential calculus, divergence and curl and 3D vectors that covers most of the these properly?

[orchid mortar]

OpenStax's calculus Volume 3?

[hazy elk]

I think you will regret it lol, why don't you try out AOPS books, I hear they are pretty good

[remote sparrow]

Starting with Blitzstein and Hwang is fine. It is a calculus-based probability book. Probability and statistics were invented to study real-world problems about random or uncertain phenomena, and so I think it is better to focus on how to appropriately use and interpret probabilities first rather than going too deep into mathematical detail.

Optionally, it may also interest you to read about the philosophy of probability.

[crimson leaf]

Please dont send PDFs discord no likey

[remote sparrow]

what do you think about some of gelfand's books pitched for pre-uni students?

[left cloud]

i’ve never seen them actually but i’ll take a look at them later

[crimson leaf]

How do you guys feel about Grimmett Welsh or Grimmett Stirzaker

[remote sparrow]

they seem fine at a glance. i do prefer the informal tone blitzstein and hwang have, though.

[safe horizon]

definitely interested in the philosophy of math and the like

[tawny copper]

What do you think of Jaynes?

its crazy how important probability is yet how tricky of a concept it is

[remote sparrow]

I've not read Jaynes.

[gray gazelle]

Why does stat and prob need calculus?

[remote sparrow]

So we can talk about probabilities as areas?

[sturdy shore]

because probability is all about measuring the likelihood of events, and you cannot measure things without integrals

unless you are in discrete land, but you definitely do not want to be stuck there

[gray gazelle]

I don't understand

Probability is in % which can be represented on a number line

0% to 100%

Why do you need area between 3% and 15%?

Do you like integrate normal distribution curve to find area there or sumthing

[willow pecan]

[sturdy shore]

🤨

[gray gazelle]

?

[remote sparrow]

I'm not getting what you're saying, but I agree all probability distributions have a total area of 1. Yes, it is a number from 0 to 1. Yes, you have to calculate an integral (i.e. area) to get that probability for continuous pdfs.

[gray gazelle]

Those emojis are very helpful thanks @willow pecan @sturdy shore

[willow pecan]

Events with probably 0 can happen

[gray gazelle]

I see why you have the honorable role

[gray jungle]

Dont forget needing measure

[sturdy shore]

at this point just open a probability book lol, we arent collectively tricking you into studying calc

it is impossible to do probability without measures, which is impossible to do (except in very specific situations) without calculus