book-recommendations

[regal creek]

can confirm

[trail hemlock]

both yall is gon get me banned

[regal creek]

for what

[ivory sable]

^

I just want a pre algebra textbook rec

So I can learn algebra

[willow merlin]

open stax pre algebra pdf google

[ivory sable]

Bet

Thx dawg

[steel cloud]

Which Folland is good ?

[remote sparrow]

there are?

[ivory sable]

Btw, if you don't want rigor look into Needham

[remote sparrow]

This book is an outline of the core material in the standard graduate-level real analysis course. It is intended as a resource for students in such a course as well as others who wish to learn or review the subject. On the abstract level, it covers the theory of measure and integration and the basics of point set topology, functional analysis, and the most important types of function spaces. On the more concrete level, it also deals with the applications of these general theories to analysis on Euclidean space: the Lebesgue integral, Hausdorff measure, convolutions, Fourier series and transforms, and distributions. The relevant definitions and major theorems are stated in detail. Proofs, however, are generally presented only as sketches, in such a way that the key ideas are explained but the technical details are omitted. In this way a large amount of material is presented in a concise and readable form.

[trail hemlock]

dude 😭

get w the times

[remote sparrow]

@steel cloud you want Real Analysis: Modern Techniques and Their Applications

[ivory sable]

He has good stuff fr

[trail hemlock]

i hate you so much

[ivory sable]

Anyway

[trail hemlock]

on a deeply personal level

[ivory sable]

It's been real

Thanks among us dude. I'll see you again

[steel cloud]

Okay thank you ❤️

[vocal egret]

gonna review all my calc rn

[torn blade]

has anyone complied all the book reviews/popular recommendations into one place, sorted by area of interest? I think that would be a useful thing

like a website

ik this server had a website but its a bit bare

[still panther]

(the website with the reviews is mathematics.gg, if anyones interested)

[still panther]

not really, if someone wants to add a review to the website they can modmail it

[willow merlin]

best intro to LA book

[gritty gale]

there's https://mathematics.gg/books but idk if that's what u mean

[gritty gale]

idk if this is the best but i found it useful https://textbooks.math.gatech.edu/ila/index.html

[regal creek]

bump

[undone fog]

StartEx offers a groundbreaking platform that connects startups worldwide across diverse fields such as technology, science, art, literature, and more. By uniting these innovative and visionary minds, StartEx fosters global collaboration and aims to drive progress and excellence for a brighter future.

united startups, successfull together

searching for an advertisement and communication person to help me advertise a visionary idea dm me if ur willing to be part of that vision

[remote sparrow]

<@&268886789983436800>

[trail hemlock]

@floral lantern

[trail hemlock]

i like langs LA, people here like to rec FIS.

[willow merlin]

FIS?

[trail hemlock]

friedberg insel spencer

[molten gulch]

FIS is goated

[floral lantern]

??

[kindred tide]

need book recommendations with moderate level sums on these topics... my textbook has a very small selection of sums

[molten gulch]

Lay lay macdonald linear algebra

Thomas calculus

Paul's online math notes

[kindred tide]

damn the first 2 books expensive af

im assuming theres no one book with all of the topics?

[loud cradle]

if you don't need a specific edition for a class, you can just buy an older edition of any calculus book, practically for free

[kindred tide]

ig i'll do that

thanks for the recommendations!

[loud cradle]

and there are several decent free linear algebra books online

if you don't need a paper copy

[kindred tide]

drop some names?

[loud cradle]

one that gets recommended is treil, linear algebra done wrong
and there's another one by hefferon

[molten gulch]

Technically wouldn't mentioning this be discussing piracy as legally people aren't supposed to host copies of these books on their personal uni websites

[azure lark]

idk, may be one of the authors is the prof?

[molten gulch]

I can check one sec

[azure lark]

nope its not. time to delete

[kindred tide]

dw it got it somewhere else

[molten gulch]

Nope it's not hosted by lay or macdonald

[kindred tide]

thanks for all the recs, appreciate them!

[azure lark]

damn, thats pretty careless for a professor

[molten gulch]

You can find a ridiculous number of books this way, but ofc I can't rlly go further into discussing this.

Now sometimes it is an official copy by the authors, I rlly like when authors can post their books on their website

[azure lark]

yep. love the ones who upload either drafts/preprints or full editions on their homepages

[molten gulch]

Absolutely

[azure lark]

I had a prof who had their finite elements book marked at 300+ USD by the publisher, and he emailed us the draft one day before he started the course for us. Absolute madlad

[molten gulch]

Goddamn that's a goated prof

[loud cradle]

in some cases the version on the author's site is better than any printed one, with all the known errata fixed and sometimes new material added

[molten gulch]

Yeah

It's great

[robust quiver]

why would you say that? i’m pretty sure it’s intentional. most people in academia would argue that scientific books should be open access, knowledge shouldn’t be hidden behind an absurd paywall

nowadays publishers mostly work against rather than for the scientific community

[molten gulch]

Yeh book publishers just want that sweet sweet 💶

[azure lark]

that is true, but in the end I believe the initiative should lie with the author. Its not the place of anybody else to decide how to spread someone else's intellectual property

If you want to propagate the knowledge for free, write your own book

[molten gulch]

It's incredibly difficult to make your book very well known without having it pubished and stuff afaik (there are ofc exceptions) and the publishers are frankly total assholes

[azure lark]

that might be so, but that doesnt give you the right to essentially pirate someone else's stuff

coz there is a reason the book was famous. The efforts of the author, the pedagogical takes and the authors own decision to monetise that effort is something to be considered before you do this. Of course, the publishers putting a huge pricetag is unresonable, and I totally agree that publishers are assholes

[robust quiver]

well, i (and many others), disagree

i view piracy as a great initiative and, in many cases, the only working alternative there is to the monopoly publishers have

on the other hand i agree i wouldn't personally upload a pdf of a book i like on my webpage like that, but this isn't usually what happens: people who do that are mostly well established professors who share useful content for their classes, out of print books, hard to come by papers, mathematical classics (which should be available to everyone!), etc. and who may even know the authors personally

[junior isle]

Was it enough?

Can someone recommend a textbook that contains all the material in the exam P for actuaries?

[long oriole]

One of my prof gives hard copies of his books who take his courses. He is incredible nice person

[orchid merlin]

Hi, can anyone recomend a book? im quite intrested in Sociology, Political Science, open strategic decision-making and manipulation, im really new in the subject of sociology and psychology, im not even sure if this is a subject but anything like it, it would be great thanks. i played a lot of chess and weiqi in contest and read a lot of books like that but i haven't truly found what i am trying to find.

[rain hound]

Academics have a fair use exception to distribute ebooks to their students as needed to do the class (at least in US). But they can’t be used outside that. I think probably the most sane way to enforce that is to post on canvas or whatever other app the course is hosted on since it’s not exposed to the open web. But ah well.

obligatory: this is not legal advice I am not a lawyer

[regal creek]

was asking for any fluid dynamics recs

[marble solar]

Are you looking for Computational Fluid Dynamics, or mathematical stuff?

I'll assume math

A lot of people recommend Jacob Bedrossian and Vlad Vicol's "Mathematical Analysis of the Incompressible Euler and Navier Stokes Equations"

My advisor asked me to read Bertozzi and Majda's Vorticity and Incompressible flows

There's also Terry Tao's two quarter sequence of notes he wrote on the subject

https://terrytao.wordpress.com/category/teaching/254a-incompressible-fluid-equations/

[regal creek]

mainly CFD but i'm planning on looking into both

[marble solar]

I don't know anything about CFD

🤷‍♂️

[amber zenith]

I am taking Differential Calculus (Calculus 1) at university, and the first topic we covered is relations and functions. However, I don't quite understand this first topic very well. Do you have any materials that could help me?

[floral lantern]

Got no clue sorry

[remote sparrow]

https://diestel-graph-theory.com/

there is a new edition of diestel's graph theory book available

it's not yet available from springer

https://www.youtube.com/playlist?list=PL_qO0UBYKVJ1myNZdh3j27fniqRtHYifm

there is a youtube lecture series by the author following the book

[molten gulch]

waitinggggg

[torpid stump]

Calulus book recommendations (I already finished Stewart looking for something more)

[molten gulch]

Spivak

Apostol

[trail hemlock]

hi30 is my goat how could you

i thought u was a physics nerd

[torpid stump]

https://tutorial.math.lamar.edu/Classes/CalcI/CalcI.aspx

This will help for all topics in Calc 1

[torpid stump]

Ok thank you

[snow saffron]

Looking for books to help pass my P Exam (Actuarial Exam)

I also use coaching actuaries but I need more information to study this spring and summer semester

[remote sparrow]

you can probably get help in the statistics server too

https://discord.gg/pVm6BztX

[snow saffron]

I didn’t even know this existed

Maybe I can get books for my FM from here?

[remote sparrow]

i think the actuary exam people also give a list of suggested references

one of which is wackerly, mendenhall, and scheaffer

blitzstein and hwang should work fine too

[molten gulch]

^

blitzstein is also free (if it's the book we're thinking of)

[snow saffron]

Where would I find this book? Also what edition

[remote sparrow]

which book

[snow saffron]

Blitzstein

[molten gulch]

Introduction to probability/stat110

[remote sparrow]

https://stat110.net

[molten gulch]

yeah that one

[snow saffron]

Okay thank you I will also ask the stat discord for their recommendations

[red ether]

Is this a gay server, bc the picture have a rainbow

[remote sparrow]

There are many gay people here. The official stance of the server is that all LGBTQ+ people are welcome, if that's what you're asking.

[molten gulch]

There's a lot of LGBTQ+ people in the server, the server icon is just in solidarity and support of LGBTQ

[red ether]

wok then im leaving

[molten gulch]

people getting butt hurt by something not even affecting them negatively....damn

[modern sphinx]

Ehh, not to be rude but server's better off without such people

[trail hemlock]

????

this cannot be real

[molten gulch]

there are people like that

[normal crystal]

he probably joined just to say that

[trail hemlock]

hes not a day above 13

and this is off topic

[next lintel]

Does anyone have any book recommendations on Probability Theory?

My prerequisites are:

• Introductory course in Linear Algebra and further self study (Hesselholt & Wahl, Lineær Algebra).
• Introductory course in Real Analysis (Eilers, Hansen & Madsen; Indledende Matematisk Analyse).
• Further course in Real Analysis with slight touches on Complex Analysis (Christandl; Analyse 1).
• Introductory course in Numerical Analysis (Lecture notes).
• Introductory course on Measure Theory (Schilling; Measures Integrals and Martingales).
• Introductory course in Probability Theory (Jacod & Protter; Probability Essentials).
• Further study of Probability Theory with focus on stochastic processes (Jacod & Protter; Probability Essenstials).
• Stochastic processes in the context of Actuarial Science (Mikosch; Non-Life Insurance Mathematics).
• Introduction to Statistics based on Measure Theory (Lauritzen; Fundamentals of Mathematical Statistics).

I'm open to anything, as long as it's on par or further level than the above.

[torpid stump]

https://www.amazon.com/dp/0521592712

Check this out

It is pretty good

[next lintel]

Will check it out. Thanks

[torpid stump]

No problem dude

[remote sparrow]

billingsley and durrett are pretty standard

there's at least a few others that get used too

[torpid stump]

I personally don't like probability or anything related to it lol

[remote sparrow]

your recommendation is too low level for OP

OP has already done some measure-theoretic probability and measure theory

[remote sparrow]

but uhh seeing as you've done jacod and protter, perhaps you want to move to stochastic calculus?

@upbeat vine likes le gall for stochastic calculus

[torpid stump]

Oh all right

Any linear algebra book recommendations?

I currently have Hoffman and Kunza and am thinking of getting

Axler's book

Linear Algebra Done Right

[remote sparrow]

you can, but i'd say as far as exercises go, they're mostly less difficult than H&K. still, the determinant-free proofs in LADR are worth reading

[torpid stump]

Thanks for the tip!

[willow merlin]

any book on linear algebra ?

[trail hemlock]

#book-recommendations message

[tribal crow]

you've asked this, or variations of it, at least a dozen times now

[willow merlin]

srry

[trail hemlock]

jus read dami's review

[willow merlin]

ok

[willow merlin]

ty

[daring lake]

I need to pick up Roman's LA

[molten gulch]

Hey chat, we want to get some books for our cousin, he's in 7th grade rn and very interested in geology and also seems to have some interest in mathematics, idk what classes he's taking rn so even some general pop-sci style books would be fine ig

[vernal tinsel]

I would let my cousin read an intro book to geometry and number theory

[daring lake]

give rudin's PMA

[wicked fractal]

I would teach analytic number theory

No books

[tribal crow]

for mathematics, I've heard many good things about Gödel, Escher, Bach

[heady ember]

In the time you have spent asking, you probably could have learnt a modest amount of linear algebra already.

[trail hemlock]

not a terrible idea tbh

[trail hemlock]

7th grade? hes ready for artin's Galois theory

no doubt in my mind

in all serioueness, Thinking Physics by Lewis Carrol Epstein is a decent one

[normal crystal]

maybe something like a Brief History of Earth by Knoll

[brave glacier]

suggest some best books in linear algebra

[marble solar]

What's your math background?

[azure lark]

imo, 7th grade is a good time to put books like Mathematical Circles in his hand

As for geology, when I was that age, I had a few books from NatGeo that were related to that topic, specifically volcanos and igneous rock structures

[normal crystal]

this poor kid is like "I like rocks"
but chat will lead CC to gifting a math textbook

[still panther]

maybe a bit too old, but smullyans logic puzzle books are pretty nice

[still panther]

7th grade is old enough to learn about abelian categories

[pliant wadi]

There's a book called 'What's the name of this book?: Dracula and other logical puzzles'

Also the art of problem solving

[pliant wadi]

There's one for younger audiences iirc

[bitter violet]

A pocket guide for identifying rocks and minerals, something low-barrier he could get into and teach himself? National Geographic has one for North America.

[winged temple]

@drifting hornet

[drifting hornet]

Thank you

[winged temple]

Welcome

[molten gulch]

TYSM everyone for your recs

he already has a ton of minecraft books and 3 copies on 3 different platforms

[gray gazelle]

Any great books on numerical analysis/methods for engineering?

[molten gulch]

Kincaid and Cheney - Numerical Analysis: Mathematics of Scientific Computing

[vocal egret]

after proofwriting, should I try Apostol's calculus or Spivak's calculus?

My brain ain't braining rn

[still panther]

just pick up a real analysis book

you ll be better off that way

[signal zenith]

Don’t curse the kid to become an AOPS kid

[molten gulch]

We'd say just start with analysis

[quick steeple]

Can somebody suggest a decent book on functions? Please 🙏🏻

[molten gulch]

There are no books just on functions, go read the chapter on functions from a precalculus or discrete maths book

[torpid stump]

Or use pauls online math notes

For functions

[molten gulch]

https://tutorial.math.lamar.edu/classes/alg/Graphing_Functions.aspx

[vocal egret]

I decided to try out Bartle's book of Introduction to Real Analysis along with Abbott's Understanding Analysis. I plan to learn from Pugh's book afterwards, but I'm still confused of which order to go with. Thanks for the feedback

I just checked Spivak, and it have very rigorous proofs. I might need some time familiarizing myself with the style of it. Thx for the advices

Agreed. But Bartle sometimes rushes some parts, so I ended up revising nearly everything I know in chapter 1

[torpid stump]

It might be too difficult though

[vocal egret]

Seems nice, but damn that's a bit difficult to pull off

[torpid stump]

Yea Bartle is much harder than Abbot.

You should try Baby Rudin lmao

[vocal egret]

Nah, a deaths sentence for me

[torpid stump]

If you have the time and also the dedication, you can do it.

[torpid stump]

Bro I know a dude on Math Stack Exchange studying algebraic topology in his first year lol

[vocal egret]

That's bloody insane

[torpid stump]

He probably learned calculus in 3rd grade lmao

[vocal egret]

seems to be

[molten gulch]

That's....normal

[torpid stump]

[molten gulch]

Like that's far from the craziest thing possible

[torpid stump]

What is the craziest thing possible?

Algebraic geometry in 5th grade?

[molten gulch]

this

Nope

not by a long shot

[torpid stump]

Cool I'm not crazy

[vocal egret]

Crazy? I was crazy once, they lo-

[molten gulch]

we wish analysis was taught in year 1 here instead of 🤮 calculus

[torpid stump]

Calculus is for babies I did calculus in 7th grade

[vocal egret]

same

[molten gulch]

Calculus isn't "for babies" but it definitely could be introduced earlier than it is

[torpid stump]

Yeah I was just joking

[molten gulch]

we're 20 now but we lack the mathematical maturity for analysis

[vocal egret]

I could've been introduce in like, 8th grade imho

[molten gulch]

we could've done calculus at 12-13 but that got fucked up due to various circumstances

[torpid stump]

And they shouldn't use stewart for their calculus text the should use Spivak or Courant

[molten gulch]

YES

or....

just jump into analysis

[vocal egret]

covid made me lose my social awareness and uh, my brain

[torpid stump]

[molten gulch]

we got covid thrice and our depression and anxiety got exponentially worse

[torpid stump]

We were playing Super Smash Bros 24/7 during covid lol

At least I was

[vocal egret]

I can't even communicate properly after pandemic, gonna try to improve rn

[vocal egret]

I just played PUBG.

My laptop did not like that

[calm kernel]

greeting.Can you pls suggest me a book about 3d trigonometry ( or calculus if it exists). I just wonder.And I can't really find good myself.
@molten gulch ? okay?

[torpid stump]

Bye i gtg everyone

[molten gulch]

we don't know of any good books on spherical geometry but I think you could pick up some of the good intuition from knowing calculus; thomas calculus, stewart calculus, apostol calculus, spivak calculus are 4 good books on the topic

[calm kernel]

btw can they almost replace institutions

[calm kernel]

or unis

[molten gulch]

you still need a degree for a vast majority of jobs

[drowsy thicket]

From a pure knowledge POV: there is the flipped classroom model (also I think the Moore method does it this way), where you self-teach yourself everything and only meet up with your instructor to discuss problems

I don't think it always works as well as a normal classroom model

[molten gulch]

we hated every time we've had this model in class

[calm kernel]

I think it is better and there is less stress when tryin to ask teacher, who is working with class and doing it harder. And a lot easier to it individually

And we can understand a lot

ourself

[drowsy thicket]

Yeah this is the model my uni uses currently for people studying in parallel to high school

I don't think it's a good idea on their side, making first-semester people (not even) having to teach everything to themselves

I think it misses the 'instructor insights'

[molten gulch]

we struggled (and failed) calculus because we had to come up with so much and at the same time the homeworks were very difficult (understandable but they were far beyond just "challenging")

[calm kernel]

ye, cons and pros

[drowsy thicket]

I read about a professor's opinion on this recently on math stackexchange

[calm kernel]

and what is it about?

[drowsy thicket]

Different profs say different things. One said he hasn't seen anyone actually successfully self-study some area by themselves. Another said he thinks it's entirely possible

There are mixed opinions

[drowsy thicket]

I completely believe that self-study works

There are many examples on this server too

And well, there is a reason there is this flipped classroom model at unis, if it didn't work then surely it wouldn't be around anymore

[calm kernel]

ye depending on people. Bc I can see someone can't actually find out about somethings without teacher or tutor. The only problem in self-studying is , that you need to search everything on the internet

The only problem in self-studying is , that you need to search everything on the internet
If there is a case*

[drowsy thicket]

This is how I learned linear algebra 1 and 2 and now analysis

[calm kernel]

is 1 and 2 is level of deep learning

[drowsy thicket]

linear algebra 2 is just the continuation of linear algebra 1

[calm kernel]

oh okay

[drowsy thicket]

It doesn't directly have to do with machine learning or deep learning if that's what you meant, but if you want to learn those probably some linear algebra will be necessary

[calm kernel]

how do you know that I am going

[drowsy thicket]

You said 'deep learning' and your pronouns are 'ILoveML'

I assume ML abbreviates 'machine learning'

[calm kernel]

why the meaning is close to ml when it's just about learning somethings deeply

[drowsy thicket]

Oh, sorry, I thought you meant the computer science concept 'deep learning'

[calm kernel]

okay bye and ty

[signal zenith]

Me personally I prefer the flipped classroom model

Mostly because I rarely feel a professor gives insights by lecturing that aren’t just in the book

The vast majority of lecturers are just repeating what you could already learn from the book so better to use the time with them to practice

Just my opinion though

[remote sparrow]

@remote vortex you might be too young to have used different books, but before axler's MIRA existed, did you enjoy any other measure theory books? if axler's MIRA didn't exist, what would you recommend instead?

[still panther]

just read bogachev 4Head

[remote sparrow]

why would you need abbott or bartle/sherbert after reading spivak? wouldn't it be better to move on to rudin, carothers, or a metric spaces book like magnus or o'searcoid?

[remote vortex]

Folland is a good book; it's more concise than Axler but not as bad as Rudin (and also if when you're learning MT, you're probably better at handling conciseness than you were when learning RA)

And Folland does cover much more and in greater generality

[remote sparrow]

oh yeah, i knew you were a folland enjoyer, but i was more wondering if you had non-folland and non-axler suggestions that were about the same level as axler

[remote vortex]

Nothing springs to mind at the moment

[remote sparrow]

that's fine

[signal mountain]

billingsley is one ive heard thrown around but maybe it doesnt actually cover much measure theory (?)

[remote sparrow]

it covers measure theory

use the search query "from: outsider7593 billingsley"

[signal mountain]

and indeed there it is!

[signal zenith]

We have both of this. I’m just saying that in a standard “professor lectures at you” course I rarely learn anything in lecture that I didn’t already learn from the textbook

[remote vortex]

It does, it's a fine book, but I wouldn't say it's Axler level of accessible

It is quite good nonetheless, especially if your overall goals are broadly in the probability/statistics area

[signal mountain]

ah right ! is it comparable to folland then?

[remote vortex]

It's been a while since I used it much, but skimming it right now, I'd say more or less yes.

This is his proof of the pi-lambda lemma/theorem

[signal mountain]

been a hot minute since i did any measure theory but seems reasonable

[remote vortex]

I think it's about the Folland level on the conciseness vs verbosity spectrum.

Less concise than Rudin but less verbose than Abbott or Axler

[wicked thunder]

Is there a analogue to the rudin series but for logic? Like how there's a progression from baby rudin->adult rudin->grandpa rudin but for the topic of logic? The field of mathematical logic is very large so I'm trying to find a good entry point.

[vivid snow]

Guys is there any workbook with algebraic factions or with complex numbers

[gray jungle]

I will say, i have been in love with bogachev style in measure theory

i wouldnt recommend it to a student thats not incredibly talented to learn from, simply cause it will be very difficult to know what to ignore on a first read, but its very well written

[remote sparrow]

i'm not really aware of a single author that has a complete multi-volume series covering the introductory aspects of each subtopic in logic

you can ask for specific introductory books to work through first though

#book-recommendations message

[wicked thunder]

Do you know a good place to start? I'm fairly new to logic and a bit lost on where to start.

[remote sparrow]

just linked some

you can look at https://logicmatters.net/tyl as well

[wicked thunder]

Thanks! 🙏

[bitter violet]

There’s also the Open Logic Project. Have not read yet, but free. https://builds.openlogicproject.org

[thin swan]

I recommend all books made by UKMT

[weary bison]

So I'm trying to learn more about elliptic curves and modular forms because I'm trying to teach myself how Fermat's Last Theorem got proven, just to see how far I can get. Does anyone have any recommendations for resources on any of those three topics? Or maybe some of the background I might need?

[molten gulch]

Diamond and Shurman - A First Course in Modular Forms

[weary bison]

Thank you! 🙏

[normal sandal]

Hey, I'm looking for a more advanced analysis text, I've had courses in real/complex, functional analysis and pdes but I want to go deeper + I feel like I haven't really seen connections between the different fields.

[foggy quest]

There are lots of connections in "Partial Differential Equations I/II/III" by M. Taylor.

[marble solar]

Stein and Shakarchi Volume 3 and 4 is the good answer for outside of Rudin/Folland

[muted talon]

I have a question

I've been meaning to get deeper into math that isn't as directly related to Computer Science (my major.) Currently, I have a calc 3 course and I'm enjoying it. However, it's going to be over soon. It's one of my last non-discrete math courses, and I plan on going on applied mathematics master's because I think I want to work in scientific computing research

So, I want to study math on my own

Is there any books recommended for stuff like calculus and linear algebra?

[molten gulch]

well after calc 3 you can go in a ton of directions

analysis, topology, diff geo, abstract algebra, etc....

[muted talon]

I would personally revisit calc because my college did a weird thing with calculus (crammed calc 1 and 2 into a 10 week course, and calc 3 into another 10 week course)

[molten gulch]

well then revisit calc 3 (stewart or thomas' calc, or pick your favourite)

and then go from there

[muted talon]

Fair enough

Thanks :3

[molten gulch]

yw

[proven lantern]

Any complex analysis for several variables resources recommendations? Didn't finish ahlfors but would like to have an idea for future planning. Would prefer the most comprehensive and concise text available.

[remote sparrow]

is there a reason you want to get into this? just want to make sure you aren't thinking that just as multivariable calculus is a "natural" continuation of introductory real analysis, complex analysis of several variables is the "natural" next step

[gray gazelle]

You can start with Mendelson's textbook, it's classic. If it feels too hard, try Kleene's textbook, it's a bit easier but covers the same topics as Mendelson +-. And both have good exercise

[celest estuary]

Suggestions for book of probability that is more focused on counting method...

[fresh skiff]

Is it related to algebra?

[drifting steeple]

anyone has a book on classical mechanics

?

[loud cradle]

there are several...

[drifting steeple]

what's the name

I want a good book

[loud cradle]

what level are you looking for? like a first course?

[drifting steeple]

yeah

[loud cradle]

kleppner/kolenkow is nice

[drifting steeple]

alr thanks I'll check it out

[rich sun]

I can also recommend Goldstein

[gray jungle]

i second goldstien

[tawny copper]

Rossi and Gunning; Krantz; Hormander

The first chapter of Rossi and Gunning could be called a "natural" continuation of complex analysis. In the preface they are honest and state that it's about a semester worth of material (it's about 60 pages). Chapter 2 is also "elementary" in a way, it is about the properties of the ring of germs (at the origin, say) of holomorphic functions in C^n. But the rest of the book is more "geometric"

[gloomy pawn]

Not a book recommendation but an article: https://link.springer.com/article/10.1007/s40687-024-00464-9

[tawny copper]

Freitag's second volume of complex analysis also discusses "modular forms of several variables", but haven't read that yet

[vocal egret]

Is Contemporary Abstract Algebra worth looking into?

I currently have Fraleigh, it's more like manual imo

[remote sparrow]

#book-recommendations message

[quick steeple]

Try the Asmus’ book on logic

[rocky flicker]

What's a good book

For learning

Set theory and zfc

For someone who doesn't have a lot of mathematical maturity

[devout tinsel]

I need to study Complex variable theory in a week. Please suggest a lecture series and study material.

[foggy quest]

https://mtaylor.web.unc.edu/notes/complex-analysis-course/

[vocal egret]

Book of Proof is solid imho

[rocky flicker]

@vocal egret im actually going over velleman

how to prove it

does it cover

the same stuff

right now i have done

some set theory

stuff

and a lot of logic

but havent seen any mentions of ZFC axioms

[vocal egret]

not really. Book of Proof covers more content such as calculus proof. I checked and velleman's book is intended to be a simple introduction for new peeps

[rocky flicker]

hmm

[vocal egret]

@rocky flicker zfc should be in thr "functions" chapter

[rocky flicker]

Alright, thank you

[rocky flicker]

to be fair the book is decent

i've been going over it

at least for proofs

n stuff

but yeah it doesnt really spread much into other domains

[vocal egret]

velleman's book is more clearer imo tho

[rocky flicker]

yeah

[slow vessel]

Anyone know abt arithmetic and geometric or pure grade 10 math text book?

[quick steeple]

What topic do u need?

Usually prealgebra and precalculus are good

[slow vessel]

i need both

just beginnner, so i can grasp it

[quick steeple]

Oh

Then u need basics first

Multiplying, dividing, power, roots etc.

[slow vessel]

i already know that, maybe kinda little advanced?

[quick steeple]

Because if u don’t know the basics u won’t understand algebra

[quick steeple]

Try James Stewart precalculus

[slow vessel]

but i think i need that also for revision

[quick steeple]

Ofc

[slow vessel]

I'll download it by eBook

[quick steeple]

U can get it for free

Just pdf

On google

[slow vessel]

alr thanks man

[molten gulch]

Discussing piracy on this server is bannable

[quick steeple]

What piracy

U just google “such and such” pdf

[molten gulch]

yeah that is piracy, the books aren't distributed legally

they're hosted on someone's uni directory normally, that's not allowed unless you're the author and have permission from the publisher to rehost

[quick steeple]

Stupidity

Books should be free

[woeful dune]

u can check pearson series

[gilded shuttle]

they didn’t post a link or file

[molten gulch]

AFAIK discussion is also discouraged

[gilded shuttle]

may be discouraged but the rules say nothing about it being bannable

book name pdf doesn’t seem to be that harmful

[quick steeple]

😎

[gilded shuttle]

everyone should know about it either way

[quick steeple]

✅

[woeful dune]

where's the combinatorics channel?

[gilded shuttle]

https://discord.com/channels/268882317391429632/576511723574525962

the old combinatorics channel was archived

[woeful dune]

ah i see

[knotty smelt]

I wonder if anyone can point me at a rigorous epistemic theory in the philosophy of probability/statistics literature (e.g. frequentism/bayesian epistemology)? Moreover, which covers different interpretations like bayesian, frequentist and information-theoretic probability? Thanks!

[remote sparrow]

https://plato.stanford.edu/search/search?query=philosophy+of+probability

https://plato.stanford.edu/search/searcher.py?query=philosophy+of+statistics

click through some links and check the bibliographies

https://www.amazon.com/Philosophy-Probability-Contemporary-Readings-Routledge/dp/0415483875

this anthology is a top result on google

i'm sure there are many others like it

[robust quiver]

is there something other than “we cannot allow posting links or files with pirated content” mentioned in the rules or is it just implicit?

[knotty smelt]

Thanks, I will try to check these link and search for the others.

[thin swan]

Gutenburg is still valid

[vocal rampart]

i want to learn about chaos theory to apply it to physics, any advice on where to start or available resources like videos or books

[thin swan]

https://www.gutenberg.org/

A website for you folks worried about piracy

[pale scarab]

I'm trying to remember a math professors page that had a pretty large collection of well written expository papers. Does anyone know what I'm talking about or possibly just something similar.

[loud cradle]

keith conrad maybe?

https://kconrad.math.uconn.edu/blurbs/

[pale scarab]

Yes that was it thank you. If anyone knows of similar resources they know of I would like to know.

[mossy flume]

hmmm I should make the name text on that sticker bigger

meh

[left cloud]

lmfao

[signal zenith]

If you’re right now taking calc 3 your calc foundations are probably solid enough already you can move on to real analysis

At least for me proving stuff rigorously was a lot of the fun & helped me understand it much better

[tribal crow]

promoting your channel is not allowed on the server

especially since this is #book-recommendations

[trail hemlock]

💀

[pearl fox]

has anyone read Abstract Algebra: and Inquiry-Based Approach by Hodge?

and does anyone have any opinions on it starting with introducing integers and stuff and then leading to rings, then fields, then groups ?

[cold tusk]

is Naïve Set Theory a good book?

[pale scarab]

I think halmos is one of the best authors in general.

[cold tusk]

Good to hear!

[foggy quest]

https://mtaylor.web.unc.edu/notes/

[wispy moss]

is "linear algebra done right" a bad book ? if yes why ?

[vital bane]

it's not a bad book

it's a weird book (for a first look at LA)

because the author hates determinants (for some reason) and does everything without determinants

it isn't necessarily bad to get a new perspective on LA, but it shouldn't be one's first exposure to the subject

it's a fun book to read once you've already learned LA

[jade rover]

What book would you guys recommend if you’re planning to take the ap calc bc exam, self taught?

[trail hemlock]

larson is nice

larsons calculus 10e is the one my school uses

[jade rover]

Alright thank you

[vocal egret]

Just decided to change from "Book of Proof" to "Mathematical Analysis: a transition to advanced mathematics"

I feel like it's more straightforward

[wet elm]

Hello. Could you recommend me some websites or books about logic and math problems, pazzles, riddles, etc.? I want to have a daily routine of these problems in my day.

[toxic willow]

https://projecteuler.net/

[heady ember]

In other words, it should be Axed for a first intro to LA

[versed meteor]

hey guys, does someone have the pdf of this book :
'problems in linear algebra and matrix theory' by fuzhen zhang

[spark jay]

Go to mods server or mathdash they offer potd
But those are sufficiently hard they can demotivate you lol

[cobalt copper]

what do you guys reccomend for self taught discrete math?

[marble solar]

Discrete Math with ducks

[reef stump]

is there any page like competitive programming but for maths? I mean without code, Only math problems with different difficulties.

[signal mountain]

yes, they're called 'math olympiads', generally aimed at pre-university students
if you search for '[country/local region] math olympiads' you might find some you can take part in

[foggy quest]

he doesn't in the latest version. He develops determinants the usual way

[reef stump]

thanks

[signal zenith]

it's a good book'

I would recommend it even for a first look

I largely agree with the author's view that most things that standard texts use determinants for are both easier and more elegant without them

although, if you're say a physicist or a computer scientist who needs linear algebra for the more computational side then maybe it's not the most useful

[storm lake]

Is there a book that provides an introduction to math in non euclidean geometry?

[broken meadow]

Wrong channel for this

read #❓how-to-get-help

thanks

(deleted post as well)

[cobalt copper]

thanks!

[analog plinth]

Is bartle and sherbert a good book for real analysis?

[remote sparrow]

yes

[hollow shore]

Hello. I am looking for books on Probability.

A self contained Measure Theoretic Probability textbook which motivates Measure Theory from the ground up.

[remote sparrow]

billingsley

[proven lantern]

Not an expert, but I would choose Kallenberg when I got to that stage. An extensive and comprehensive treatment of measure theoretic probability theory

[hollow shore]

My analysis is not that strong tho

[remote vortex]

Billingsley's "Probability and measure" is the classic recommendation for measure-theoretic probability

[hollow shore]

Okay. Besides Analysis in R, should I also pick up some metric space topology?

would that be relevant?

[remote vortex]

Not hugely, although it will probably make it easier to think of various modes of convergence.

[hollow shore]

Gotcha

[remote vortex]

But I wouldn't call it essential in the way real analysis is.

At some point in probability (characteristic functions) you'll also want to know a few things about complex numbers and basic complex analysis.

But that happens at a fairly late stage, around the central limit theorem usually

[hollow shore]

I see

[rose hazel]

Whats the recommended book for a ug-level introductory course in abstract algebra?

[toxic willow]

#book-recommendations message

check out pin message

I also heard pinter is great 🙂

[cobalt copper]

is Stewart's Calculus still reccomended for self learner?

[rose hazel]

what do you think of artin? is it good for a first course?

[vital bane]

I'm sure he develops determinants in the usual way, he even has a chapter on multilinear algebra which is very cool, but doesn't he still introduce eigenvectors and eigenvalues and characteristic equation without determinants? it's not a problem for someone who's already seen that stuff though

[rose hazel]

Ignoring my previous discussion, i have a fourteen year old cousin whose birthday is coming up, and i would really like to gift something educational (preferably a book), any recommendations?

He mostly does programming as a hobby, and has taken a not-so-formal real analysis course in high school, but is not particulary interested in mathematics.

[vital bane]

not-so-formal real analysis course in high school

I think that's called a calculus course

[vital bane]

"Ignition!: An Informal History of Liquid Rocket Propellants" by John D. Clark

[rose hazel]

call it advanced calculus, it was named real analysis and it certainly covered much of the proofs, it just wasn't as rigorous in the sense that well, hard to explain but it wasnt rudin or anything you would read in a ug course.

[rose hazel]

thanks

[still adder]

Am I the only one who thinks Rudin is too dry

[vital bane]

you're not alone

Rudin is for people who already know analysis

[rose hazel]

I am no expert by all means, but i think real analysis as a subject tends to have a dry treatment, even in books such as tao.

mostly because why include the non-abstract "interesting" applications of it when you have already done it in a calculus class?

[vital bane]

Abbott is not at all dry and is quite full of water such a well written and well motivated book

[remote vortex]

Nowhere near, Rudin's PMA is a controversial recommendation as an introduction to real analysis (although I think it's universally praised as a book in its own right, and very recommended as the second read)

[still adder]

Funny cuz I was recommended "topology without tears" as supplemental material for abbott (main text spivak), and tears are very wet

[remote vortex]

But also what Neamesis said, Abbott's "Understanding Analysis" is a much more accessible introduction to the subject, which I wouldn't call "dry" at all.

[rose hazel]

i just ended up using tao because he develops much from scratch, and honestly i think tao's litte hints in the exercises and his writing in general just helped a ton.

[undone fog]

guys pls give me courses to linear algebra calculus and probability to go deeper in AI i need courses pls i want u to guide me because i foudn out that if i am not guided with a real organised program i cannot advance and the advancement part will take lot of time so pls help me i am sure you are experiemented

[spiral sky]

Def not prefer carothers

[hardy patio]

That’s the first book I read and my first encounter with math. It was a great introduction

[vital bane]

same! ikr it's amazing

[hardy patio]

Then I went on with linear algebra done right and also liked it

[rigid flint]

Anyone have any good books for starting physics with calculus?

[vital bane]

check out this thread in the #resouces channel of the physics server

[rigid flint]

Thanks, I was just trying to find something like this on the physics server but gave up lol.

[peak hawk]

where can I get help in electricity question ?

I am stuck

[remote sparrow]

#book-recommendations message

[daring lake]

if it doesnt fit here, then see the EE server in #old-network or search stack exchange

[trail hemlock]

i love rudin

[dim sierra]

no you aren’t rudin sucks

[snow plaza]

I'm reading rudis real and complex analysis and it's dense and hard to grasp but honestly after I manage to get through a chapter and solve the exercises I feel like I have a really firm grasp on the topic but it's for sure not easy

Although I have no formal education in maths besides high school for now

[mystic orbit]

it kinda is kekw

[gray gazelle]

How old are you?

[snow plaza]

About to turn 19 got unlucky with birthdays/school years

[gray gazelle]

Good for you, you enjoy rudins complex analysis?

[snow plaza]

Honestly yeah

[gray gazelle]

I'll have to check it out, how did you learn about it?

[snow plaza]

A friend from class gave it to me because our professor gave it to him but he wasn't too interested

[gray gazelle]

That's a nice gesture from the professor

I'm currently reading James Stewart's calculus series

[snow plaza]

She just dumped 10 books on him because she had extras and told him to return them someday

[gray gazelle]

What a blessing

[snow plaza]

Yeah he couldn't believe it either

[gray gazelle]

This is in the United States?

[snow plaza]

Nah

[gray gazelle]

I take it your friend is good at math?

[snow plaza]

Yeah he is

I mean we all were good at maths

He's going to study maths as a major now so those books are gonna come in useful

[snow plaza]

For rudin I just take my time and really try to understand it but I like how he builds everything up starting with basic topology

[gray gazelle]

Ill have to look into it shortly

[trail hemlock]

um darq

what?

[pale scarab]

The problems are good.

[jovial parrot]

LOL

[trail hemlock]

HI AMUKH

[foggy quest]

He defines the characteristic polynomial using generalized eigenspaces instead of determinants. All linear algebra books I know of cover generalized eigenspaces not long after determinants, so his treatment is not really different than other treatments.

[upbeat swift]

Are there books of practice questions, maybe a sprinkle of olympiad questions for high school?
Or maybe books about high school math?

[normal crystal]

well, which do you need
books to teach you high school math
or books to give you problems for olympiads

[upbeat swift]

problems for olympiads

extra points if it also includes common problems found in normal exams or small summaries

[south elbow]

book on differential geometry (what prerequisites does it need?)

[timber mesa]

a text like Do Carmo's curves and surfaces assumes you know multivariable calculus and linear algebra, to read others like Lee's series it would be good to know some real analysis/basic point-set topology and abstract algebra

[trail hemlock]

spivak?

[drowsy nacelle]

Thought Lee ITM covers point set from first principles

[cobalt maple]

Any recommendations for books on 3-manifolds that are meticulous and very rigorous (especially topologically) and preferably mostly self-contained?

[plush venture]

Hello everyone, i am uh, suffering from a problem: I find it very hard to imagine geometry and solve geometry-related problems, it's not that i can't solve them per say, but my brain just gets overwhelmed whenever I encounter one and i go full anxious mode.

i have avoided geometry for the longest time, but i dont think it is plausible if i want to do any "actual" math, so is there anything i can do to help this?

[vocal egret]

Having problems with Abbott's Understanding Analysis... I tried to find resources for the exercises, but the supplement I found is near to none. Tho book's really good as an after exercise with bits of afterthoughts. Any recommendations of supplement? Any would be fine, I just can't stand Abbott's book in general

[heady ember]

@vital bane Abbott shill, I call upon you! I see slander right here!

[novel hound]

You could try the first few chapters of Spivak, the chapters on limits, continuity, IVT, least upper bound and the significance of the derivative. And, you could also try the video lectures for 18.100A mit ocw esp to get started and for chapters 1 and 2. If you want more info on topology stuff in chapter 3, francis su video lectures (specific to that chapter) are good.

[vocal egret]

tysm

[remote vortex]

Skip all the imitators and learn from the OG: https://en.wikipedia.org/wiki/Cours_d'Analyse

[vital bane]

specifically lots of multilinear algebra

[vital bane]

tf (tbh I don't have time to quarrel with people's opinions, I am busy )

[vital bane]

Resources for the exercise?

what do you mean?

[vocal egret]

I meant for more comprehensive examples and explanations. Bartle's book is very good for this, but it's lacking some steps and feels very rushed.

[wispy moss]

I am a cs student , any other book as second read to help me on the computational side ?

[vital bane]

??? I feel like you rushed through Abbott and didn't read it properly, it has lots of comprehensive examples and explanations

Bartle is also really good in that regard

which topic did you find lacked examples and explanations?

[vocal egret]

In examples of 1.2, Abott skipped over some stuff afaik

Some of the explanations are vague, and the exercises end up making me rely on other books

[vital bane]

"1.2 Some Preliminaries"?

[vocal egret]

Ye. I just started and i forgot almost every set rule beforehand

[gray jungle]

1.2 seems to be set-theory background so its meant to be a revision to be fair

[vital bane]

If you find 1.2 to be lacking details

maybe you will enjoy Paul Halmos' "Naive Set Theory"

I want to read it myself some time, it is quite critically acclaimed

[vocal egret]

Thanks for the reco

[remote vortex]

Quite so:

This should be familiar territory

And to be fair all you need is familiarity with the concept of set, belonging, inclusion and set arithmetic.

Cardinality is covered in the book with some detail (well, as much detail as needed for real analysis, i.e. not much, but he doesn't seem to assume previous familiarity with the notion)

Sir, this is a #book-recommendations

[cobalt maple]

Oh shit

My bad

[remote vortex]

Happens to the best of us!

[shrewd tangle]

Hello, I have just started college and I have a geometry class. My level of geometry is the one of a 10 year old (due to my country's education curriculum) but I know everything else that's expected from a freshman. I need a book that goes through the basics but is rigorous enough for college

So like, I need everything proven (for example, I need a proof that the sum of the angles of a triangle is 180º, a proof that opposite angles measure the same, etc)

[vapid halo]

A geometry book I have on my self is "Elementary Geometry for College Students" by Alexander and Koeberlein

[toxic willow]

Hi, I need some set theory background. However, I forgot those knowledge I learned several years ago. Pin message recommends Elements of Set Theory by Enderton. I also heard Naive Set Theory by Halmos. Which one should I choose?

[still adder]

Halmos is the more famous one imo

[gray gazelle]

does someone have a super intro level dynamical systems text that just includes ODEs

[remote sparrow]

#book-recommendations message

[remote sparrow]

enderton goes further. it's also more formal, but that depends on whether you care about such things

[shrewd tangle]

Thank you! I'll take a look at it :D

[toxic willow]

thank you

[gray gazelle]

Is anything for a broad comprehensive introduction to mathematics going through each topic better than Euler's Algebra?

[restive nexus]

Does anyone have any good book recommendations that explain the connection between complex geometry and algebraic geometry in a detailed way? I've heard of stuff like the analytification functor but haven't seen a detailed exposition. Even though it's clear to me that there is a strong connection I can't seem to understand how exactly you can use results in AG that very clearly should imply results in CG. I've seen this done on Stackexchange a lot without a justification for why this is possible

[remote sparrow]

@dapper root

[dapper root]

I went through Arapura’s book algebraic geometry over the complex numbers

Enjoyed it

[restive nexus]

Does it explain complex manifolds using AG and a way to switch back and forth between both languages?

[wispy timber]

hello, im looking to learn about multilayer networks as defined here: (https://en.wikipedia.org/wiki/Multidimensional_network). does anyone have a good source to begin on?

[dapper root]

You’re talking about GAGA which is at the end of the book yes

It sort of covers complex geo and algebraic geometry at the same time in some sense

[restive nexus]

Woa ok then that's def what I'm looking for

Thanks

[spark jay]

Any suggestions for books on graph theory (with good problems and not just theory)

[remote sparrow]

https://diestel-graph-theory.com/

https://link.springer.com/book/10.1007/978-1-4612-0619-4

https://link.springer.com/book/10.1007/978-1-84628-970-5

[molten gulch]

diestel <3

[hoary wagon]

Not a textbook, but a website.
satprepteacher.com
SAT, ACT, EOC (End of Course), they have everything. There are PDFs available for studying. Click on SAT Preparation at the top of your screen (Don't worry, there's more) --> Resources to access free resources. I would link all the PDF files, but theres too many.

[trail hemlock]

has anyone read “Contemporary Debates in Metaphysics”, and if so, is it a good introduction to reading metaphysics?

oh its not letting me attach the image

[dim sierra]

I doubt something about contemporary debates is good as an intro

you should read plato 😄

his dialogues are super friendly

[remote sparrow]

any philosophy anthology is good if you read critically

[trail hemlock]

oki

[strange coral]

Are there any good introductory books that are recommended for cultivating an interest in math?

[normal crystal]

If you don't have any previous exposure to metaphysics, and you're not in a class, I would suggest reading something like the intro book by Sider before that

[trail hemlock]

yes i am not in a class and im very intro

thank you for the rec

[hollow drum]

Where can I learn about mapping class groups of surfaces? I looked in hatcher and didn't see anything about them.

[toxic willow]

What Is Mathematics? An Elementary Approach to Ideas and Methods by Richard Courant

Some chapters are not so easy though, however, I love this book

[remote sparrow]

https://www.amazon.com/Mathematics-Human-Flourishing-Francis/dp/0300237138

this seems good

[marble solar]

A primer on mapping class groups

Benson Farb is one of the authors

[strange coral]

Oh okay. And could you please give your opinion on these book titles. Like are they good for introduction to maths?

• https://www.goodreads.com/book/show/17356911-the-great-mathematical-problems
• https://www.goodreads.com/book/show/208916.The_Music_of_the_Primes

[remote sparrow]

idk either

[hollow drum]

This look great thank you so much

[strange coral]

Ook. Thanks for your suggestions!

[spiral sky]

Is the book "field and galois theory" by js milne a good book for galois theory? I have background of abstract algebra and some galois theory

[signal zenith]

<@&268886789983436800>

[signal zenith]

They’re mentioned in most low dimensional topology books. For example, “Lectures in 3 manifold topology: an introduction to the Casson invariant” by Sobaliev includes a proof that they’re generated by Dehn Twists if I’m remembering correctly (I did a reading project on this book last sem)

Though I don’t recall going too in depth into them

[remote sparrow]

i like david cox's book on it, but it could be too introductory for you

[timber mesa]

I don't think this person is advertising their own service and there indeed are some free resources in that webpage

so it's fine

[signal zenith]

Ok fair enough. I thought it was sus bc they joined pretty recently

[shut yew]

i am newbie in math

what book should i read

[spark jay]

Thanks

[mystic orbit]

this tells us nothing about your background

you could start anywhere from "basic mathematics" by lang to "artin's algebra" or "abbott's understanding analysis"

[shut yew]

i just know basic mathematics and i am going to join a competition in next year

[mystic orbit]

so you wanna do competition math?

[shut yew]

yeah

but next year

i just prepare for it

[mystic orbit]

you can do the art and craft of problem solving

[shut yew]

and i want reading book to boost my vocabulary too

[shut yew]

online book ?

[mystic orbit]

it's a book

I dunno whether it's online or not

you can google the name and you should find a pdf lmao

[mystic orbit]

don't read math books to learn english

it only sounds like a good idea in theory

[shut yew]

check dms

[shut yew]

am not

[trail tundra]

@sour haven here you go, here’s the book! http://www.wallace.ccfaculty.org/book/Beginning_and_Intermediate_Algebra.pdf

[sour haven]

does that cover all of algebra?

im asking because i don't want to get confused thinking ive covered most of the algebra

[trail tundra]

there’s some stuff it doesn’t cover like matrices, conic sections and trig but you’ll be able to find those elsewhere. it’s generally a good practice to learn from multiple textbooks at once anyway, cause some miss out on things that you can easily get from others

[sour haven]

can i cover these with khan academy algebra, clculus etc

in 1 year and 10 months i have final exams ,physics,maths,chemistry , im a complete 0

[trail tundra]

i wouldn’t say you should use khan academy as a single thing to learn from, although it is a very good resource to use. and calculus is another thing entirely that you’ll be able to find a textbook for

[sour haven]

okay

[trail tundra]

textbooks are generally the way to go with learning imo, cause they explain concepts in much more depth than you’d get from a youtube or khan academy video. but they are still helpful to aid your learning journey

[sour haven]

what about algebra (all of it)

[sour haven]

I think you are right

[trail tundra]

just start with the book i linked first, then you’ll be able to find some other textbooks that cover algebra 2 and trigonometry

[sour haven]

wait, algebra 2 ?? what is this

my class was doing that f(x) thing before schools ended

[trail tundra]

it’s beginning and intermediate algebra, so it has mostly algebra 1 with a tiny bit of algebra 2

[trail tundra]

ah you were learning about functions?

[sour haven]

so need to worry?

[sour haven]

yes, but i know nothing

[trail tundra]

no, and it’ll be good to go over the foundations anyway. especially since you don’t know anything rn. if you don’t know anything about prealgebra, then definitely read up on that as well cause getting your foundation is the most important thing. you can’t build off anything if there’s nothing for you to build off

just take your time to really make sure you understand things before moving onto the next topic

[sour haven]

i don't know what pre algebra is (that name) but i definitely know most things about it

english is not my native language.

[trail tundra]

ah okay, i see

okay we should move back to #math-discussion

[gray gazelle]

What are some books about probability, stochastic processes and maybe stochastic calculus aimed at pure mathematicians instead of aimed at applied ones?

[crimson leaf]

What's your current level

[gray gazelle]

I know basic measure theory and Lebesgue integral stuff, I also know basic stuff about metric spaces and topology and I know what Banach spaces are. There's other things I know about like some agebra, cat theory and model theory but those are probably not as relevant

[crimson leaf]

Yeah I was going to say Billingsley but that might be below your level, probably worth a look anyways though, maybe Lawler's notes though they're not complete afaik https://www.math.uchicago.edu/~lawler/probnotes.pdf

[remote sparrow]

i heard le gall is good

https://link.springer.com/book/10.1007/978-3-319-31089-3

small warning about billingsley; the fourth edition allegedly has a lot of severe typos. go with the third edition instead.

[small silo]

what are precalc and calc books that transition almost seemlessly when learning calculus

also should i get a algebra separate book with pre calc too or is just precalc enuf?

[remote sparrow]

you could use stewart's precalc and calc books

[spark jay]

For concepts u can go for 3blue1brown series on essence of calc and calc made easy
For learning how to use - Stewart
For rigor - spivak or apostol

[remote sparrow]

lang's Basic Mathematics would go well with spivak or apostol

[willow merlin]

Book that explains orthogonal projection of two vectors or between a vector and a subspace

oddly specific

[cursive orbit]

any linear algebra textbook

[willow merlin]

Im reading intro to linear algebra by anton and can't find it

Are u sure

@cursive orbit

[remote vortex]

"Elementary Linear Algebra" by Howard Anton and Anton Kaul does cover orthogonal projections

In several sections, in fact

[umbral field]

projecting onto vectors chapter 3.3 projecting onto subspaces chapters 6.3-6.4

[willow merlin]

Found it ty

[remote vortex]

Protip, most books have an index at the end

Which lists the pages where you can find a specific topic

[willow merlin]

Yes, srry

[remote vortex]

I honestly assumed you might not have known that indexes are a thing

[willow merlin]

Yea

[gray gazelle]

how much algebra do you need for algebraic number theory? emphasis on the word need

[spiral sky]

I'm also interested about this, but not for ANT but class field theory

[sage python]

Well CFT is just gonna be an outgrowth of ANT

[spiral sky]

I watched a series of videos on YouTube by math curator zanachan, and really got lost in every single one, I know minimal galois theory that's probably why

[small silo]

i just didnt see many people online who were following these two books in order so i figured it wouldnt have many resources

[trail hemlock]

stewart is extremely popular. larson is good as well (they are basically the same)

[small silo]

btw do you think i would need to follow a separate book for algbera or precalculus is fine?

[trail hemlock]

i mean

did u take algebra I and II in school?

maybe do some khan academy but i cant justify reaeding an entire algebra textbook just for stewart or larson

[foggy quest]

I read a lot from "Brownian Motion and Stochastic Calculus" by Karatzas and Shreve, and it was very mathematically solid.

[sudden kindle]

Class field theory is yummy

Scrumptious even

[mossy relic]

Does anyone know what book (or website?) my professor gets these differential equations from?

y = xsin(x+c) [eliminate c]
cosydx + (1+e^-x)sinydy=0; x=0,y=pi/4

Our assigned textbook didn't have questions like these so I kinda wanna see more of these problems which I found difficult during the test.

Book where these are from? Or DE book reco with hard problems and answers

[tawny crater]

does anyone know of a more lighthearted logic book than a mathematical introduction to logic

i don't know if it's possible - the book is already pretty lighthearted, it's just the subject which can be tedious

a lot of dry manipulations

especially sections like 3.3 it's too detailed for me and i don't understand the bigger picture

[remote sparrow]

what book are you reading

[tawny crater]

a mathematical introduction to logic by herbert enderton

[remote sparrow]

https://milneopentextbooks.org/a-friendly-introduction-to-mathematical-logic/

https://www.amazon.com/Propositional-Predicate-Calculus-Model-Argument/dp/1852339217

[tawny crater]

thank you

[slim nacelle]

Homological algebra (group cohomology) mostly

That and basic familiarity with local and global fields and their absolute Galois groups as profinite groups, and Adele rings

[edgy pulsar]

#❓how-to-get-help Hi all!
I need textbooks for GED test prep. Specifically, GED Mathematics and GED Science. If you have GED Prep books, please share with me.

[spiral sky]

Thanks a lot! This could be a lifetime learning project!

[slim nacelle]

yeah it could also be something you learn over the course of a summer or a year

[spiral sky]

I said that bc from past seminars I've seen it seems that absolute galois group over the rationals is profound object of study, "mysterious" they called it

[slim nacelle]

indeed it's quite mysterious

class field theory is much easier than the general picture around this though

class field theory tells you just about the Abelianization of the absolute Galois group, that is the Galois group of a maximal Abelian extension. This is WAY simpler than trying to describe the whole non-Abelian mess

[spiral sky]

Oh I see, I'll remember it as my intuition when I approach this, thanks again

[pliant wadi]

Is there a book out there that talks about the history of model theory and logic from any point of time?

[wispy moss]

calculus book ?

[torn crypt]

Hodges includes some data in his chapters about like, here’s some historical or bibliographic data

There’s probably some biographies about particularly famous logicians

But idk any further than that

[vital snow]

does anyone have any good book recomendations to study for a putnam problems? I vaguely know what the problems are asking I just dont know how to get there or what field of math it requires

[molten gulch]

stewart

[small silo]

spivak

use stewart though

spivak only if you want tough problems while studying stewart

[spark jay]

for a beginner the language might be a little tough and the ques too

[dawn echo]

good introductory texts for algebraic k-theory?

[mellow wren]

Weibel's book for the classical treatment and there's a set of notes by Florian Adler for the more modern treatment using infinity categories
https://florianadler.github.io/AlgebraBonn/KTheory.pdf

[dawn echo]

Thanks 🙏

[pliant wadi]

Ah, thanks. Gotcha.

[remote sparrow]

well, for one thing, logic as a mathematical discipline (obviously philosophical discussion of logic existed far before) has only really existed since the early 20th century. it's a fairly modern subject compared to analysis and algebra.

i'm not sure there can be a proper history of model theory in particular for now.

one might be able to say "so-and-so fact was discovered by so-and-so person on so-and-so date," but proper historiographical analysis is currently lacking

[torpid stump]

Stewart all the way. Or if you want to challenge yourself use Spivak's text and then get some real analysis texts like Abbott or Baby Rudin.

[remote sparrow]

what interests you more?

[torpid stump]

Abstract algebra 100%

[remote sparrow]

doing abbott after spivak is mostly redundant except for the fact that abbott goes over the topology of the real line

[remote sparrow]

#book-recommendations message

[torpid stump]

In my opinion

It is what I did

[remote sparrow]

i did stewart and just moved to abbott

#book-recommendations message

linear algebra suggestions

[gray gazelle]

how did you find that transition?

[torpid stump]

Sorry I don't get it be a bit more specific

[gray gazelle]

just curious as to how easy the transition was for you from spivak to abbott

[gray gazelle]

also if you've already had a gentle introduction to algebra and are really interested in the subject, I'd recommend D&F. it's encyclopedic af but it really gives you all the details, lets you explore a lot of topics that might not be offered at uni

fair enough

oh wow

yeah Rudin is no joke

how long did it take you to complete abbott?

[torpid stump]

I was working through them simultaneously and I completed Abbott about 1 week ago, while I completed Bartle and Sherbert just yesterday.

[gray gazelle]

congrats!

[torpid stump]

Thanks!

I don't know why I choose that emoji

[gray gazelle]

hahahahaah

[torpid stump]

This one is better

I am in high school so time was also quite limited

[vital snow]

any intro number theory books?

[torpid stump]

This channel inspired me so much though: https://www.youtube.com/@mathematicaladventures

[torpid stump]

An Introduction to the Theory of Numbers, by G. H. Hardy and Edward M. Wright.

Best book on number theory

[gray gazelle]

enviable days!

[trail hemlock]

u read abbott's analysis and now ur doing rudin?

why

[torpid stump]

Just to get a better understanding of the subject

Also for fun

[vital snow]

thanks. any for linear algebra?

[torpid stump]

I enjoy challenging my self

[torpid stump]

I don't know sorry

Ask anyone else

[gray gazelle]

first or second course?

[trail hemlock]

is rudin not a superset of abbott's coverage?

and depth

[vital snow]

both

[torpid stump]

Correct. But as I said I enjoy challenging myself.

[trail hemlock]

ok

[torpid stump]

And it is not like I am in university and I have to stick to one book and finish it quickly. I am self-studying.

[gray gazelle]

for first course I recommend a freely available book that I used for my uni course:

https://lyryx.com/first-course-linear-algebra/

for a second course (proof knowledge preferable):

linear algebra done right

[torpid stump]

I worked through all three simultaneously

[trail hemlock]

i think FIS is a great LA book

[torpid stump]

Just didn't finish Rudin yet

[vital snow]

thanks

[trail hemlock]

yeah the recommendation is to read chapters 1-8 and use a different text for multivariable

im nearly done wih ch7 lol

[gray gazelle]

the first book has some applications to chemistry and physics which you can skip

[trail hemlock]

but my apush hw 😔

[gray gazelle]

like balancing chemical equations and resistor networks

one complaint i have is that vector spaces are introduced rather late, but i digress

[torpid stump]

@gray gazelle Check this channel out: https://www.youtube.com/@mathematicaladventures/videos

It inspired me

[gray gazelle]

oooh will do, thanks for the recommendation

very cool i'd say! self-studying is really cool

[torpid stump]

👍

[remote sparrow]

no one goes past chapter 8

[sturdy jasper]

Have anyone read no longer human?

input on the book would be good

[normal crystal]

Can I guess you were inspired by a recent anime?🤡

[sturdy jasper]

Nahh i heard the author suicided after writing that book..

so uhh have u read it?

[normal crystal]

tbh, I feel like I did read part a long time ago, but I'm not sure
I've read other Japanese novels from that time period

[normal crystal]

I'm not sure what you mean by that other than stating historical fact
but I meant there is a current anime using Dazai as the MC in a fictional setting

[torpid stump]

[remote sparrow]

nothing bleak about that, the exposition past chapter 8 isn't good

it's much more worth it to use other books

[copper glacier]

Dude, I'm trying to learn basic math, but I already have a base, it's not very good, does anyone have any tips?

[remote sparrow]

relearn whatever counts as your "base" until you want to say it's good or very good

[copper glacier]

I'm currently trying, I'm almost finished with the base, it even includes complex numbers

[trail hemlock]

bit of an off topic book request, anything yall got for AP bio? not the prep books, like a textbook that follows the curriculum

like how larson has the ap edition of his books

something thats a bit dense, cuz i think bio is rly interesting

[normal crystal]

there probably are AP editions of the main Gen Bio college texts, but why bother
Campbell, Sadava or Hartl is fine

[trail hemlock]

yeah campbell

is what im going with

[remote sparrow]

i used campbell for hs ap bio

[trail hemlock]

yay

me 2 frm now on i guess

[remote sparrow]

nothing special, it was just my assigned textbook

[copper glacier]

Do you have any algebra books to recommend something intermediate?

[trail hemlock]

aops has 2 algebra books

[copper glacier]

aops?

[trail hemlock]

https://artofproblemsolving.com/store/book/intro-algebra

https://artofproblemsolving.com/store/book/intermediate-algebra

wait do u mean like abstract algebra ?

[copper glacier]

no, not the same

I want to increase my algebraic manipulation, I want to improve my mathematics before starting in electrical engineering, here on the server how far do you learn mathematics so I can know?

[trail hemlock]

any algebra workbook should suffice, and as sour drop said, whatever you count as your "base" is what you need to drill and kill

[copper glacier]

ok, I had doubts regarding the progression I should take to expand my knowledge in mathematics, I started with algebra, followed by arithmetic, then geometry, trigonometry, spatial geometry, complex numbers and finally combinatorial analysis and probability, would it be correct to follow this list? I saw it in some places, but I don't know if it's really the right thing to do

[trail hemlock]

yeah that sounds good

but you should be asking if it fits your needs, as a prerequisite to EE

[copper glacier]

yes yes, they are prerequisites since I will see calculus 1, 2, 3, 4 and I will also see many aspects of this content, I am a technician in the area but I am not as familiar with mathematics as you, I just have the knowledge from school

[trail hemlock]

you are probably more familiar with math than me, im in Hs.

[copper glacier]

sorry I'm young, I'm 20 years old but I really have trouble understanding abbreviations lol

what is Hs?

[trail hemlock]

high schol

[copper glacier]

ha

I don't feel that way, I see the server full of calculations and questions that I would love to ask, but lacking knowledge, I was very interested, so I wanted some light so I could better understand these questions.

[trail hemlock]

yeah so follow an algebra book, aops is good, so is Lang's basic mathematics, or khan academy

[copper glacier]

ok nowadays I have 100% of my time to dedicate myself to studying I'm going to start reading some books tonight I'm going to follow Khan Academy.

[trail hemlock]

fire

[winter ice]

hi do you have any recomendations about advanced algebra books about 3d projection into a plane, and transformations

[fresh skiff]

Advance algebra reminds me of Homological, commutative, noncommutative algebra etc

[signal zenith]

Sounds like you’re looking for a linear algebra book?

Those are the books that will talk about projections of 3d onto planes

[swift eagle]

I am an undergraduate student in mathematics. I feel that my knowledge in mathematical analysis, particularly in integration (indefinite integrals, definite integrals, improper integrals), is insufficient for dealing with ordinary differential equations and electromagnetism in physics. The focus on proofs means that I cannot solve these integrals. any book recommendation？

[remote sparrow]

open a book like stewart

there's plenty of problems to practice with

[lethal plinth]

hello, can anyone share maths book for questions?

[swift eagle]

thank you

[pliant wadi]

Ah makes sense, thanks

[restive nexus]

Complex analysis with applications by grafakos and asmar is a really good read imo

One of my top 10 reads of all time

[torpid stump]

Is the Alfhors book good?

[restive nexus]

Haven't read it so I don't really know

[torpid stump]

Ok

[restive nexus]

I liked grafakos because when you're in your first few semesters you like to see more computations from time to time which the book covered by giving you a problem to solve as well as a solution. There are also a bunch of other exercises which can go over a few pages

And a bunch of pictures. Most math books don't have any pictures at all

[torpid stump]

Alright.

[torpid stump]

I don't really prefer colorful picture-y books

[restive nexus]

I think it's the only book I've ever seen use colored images lol

The pictures in the book helped me a lot personally but ig you could wait for someone else to give their opinion as well

[torpid stump]

Yeah. Thanks anyways

A challenge for someone to answer. Can someone provide book recommendations from all math subjects in high school, undergraduaute math, and graduate math. There should be two books each (at least)

[winter ice]

probably, if you have any recomendation on a book or a pdf, would be great

[signal zenith]

Tbh I don’t actually know what’s usually used for lower division/calculation based linear algebra

[molten gulch]

narasimhan's book and freitag's 2 volume set I think are 2 good options, gonna wait for more ppl to weigh in

[torpid stump]

Thanks

[novel hound]

How hard is Freitag, say compared to Ahlfors? Can it be handled after say baby Rudin and/or whether it would be better to do an intermediate complex analysis book like Gamelin before?

[torpid stump]

Many people say Spivak is too hard

[novel hound]

Abbott and his book are inspired by Bartle so I feel like it would be better to pick something else for a second pass (just for variety).

[torpid stump]

Ok

What would you recommend as a second pass

[novel hound]

Apostol and Rudin together perhaps. But, only if you like Apostol's style.. can be a bit dry.

[torpid stump]

I saw it on pdf, his calc book.

Didn't like it

[molten gulch]

Rudin

[torpid stump]

Or

[molten gulch]

Stewart -> Abbott -> Rudin

[torpid stump]

I can use all three of them

[molten gulch]

AFAIK is a p, common way of doing things

we're very very slowly doing abbott ourselves rn

[torpid stump]

Stewart -> Abbott and Bartle -> Rudin

[molten gulch]

we used Thomas for single variable and stewart for multivariable calculus (school switched req'd books on us grrr)

[torpid stump]

@molten gulch Is it like a disorder or just choice? The DID thing (if you don't mind telling me just curious)

[molten gulch]

disorder

we'd never wish on anyone else the types of things we've seen that fucked us up this bad

[torpid stump]

Oh

I am sorry man

[molten gulch]

it's fine

[torpid stump]

Hope everything goes well

[molten gulch]

surviving day by day

[torpid stump]

Good luck in your mathematical endeavors!

[restive nexus]

I know someone with DID on a different server. They use tupperbox for each personality

[molten gulch]

yeah we want to do everything which is kinda impossible, and the reason this madness exists

[torpid stump]

Don't you guys prefer physical books

[molten gulch]

the only physical maths textbook we have is our copy of thomas calculus

[torpid stump]

https://www.bookfinder.com/

Best website ever

[restive nexus]

I have a bunch of unread books in my shelf just because it's neat to have them

[torpid stump]

Yes

[restive nexus]

And from time to time I'll just look through them which is really fun

[torpid stump]

It's fun to spend money

[restive nexus]

Relatable

I made a meme about this a while ago

https://www.reddit.com/r/mathmemes/s/NNMNw7RTRd

[torpid stump]

Lmao

[molten gulch]

@torpid stump do you mind if we send you a friend request too

[torpid stump]

No at not all

I love making friends

I sent you one

My parents may be against it

Since I am a tiny 14 year old

[restive nexus]

Damn you're doing math at 14?

Based

[molten gulch]

math at 14 is quite normal

[restive nexus]

Not that kind of math

[molten gulch]

yeah we use pluralkit instead

[restive nexus]

I started real math at 16 but only because I knew someone who was into it

[molten gulch]

we started at....19?

so last year

[restive nexus]

Before that it was only YouTube videos and Wikipedia

[restive nexus]

Same

I'm 17

[restive nexus]

Wait I think I was 15

I can't count

December 2022