book-recommendations

[royal bone]

I am searching for school geometry book WITHOUT stuped colorfull drawings , in which will be coverd every school geomatry topic with problem practice and priblems should not be elementary like those you give to a stuped student to boost his confidence and self esteem by solving those elementary problems

[copper axle]

euclid elements

Apollonius conics

things like that?

[royal bone]

school book

not sciefintic

[sterile pelican]

Lang has a good geometry book for a high school student

[royal bone]

most of tasks are 0 lvl

I am starting to think that there is no good geometry book written in english

[copper axle]

Probably some math olympiad books

[elder stratus]

looking for book recommendations on geometric combinatorics and any prerequisites for that

[royal bone]

I do not need olimpiad lvl problems. I need normal and hard lvl school problems

[elder stratus]

for a geometry book try: pogorelov’s geometry

you should be able to find a pdf just by googling

part 1 and 3 should be of relevance to you, ignore the rest

[hollow shore]

which one?

[sterile pelican]

It's called "Geometry: A High School Course" by Serge Lang

However it isn't your standard geometry book that you see in schools

[glad perch]

Hey I'm trying to learn complex numbers what books recommend?

[iron heath]

I'm interested in the intersection between mathematics & philosophy so a book I find very interesting & recommend is "When Einstein Walked with Gödel - Excursions to the Edge of Thought" by Jim Holt

[oblique hatch]

What prerequisites are there for Silverman’s The Arithmetic of Elliptic Curves?

[sterile pelican]

One other book I recommend is "Gödel's Theorem Simplified" by Gensler

[iron heath]

thanks! ill look into it!

[sterile pelican]

It's a mere 85ish paged book about Gödel's theorem and what it inherently means. The author requires you to know only some high school maths, knowing logic is good though, and pulls no punches of what is Gödel's theorem signifies, and is far better than most videos out there.

[iron heath]

My library system seems to have every book on Gödel except this one, lol. Gonna check out my favorite bookstore for it this weekend. This sounds like a fascinating book.

NGL though this search brought up some VERY interesting related book suggestions! I definitely appreciate the suggestion @sterile pelican !

[hearty tree]

anyone doing a level maths here

[remote sparrow]

kiselev's geometry volumes

[hearty tree]

oh ok sorry

[royal bone]

i will search that

[vagrant thistle]

Hey y'all. My son is 11 years old and has been consistently into maths for few years now. He's finally at the point I feel he can start to learn by himself. I have Ka Strouds engineering mathematics that i used for my engineering studies, but I would like a more "pure" maths book for him, but similar to ka strouds, that quickly covers the basics and carries him into more advanced maths.

I think he finds it cool to have a massive book of maths, so a single tome is not a drawback or scary

[viscid hemlock]

TheMathSorcerer has great book recommendations. I'm not sure whether this is listed here. He has a youtube channel and reviews lots of math books

[pine tundra]

https://youtube.com/playlist?list=PLO1y6V1SXjjM-1azbCNYq2-A1_7KaioNr&feature=shared

Also this https://youtube.com/playlist?list=PLq42v-9QqE1Taf9RlihKYgm2lWgO5Bbwj&feature=shared and this https://www.youtube.com/watch?v=aCcoq6U-4sQ might help

[vagrant thistle]

Thanks! Great, I'll check those out

[remote sparrow]

could you let us know what your son has previously covered?

[vagrant thistle]

I havent wanted to interfere too much until now with what the school is teaching. He's at powers now in school

He says he wants to become a physicist (i know.. i know, but still, it's what he wants, so while he wants that, I'll put the books in front of him)

So that means pretty basic so far, arithmetic and no algebra so far.

[remote sparrow]

https://www.hachettebookgroup.com/imprint/workman-publishing-company/page/big-fat-notebooks/

you might appreciate the big fat notebooks

khan academy will also be helpful

[vagrant thistle]

I would like to avoid screens, we're not super strict, for a few more years he wont have a screen with internet in his room

[remote sparrow]

the big fat notebooks are available as paperbacks, but i can understand keeping your son away from screens

i would like the pre-college math curriculum to be more rigorous (although certainly without making the mistakes of the new math of 1950-1970s), but i don't believe any such books exist yet. hung-hsi wu has written some books for math education researchers and teachers about pre-college mathematics

https://math.berkeley.edu/~wu/

[north heron]

Hello, i'm looking for books with exercices about norm and vectors sequences convergences ( with corrections ), do you know any please ?

[sick river]

Any introductory books in knot theory for someone with a standard graduate level mathematics background?

[flat marten]

Not quite a book, but I'm looking for a lecture series for logic, looking to pair it with logic and structure (van Halen)

[prime oak]

i read rudin, then bartle and sherbert, then rudin
i didnt have any problem understanding the chapters i read in my second reading, i understood nothing in my first reading

recommendatiosn for introductory reading in algebraic geometry?

[remote sparrow]

hartshorne

[sterile pelican]

[heady glacier]

💀

Fulton algebraic curves is more beginner friendly

Vakil and Hartshorne are excellent books though

[sterile pelican]

Cox, Little, and Shea's book called "Ideal, Varieties, and Algorithms" is my personal favourite

[heady glacier]

If you want a fuller picture including Grothendieck’s development of the study

[sterile pelican]

They are but not as a first book :^)

And Hartshorne scares me too much

[fierce hedge]

Is that the same cox as in cox Zucker machine?

[sterile pelican]

Very likely

:^)

[sterile pelican]

Just checked and yes the same David A. Cox :^)

[fierce hedge]

Lmao, nice

[royal path]

Is Gilbert Strang's calculus book any good

I'm just starting out, I want to get a complete conceptual understanding

Most books i currently have on calculus are pretty dry, memorizing formulae and other crap

[royal path]

'Cox zucker machine' 💀

[sterile pelican]

I don't know about Strang but I do like Serge Lang's Short Calculus :^)

But since Short Calculus is Single variable you would also need to get his Several Variables Calculus book

[cold elbow]

naw 💀

[fierce hedge]

I mean it's real - https://en.wikipedia.org/wiki/Cox–Zucker_machine

[cold elbow]

no way

[open laurel]

mathematicians gotta have fun too

[sterile pelican]

Who says mathematicians has no humour?

[cold elbow]

not me def

mathematicians has W humour

[royal path]

Bruh

[nova copper]

Recommendation: maths books are lame and a waste of time

Read lecture notes like a real man 🧑‍🦽

[fierce hedge]

I wonder if I should sully this or so true this

[elder stratus]

lecture notes are kinda based actually

but books have their place as references for sharper/ more general versions of things

[fierce hedge]

Yeah but you need to read books to make lecture notes

[nova copper]

Aye let’s be real here math majors do not need books

[fierce hedge]

Not you per se but the instructor had to

[nova copper]

Waste of time

[fierce hedge]

[nova copper]

Just give me the definitions and theorems and move on thanks

[finite gale]

L take

[nova copper]

Interested to see someone else’s take

[elder stratus]

books are the bricks that shoulders of giants are built with

[fierce hedge]

This is probably one of the most L takes since the dawn of humanity and humanity has taken a lot of Ls

[nova copper]

Tell me why

Genuinely curious

[elder stratus]

what are books if not refined and well organized lecture notes?

[nova copper]

A waste of time I’m telling you

[fierce hedge]

Cause like lecture notes are not standardized, one almost always recommends standard books. Plus a lot of books started as lecture notes, they are usually more refined

[nova copper]

All you need is some proofs, that’s the entire point innit

[fierce hedge]

NO, wtf

[elder stratus]

also you can burn books in case of emergency

[nova copper]

Ok bra applied sciences I see kinda cringe

[elder stratus]

what a measly fire lecture notes will provide you

[fierce hedge]

I should ask someone more advanced to explain

[royal path]

Yes. The books you're criticizing are written by people better than you 'innit'

[finite gale]

Or take this to #discussion instead

[fierce hedge]

Yo @fallow cypress would you like to add something here

[royal path]

Go drink milk and do basic arithmetic

[nova copper]

Absolutely not arguing on that

[fierce hedge]

This is very fair actually

[nova copper]

That does not mean I will read them

[royal path]

Yes. Thought so

[nova copper]

Kinda disappointing arguments here

Have a good one

[fierce hedge]

Discussy is more suited for this

[elder stratus]

fact: lecture notes contain less content than books

boom

[royal path]

Petition to add debate channel

[fierce hedge]

Bro disappointed that he couldn't have beef LMFAOO

[finite gale]

That's just discussy

I don't think there's need for personal attacks here

[royal path]

Yup sorry

That was a dumb thing to say

[nova copper]

No offense taken pal 🙂

[royal path]

🙂

[amber inlet]

So does that mean lecture notes or handouts are better than the books itself?

[sterile pelican]

It depends on the individual really. Lecture notes to me are useless unless the lecturer can properly motivate you the ideas behind it, because lecture notes are super concise over say a book. In addition, the lack of exercises from said notes is just as useless since maths isn’t a spectator sport.

A good book must encompass a narration of ideas then properly test those ideas conceptually, especially as a first course

[pine thunder]

topics:
measures of central tendency.
measures of dispersion
introducing to correlation
introducing to regression
curve fitting
i want a boik with these topics plz help and thanks

[turbid fox]

Hi, any good book recs for enumerative combinatorics? I have a background in group and ring theory, linear algebra, real analysis, am mostly interested in puzzle-type combinatorics rather than anything too deep atm. I’m not too versed on the branches of combinatorics so I hope my last request is not silly

[remote sparrow]

A Walk Through Combinatorics by miklos bona

[turbid fox]

thanks for the speedy reply

[worthy karma]

Does anyone have some good reccomendations on books for learning PDEs? I've taken an undergrad level course in Real Analysis, Differential Equations, and Linear Algebra already

[subtle fractal]

any good books with complex numbers(geometry) im just looking for problems preferably imo to bmo level

[gray gazelle]

book for engineering mathematics??

[iron heath]

thank you for this recommendation! My daughter is preparing for the high school entrance exam rn and she struggles in math. She has a tutor, but I want to help her feel as confident as possible as she's going to need to practice math a little every day until the test. This book looks like it might present math in an interesting and colorful format to be more memorable. Very grateful for this suggestion. Thank you! 🙏🏽

[iron heath]

Why do you say that? I'm a math major and I wish we were using a book. Mainly to have more practice problems and to make sure I thoroughly understand the concepts. Having to search all over the world for additional resources like YT videos to explain what my Professor insufficiently explained once already is annoyingly time consuming. I definitely prefer a textbook, though I can admit I am usually an outlier. My mind works different than others usually. So I am genuinely curious why you say math majors don't need books?

[nova copper]

A big part of getting better at university pure mathematics for me has been writing and reading proofs. A wordy text takes away from the main idea imo.

[iron heath]

oh yea... I agree for proofs. I had an EXCELLENT Pre-Calc Professor once who had basically created his own condensed version of a textbook and his explanations were so short and sweet ESPECIALLY when it came to proofs. I loved it so much I asked him what book was the pages from that he was giving us so I could go buy it. That's when I found out he just made them himself. He felt the same way as you - that regular textbooks were much too wordy. Thanks for answering. Now I understand.

[nova copper]

To elaborate a little bit: when I compare courses that work with lecture notes (that is the structure of definition-lemma-proof-theorem-proof) to courses that use textbooks I find the ones with the textbooks to be so bothersome and time wasting

Like idfk about your literary wording and philosophy stop wasting my time pls

[oblique hatch]

For me it’s been very hit and miss whether textbooks or lecture notes are better
I’ve only ever fully read 3 textbooks (Ahlfors, Rotman Intro to theory of Groups, Silverman and Tate)
But like… CA was something I could never get through lecture notes, Rotman is like a massive cross section of stuff that might be covered over 2-4 courses
And Silverman and Tate was my brain deciding it just wanted to consume a book, at which point more detail is better

[wide ruin]

Hi, I'm a software engineer, that, back in the day, used to hate math 😓 and now I'm re-discovering and really liking it as, as I've become senior I'm being tasked with stuff that needs math (it's hard when you don't know much math T_T), I would like to take math seriously from now on, and I'm looking, for a set of books to accomplish that objective, I'm absolutely fine by studying by myself and books is my go-to option as I find them to be quite relaxing, I would need to start somewhere around geometry and trigonometry, as that's as far as my knoweledge goes, I know nothing about pre-calculus onwards, please recommend me some books! I really need them ❤️

[sterile pelican]

Like I said earlier it depends on the individual really. For me Lecture notes are useless unless the lecturer can properly motivate you the ideas behind it. I need to know why I should care about this theorem/proof. For me lecture notes are too concise to give me a damn of said ideas over say a book.

In addition, the lack of exercises from said notes is also just as useless for me, since maths isn’t a spectator sport. For me at least good book must encompass a narration of ideas then properly test those ideas conceptually, especially as a first course.

As you go for a more graduate level then books tends to be more concise, and thinner, so I can understand at that perspective where you don't beat around the bush at all. But books like Silverman, Anderson, Cox, Hodges and Bloch, gives me either the nitty gritty details, the historical reasons, and of course the exercises that yield interesting results.

[subtle fractal]

https://artofproblemsolving.com/store/book/intro-geometry .(geometry) https://www.cfdyna.com/Home/Maths/Trigonometry-Loney.pdf .(trig) https://theswissbay.ch/pdf/Gentoomen Library/Maths/Calculus/Michael Spivak - Calculus.pdf. (calc)

[nova copper]

I mean as long as the course includes proper exercises, which it always has for me I mean it’d be ridiculous if there wasn’t any, I find I learn a lot more from trying to figure out what it’s all about myself. That’s the one thing that has really clicked with me. I however retract my obtuse statement and admit that at the end of the day it is very subjective.

[wide ruin]

Thanks! Can I read this calc book without having done pre-calc? I may have said that wrong, I haven't done pre-calc

[subtle fractal]

yup

[wide ruin]

one last question, keeping in mind that I read those books, when should I read about linear algebra, after those 3?

[sterile pelican]

Most good books in my view should at least give you a sort of landscape, albeit geometric, algebraic, analytic, and all. But yeah I agree some do not like that but I am sadly not like that. For me at least I see textbooks as how I see novels if written well you get an imagery of what these objects are, while bad ones wastes your time and money

[subtle fractal]

idk depends on you

[nova copper]

Wonderful take, thank you!

[sterile pelican]

You're welcome!

That was an interesting talk though

[nova copper]

Absolutely what I was hoping to find in the end

[subtle fractal]

if you need complex numbers i would recomend this https://thunhan.files.wordpress.com/2008/08/tituadreescu-complexnumbersfromatoz.pdf read to page 30 and if you need vectors https://www.math.mcgill.ca/rags/JAC/DDB/VectorNotes.pdf (note read vectors first)

[wide ruin]

thanks again, I will make good use ❤️

[subtle fractal]

i hope so

[gray gazelle]

does anyone have a recommendation for probability that also covers the measure theory part?

[fierce hedge]

You couldn't possibly have found high quality lecture notes for every maths topic unless you're at uni

[fallow cypress]

This is based, learn all mathematics by emailing random professors and getting them to explain stuff to you instead of via books

[fierce hedge]

Omw to email riehl to personally teach me cat theory via email

[fallow cypress]

stanley enumerative combinatorics is standard and comprehensive

but kind of a slog to read through personally even though the results are cool

😭

[nova copper]

very true, my university makes them available to us

though going on a proper search could get you very far more often than not imo

[finite gale]

why even go to class at that point

[sterile pelican]

Why even pay tuitions at this point?

[scarlet pumice]

Anyone got any recommendations on books/resources to prepare myself for math in university? I haven’t done any difficult math in ages now and I will be doing calculus one variable and linear algebra in 5 months.

[finite gale]

if you're going to do proof based math, you could always familiarize yourself a bit with proofs i guess

you could also choose to start reading ahead a bit if you want

but only do as much as you actually want to since you won't want to be burning yourself too early

[scarlet pumice]

Anything specifically for engineering?

[sterile pelican]

For some reason seeing the twist of engineering at the end sounds like putting a knife behind the proof book's back

[wooden cape]

Besides academic books, what books do you guys recommend reading in your free time?

[sterile pelican]

Read "lighter" academic books or papers

[gray gazelle]

։

[old elk]

What book do you recommend for differential geometry, I am finishing my studies in analysis and linear algebra?

[cold elbow]

any free good calc books

[old elk]

I was selecting for Do carmo but I see it as quite complex.

[white wolf]

#prealg-and-algebra message

[turbid fox]

I’ve had a look at that one, but I think it’s out of my head atm. I am hardly even familiar with any of the topics mentioned in the chapter of vol 1, and I’ve not done an intro combinatorics course yet. My only exposure to the subject is just picking random problems from problem books

[fallow cypress]

Yeah fair enough

[turbid fox]

either way thanks for the suggestion 😅 combinatorics is a future focus

[crimson leaf]

An easier one I like is by Guichard it's free on his website: https://www.whitman.edu/mathematics/cgt_online/book/

[wary compass]

Could anyone recommend textbooks for studying fractal geometry? I'm using the Falconer book, but I'm looking for another one to complement it, maybe from a little different perspective

I heard that a short book by Hillel Furstenburg called Ergodic theory and fractal geometry is good, but I couldn't find a pdf version online..

[glacial spire]

What's the standard textbook on inverse problems?

[cold elbow]

can anyone recommend me free problem books for calc and other high school materials

[finite gale]

Khan academy

[warm veldt]

Try calculus by I.A. Maron

[heady glacier]

“Fractals Everywhere” by Barnsley is a phenomenal text

[wary compass]

Great, I'll take a look

[cold elbow]

tytyty

[remote sparrow]

https://web.archive.org/web/20210413023953/math.ucdenver.edu/~jmandel/classes/5070s08/analysisSyllabus-08.htm

the original website is down but luckily it's archived

it's a prelim exam syllabus for applied analysis

includes rudin and schroder

[fierce hedge]

Is everything archived?

I'll archive a copy in any case

[remote sparrow]

well it's just a syllabus

[fierce hedge]

No homeworks or assignments?

[remote sparrow]

there's selected exercises from rudin

and the author said every exercise from schroder from the required sections is good prep for the prelim

[fierce hedge]

Interesting

[remote sparrow]

it's not a syllabus for a class, it's a syllabus for a preliminary exam

like for a phd

[shell yarrow]

anyone have any book reccs for ordinary differential equations that's a good balance between theory and application?

[remote sparrow]

https://www.math.usm.edu/schroeder/bookspage.htm

[fierce hedge]

Oh, that makes sense

[remote sparrow]

schroder has an errata and comments sheet for his analysis book

https://math.berkeley.edu/~gbergman/ug.hndts/#Rudin

there are notes for rudin and additional exercises

[fierce hedge]

I tried to find some courses that use Browder but there was like only one and that too a bit ancient

Ross or Rudin are pretty much the standard at this point

[remote sparrow]

a quick google search yields tons of syllabi following abbott

[fierce hedge]

Lmao I forgot Abbott, yeah that also

[sterile pelican]

There is Bloch...provided you don't mind the pace and dryness :^)

[fierce hedge]

But like Honours or advanced classes almost exclusively use Rudin

[fierce hedge]

Faster than Rudin? Or like too slow

[sterile pelican]

Very slow

I used that book for self study

Also he constructs R starting from N

Most books ignore that tidbit

[fierce hedge]

Similar to Tao?

[sterile pelican]

Kind of but I feel like Tao's isn't as thorough

But Tao is a bit faster and no I did not finish Tao so I cannot say much

Bloch is really slow

[fierce hedge]

Slower than Tao

I should check the book once

[sterile pelican]

You won't get to see R until chapter 2 :^)

And chapter 1 is quite long

So you would spend the first 2 chapters just constructing R from N

[remote sparrow]

https://www.math.colostate.edu/~clayton/teaching/m317f10/
https://pi.math.cornell.edu/~zbnorwood/3110-s19/
https://mathcs.holycross.edu/~groberts/Courses/MA242/homepage.html
https://users.math.msu.edu/users/chamatth/320spring19.html

here are some course webpages following abbott, all of which include homework and exams

https://web.archive.org/web/20150104024351/https://math.unm.edu/~skripka/Math510.html

here is a course webpage following carothers, with additional homework

http://bueler.github.io/M641F19/index.html

https://pages.mtu.edu/~trolson/ma4450_10.html

here are a couple other webpages which follow carothers, with homework assignments

[remote sparrow]

https://people.math.wisc.edu/~lestovall/521.14s/
http://wwwarchive.math.psu.edu/anovikov/math403/
https://yifeizhu.github.io/301/

some syllabi following browder

with homeworks

[fierce hedge]

holy shit, thanks!!!

do you have all this saved or are you quick with google searches? @remote sparrow

[remote sparrow]

googlefu

[crimson leaf]

I was given Real Analysis with Point-Set Topology by my analysis professor by Stancl and Stancl and it's kind of weird cause they start off by saying:

"This book is designed as a text for a first course in real analysis. It is
specifically addressed to students who are unlikely to proceed to advanced
degrees in mathematics and for whom their first course in real analysis will
also be their last."

But it doesn't feel like I'm missing out on anything when I look at what I'm reading here and else where (I'm on chapter 4) I do really appreciate the topology and the kind of gradual introduction they're doing, like instead of doing all of the topology at once they interweave it with the analysis so far

[fierce hedge]

Ohh, like what was your search term for finding the courses that use Browder?

[remote sparrow]

i write the book title, author's last name, and the term "syllabus"

[subtle fractal]

any good books that cover everything important about olympiad trig(all basic formulas, identities, area formula, cheva, law of the sines and so on...)

[heady glacier]

Cool! I hope you enjoy it!

[livid lichen]

whats a good book for high school placement test preperation?

[livid lichen]

I think any basic trigonometry book you can find with good reviews would be fine.

[gray gazelle]

has anyone rad Calculus With Applications by Lax

would you recommend it?

[gray gazelle]

polynomial by barbeau

[hushed lynx]

what resources are recommened to help with geometry and trigonometry? i've taken calculus and linear algebra and am going to take multivariable calculus, but i've noticed especially in calculus that trig has been one of my weak points
i'm looking for practice resources and resources to gain intuition

[cold elbow]

oka ttyytyty

[small cobalt]

Does anyone have recommendations for rings first intro abstract algebra books? In particular I was looking at Aluffi's Algebra: Notes from the Underground and Anderson/Feil's First Course in Abstract Algebra if anyone is familiar with them

[heady glacier]

I like Weintraub’s approach via module theory and Dummit and Foote (dense but has all you’d ever need)

[dim sierra]

Why do some people say DnF is super wordy but others say it’s super dense

Personally I like it but how is it “super wordy” lol

[sterile pelican]

I'd recommend Anderson it is the only algebra book that I know starts with rings first

[uncut zealot]

Does anyone have a good algtop Hatcher-equivalent if that book just really doesn't work for me? In particular I need something that covers the equivalent of chapters 0 and 1

(This is for a course that I'm in that's following Hatcher chapter 0 really really closely and is theoretically meant to move into chapter 1 material at some point)

[remote sparrow]

the book was probably a terminal course in its day if the standard then was still rudin

[crimson leaf]

Yeah it was 1988

[hollow shore]

instead of syllabus I type "assignment schedule"

works like a charm

"course" sometimes works too

also duckduckgo is good for this

[remote sparrow]

https://www.amazon.com/Real-Analysis-Lifesaver-Understand-Princeton/dp/0691172935

i found a book written as a companion to baby rudin

[latent moat]

hmm

[fierce hedge]

Ohh, interesting

[coral prawn]

anyone read cumming's real analysis book? How does it compare to the others (rudin, tao abbott etc)?

[storm fossil]

Anyone happen to know of a course that uses Spivak's Calc? An online one with lectures, etc.

[hollow shore]

https://math.stackexchange.com/questions/1793857/is-there-a-list-of-recommended-problems-to-do-in-each-chapter-of-spivaks-calcul

[nova breach]

Does anyone here have experience with Jacobs’ Elementary Algebra?

[storm fossil]

I did end up seeing that one. The lecture notes should be enough. I don't think many courses use Spivak as the main book.

[fervent marten]

can anyone recommend me a good algebra 2 textbook, to try to skip algebra 2 in 8th grade

[zealous moss]

If anyone is looking for a good Dystopian trilogy i would suggest Article 5 by Kristen Simmons

[vale marsh]

Is there a book that goes more into depth about the Lambek-Moser theorem with examples of applications?

[opaque ginkgo]

would you recommend sullivan or james stewart for precalc ?

[gray jungle]

I'm looking for a good problem book in undergraduate real analysis with solutions if possible , this is not for learning purposes i know real analysis but my goal is to brush up on old techniques i may be rusty with so the book should not be too basic.

[fallow cypress]

have you already tried rudin principles of mathematical analysis

I think all of those problems probably have solutions somewhere on the internet

and they range from quite easy to quite hard

[gray jungle]

Yeah im familiar with many rudin exercises , need something else lol

[chrome yacht]

i know thomas korner's a companion to analysis ends with about 340 theorem level problems in analysis ||(and on the right website you can find a pdf with partial solutions attached with the book pdf)||

[storm fossil]

Not sure if this is something that exists in the way that I mean it. Is there a modern version of Euclid's Elements? I don't mean a translation or something, but rather a rigorous, purely geometric book.

Something that starts with some basic geometry axioms and builds on them.

Mostly just for fun, but also for the sake of learning. I'm not sure if "rigorous Euclidean geometry" is a thing. It almost always ends up being set-theory and somewhat advanced algebra. In which case, it doesn't make sense to call it a geometry book.

Preferably something at the 1st/2nd-year undergrad level. Really simple, but rigorous geometry.

[sterile pelican]

There is one but you still need Euclid's Elements as a supplement

It's called Geometry & Beyond by Hartshorne

[storm fossil]

Thanks, I'll see if they have it at my library. My library fortunately has a great math section.

Gonna head there in a minute, so I'll give it a look.

[sterile pelican]

Yeah have a look and see if it holds for you

[storm fossil]

Gonna grabb the elements as well since I've always wanted to read through it

Take care

[lusty ermine]

What book do I need to solve this???

\section*{Problem}
Factor the polynomial ( p(x, y) = 8x^2 + 4xy + 18x - 12y^2 - 33y - 18 ) in ( \mathbb{Z}[x, y] ) and determine the sum of the constant terms of the prime factors.

\section*{Options}
\begin{enumerate}
\item 2
\item 3
\item 0
\item -3
\item 4
\end{enumerate}

@tender river

[hasty eagle]

renato (ping if reply)

[hybrid sparrow]

To ask for mathematics help on this server, please open your own help channel or help thread. See #❓how-to-get-help for instructions.

[nova breach]

Anyone have some enjoyable math reads? Kind of a Goldilocks spot. Not so rigorous as to be a textbook (e.g., I’m not trying to read grad-level analysis texts on the plane), but not so shallow that it’s a pop-sci book. (Even as a kid, I hated pop-sci books. “Imagine the solar system like a big funnel that the Earth is spinning around.” Shut up, Tyson.)

One example I can think of are much older texts. Some of the pre-newton stuff is just so fun. Geometric proofs, early attempts at logic, early attempts at proofs, etc. I remember watching a lecture from Tao where he did a small history lesson on calculating the size of the planet. Seeing how the ancient Greeks derived some of this stuff from eclipses and basic trigonometry and getting reasonably correct answers was inspiring and fun.

The math isn’t much harder than trig, basic logic, some geometry or algebra, but it forces you to think very differently. And to me, that’s a lot of fun when I’m just trying to relax at the park.

Preferably something with some of the actual math, so I can try to visualize the world using only their tools/math.

Hope that’s coherent. Just like reading math. This one is a personal request, not for my class. 🙂

I suspect there would be some good content from East Asian history if it’s been translated.

[lapis heart]

random: "flatland"

novel

[sterile pelican]

One book that fits that mould would be Gensler's Gödel's Theorem Simplified. The book requires a high school background, but it's good if you know a few things of logic like implication. The book holds no punches in exploring the topic and it doesn't follow the "pop-science" of the subject like the YouTube videos you see. I highly recommend reading that book and it's only a mere 85 pages! However, despite my praises I do felt like the last chapter is quite confusing but as he said on the preface it's an optional read. Overall have a look at that book and see if you like it.

[storm fossil]

I think I finally found exactly the kind of book I've always wanted. Basic Mathematics by Serge Lang. I'm sure it can be improved, but this is exactly what I've been searching for. So, if anyone ever happens to need a mildly rigorous high school math book (Alg 1, 2, and geometry), this might work for you.

Feels like the subjects are treated seriously and not just algorithmic gradeschool books with a kid on a skateboard and obnoxious amounts of graphs.

Figured I'd mention it in case anyone else needs it or wants to recommend it to a niece or something.

[sterile pelican]

Serge Lang's Basic Mathematics is a great book on precalc! I always recommend it over other precalc books

[storm fossil]

It's so nice. It's literally exactly what I wanted. I wanted something that at least attempts to show why some of this stuff works, not just "here's the algorithm. And here are some applications that no one in 9th grade cares about."

This is great. I hope I can find a physical copy for a reasonable price.

Being poor is not the best financial status for needing textbooks.

[sterile pelican]

Yeah and if you want to learn calculus, which is sort of a sequel to Basic Mathematics, I do suggest Lang's other book called Short Calculus

A great single variable calculus book

[storm fossil]

I've been having a tonne of fun with Spivak's. I know it's considered really hard* (for a first-time calc experience), but this is for my own enjoyment as I wait for the semester to start.

So, it's not the end of the world if I get stuck. I have, but it's been fun. Easily my favorite math experience so far.

[sterile pelican]

Which book? Because Spivak has one deceptively called Calculus which is more like an analysis book, he even said in the preface on his later editions that it should be called analysis.

However, I do love Spivak's writing style

[storm fossil]

The Calculus book. It's definitely analysis, but that's what I wanted. I would get really frustrated with applied math textbooks because it just felt like magic.

I'd rather get stuck because I'm trying to understand why it actually works than get frustrated because it feels like I'm just plugging in algorithms that the book tells me to.

Plus, it does go over limits, derivatives, and integrals, so it works as a calc book. Just a step-up from the basic calc books like stewart.

[sterile pelican]

I do agree about Stewart's book and I absolutely despise that book, which is why I do think Lang's Short Calculus is a good in between, at least in my view. Regardless, I do think Basic Mathematics is a great book to get started to. In regards to "applied maths" there are great applied maths books out there, for instance Gregory's Classical Mechanics is a great book, it's just most are being obscured with terrible books due to the promotion to Pearson's MyMathLab - a terrible software in existence!

[storm fossil]

I think it's mostly just the high-school type books that left a really bad taste in my mouth. Many times I'd ask "why?" and I felt incredibly stupid because it seemed like everyone else thought it was obvious.

The questions I would ask are the questions answered in the beginning of Spivak's Calc. And I am certain I would have been infinitely happier in school if I had been exposed to it. There were answers to my questions and it turns out it isn't trivial.

So, textbooks that aren't particularly proof-based just kind of don't vibe with me at all.

I'm sure there are some applied ones with proofs.

[narrow relic]

I wouldn't recommend anything by Lax based on my negative experience with his linear algebra books.

[latent moat]

Is this channel only for maths book?

[sterile pelican]

From the channel description it doesn't seem to be, which is quoted as, "Use this channel to ask for book recommendations. Tends to be mostly math but feel free to ask about other literature (YMMV)."

[latent moat]

Oh ok so ig it's mostly for study 📚✏

[storm fossil]

You can ask or recommend about any type of book based on the description.

[latent moat]

Alr gotcha 😼👉

[sterile pelican]

Make sure it doesn't violate the #rules

[hearty steppe]

Yea I’m going to move on to Tolstov’s Fourier Series.

S&S definitely too heavy on rigor and feels short handed on being more detailed in a broken down manner. Definitely much like Brian C Hall’s writings. Not my flavor of exposition, going to move on. I can see why people like S&S though and that’s respectable. Definitely not my flavor of read.

[crimson leaf]

I don't want to sound rude but from everything I've seen you say on this topic and other ones I think you might be best suited with something like Kreyzig engineering math or other engineering focused texts for a lot of your math. (I do think from everything I know Tolstov might be a good choice for you as well)

[hearty steppe]

I think I remember bumping into Kreyzig engineering math book. You are not referring to the functional analysis book right? I liked that one until it got to chapter 8

[crimson leaf]

No no advanced engineering mathematics it's basically a hodgepodge of math you would need for engineering

[still umbra]

Could pickup a game theory textbook or network science textbook

althought it's true they're still textbooks

hopefully the content is more interesting

[south portal]

I have not studied math at my senior high school. Now as I'm studying economics I want to study maths and statistics but I'm having difficulties.
I have also forgotten much of the maths I studied earlier also.
Now I'm requesting some recommendations of books and advice about how I began studying mathen?

[hearty steppe]

Ok yea I think I remember bumping into that book but I haven’t read it yet

Interesting how engineering math books kind of fit my niche but I’m not an engineer 😆

[hearty steppe]

Anyone familiar with this book? https://books.google.com/books/about/Applied_Analysis_by_the_Hilbert_Space_Me.html?id=OvzLZJNUCpIC&printsec=frontcover&source=kp_read_button&hl=en&newbks=1&newbks_redir=0&gboemv=1#v=onepage&q&f=false

[humble zephyr]

Does anyone know of good, proof focused calculus books for free? Does anyone have any experience with the ones listed here under "calculus"?

https://aimath.org/textbooks/approved-textbooks/

These are just some of the ones I've found; I'm open to suggestions.

I don't mind some computational work, but I'd like to better understand calculus from a fundamental level.

[sterile pelican]

Serge Lang's Calculus books has proofs with computations. I highly recommend them, he has two which is Short Calculus and Calculus of Several Variable.

You only need precalc at the level of his other book called Basic Mathematics

But even that Short Calculus gives you enough reviews of said topics to proceed

[humble zephyr]

Thanks for replying!

Is there a place where I can get it?

[sterile pelican]

ebay or amazon should do

[dim sierra]

What’s the end all be all reference for complex analysis?

[finite gale]

wikipedia

(don't take this seriously)

[keen flare]

What's a good book for fourier analysis?

[loud cradle]

stein and shakarchi volume 1, if you know some elementary real analysis and want a math-oriented treatment

if you prefer something more application-oriented, you might check out folland's "fourier analysis and its applications"

[tulip blade]

I like this https://www.cambridge.org/core/books/fourier-analysis-on-finite-groups-and-applications/8662B523E28C44A6F245AB50A2B06EBD

[remote sparrow]

discord search "from:sour_drop cummings"

[coral prawn]

~~geez are you a libarian or smth u know quite a bit abt every book ~~

[past blade]

Does anyone have good recom of texts on measure theory after reading Baby Rudin's first 8 chapters?

Also what's a good transition from baby Rudin to studying ODE and PDE somewhat rigorously?

[finite gale]

i literally just linked you the book review

[past blade]

oh sec where is it

[finite gale]

#book-recommendations message

[past blade]

ah

thanks a lot!

[bitter sail]

Hi

guys

i cant really find a way to describe my mathematics skills

i really lack on everything since not everything came for free , so i have to go bymyself now , my elementary school wasnt helpful , not even my highschool

so i should start again

anyway on finding a book that helps me get myself my math skills back ?

im good at operating only

not good with equations

good with geometry

and everything else i hate learning in concepts and remembering concepts

idk what to learn first

where to start what to study first so i get great starting steps

[daring lake]

I suppose you can start with basic algebra and trig?

[gray gazelle]

algebra dude

[covert bane]

does anyone have any good references for/introductions to (dependent) type theories?
for context, I'm doing some writing on internal languages in categories/topoi, but I can't find anything sufficiently introductory

[sleek hawk]

https://people.mpi-sws.org/~dreyer/courses/catlogic/jacobs.pdf

When in doubt, check the nLab references

[covert bane]

I looked through a few but appear to have missed this one

thanks!

[sleek hawk]

https://tm.kehrenberg.net/series/introduction-to-dependent-type-theory/

https://www.cs.kent.ac.uk/people/staff/sjt/TTFP/ttfp.pdf

[covert bane]

looks like this is going to be a long weekend 😭

[sleek hawk]

I am just linking a bunch of the references if you don't want to read the nLab reference section yourself

No pressure to look at all of them haha

[covert bane]

I mostly saw a bunch of Lawvere's stuff on clicking through nlab links

and most of them were a little deeper than I am able to read

but those 3 look good at a first glance

[sleek hawk]

I just went here: https://ncatlab.org/nlab/show/dependent+type+theory#references

[covert bane]

ah, I was looking at the internal logic page or just logic I think

[sleek hawk]

Ahh that might do it

I don't know how to codify it well but oftentimes these pages have a varying level of references depending on the specificity of the topic and other things

If you get familiar it can become quite easy to "sniff out" the top level subject page that will have more general references

[subtle fractal]

is there a book covering matrixes with complex numbers and how to express points with them

[gray gazelle]

guys i am doing pure maths any book recomendations

[unborn oxide]

guys i have a extremelly difficult algebra and trig competition coming up in 14 days, i really need some resources to make a good revision. im looking for some very condensed and complete "summaries" or lookup tables that i can use together with solving previous years of the exam in those subjects. mainly struggling with matrices, complex numbers and trig in general, its all olympic level stuff... anyone could help guide me to those resources? you can dm me! please!

[drowsy mesa]

Hey guys, best books I found on the history of Trigonometry:

– The Doctrine of Triangles: A History of Modern Trigonometry

– The Mathematics of the Heavens and the Earth: The Early History of Trigonometry

|↑↑↑↑↑↑↑↑↑↑↑|
Excellent books

But if you want something quicker and more summed up MAA has a nice course regarding this called "Teaching and Learning the Trigonometric Functions through their Origins" using some resources of the TRIUMPHS (transforming instruction in undergraduate mathematics via primary historical sources). It's composed of 6 parts:

– Teaching and Learning the Trigonometric Functions through Their Origins: Episode 1 – Babylonian Astronomy and Sexagesimal Numeration
– Teaching and Learning the Trigonometric Functions through Their Origins: Episode 2 – Hipparchus’ Table of Chords

–Teaching and Learning the Trigonometric Functions through Their Origins: Episode 3 – Ptolemy Finds High Noon in Chords of Circles

–Teaching and Learning the Trigonometric Functions through Their Origins: Episode 4 – Varāhamihira and the Poetry of Sines

–Teaching and Learning the Trigonometric Functions through Their Origins: Episode 5 – al-Bīrūnī Does Trigonometry in the Shadows

–Teaching and Learning the Trigonometric Functions through Their Origins: Episode 6 – Regiomontanus and the Beginnings of Modern Trigonometry

Here:
https://maa.org/press/periodicals/convergence/teaching-and-learning-the-trigonometric-functions-through-their-origins

[bitter sail]

nice

[bitter sail]

everyone is saying this

i dont want to learn it it my own language

only in english

[keen flare]

Hi guys - recommended text for reviewing undergraduate algebra fast that isn’t a drag to read like d&f?

[crimson leaf]

I think Lang is pretty exciting but you should probably check pins

[fierce hedge]

Usual recommendations are Artin, for a good free book you can try Judson

[mossy flume]

Artin good

Heard good things about Aluffi Chapter 0 if you wanna get categorical

[fierce hedge]

I just noticed the person said reviewing UG Algebra, for quick review probably Herstein although it doesn't do group actions properly

[fierce hedge]

I think Chapter 0 is a bit more grad level even advanced ug can definitely read it

[mossy flume]

Well they said review

[fierce hedge]

Fair

[crimson leaf]

Yeah they want a quick review of undergrad

Maybe even finding some lecture notes would be good for them

[fierce hedge]

I think Milne has a good pair of notes on algebra

I know his group and Galois theory notes, he probably also has ring, fields

[gray gazelle]

best books on number theory?

[fluid halo]

IPO questions?

[south portal]

Suggest some books to get started with pre-computational mathematics.

[remote sparrow]

you should probably specify whether you mean his ug or his grad text

[gray gazelle]

suggest me some good books on boolean algebra?

[crimson leaf]

I forgot he even has an undergrad book

[abstract hollow]

Hey, I just took my first course in algebra and I'm a little bit confused About symbols and operators and all of this stuffs, is there any chance I can find a well simplified book?, please suggest some

[abstract hollow]

" basic Logic "

[ripe dock]

Probably the wrong channel but

If I'm going through a textbook by myself, whats the best way to check if my proofs are right?

[remote slate]

Principles and Techniques in Combinatorics" by Chen Chuan-Chong and Koh Khee-Meng
is this book good enough for learning combinatorics from scratch?

[gray gazelle]

A question about Chartrand, Polimeni & Zhang proofs book

Do the latter chapters (12-19) for example "Proofs in Ring Theory" require you to already know Ring Theory or do they restrict it to simplified versions using only what we've learned from the book?

[subtle fractal]

is there a collection of geometry problems(imo level) that can be solved by complex numbers

[supple ferry]

I'm looking for supplementary reading of Rudin's chapter on functions of several variables in his book PMA. I'm looking for books or online lecture notes.

I'm looking for something more modern.

[tawny copper]

Evan Chen has a handout on that

[subtle fractal]

thanks didn't know that

[tawny copper]

you should join the olympiad discord server, you will find more of this stuff there

[subtle fractal]

also didn't know that existed

thanks

[tawny copper]

here is more like higher math things, MODS is a better place for competition math @subtle fractal

[gray gazelle]

I got this book.
Is it good? Is there anything better?

[magic moth]

@gray gazelle look for ordered sets by Bern S.W Schroder

might be worth ur time

[fallen hearth]

whats probably the best/recommended book for secondary school level? the book that teaches in a clear way and makes u think like a mathematician?

(please ping when replying)

(I know definition of best differs, but please suggest a good book)

[gray gazelle]

Opinion on Lang's calculus book? I don't plan on reading this book but just want to know what people think

[misty wyvern]

Any fun rigorous math books for light reading for a PhD-level researcher?

Yeah I know "rigorous" and "light reading" don't go hand-in-hand but I think there are definitely textbooks/monographs that can be breezed through at bedtime.

With the right background ofc

[tulip blade]

never heard of it

[woeful ravine]

Graph Theory by Bollobás is a good introductory book while also being fairly challenging to the reader

Assuming you've already took an undergrad combinatorics/discrete math course

Otherwise, I think most discrete math books nowadays have at least a chapter dedicated to introductory graph theory

[keen flare]

bruh lang covers more than I know in like 130 pages

I used like artin & d&f back when I took the classes

god i know like nothing

[tawny copper]

the millenium prize problems (like the official articles, its a book)

first time I saw $\sha$ 🙈

tf how do you latex that

[gusty smelt]

mathematical structure of quantum mechanics by strocchi. For me I already knew the math so its like, light reading bc its just putting it into context (this book puts QM in C* context)

[misty wyvern]

oh damn, i think strocchi has another qft book i know

[tawny copper]

"Glimpses of algebra and geometry" is also cool, I read spare sections from time to time

and I want to read Weil's "NT an approach through history", its probably bed-readable

[remote sparrow]

A Friendly Introduction to Mathematical Logic by leary and kristiansen

most people aren't really concerned with foundations so maybe you haven't read anything concerning foundations either

[misty wyvern]

you got that right, i have never thought about foundations except whether something is isomorphic to choice

[ocean mulch]

Galois’ Dream: Group Theory and Differential Equations by Michio Kuga

the target audience is bright undergrad, so for PhDs it should be a children book. But still fun to read if you're not familiar with modern differential equation theory

[tawny copper]

I also recommend Hardy's "Ramanujan 12 lectures on subjects suggested by his work and life"

there is a readable pdf out there

[storm fossil]

Can anyone recommend an intro number theory book that begins with something like the peano axioms? One that doesn't, at least at the beginning, use set theory. And one that doesn't assume too much prior knowledge. For example, Apostol's book assumes you've taken at least one proof-based course and doesn't shy away from that terminology.

[median saffron]

@remote sparrow

Thanks, you helped me get my first math book evah . I decided to go with Villeman like you said and I have it with me in person I am loving it so far

[remote sparrow]

Other readable texts you might be interested in are Cutland's Computability: An introduction to recursion theory and Boolos, Burgess, and Jeffrey's Computability and Logic. Do note that while Boolos et al. maintains mathematical rigor, the book is aimed at those with no mathematical background. For what it's worth, diligentClerk still recommends it. A Walk Through Combinatorics by Bona is readable too.

[fallow cypress]

good choice :)

[fallow cypress]

if you're interested at all in this sort of stuff, isaac goldbring has an excellent and easily readable set of notes on nonstandard analysis https://www.math.uci.edu/~isaac/NSA notes.pdf

also you've prob taken difftop already, but if you haven't, tu's intro to manifolds sounds exactly like what you described lol

[misty wyvern]

I have but do you have a recommendation for a followup to diff top (maybe with a Hodgey feel)

[fallow cypress]

I have no idea unfortunately 😔

topology from the differentiable viewpoint is also a fun one, has some stuff on cobordism and stuff towards the end

[sage python]

@misty wyvern which difftop have you done so far?

[misty wyvern]

Only picked up the basics useful for physics unfortunately. So basic co/homological theory, Frobenius theorem, that kind of stuff. I'm using a basic statement from Hodge theory in my current research project so it's been on my table to learn diff top and Hodge theory in seriousness at some point.

[sage python]

Ah sorry I was out. So real Hodge theory boils down to, in any De Rham cohomology class you can find a harmonic form

I think last chapter of Warner talks a bit about it. If you want the stuff over C, where you deal with (p,q) forms and the like... Voisin seems to be the standard, which I've glanced a bit at but which felt a bit tricky

[misty wyvern]

Yeah, that's basically the one thing I needed from Hodge theory for my current paper.

lol

But it'd be nice to know more

[sage python]

Which thing, harmonic forms realizing de Rham classes or the (p,q) stuff?

https://webusers.imj-prg.fr/~fouad.elzein/Hodge.pdf is one I've glanced at as well and think I prefer to Voisin. Probably what I may use if I take a more serious dive into this

[misty wyvern]

Harmonic forms on Euclidean space, the simplest. I'm looking at a stochastic PDE operator and am using a Hodge-type decomposition to simplify computations.

It's a bit of a black box to me as a stochastic analyst so I should learn more

[sage python]

Ah in that case maybe Warner then

This black boxes the analysis input of stuff like elliptic operators

And is more focused on the very algebraic stuff

[misty wyvern]

Got a link to Warner

?

https://link.springer.com/book/10.1007/978-1-4757-1799-0

this?

[sage python]

Yeah. You'd only look at the last chapter though, it proves your theorem

Another option, which now that I think about it might be your style

Is "Laplacian on a Riemannian Manifold" by Rosenberg

[misty wyvern]

That book has a very specific audience in mind lol

[sage python]

I've been meaning to take a dive into that as well

[misty wyvern]

And it looks like I might be it

[sage python]

Yup I just thought of it after I said Warner lmfao

It does topology on manifolds via the Laplacian and the heat equation, among other things

Atiyah-Singer index theorem and whatnot

[misty wyvern]

Hmm I might wanna check out Warner. Doign some sheafy manifold theory was also on my bucket list

[sage python]

Ah yeah in that case Warner's good too. Proves equivalence of sheaf, de Rham, and singular cohomology

[misty wyvern]

I don't think I'm ever going to have a use for sheafs but they seem very natural for physics.

Even though physicists don't use them

I'm chalking that up to a language gap

[sage python]

Opportunity to be a trailblazer!

[misty wyvern]

[sage python]

Are you interested in statmech type stuff? Since you mentioned stochastic PDE and physics that feels like an intersection point

[misty wyvern]

Yep! I do statistical field theory in fact.

The SPDE I'm looking at is related to a stochastic renormalization of a type of molecular dynamics.

[hollow shore]

is anyone here familiar with the 3 volumes on Analysis books by Amann Escher?

how does it compare with something like Pugh

[fierce hedge]

I think @karmic thorn was using them

[fierce hedge]

I think Pugh is like vol1+2 compressed

[karmic thorn]

Yes, I've read about half of V1 I think

Yeah, AE is far more thorough and takes its time through things

I've mentioned before that AE has the problem of being difficult to read through from the middle

Lot of weird notation and choices of content sequencing

But it is good for a class going along with it

For learning by yourself, Rudin with Pugh as a supplement works (this is what my analysis class has been doing)

[fierce hedge]

I think I have never found any classes that use AE

At least none that are online

@remote sparrow have you seen any classes using Amann and Escher?

[remote sparrow]

i did a google search, but i'm pretty sure even the most prestigious american universities don't introduce students to real analysis with anywhere near the level of abstraction in amann and escher. they all use rudin or something about the same difficulty as it. i would venture that most european universities don't either. any syllabi would probably be in german, which is a language i'm not familiar with.

[karmic thorn]

Yeah, it's used in some places in Germany I think

Not very popular elsewhere

[fierce hedge]

Understandable

[elder stratus]

looking for some books on geometric combinatorics
I'm particularly intersted in Sperner's lemma and Tucker's lemma

[indigo mesa]

AE my beloved

Bought physical copies of the first two and used them as a supplementary source

[bright pulsar]

Book recommendations that discover Math Philosophy ?

[tawny copper]

I read Shapiro "Thinking about mathematics", an easy read

[tawny copper]

.

[worthy mirage]

Hello.Who has this book ?

https://www.amazon.com/Gateway-Number-Theory-Applying-Algebraic/dp/1470456222/ref=sr_1_1?crid=KR8XCBQIN0JW&keywords=A+Gateway+to+Number+Theory%3A+Applying+the+Power+of+Algebraic+Curves&qid=1695555746&s=books&sprefix=a+gateway+to+number+theory+applying+the+power+of+algebraic+curves%2Cstripbooks-intl-ship%2C336&sr=1-1

[fallen hearth]

this please

[dark elm]

there are a lot of books about mathematics, and most of them are leaning more onto a certain subject, so what kind of math are you looking for? trigonometry? precalculus? algebra? or mathematics in general for secondary levels?

[lime vessel]

makes u think like a mathematician

Learn logic at least

Thinking mathematically generally comes from exposure to math

[dark elm]

i would like to ask too though, any recos that talks about dedekind cuts and countable and uncountable sets?

[fierce hedge]

Any standard intro analysis textbook talks about them, you can also look at notes or individual videos for them

[soft grove]

I recommend you Dostoevsky's book "Crime and Punishment"

[fallen hearth]

in general. like the ones taught in high schools. covering a little bit of everything. good ones.

[fallen hearth]

I know programming etc. Is that fine?

[lime vessel]

No

Logic as in "contrapositive", "for all", "there exists"

Also basic proof techniques

Induction etc

[fallen hearth]

I do not know what all that is. Where to begin? Any books/starting point?

[fallen hearth]

...please?

[lime vessel]

https://math.berkeley.edu/~hutching/teach/proofs.pdf

[soft grove]

I would like to recommend you the literary work "Kolobok"

[fallen hearth]

that is a nightmare

what is even that?

"The Little Roll"....

[soft grove]

This is a good book

[fallen hearth]

Looks like Russian version of teletubbies

[fallen hearth]

So I should read this story called "The Runaway Bun"?

[soft grove]

By the way, yes

[fallen hearth]

thank you.

[lime vessel]

Also check out #books-old

[fallen hearth]

thank you very. much i will.

[soft grove]

I can also recommend the story "Ryaba Hen"

[fallen hearth]

most of the books there are phd level or very advanced that even the titles don't make sense to me. but one day they will....

[fallen hearth]

done 👍

[lime vessel]

(See the top several in particular)

[hearty steppe]

So far, and I’m not very far into it… I gotta say Tolstov’s “Fourier Series” has quite beautiful exposition. Especially with the algebraic manipulation.

Man I probably have so many books that have comparable flavor that I found. I am confident that I will be able to crack some good intuition on Fourier Series now 🙂

You guys really know your book recs much love for this server

[glad arch]

Has anyone read the book "Ordinary Differential Equations" from Nohel and Brauer? Is it a good book?

[remote sparrow]

hamkins' Lectures on the Philosophy of Mathematics

he also has a youtube lecture playlist following this book

[leaden jasper]

Any goods books on category theory ? A handful are available in my school's library

The name "Categories for the working mathematician" rings a bell but idk hwo good it is

actually that's the only math-oriented one here i think

[manic cairn]

That is a classic, but it assumes a lot of math on your part already

for the examples

[leaden jasper]

fwiw the examples in the introduction are accessible to me

[manic cairn]

that’s good

in that case, feel free to use it

It was originally developed to simplify homology theory in algebraic topology

[leaden jasper]

had to think for a second about the tensor product of an abelian group with ℤ being an identity since i haven't studied them formally yet

but it's not very complicated

[manic cairn]

that’s good

if you know topology and a decent bit of algebra already, you should be good

[leaden jasper]

this year i'm taking an advanced algebra class and a logic class so i'll probably catch up on most of the stuff i haven't understood

[manic cairn]

good

[leaden jasper]

ye ye

1st year of masters

[manic cairn]

you’re more qualified than me probably

I’m just a high school graduate

[leaden jasper]

i see

thanks for rec anyway

[manic cairn]

Anybody have a recommendation for locale theory?

I was reading this categorical formalization of Kant’s transcendental logic, and it mentions this off-hand:

I don’t know any locale theory, and I don’t know where I would start.

[fossil nest]

i know this is a somewhat of an oxymoron but what's an introductory category theory book assuming the least background knowledge

[remote sparrow]

could look at leinster or awodey

[manic cairn]

I don’t know how to kill the embed

https://github.com/hmemcpy/milewski-ctfp-pdf

This is something that I’ve seen programmers use, and it requires far less math than MacLane or Riehl

[fossil nest]

thank both

[bright pulsar]

thank you!

I checked it out , it's really nice

[snow gate]

are there any books on game theory anyone can recommend for a beginner?

[remote sparrow]

what does "beginner" mean?

[heady ember]

Look at clerk's recs

[storm fossil]

Not sure if podcasts would be on-topic. If not, just let me know and I'll move it to a different channel. Does anyone have recommendations for podcasts (doesn't have to be currently active) that has research-level mathematicians as guests? I'm trying to find something where they don't just talk in analogies, but genuinely talk about their field, math, maybe some of the history.

I would also count theoretical physics as long as it's not NDT and Bill Nye lol.

Or it could be a single-man podcast that doesn't have guests, as long as they talk about research, math details, etc., and not just pop-sci stuff.

[remote sparrow]

https://kpknudson.com/my-favorite-theorem

[storm fossil]

That's perfect! Thanks

[dense fjord]

Quick question. I am currently doing a Computer Science senior project on Partially Homomorphic Encryption, namely additive ElGamal and Paillier; however, I have no math background whatsoever (besides introductory Linear Algebra and Calc 1 courses). Would any of you have some book recommendations that could help me understand the math behind these algorithms before I proceed with their implementation? Or just a basic outline of what math concepts I'd need to know. Thank you in advance!

[thick niche]

https://www.amazon.com/dp/1723923893?tag=uuid10-20

Not the best choice but its the only things that comes to mind right now because homomorphic encryption falls largely under code breaking in most books

[civic nebula]

for probablity and random variables is peyton peebles book good or are their any other good alternatives??

[gray gazelle]

any good jee math book except black book?

[frail pendant]

add link between <>

[manic cairn]

ah, thanks

[honest fog]

I'm looking for a textbook that covers general mathematics and like the very basics to do Probability and Data Science

what are some good recommendations?

[misty glen]

you may as well just pick a calculus, linear algebra and probability books and read them separately

[soft grove]

I would like to recommend you a literary work called "Kolobok"

[magic moth]

@wind pilot ```md

1- Discrete Mathematical Structures
B. Kolman R. Busby S. Ross

2-Discrete Mathematics and Its Applications
Kenneth H. Rosen

3- The Discrete Math Workbook: A Companion Manual for Practical Study
Sergei Kurgalin, Sergei Borzunov

4- Introductory Discrete Mathematics (this one is a dover so should be ez to find in physical form too).
V. K. Balakrishnan

5-Discrete Mathematics and Its Applications
Sussana S. Epp

6-Discrete and Combinatorial Mathematics: An Applied Introduction, Fifth Edition by Ralph P. Grimaldi.

[wind pilot]

thank you so much!!

[magic moth]

ill be updating it with more books so wait a sec

[soft grove]

@wind pilot Read this

[wind pilot]

lol what is that

[cobalt arch]

Where is this excerpt from?

Found it

[abstract spire]

What are some books to study group theory?

[rigid barn]

There are many, with varying degrees of sophistication. If you're completely new to the subject and don't have a lot of math background, try "Visual Group Theory".

[abstract spire]

Whats usually used in most uni courses?

[gray gazelle]

Does anyone have recomandation about formal logic, quantifiers and quantification and beyond maybe?

[rigid barn]

Again, it varies. Normally, students meet groups for the first time not in a specialised course, but in an "algebra" course, where the basics of groups, rings, and fields are covered. For this, there is (again) a multitude of texts. You can try something simple like Fraleigh/Artin or something more sophisticated like Dummit&Foote or Knapp. Another standard university text that only covers groups is Rotman's "Introduction to the Theory of Groups". This requires 0 prior knowledge, but some maturity.

[abstract spire]

My bad, I wanted to ask bachelor's courses. Il look into the books you recommended. Thanks.

[umbral basin]

Can anyone tell me whether the indian adaptation of Tom Apostol's Calculus is good?

[magic moth]

Discord

has anyone read this?

i kinda think it's alright for a formal treatment but idk if it's enough or i should check álgebra done right by axler too

[dusty forge]

Any good books for Algebraic Geometry

[mystic orbit]

how much category theory do you need?

if you only need a few lingo bits and a decent amount of examples then aluffi's algebra 0 is really good

actually, that's a bad recc lmao, it's sprinkled all over

[fossil nest]

i’ve just glanced over awodey and even just the first chapter there seems to be plenty

but thanku

[sage python]

What type? Complex AG? Varieties? Schemes?

[sage python]

Can you post the TOC?

[magic moth]

sec

Discord

@sage python does that help?

[rigid barn]

What complex analysis book covers singularities/meromorphic functions well? I've had this probably twice already, where I set out to learn CA, end up understanding the fundamentals well (e.g. Cauchy theory), then get to singularities and fizzle out for w/e reason. Is there any text that covers this particularly well?

[sage python]

This looks good. Maybe a bit of SVD and low-rank approximations to matrices?

[crude sage]

How is Artin simpler than D&F?

[rigid barn]

It just is, I don't know what you want me to say. Plus D&F is a doorstop.

[crude sage]

I wasn't sure if you meant that it covers less, or it's less rigorous, or the exercises are easier, or something like that

[cobalt maple]

Does anyone know of any place I can find supplementary exercises to Hatcher? I feel like his problems are a tad bit too difficult at first; I would like some really simple and easy exercises to first exemplify the ideas and general constructions before I delve into harder problems

[gray gazelle]

Someone knows something that i can use to study teorems?

[sage python]

Artin covers less (in part because it is shorter). Idk about the exercises. Though I will say D&F takes a loooong time to explain some topics, locally it might be less dense than Artin (Artin spends more time on matrix stuff in linear algebra, and spends more time being careful about the geometry underlying symmetry groups I think)

[crude sage]

Hmm thanks. It seems that artin is better for an algebra student in a hurry

[sage python]

I mean what's your background?

If you already know (proof-based) linear algebra, and are moderately quick on the uptake, there's a chance both Artin and D&F will be a bit slow

[gray gazelle]

Hi,
How can I prepare for calculus and discrete mathematics in college if I don’t have enough time to review all the school mathematics topics and I don’t know which books and problems are suitable for my level?

[narrow relic]

I recommend just trying a book on each topic and seeing how you feel about it.

[magic moth]

i posted a list earlier for discrete math let me find it for u

[magic moth]

here

[narrow relic]

Would you consider adding Grimaldi to that list? It really helped me.

[magic moth]

@gray gazelle

give me the name of the author and name of the book

[narrow relic]

Discrete and Combinatorial Mathematics: An Applied Introduction, Fifth Edition by Ralph P. Grimaldi.

[magic moth]

done

[gray gazelle]

thanks for that 🙂
I'll save it for 2025, rn I need for relearning all math before calculus

[narrow relic]

Hey thanks. I hope it helps people

[magic moth]

ehh

[narrow relic]

I would check out books by Mary P. Dolciani if you can find any

[magic moth]

well go at ur own pace

[dusty forge]

Intro

[narrow relic]

E.g. this is an 8th grade algebra book: https://www.amazon.com/Modern-algebra-Structure-method-Book/dp/B0007GU5S4/

[gray gazelle]

oh okay, I'll search for it, thanks

[narrow relic]

She has many books that cover the middle and high school level material

I don't remember their names but you can check them out

[narrow relic]

The pre-calculus one is called Modern Introductory Analysis

[crude sage]

Hmm I do know proof-based linear algebra, so most of the introductory matrix stuff in Artin and a good bit of the general linear algebra stuff later on is review. I am sort of using the book as a way to review linear algebra carefully (as well as doing the other algebra). Do you have any recs?

[narrow relic]

https://archive.org/details/modernintroducto00dolc

[sage python]

Ah if you wanna review linear algebra Artin's fine. It's also good at connecting algebra to other areas of math

[gray gazelle]

mm I get it, I'll search for those books, thanks for the resources

[sage python]

I guess if someone doesn't intend to review linear algebra and is quick on the uptake I'd probably recommend Jacobson? That's my personal favorite

[magic moth]

so jacobson is what you would consider for courses in linear algebra for math undergrads?

[sage python]

No this is in abstract algebra, for people whose linear algebra is already solid

[magic moth]

ahh

[sage python]

I have a pinned review of a bunch of algebra books in this channel

[crude sage]

Oh lol I missed that only saw your LA recommendations

[sage python]

The gist is, Artin's good for people who don't know LA yet and who are skeptical that algebra's interesting. D&F is standard, good reference but very slow and dull. Jacobson's my favorite, more writing than symbols (eg defines an R-module as an abelian group M with a homomorphism to End(R), rather than a map RxM->M satisfying axioms)

[magic moth]

im thinking Friedberg, Insel, and Spence

[crude sage]

I guess I'd better take well-motivated treatments of stuff where I can find them. Thanks

[sage python]

Lang's high powered, possibly too high powered. Hungerford is diet Lang. Knapp is (heavily) souped up Artin. Herstein's old school, efficient but also deficient contentwise, and uses nonstandard conventions. People here like Rotman, seems like it's got non-standard organization

[narrow relic]

What do you think of Vinberg?

[sage python]

Idk that one

[narrow relic]

I haven't had time to read it but it looks really good to me

[sage python]

Tbh there are fucktons of algebra books I don't know super well. Maclane Birkhoff is supposed to be good too, Isaacs, etc

[magic moth]

i think ill try bass when im done with sherbert

[narrow relic]

For analysis?

[magic moth]

i saw no complex analysis books and i think ur list for real analysis is aimed at grad students

[manic cairn]

The fish or the instrument?

[magic moth]

yeah

[narrow relic]

Bass is kind of lacking in motivation, I didn't like that aspect of it

[manic cairn]

that’s a book?

[sage python]

Presumably "Real Analysis for Graduate Students"?

[magic moth]

tell me more

actually that is its name

nvm

[sage python]

I think I have a pin for grad analysis books as well

[magic moth]

complex analysis?

[sage python]

That too

[magic moth]

but i dont think ill need that in my lifetime tbh

[narrow relic]

Have you ever looked at the Kolmogorov and Fomin Introductory book?

[magic moth]

@sage python you should eventually review some bourbaki

[sage python]

So there are two English variants of K&F. The one you're talking about is not as faithful to the original, the other one is "Elements of the Theory of Functions and Functional Analysis"

[narrow relic]

Yes 😄

[sage python]

The reference for (the second half of) my second quarter of analysis was the "Elements" K&F

[narrow relic]

The "Introductory" one actually has problems throughout it unlike one of those original K&F volumes (forgot which one)

[sage python]

I read some of it and quite liked its expo

[narrow relic]

I was thinking of just forgetting my personal syllabus and going with that one book

[sage python]

But it uses out of date terminology

[narrow relic]

But it seems to be missing content, as usual

[narrow relic]

Ahh okay.

[sage python]

What are you trying to learn exactly

[magic moth]

who me?

[sage python]

joesmith, but also if you want suggestions I can try to give them

[narrow relic]

The math you'd need to understand papers in Bayesian statistics (this includes Markov chain stuff so measure theory, some topology comes in there for identifiability arguments) and probably some mathematical "machine learning" or whatever, I haven't looked into that for years now but probably the Hilbert space stuff of functional analysis

[magic moth]

digital signal processing, ML, mathematical programming (optimization) and maybe some operations research?

[sage python]

Hmm, that's tricky for me since a lot depends on how much exactly you need. Tbh I didn't know ML involved much functional (it's plausible to me that some research level stuff involves it but I hadn't known precisely). As for Markov chain stuff, some stuff you can get away with without measure theory: see Lawler stochastic processes. If you do need some, then maybe you'll like Schilling as a probability-oriented measure theory book

dandida if you wanna do ML then you very much want singular value decomposition

[narrow relic]

Thanks. Yeah, I have Schilling and have read some of the first 11 chapters

[sage python]

My ML is borderline nonexistent but my vague impression is

[narrow relic]

My current reading is Carothers, but I haven't had time to work on it for months, it is very time consuming

[sage python]

Let's say you are dealing with a dataset that depends on a loooooot of features

[narrow relic]

I spent about 4 months doing the first 2-3 chapters if I remember right. I did all the triangle problems

At that rate it would take me a few years to do the 15 chapters I wanted to do

[sage python]

Like you do linear regression but it's an approximately fuckton x fuckton-dimensional matrix

You may want some dimensionality reduction to isolate which features are most important (presumably for the sake of less computational power?). So you want a low-rank approximation to the matrix

The way you do that is via singular value decomposition

[narrow relic]

Yeah.

[sage python]

Okay good you confirmed that increases the probability that I'm not talking shit lmfaoooo

[narrow relic]

So if I finished Carothers it would probably take a few more years. Then I guess the Schilling book would take another year to do the first 13 chapters or whatever

[magic moth]

i might have to say i need to learn DE too

so

[narrow relic]

It's kind of discouraging.

[sage python]

dandida: Idk differential equations much

joesmith: do you need Carothers to do Schilling? At a glance it seems like it does a little bit of the topology it needs within the book

[magic moth]

operations research?

[narrow relic]

I'm not sure. I kind of went back to basics because it was hard for me to understand some of the sequence type arguments for sets in Schilling

[sage python]

Did you look at appendices A and B?

[narrow relic]

I did, but every time I see something like that, I usually decide to just go work through a real book on those topics

[sage python]

Oh I'm not saying I think it's not important for you, I literally just don't know much about the topic lmfao

[narrow relic]

Since otherwise I feel like I won't really understand what I'm doing

[sage python]

Fair enough joesmith

[narrow relic]

Heh but I am always trying to find ways to shorten down this process

Since I am honestly a bit discouraged with the mountain of material I have to do

That's why I thought about switching from Cathers to the K&F book.

And skipping the topology book I had planned since K&F covers some of that too

They also cover the Hilbert space stuff

@sage python Do you have a syllabus or recommended problem list for those K&F volumes (or the single volume English one)?

[sage python]

The class I used didn't follow K&F super super closely, and was more the functional analysis bit of it than the topology

Also only for the second half of the class

[narrow relic]

If I just went with that book to save time, how should I decide which problems to do?

[sage python]

And our problems were written directly by the prof (kinda hard ones, not very generic, since it was an honors class)

[narrow relic]

Thanks for your advice though

[sage python]

Sure thing yea

[hearty steppe]

Hey guys any book recs to learn more about this stuff

https://en.m.wikipedia.org/wiki/Reaction–diffusion_system

https://en.m.wikipedia.org/wiki/Lotka–Volterra_equations

[fierce hedge]

I've only read a bit of Vinberg so not very sure of the whole book but it tries to be a geometric approach similar to Artin but I guess more expanded upon Artin. I read the determinants part and I think this is the only book I've seen which motivates determinants as signed areas.

[narrow relic]

I've seen other books that do it, it's a great approach (I think Treil does that and also another book that shall remain nameless)

[narrow relic]

Which parts did you read?

[fierce hedge]

Mostly the section on determinants cause most books I have do it via multilinear algebra so I wanted to know if there's another way of doing it and came across Vinberg in a mse recommendation

[narrow relic]

Oh cool.

[gray gazelle]

Any book recommendations for game-theory?

[fierce hedge]

I just checked and no Treil also does it via the multilinear approach albeit a bit indirectly, constructing it via some properties it should have

[gray gazelle]

Have you found anything yet?

[remote sparrow]

#book-recommendations message

[remote sparrow]

#book-recommendations message

[gray gazelle]

damn

TY

[narrow relic]

Oh I'm sorry I got you to waste time checking that out

[woeful ravine]

Does anybody have any recommendations for more advanced works on convex & discrete geometry?

[fierce hedge]

I am sure this wasn't meant to sound sarcastic but just to make sure it's not sarcasm right?

[lime vessel]

When overapologetic:

[hollow shore]

https://mitpress.mit.edu/9780262539791/proof-and-the-art-of-mathematics/

@remote sparrow @fierce hedge an intro proofs book which is actually good!

joel david hamkins is a household name by this point

[remote sparrow]

i'm aware of this book

[fierce hedge]

implying other books are bad or is this superior in some sense?

[remote sparrow]

#book-recommendations message

[hollow shore]

I mean, it just brings smth new to the table

[remote sparrow]

https://www.reddit.com/r/math/comments/o8re9z/review_of_proof_and_the_art_of_mathematics_by/

my original post is pretty much irrelevant, but there are some interesting comments

[hollow shore]

tbf that amazon review reads very weird

I will read a few chapters and let you know

[golden salmon]

Any reccs for microlocal analysis?

[remote sparrow]

@finite crane

[tawny copper]

check out Igor Pak's notes

I love them

well I'm not sure if you would consider it as "more advanced work", kind of an unclear request

[orchid mortar]

Maybe look into Matousek's work, and those who cite from him?

Though I'm not sure how involved Matousek was in convex geometry

[novel obsidian]

I want to learn some plane, hypolerbolic, spherical etc. Geometry. Does anyone have opinions on 'Geometry: from Isometries to Special Relativity' by Nam-Hoon Lee' or have any other textbook recs?

[storm fossil]

Are there any books that are similar in prestige/style as Euclid's Elements. A bit hard to explain. Obviously, Euclid's Elements shows you the world of geometry and geometric proofs. And it's so well written and structured that it can make you really fall in love with geometry/math. And since it begins with axioms, there are no real prerequisites. It's hard, but literally anyone can follow along if they try.

Did anyone in history write a book that treats some other math subject the same way? My best guess would be some sort of number theory or logic book. Honestly, in a different time, I could imagine Tao's opening chapters to Analysis being something like that.

Just curious if anyone ever attempted to do something similar for another math subject. 🙂

[vivid fern]

Prestige-wise, maybe Bourbaki?

[small cobalt]

Gauss's Disquisitiones Arithmeticae was the first thing that popped into my head for prestige

you're going to be hard pressed finding much matching the significance of Euclid's work though

[manic cairn]

Archimedes’ The Method

[small cobalt]

A couple other suggestions would be van der Waerden's Algebra and Hardy's A Course of Pure Mathematics

[covert bane]

Whitehead and Russell's Principia Mathematica as well

[halcyon scaffold]

Maybe hilbert’s foundations of geometry?

Cause it’s literally a modernized elements

[fallow cypress]

here's a list of recs of math bio books you may be interested in in no particular order

They all touch upon similar topics to the ones you posted

[narrow relic]

I was not sarcastic, I really meant I am sorry that I wasted your time

[fierce hedge]

Lmao np

[storm fossil]

Thanks a bunch folks. Just got around to reading the recommendations. 🙂

[hearty steppe]

Man you are incredible as always. Always enjoy your recs and words of advice 🙂

I have Murray but I don’t have the others. I’ll definitely prioritize giving Murray a read at some point

[fallow cypress]

no problem! :)

[gritty zodiac]

my real analysis course is currently following pugh's real mathematical analysis. what are some books similar to it but slightly easier/less terse that I can use for problem-solving practice?

especially for metric space related stuff

[finite gale]

i recall tao's analysis books are pretty nice to read

[remote sparrow]

abbott doesn't cover metric spaces until like the last chapter (and it's only treated very briefly through a series of exercises), but it's a nice supplement

there is also carothers for more metric space material

gamelin and greene's topology textbook devotes a lot to metric spaces

rudin has good problems even if you don't want to really read the rest of the book

schroeder's Mathematical Analysis: A Concise Introduction covers metric spaces in the second half

[novel obsidian]

do people have opinions on Hartshorne's book, "Geometry: Euclid and Beyond"?

[kindred crest]

A good book that deeply explains sets?

[warm haven]

might be a shot in the dark but does anyone know of a textbook that introduces essential fourier and functional analysis topics in the context of measure-theoretic probability?

[hearty steppe]

I am probably going to hedge bets on Folland's text which I might read since I really loved his real analysis text was a focus on general measure theory and its applications. I know his real analysis text is an absolutely spectacular read even though it thoroughly kicked my ass in more ways than one. I still loved reading it and I went through all the chapters. Man even the last 3 chapters are super trippy and spectacular way to end on a high note. One of the best books I ever read with an absolutely spectacular ending series of final chapters. You really should go through that book.

That being said I am selling myself on going through Folland's Fourier Analysis text possibly. I hope it has the same amazing flavor of exposition as his real analysis text, although I can't confirm that.

Right now I am really enjoying Fourier Series by Tolstov, and I would say even though it is a much lighter approach in exposition, it is both algebraic and measure theoretic in principle I would believe.

[loud cradle]

fyi, folland's fourier analysis text is much more application-oriented and less mathematically rigorous than his real analysis

it's a good book but the focus is very different

[versed citrus]

Suggest me a book/video/playlist or anything else that actually explains why and how to use probability and statistics. Preferably, something even a dummy would understand.

I feel like I've learnt half-baked stuff and confused myself with a lot of concepts during classes, especially with the hypotheses testing concept. So, I wanna relearn from the beginning (and if possible, unlearn as well). Tag me for reply

[inner token]

@versed citrus https://youtu.be/ELgjmaSGsWs?si=1VZrxrZ8pJ7l2Pdd

I leaned pretty heavily on this channel when I took p & s in grad school

[hearty steppe]

how do you compare it to Tolstov?

[loud cradle]

i'm not familiar with the latter - does it only cover fourier series as the title suggests?

folland's covers fourier series, fourier transforms, distributions, etc. so it probably has broader coverage

[hearty steppe]

yea I remember his real analysis text being super thorough. I will work through Tolstov first

man especially the chapters on Fourier Transformations, Distribution theory, Topics in Probability theory, and the final chapter on More Measures and Integrals. That book is a real trip. It ends with one of the biggest darn bangs ever.

it felt like multiple bangs going off in my brain. So much pleasure in reading.

I'm not sure if all of Folland's books are like that but man I have so much high hopes for his fourier analysis text. Really looking forward to reading it. His writings are absolutely remarkable.

I just realized he has a quantum field theory text. Has anyone read that?

[sand crescent]

join me on Classical fourier analysis 😻

I am doing some guided reading on that rn

[hearty steppe]

What text are you going through? Folland? I’ll work through folland after Tolstov but sure hit me up in DMs we can try to put a group together

[sand crescent]

Sorry, that was the title of the book

[burnt cairn]

I’m currently a senior in high school who’s taking precalc looking to prepare for cs math. Does anyone have any book recommendations

[rare jetty]

you dont need much calc for cs tho. just go through https://ocw.mit.edu/courses/6-042j-mathematics-for-computer-science-spring-2015/resources/mit6_042js15_textbook/

[wide quail]

Imo there aren't a lot of resources surrounding this book and not much of a community of people who read this stuff. It's easy to get stuck for a long time trying to understand the proofs and the fact that there are no solutions (and not many online generally) doesn't help when the problems are based on ad hoc tricks instead of skill building

When I read stuff I'm generally focusing on the purposes of

-Picking up concepts that illuminate things that would otherwise be chaotic or confusing
-Building skills or picking up certain techniques (which makes more sense to do if the solutions are provided instead of spending lots of time coming up with a jank unilluminating method on your own)
-understanding the logical flow of an area e.g. what results are used to prove other things, what's more fundamental, what kind of things do I need to read more about to understand why X is true

The book makes it quite hard to do 2 and also 3 since the proofs are sometimes hard to understand and there's no community online surrounding this where you can ask for help to get unstuck

[ripe dock]

Anyone has a good reccomendation for book/s on the history of math? Ones ehere you don't need to know the math to unserstand what's going on

[urban summit]

Anyone can recommend book of Calculus 1-5 for me? Im interested at calculus

I bought the calculus comic book that makes me better at visualization

And easy for learn

[burnt cairn]

I need calc for college

[valid monolith]

Anyone has read the linear algebra books of the UTokyo engeneering course?

[finite gale]

This sounds way to specific and vague at the same time

Which book specifically are you taking about

[valid monolith]

Either of the two

Basic concepts

Or

Advanced topics for applications

[finite gale]

What

Who wrote the book

[valid monolith]

Kazuo Murota and Masaaki Sugihara

Published by World Scientific Publishing Company in 2022...but both had a release in japanese in 2013 and 2015 published by Maruzen press

[gray gazelle]

Anyone have opinions on Michael spivak for calculus

[magic moth]

does someone here have stanley I. Grossman S. book on linear algebra?

[valid monolith]

Elementary linear algebra?

[magic moth]

the title of mine is in spanish so idk if its called that in english

it just says linear algebra

would sending the TOC help

?

[valid monolith]

Maybe, send it

[magic moth]

multiple pictures

cause its long

sec

[valid monolith]

... Why is the title in spanish

[magic moth]

cause i have the book in spanish

[valid monolith]

Like, if you understand Spanish and English, you can't translate?

[magic moth]

well yes

but the word elementary its not in the title

[valid monolith]

Ah

Is that 700ish or 200ish pages

[magic moth]

7th

[valid monolith]

Then probably is just the one that is not applications

Let me see

[magic moth]

so is this good if i want a proof based approach?

weird thing is

[valid monolith]

Send a photo of the cover

[magic moth]

in the course that used this

we didnt do proofs

[valid monolith]

I found one in Spanish called algebra lineal

[valid monolith]

You want it in English?

[magic moth]

sure why not

[valid monolith]

No like

Was just asking

Before i don't think his other book in english is the same

[magic moth]

the thing is i have another book of linear algebra, but i want it with exercises with no answer

their different?

ohh

well I want a book that teaches me the methods for proving stuff in linear algebra

so if it helps that

sure

[valid monolith]

Umm I'll send through dm, a wetransfer link for the book of the photo above, spanish

[magic moth]

ok

[valid monolith]

Actually idk the English one also has 700ish pages

[magic moth]

was it a good book though?

i can always get axler i think

[valid monolith]

send me a message

cant load the profile box to send you one

[quasi kiln]

queeeee

hablas español?

[magic moth]

yes

[quasi kiln]

:OMG:

[magic moth]

i found at least 1 more spanish speaker in this server

also if u wanna talk we should go to another channel

[quasi kiln]

No xd I just thought that Spanish was your native language

[magic moth]

it is

[finite crane]

late reply but
Grigis- Sjostrand for the quick and dirty. Lecture notes online would also be good (regardless of whom).
Hormander's original paper (Fourier integral operator I & II) is great. Hormander's series of books that spawn from his paper is.... for the masochistic.

I really want to get back to doing stuff with microlocal

[misty wyvern]

i kind of like that typesetting, how do i get the bar with the chapter number to the left of the name in tex

[dim sierra]

Hello, i am starting in quadratic ecuations and i'm looking for a book or article about it, any recommendations?

[golden salmon]

ty!

[sonic owl]

if anyones familiar with "Trig without Tears". could you recommend something similar but for Calculus 1? if one exists that is

[swift dome]

stewart

[jolly ether]

is there any book that shows you how theorems are proved? Simple ones please(preferbally one that can be borrowed from the library)

[fresh palm]

to anyone who does not wanna scroll up ^^^

[remote sparrow]

trig without tears seem like notes. you might be interested in paul's online math notes for calculus. you can also pick up a copy of Calculus All-in-One for Dummies by mark ryan if you wish.

[fresh palm]

I replied to it so i dont lose it

[sonic owl]

ive already checked out pauls math notes and its probably what ill rely on if i cant find a similar resource

ill check out your other recommendation, thank you!

[remote sparrow]

math books already show you how to prove theorems. that would be the proof of a theorem. are you instead interested in learning techniques that might help you read and write your own proofs, e.g. proof by contradiction, mathematical induction, what it means to prove a universally quantified statement, etc.? then see any intro to proofs book.

#book-recommendations message

[jolly ether]

oh ok thanks

[cold elbow]

any books for studying hs competition math

[versed citrus]

Thanks for the video! Have a great day😄🍀

[ripe dock]

?

[swift dome]

Not a book , but AOPS is quite a good resource for what you looking for

[prime oak]

does anybody have recommendations on books about the history of fermats last theorem

[tawny copper]

the one Wiles read or Simon Singh's book to include Wiles in the story lol

[lavish void]

Hi I am looking for intro to linear algebra txtbook

Preferably with solutions and questions to it

[remote sparrow]

#book-recommendations message

i believe i previously responded to your query several months ago

[lavish void]

wtf

i didn’t even remember saying that

[white jasper]

Guys anyone knows about a a good book with middle school math explanations

[lavish void]

thanks @remote sparrow

[remote sparrow]

what is the content of middle school math

[finite gale]

Sour drop lost active

[halcyon scaffold]

Ladw is pretty good

[ocean spindle]

I used Gilbert strang

[prime oak]

lang

[gaunt sky]

Is Book of Proof by Hammack a good intro book to pure math? I am studing from it and I almost finished chapter 1, are there other ones similar? I want to use it as an intro to set theory and topology, another book to learn from at the same time could be useful, to try different exercises and approaches.

[tawny crater]

intro to set theory and topology?
Can you expand a bit on what you want to study and why and your background please

[gaunt sky]

Intro to proof math in general but in particular to those subjects, I have a very scarce background (high school) but I did some extra courses

I have never done a proper math proof in my studies so that's the aim for now

[remote sparrow]

yes

you should also consider looking at Topology without Tears by sidney a. morris

https://www.topologywithouttears.net/

[gaunt sky]

I found that! Very interesting and my next read.
I have already read first chapter some times ago and it was what I wanted but when I was asked in the exercises to prove something it wasn't easy

[analog lava]

hi everyone

is Tu's differential forms in algebraic topology a good book for someone wanting to learn some basic AT ?

i know only very basic diff geo not even a complete course

[analog lava]

yea nvm

[sand crescent]

Try Hatcher for basic AT

[analog lava]

idk why but i just hated it for some reason

too many pictures or idk

[tawny crater]

I just don't understand why you want topology it's considered a more difficult subject than the ones people tend to start with