book-recommendations

[wet sentinel]

analytic number theory studies the integers (more specifically primes) using tools from analysis/calculus

like the distribution of primes and these things

it studies a certain type of functions which are closely related to the distribution of primes, these functions are called arithmetic (or number theoretic) functions

[barren pollen]

I see

so analytic number theory is the main subject

[wet sentinel]

usually complex analysis is required, but for apostol you can get away with calc (along with multivar calc), tho a good chunk of the book doesnt even need multivariable until later

[wet sentinel]

well, number theory is actually divided into more than just analytic number theory, there are other things like algebraic number theory. But from what i know these are like the main ones (or lets the most popular ones?)

algebraic number theory on the other hand uses tools from abstract algebra and algebraic geometry etc.. to study the integers/rational numbers and other similar/analogous objects in a different setting, tho idk much about it so i cant say more lol

tho i cant help you much if you want to study number theory for cryptography and these things since idk about them

i dont recommend going through a textbook on elementary nt tbh

[cunning elk]

at least to get some background?

[wet sentinel]

like most of the facts that you will get out of such a textbook can be found in textbooks on abstract algebra and in a more general setting

so i feel like it might be a waste of your time

[barren pollen]

still never regretted reading a book haha

[wet sentinel]

tho if you insist on studying elementary nt then sure ig hahaha

#book-recommendations message here is a list of elementary nt books (tho as i told you apostol essentially covers more or less all ent that you would want to know)

#book-recommendations message there is this one too

[slow roost]

me too. People who strongly dislike certain books are somewhat of a mystery to me

[fresh skiff]

I am trying to learn some probability, so my plan is to watch statistics 110 video and read the professors book (instead of doing much problems from the book i plan to do homework problems) does it sounds good?

[mortal iris]

Very nice lectures. Even nicer book. Should be a good start.

Though if you want something rigorous you should probably look at a text like Billingsley's Probability and Measure provided you have some background in Analysis.

[fresh skiff]

oh i got it, yes i do have some background in analysis. But not much strong background in measure theory. But yes i am following Blitzsein's book and lectures, and beside this taking some look at sheldon ross's book

[mortal iris]

Billingsley's text develops the measure theory stuff as well so you wouldn't be lost. So if you want rigor you had best go there. Granted, Blitzstein's course gives you better intuition so you should still work through it. (Ross's book I don't like very much lol)

[fresh skiff]

understood, thank you so much for you opinion i appreciate it

[barren pollen]

which part of mathematics deals with error propogation and arithmetic with decimals? like we're told use 3 decimal places for intermediary calculations in engineering but I want to know that this will not impact the final answer. (I also don't really think it's true)

[slow roost]

it's called error analysis: https://en.wikipedia.org/wiki/Error_analysis_(mathematics)

could also be said to fall under numerical methods, broadly speaking

a standard text for it is Taylor

it has a memorable cover

I fuckin hated that subject though

it played an important part in getting me to switch majors from physics to math

[vital bane]

I do this all the time

Just look at #1059828221887135774 and #1397223478762930337 there's a lot of errors

[vital bane]

Mid 🥀

jk

[bronze quest]

Stfu

[vital bane]

https://tenor.com/view/mewing-bird-gif-16835999897918525830

Not yet

I'm on chapter 7

I'm doing a master's now so it's kinda hard to find time to do Abbott

thanks

[hasty sluice]

What book did you use when you take analysis?

[cursive burrow]

https://tenor.com/view/another-easy-steal-steal-gif-gif-steal-gif-gets-stolem-gif-7935542554022949277

[cursive burrow]

yeah this is mid

(im at prison for stealing gif btw)

[vital bane]

Understanding Analysis by Stephen Abbott, this book is literally so peak, absolute cinema 🔥

[jolly dawn]

How does manga ver. of evangelion compare to the movies? I liked the movies a lot 😀 (excluding the end of evangelion movie ofc 😅)

[jolly dawn]

To be fair chapter 8 of Abbott is more like a buffet: just an arrangement of interesting topics. I also just stopped at chapter 7 😓

[hasty swan]

they gave me this book like 3 times with all of my required lab classes and we never used it lol

"here... if you even care.."

[vital bane]

That's the best part though

All the juicy fun stuff is in ch 8

[tame tree]

is there such thing as a digital version of rudin

[tender river]

rudin the person or rudin the book

[remote sparrow]

there is an unofficial version with modern typesetting

[tame tree]

where 👀

[tame tree]

where may i obtain a copy of mathematician walter rudin’s digitally uploaded consciousness

[remote sparrow]

where you would expect

[tame tree]

i don’t know

[remote sparrow]

you seem to know where based on your message history

[naive lava]

Why, do you want to be a sadist?

[rain wren]

dms

[torn blade]

i think i know where but i have to check again

[tender river]

where you find any other book

[heady ember]

Aye aye captain

[vital bane]

all hands on deck

[remote sparrow]

https://www.rxddit.com/r/math/comments/1ply6u6/functional_analysis_textbook/

https://link.springer.com/book/10.1007/978-3-031-88819-9

found this open access book

[odd cargo]

https://tenor.com/view/xxiisoul-thanos-gif-23843096

[daring wolf]

tfw searching Hartshorne's algebraic geometry

[midnight gulch]

here is every open access springer math textbook if you were curious https://link.springer.com/search?query=the&content-type=Textbook&openAccess=true&dateFrom=&dateTo=&facet-discipline="Mathematics"&sortBy=relevance

[barren pollen]

sweet! im taking Numerical Analysis and Computational Methods next semester!

[royal elm]

read ender’s game

[hallow oriole]

mathematical 'coffee table' books. like not popmath but books that another math undergrad could pick up and read. ex. mathematical constants 1/2 by finch, the integral books by valean, proofs from the book, the symmetries of things, excursions in nt, alg, and anal, mathematics made difficult(~), a short book on long sums, the cauchy-schwarz master class, fractal geometry of nature, etc

thanks xx

[midnight gulch]

princeton companion to math

its a thick one

[hallow oriole]

oh good shout

[granite radish]

how to solve it- polya

[meager python]

Read infinite powers guys its soo good

[slow roost]

God Created The Integers is pretty cool. Stephen Hawking put together a selection of excerpts from important papers of famous mathematicians, and gives biographical info for all of them

most of the papers are challenging reads, but it's eye opening to read the works of those greats, in any case

[vagrant plaza]

What is Mathematics ? By Courant and Robbins, it's an old good book but with an updated epilogue by Ian Stewart.

[minor whale]

anyone have any book recommendations for basic symplectic geometry

[slow roost]

any recs for a book covering quaternions, octonions, and the Cayley-Dickson construction?

oh, Conway wrote one

[mortal iris]

The Road to Reality by Roger Penrose. Admittedly it's more about physics but the first half of the book is about the math and a bit of metaphysics sprinkled in.

[mortal iris]

I've heard good things about this book but never quite picked it up myself. For an introduction you can also check out the later chapters of Spivak's Physics for Mathematicians or Arnold's Mathematical Methods of Classical Mechanics. Though focused on the physics, the introduction to symplectic geometry itself is done well in both.

[wispy bison]

Analysis on Fractals by Strichartz (author of The Way Of Analysis) https://www.ams.org/notices/199910/fea-strichartz.pdf
This explains a notion of what it means for a continuous real-valued function on the Sierpinski gasket to be harmonic, and defines the Laplacian on it. The definitions at the beginning are surprisingly elementary, and I could follow them even though I don’t know much about Laplacians or PDEs

[merry sphinx]

kinda unrelated, but this is like the one font i might use over the computer modern (well, i use mlmodern so slightly bolder, but same font) one. but you gotta pay for it, lmao

[remote sparrow]

https://www.rxddit.com/r/math/comments/1pmxs7j/springer_sales_of_hardcover_books_2361_each/

[floral lantern]

visual group theory

[molten gulch]

<@&268886789983436800> requesting pirated resources

[remote knoll]

Please don't request pirated textbooks, we can't provide them, and discord would get very angry if we did

[tough dragon]

Can someone tell me how to became good in maths

I am average

[remote knoll]

Practice

[tough dragon]

Only practice???

[remote knoll]

I mean, it is the most important component.

What level of math are you doing?

also join me in #study-discussion

[tough dragon]

Class 10 cbse

[distant nest]

I need book for real analysis

[dim delta]

Does anyone have any experience with Leon Linear Algebra and its Applications? It’s the book that my school uses for its second linear algebra class.

[vital chasm]

tao, apostol, pugh, bartle and sherbert, etc, plenty of options
if you are feeling brave, even rudin

[dusky seal]

Isn't Apostol's textbook more of an elementary analysis book? I'm talking about his two-part calculus series.

It's like a mix between calculus, analysis, and even linear algebra.

[vital bane]

I think they're talking about Apostol's "Mathematical Analysis" book

[dusky seal]

There's the Real Analysis Trilogy by Amann and Escher. Compared to other analysis textbooks, it has the most breadth.

[dusky seal]

Oh right, he has an actual analysis textbook.

[distant nest]

Contains everything?

[dusky seal]

Yes, from the bare basics (e.g. counting, truth tables, basic algebra) all the way to advanced stuff (e.g. partial derivatives).

[vital bane]

I wouldn't go for breadth when learning a subject for the first time, I think you should focus on mastering just the core concepts

[dusky seal]

Although, it's pretty hardcore and not recommended for beginners.

[dusky seal]

I would know this because I am a dumb dumb.

[vital bane]

Which will make it easier when you want to learn more/more advanced concepts which build off the core concepts

[vital bane]

Me too 🗣️

[dusky seal]

For those who want to transition to analysis but slowly and smoothly, I would recommend Apostol's Two-Part Calculus books:

It even teaches linear algebra. It does all this from a proof-based approach without becoming insanely abstract. It strikes a good balance.

[distant nest]

Can you send the pdf for me

[odd cargo]

any book lmao

any good book *

i only have two calculus books right now, one by piskunov (which i use for higher calculus) and one by peter lax

both are alright but theres def better out there

[tame tree]

tbh just read abbott

goes into more generality than spivak

not very hard

[tame tree]

indeed

[dim delta]

In a lot of places, I found Abbott to be significantly easier than spivak

[regal ledge]

Any book for linear algebra just after finishing class 12th?

I am also thinking to do the linear algebra course for undergraduates from mit ocw Gilbert Strang one

Any book i can use?

[molten gulch]

Friedberg insel and spence or hoffman and kunze

[regal ledge]

Thanks man appreciate it 🙏

[remote sparrow]

those copies look nice af

https://old.maa.org/press/maa-reviews/introduction-to-real-analysis-2

sent this review before but this is a nice measure theory book

wait did you buy this from amazon or direct from springer? meant to ask this last time

[daring wolf]

springer

[remote sparrow]

yeah i'm just not gonna buy hardcovers from 'em again (unless the book has tons of color, like tapp's diffgeo of curves and surfaces book since they use thicker, glossy paper for those, which helps a bit even if the books are still ultimately gluebound and hard to lay flat)

[mortal iris]

Your username suggests an interest in quantum physics. Hoffmann and Kunse is an otherwise rather dry text with close to no regard to applications. I would instead recommend Shilov.

[daring wolf]

i think springer nowadays js sells books that are relatively unpopular in glue bounds
idk if they have sewn editions nowdays however at least i have like 2 sewn editions in recent orders

[mortal iris]

Idk why. I used the first volume in my first Calc course way back when and found the writing style very dry and boring. Also the second volume is a bit all over the place.

[regal ledge]

Thanks sir 🌹

[remote sparrow]

i have heard axler's LADR and MIRA get sold as sewn editions

well i have mira

it is sewn

ladr 3e was sewn for me, not 4e

got unlucky ig

[daring wolf]

oh thats a good news

[remote sparrow]

but some ppl's 4e copies are sewn

[daring wolf]

i also have ladr 3e sewn

[remote sparrow]

which books do you have that are sewn?

[hybrid sigil]

I've bought Gamelin's "Complex Analysis" paperback this sale, my first direct buy from Springer, will see how it goes. It's print on demand

[mortal iris]

Bud no need for that archaic formality lol. Enjoy

[daring wolf]

hartshorne (as i said last time)
and Lang

[remote sparrow]

it's a great intro

[remote sparrow]

both new?

wow

do you live in europe by any chance?

[daring wolf]

(which are recent orders)

no

,ti

[hasty eagle]

The current time for _0mem is 03:05 AM (KST) on Tue, 16/12/2025.

[remote sparrow]

oh right you showed you were korean that one time before

[hybrid sigil]

Cool! I've sampled the first chapter and problems, looks good, I like the style. But it seems like there are many good books on Complex Analysis

I suspect I will end up with buying several eventually 🙂

also, I like that he covers a lot of stuff, so might be useful even for more advanced studies (Part III)

I recently discovered that I can look at whole series on ZBMath, say, Springer's "Undergraduate Text in Mathematics" and order books by citations number to get a sense of how influential/popular they are. Does anyone else do this too?

https://zbmath.org/serials/9079

It's also possible to do it for articles, say, go and find the most cited article from American Mathematical Monthly in expository number theory or something like that

[remote sparrow]

that's the first time i've heard anyone do this

i mostly stick to what gets recommended on reddit, math stackexchange, and math overflow

[hybrid sigil]

Apostol and "Ideals, Varieties and Algorithms" by Cox seem to be quite infliential, out of undergrad books, not surprisingly perhaps

[hybrid sigil]

Yeah, it's not like this ZBMath mining is better than that, just different

[remote sparrow]

cox is also an intro to computational algebraic geometry with very minimal prerequisites and i'm sure methods inspired by the book have been implemented in many applications

[hybrid sigil]

I also like that it's free and you can do all sorts of queries. For example there are categories for expository books/articles in all sorts of areas in mathematics, and also most books have reviews right there

[remote sparrow]

MAA is a good source of reviews

most reviews don't seem to have migrated over to the new website

[hybrid sigil]

yeah, I often read those too 🙂

yeah, this is somewhat annoying, they could have done a better job migrating their site 🙂

otherwise one needs to do that "old.maa.org" trick

[hybrid sigil]

also, on ZBMath it's easy to actually quickly see all the books a particular series with all the data, their UI is also quick and responsive, and the site is free to use

[mortal iris]

It's fairly elementary. If you feel like Shilov is too hard for you, then sure, it would serve as a good bridge if you are comfortable with all the vector algebra they teach in 11th and 12th in India (I assume you're Indian). That said working through Shilov with some effort is a better bet atp. You can supplement with 3B1B videos to a degree and even Strang's text for stuff that might not come as easy in the beginning.

[remote sparrow]

#book-recommendations message

[regal ledge]

Yes I am comfortable in matrices and I am Indian. Vectors is a bit tough for me but I will master it before my class 12th ends

[mortal iris]

I would strongly suggest using the 3B1B Linear Algebra alongside your school topics upto Cramer's rule. It gives you a better visual intuition for what is going on compared to what your RD Sharmas or NCERTs would lol.

[mortal iris]

I believe this is very commonly used to teach in German math programmes. Correct me if I'm wrong.

[mortal iris]

Cummings is great. Abbott too. If you have already done a course on par with Spivak for Calculus then Zorich is brilliant.

[regal ledge]

Sure I will start doing it too

[odd cargo]

there are interactive resources available for free online

for vector analysis

i can link one if you want

[regal ledge]

Sure

[odd cargo]

https://mathinsight.org/thread/math2374#s35

[regal ledge]

Oh I have seen a few videos of this channel

Thanks @odd cargo

[slow crest]

hi i'm in high school looking for some interesting reading like first year uni stuff. does anyone in uni have recs for textbooks to learn advanced maths. im looking for something like group theory or set theory etc

[odd cargo]

no reason to rush yourself if you're eventually going into uni for maths

just find problem books

[odd cargo]

Just read another text from a book where the author is seemingly afraid of making an obvious statement

[slow crest]

do you recommend one in particular

[odd cargo]

plenty of problem books around bubba

[slow roost]

this is currently on sale (in hardback!) for $23.99

[slow crest]

thanks!

[molten gulch]

What book?

[mortal iris]

The entry point into uni math is typically a course on proofs. You can pick up a few things you mentioned over here and get a good view of math at uni might look like.

[remote sparrow]

https://www.rxddit.com/r/math/comments/136sb5m/is_there_a_measure_theory_book_for_dummiesidiots/

[slow roost]

afraid I don’t know any for dummies or idiots, but I’ve got some great choices for morons and dimwits

[mortal iris]

It would be real funny to recommend Bogachev to this fella lol

[empty junco]

for purely selfish reasons

[normal crystal]

for profs, or anyone, who self publish on amazon, I wonder if there is a reason to limit the format available between paperback and hardcover
I can understand the ones who choose not to release a kindle ebook, or guess why
but usually the hardcover price is a only modest increase in price when both are available to order
for instance, idk why this isn't offered with a hardcover option
https://www.amazon.com/Simple-Infinite-Joy-Mathematical-Statistics/dp/B0BD1YPQRN/

[tender river]

https://www.cambridge.org/us/universitypress/subjects/mathematics/algebra/algebra-notes-underground?format=PB

[normal crystal]

you can look at the ToC on their site

[stark cobalt]

Okay sorry about that , ill keep that in mind from next time onwards

[normal crystal]

🤡
https://www.amazon.com/All-Rave-Shawn-Fannings-Napster/dp/0609610937

"An A-Z Guide to AI Prompt Engineering for Life, Work, and Business- NO CODING REQUIRED"

PART OF A TWO BOOK SERIES

[cunning elk]

it's trig + basic $\mathbb{C}$ + basic linear algebra (up to determinants) + vector geo

[hasty eagle]

elrichardo1337

[hallow oriole]

linalg up to determinants? 😭

unless ur doing the axler approach this is like ten things right

[cunning elk]

i have some issues with how it's presented in that text

but they do vectors and matrices in $\mathbb{R}^2$ and $\mathbb{R}^3$

[hasty eagle]

elrichardo1337

[trail void]

i told you bro you didnt believe me 😭

[vital bane]

Springer's hardcovers are bad?

[remote sparrow]

?

hardcovers are good and better than softcovers when they're made well

when they're made poorly, they're awful

that's always been my position

[remote sparrow]

new ones yeah

most of the time

[vital bane]

local man finds out poorly made things are awful

[trail void]

paperbacks arent really awfully made though

[vital bane]

That depends to be honest

They can be

[trail void]

youre not really tryna keep a book to give to your great grand children you know? for that purpose most paperbacks are fine

[remote sparrow]

did i say paperbacks were poorly made

[trail void]

.

responding to this

[vital bane]

huh?

[trail void]

im responding to sour drop when he inquired if he asked that to which i replied he did not but you did

[remote sparrow]

i want a book that takes no effort to lay flat and i would prefer a book that doesn't wear out in my bag or when shelving and reshelving

[vital bane]

I didn't reply to anyone, I was making a joke lol

[remote sparrow]

does it matter if i want to pass it down or not?

[trail void]

mb i didnt notice 😭

[vital bane]

Also hardcovers just feel nicer tbh

[trail void]

i have paperbacks i take everywhere and they lay flat

[vital bane]

Just a personal opinion

[remote sparrow]

you don't have to accept shit quality things just because you aren't going to pass it down

[trail void]

for me personally
if its a textbook of more than 800 pages, or sort of wide, hardcover it is

• if im planning to study it for years
  if not, then paperback is fine

[remote sparrow]

must be nice wherever you live then, because they need to lay flat on every page, not just the middle ones

and without mangling the spine

[trail void]

oh i should say i do train my paperbacks so they dont cause an issue

maybe im sort of accustomed to it so they work best for me, i understand however preferences are a thing

[remote sparrow]

breaking in a paperback can only do so much; it's simply not the same as a sewn-bound book

[static idol]

Is stewart precalculus considered good/the best?

[mortal iris]

I might be the odd one here but I prefer spiral bound.

[mortal iris]

Best is subjective. It is pretty decent. I prefer Stitz and Zeager tbf.

[remote sparrow]

no gluebound book can flex open like this, only sewn books can

[trail void]

i think that it shows the book is well used, i used to concern myself with them when i first started reading seriously but now its sort of nice to see

i think its mostly preference but as one reads more and more eventuall one most of the time concerns less with book covers or condition aslong as its readable

[static idol]

Thanks for the advice, I usually practice with problems that are harder than those of the book and research a little bit more of theory to try to compensate its faults

[mortal iris]

I usually print out open access stuff for personal use and bind them myself. I use good pages too. Spiral binding them makes usage easier. I wish sellers would actually sell spirally bound books. Maybe not spiral but with a cylindrical spine so that pages open out flat.

[trail void]

on the left image im planning on getting a standing table for reading too, bless my poor spine

@mortal iris i took your recommendation and will use zorich's analysis I and II with abbott and hubart as supplementary, i will get to it soon hopefully, but i have one last question? usually theres analysis I, II, and III right? does zorich's bookset contain that too or would i eventually have to get a seperate one for analysis III?

[mortal iris]

I don't think there is any such convention for analysis. If there is, idk what they stand for. Zorich covers real analysis of single variable, mutlivariable functions and introductions to topology, manifolds and Fourier analysis. In the appendices he covers a bit of numerical merhods, generalised functions and some series methods to solve different kinds of problems. Pretty evident if you have looked up the books.

You're better off learning about the Lebesgue Integral when you get to measure theory anyways so you won't find it in Zorich. And although there is a bit on complex functions in there, no proper complex analysis is covered here. Needless to say without measure theory there is also no coverage of functional analysis (besides some differential calculus on normed vector spaces).

[trail void]

understood, thank you very much!!

[mortal iris]

I should remind you. This is not a book or a topic to be taken lightly. If you got no experience writing proofs regardless of your background in Calculus or linear algebra, then you will likely very quickly get stuck while working through a book like Zorich.

[trail void]

do you have a personal fave for proof writing before heading into analysis? or is discrete mathematics enough?

[tender river]

have you taken discretemath already

[trail void]

yes

i was planning on reading hammack before heading into analysis after linear algebra is completed

[tender river]

what kinds of things did you cover

[trail void]

logic, proof techniques , basic set theory, elementary number theory etc

[tender river]

thats good enough to start with analysis

[trail void]

i would like to tone up my skills in proof writing however, if you do have a rec?

[tender river]

yes, analysis

[trail void]

interesting

thank you

[mortal iris]

If you've already done what you have said then just begin with Analysis.

[orchid vortex]

I heard that Zorich's book is used in 4-semester course (calculus + analysis) alongside of that in sem3 and sem4 they cover Topology and Lebesgue theory respectively according to this Math StackExchange answer. For Analysis III course, I believe is mostly cover Lebesgue theory for example ETH Zürich Analysis III syllabus.

[trail void]

thank you!!

[sacred thicket]

why not, if they find it fun, there is definitely no harm in learning uni stuff in highschool

[sacred thicket]

idk if non-naive set theory will even be interesting at this point, but there are a lot of beginner friendly abstract algebra books (you can find a lot of them here or on forums)

[gloomy cosmos]

Hi Everyone, I need to start refreshing undergraduate level of math , it's been 20 yrs , I am not learning actively anything related to math , it's all work, I am out of practice, any elementary probability book with lots of basic probability concepts?

[tender river]

http://probabilitybook.net/ this is recommended here often, theres sheldon ross's first course in probability too that is well liked

[remote sparrow]

https://stat110.net

[stable axle]

Any recommendations on general purpose homological algebra textbooks?

I have a lot of algebra books which deal with homological algebra in the context of something else (for example, rings and categories of modules by anderson and fuller) but I don't have a book that serves as a study of the theory by itself.

I've seen that MacLane is a very common introduction but it seems like a very old book to be using

I'll say that in general I like it when a book is a bit more conversational as well and at least gives some historical context for what it treats with

If there are any books that fit this bill then please let me know

[remote sparrow]

rotman

https://link.springer.com/book/10.1007/b98977

it just so happens to be on sale btw

[stable axle]

Nice, I'll scoop it up

Thanks

[dim widget]

Anyone have any strong recommendations on diff top books?

[vital bane]

Abbott

[finite gate]

This is probably a very repeated question here but: Is there a more recent calculus book that is as good and complete as Apostol or Spivak?

[sacred thicket]

i started reading Weibel and its very good so far

[scenic sequoia]

Best calculus books written by man.

[woven sentinel]

anyone know good books or resources for studying quantative finance

[mortal iris]

Cummings' Real Analysis is very good. Don't let the title deter you. It's at the same level as an Apostol or Spivak Calculus covering a wee bit more material that you typically see in an Analysis course.

[slim canopy]

I’m balling out on books for Christmas , what books should I get for calc 3, for linear algebra , for proofs , for differential equations and for number theory

[odd cargo]

Multivariable calculus: Application by Peter lax is a decent calc book

[molten gulch]

I like hubbard for multivar, FIS for linear, not a fan of any proof books, DE kinda depends on rigour but there's arnol'd, diprima, etc..., and what type of NT, analytic or algebraic? If you mean classical, just go read an abs alg book for the most part

[slim canopy]

for the stuff bout rigor do you mean like difficulty ?

And also idk the types of number theory I’m just learning it now

[molten gulch]

analytic number theory is mainly about using complex analysis to study stuff like primes

algebraic number theory is...about the number theory of algebraic numbers (solutions to polynomials with real (rational?) coefficients)

milne has some notes on algNT but they are way above your level rn

you need some commutative algebra for them I think

[slim canopy]

What’s the beginner kind of number theory because I don’t know complex analysis

[molten gulch]

I'm CCing @wicked fractal into this because they know way more NT than I do

[molten gulch]

most of the NT you need there can be covered out of an algebra textbook

[slim canopy]

Ok then what do u recommend for that

[mortal iris]

Hubbard and Hubbard is a very good choice for vector calc and linear algebra . Also Arnold's ODE book and maybe Tenenbaum's. For Elementary Number Theory Burton is great.

[slim canopy]

K thanks

[molten gulch]

Burton is nice for elementary stuff yeah

a lot of the basic ideas you can also get from an algebra book like Judson (free online) or gallian or artin or like

yeah

there's a lot

[mortal iris]

If you do not know what rigor is I wonder if you actually studying math lol. Would strongly also suggest getting Cummings' Proofs to get a taste for the what and why of rigor.

[slim canopy]

Is vector calc same as calc 3

[scenic sequoia]

Hull's Options, Futures, and other Derivatives

[slim canopy]

They don’t cover this in calc bc

[mortal iris]

No idea what Calc 3 is but Hubbard and Hubbard is definitely a great book to have.

[mortal iris]

What's Calc bc?

You have to realise that code names for courses and their contents are not globally identical.

[molten gulch]

Differential and Integral Calculus in highschool

(of one variable)

[molten gulch]

Depends on the institution, some split it as calc 3 being multiple deivatives and integrals and calc 4 as vector calculus, stokes' theorem, the change of variables formula, etc...

[mortal iris]

Yeah okay. Rigor is an afterthought in school programmes

[woven sentinel]

Appreciate ot

[wicked fractal]

Do not take any calc 3 or differential equations book imo. For number theory, I just recommend doing abstract algebra instead. For linear algebra there are a lot of books out there just pick the one you vibe with

[mortal iris]

If you are coming out of high school then possibly add a good single variable Calculus book like Spivak

[wicked fractal]

For calculus 3 and DEs, might as well pick a physics book

[slim canopy]

Ok

[mortal iris]

Yikes. No. Been there done that. Not a great idea.

[wicked fractal]

Unless of course you want a rigorous treatment in DEs in which case you need a solid analysis background for that

[mortal iris]

The physics intuition is super helpful but they treat the subject horribly

[wicked fractal]

For calculus 3 just pick up differential geometry

[slim canopy]

What’s that

[mortal iris]

Very bad advice for someone fresh out of high school without much exposure to math.

[wicked fractal]

[mortal iris]

It's fine to pick up a text that eases you into diff geo stuff but to pick that up from the outset is not advisable unless the student is ready and knows what it is to some degree. I personally would not advice anybody to pick up a proper diff geo book prior to doing analysis.

[wicked fractal]

There are many differential geometry textbooks which go easy

It's fine I've done it

[mortal iris]

If only one person could be representative of the general human being lol.

[slim canopy]

What if I’m still in hs tho

[mortal iris]

And most of them are either not rigorous or flat out wrong

[wicked fractal]

So it's worse than finishing a calculus 3 book and have no idea wtf is stokes theorem?

[mortal iris]

There are plenty of good vector calc books that ease you into the subject and bring in the geometry at a basic level but they are fundamentally not diff geo texts

[mortal iris]

If you are into math then I suggest picking up Cummings' Proofs and Real Analysis and then Hubbard and Hubbard. Tenenbaum's book will probably be very helpful for ODEs. Arnold's requires a little more mathematical maturity to appreciate.

They should complement what you have learned already and will greatly help you in your first couple years at uni.

[wicked fractal]

In a standard calculus 3 course what is there other than bashing out students with physical applications and make them question wtf is a differential form?

Waste of time

Anyways do whatever you want

[mortal iris]

Man guys like citytutoring really get to you eh xD

[molten gulch]

Who is CityTutoring?

[mortal iris]

Math ragebaiter on YouTube

[mortal iris]

I am yet to see any high school Calc text even remotely even get close to mentioning what a one-form is. What I recommended was mostly for after school anyways but to say pick up differential geometry for high school Calc is just nuts.

[sage python]

There is usually gonna be some content of calc 3 that strictly precedes diffgeo

The tail end of it, where you do curves/surfaces and Stokes' theorem, sure

But take the stuff that's strictly foundational

[odd cargo]

Multivariable calculus: Applications by Peter lax

[sage python]

Limits and derivatives in higher dimension, chain rule, possibly Lagrange multipliers, change of coordinates, Fubini theorem

[molten gulch]

YIPPEE

[finite gate]

Thank you!

[remote sparrow]

https://matrixeditions.com/5thUnifiedApproach.html

https://www.amazon.com/Linear-Algebra-Cambridge-Mathematical-Textbooks/dp/1107177901

https://www.amazon.com/Introduction-Through-Number-Applied-Undergraduate/dp/1470470276

https://www.amazon.com/Nonlinear-Dynamics-Chaos-Steven-Strogatz/dp/0367026503

https://www.amazon.com/Elementary-Differential-Equations-Boundary-Problems/dp/0470458313

don't worry about the price on this last one: just pick a used copy of quality "Good" or better

[lilac canopy]

Hello there! does anyone know about Category Theory? I'm an undergrad and I'm trying to read Mac Lane's book but it feels a little cumbersome with all the references to other mathematics' branches. It would be a good introduction books like The Joy of Cats or Lawvere's Conceptual Mathematics? Any recomendations?

[slow roost]

I don't recommend trying to learn it for the first time from Mac Lane

the title isn't kidding around when it says "for the working mathematician"

Lawvere's Conceptual Mathematics is by far the gentlest intro to it I've seen

[remote sparrow]

leinster or awodey are good starts

[mortal iris]

Lawvere is a fantastic introduction.

[slow roost]

agreed!

[lilac canopy]

Hahaha I thought the same. It was the only reference about categories my professor used. I'll pursue learning through Lawvere, then

[lilac canopy]

I'll check them out too! thanks

[slow roost]

it may seem deceptively almost too easy at first

but it gets to some pretty serious stuff

[mortal iris]

Indeed, it gets pretty hard as you go deeper. For the latter half (part 3 onwards) of the book it helps to know logic, some abstract algebra and discrete mathematics.

Still not remotely as hard as some other rather impossible to read category theory texts I've seen. Ik a couple of high school students working through early parts of the book as a seminar.

[lilac canopy]

Yeah. Categorical concepts are daunting, but I have a hard time trying to grasp them from places like nLab (which is great, but I soon get overwhelmed with the hyperlink labyrinth). Maybe after I cope with Lawvere ,I'll ask for some of those harder books. Thank you for your suggestions!

[mortal iris]

Lawvere lists several next step books in the end as well. Tbf you'd have been introduced to most of the subjects without having to jump into algebraic geometry so most next steps would take you along that route. It would really depend on why you want to learn the subject as to how you proceed with it. The computer scientist would be more than happy with categories as presented in Lawvere but the geometer may not be.

[slow roost]

I think there are a lot of good options for a next book - the aforementioned Leinster and Awodey, Riehl, and Fong & Spivak

[odd cargo]

lecture notes or a book?

[mortal iris]

Book

[odd cargo]

categories of continuum physics?

[slow roost]

Conceptual Mathematics

Fong & Spivak is on the arxiv: https://arxiv.org/abs/1803.05316

super cool book, could also be a great first book

[odd cargo]

yall got an introductory book to measure theory yall recommend?

[slow roost]

I don't know of one just on measure theory, but for me the most helpful book was Pugh's Real Mathematical Analysis

just the last chapter is on Lebesgue measures

[mortal iris]

Axler is good if you have already done Analysis. It's a natural continuation. If you want something very comprehensive you can try Bogachev but it is not a gentle intro by any means.

[mortal iris]

Yikes. Just looked this up. Way too advanced for a beginner. Dunno why someone would use categories for continuum physics tbf.

[slow roost]

woah, that looks really interesting

apparently it has to do with “synthetic differential geometry”

[ancient basalt]

Any decent books for ode? :p which gives a good understanding about power series solutions and stuff?

[midnight gulch]

i mean pretty much any ode textbook is going to have a chapter on series solutions

[ancient basalt]

Ik

[midnight gulch]

so what are you looking for in particular?

[ancient basalt]

But the one in using just goes so fast over that , I can't understand shit

[ancient basalt]

A book that would give me a better understanding about power series

[slow roost]

I found Zill to be ok

what book are you using?

[gray gazelle]

I have a strange question (sorry to interrupt the above; want to ask before I forget):
Is there a more modern book similar to this one? https://en.wikipedia.org/wiki/Proofs_from_THE_BOOK
multiple proofs and related results for each theorem across a variety of mathematical fields
only thing that comes to mind for me is The Princeton Companion to Mathematics, but that seems quite a bit different
I'd like a nice coffee table reference book with a variety of proofs for a variety of theorems, if anyone knows a modern one
(or is the one I linked very good maybe, even though it's published 1998; idk)

[normal crystal]

the newest edition is 2018

[gray gazelle]

ok, yea I was just wondering if there were a more mainline reference book that came to mind but that works

[mortal iris]

Tenenbaum's is pretty detailed.

[vital bane]

@tiny gulch You might find this interesting

[tiny gulch]

Yes I’ve read through this

[tiny gulch]

Though maybe it’d be worth a re-read

[normal crystal]

<@&268886789983436800>
no piracy

[molten sapphire]

👅👅

[wispy pebble]

@molten sapphire very mature. take a day off

[daring wolf]

vro took L

lmao

[vital bane]

Author's name is "Death"

[naive lava]

Holy hell, a Cambridge monograph

Istg every single one of those books is great

[slow roost]

Ive been reading my old undergrad complex analysis book Brown & Churchill again.. it’s been ages, I don’t think I ever reviewed from it while in grad school

I’m pleasantly surprised to find it’s very good

I don’t remember liking it this much back in the day

I guess sometimes books just grow on you

[main hemlock]

for analysis 1, would you guys recommend Understanding Analysis by Stephen Abbott or Mathematical Analysis by Zorich

[vital bane]

I don't remember liking it very much either

[vital bane]

Idk about Zorich, I think Sour Drop would recommend it but Stephen Abbott is absolute cinema

it's peak exposition 🗣️

Amazing book

[main hemlock]

sounds good

[daring lake]

Bartle is good, also Rudin is nice

[main hemlock]

im starting my uni undergrad next year and they use Zorich, but Abbott might be better for self study right now

[daring lake]

Abbott is also nice, good exposition and simple to follow

I also liked Jay Cummings book. Filled quite a bit with memes too.

[vital bane]

Oh really?

[main hemlock]

Cummings, thats his real name?

hahah

[daring lake]

well, it is

https://longformmath.com/

[daring lake]

Yes

[merry cove]

In terms of the exercises in the books, do u guys do them all?

Like for analysis by abott

[hasty stratus]

no u shouldnt read in the order of the book either

[merry cove]

How long should I ponder on a solution before I end up having a seizure?

This has happened too often for me in real analysis

[merry cove]

Do u take notes when reading or just casual?

[hasty stratus]

idk sometimes its good to waste time on a problem for ex a few days but sometimes its not

[merry cove]

I never really understood reading math textbooks

[hasty stratus]

i do mind maps to have the general concepts in mind

[merry cove]

Yes this has happened for STEP questions 😅

[merry cove]

After u complete a chapter?

That’s a good idea Ty

[hasty stratus]

at the start too

like i try to read the titles only and a few lines to see what the talk is abt

i dont focus on the details at the start

[merry cove]

Ah fairs

[hasty stratus]

ya

but see what works for you

[merry cove]

I think im more of a falashcard person when it comes to learning things

Just active recall each day, maybe I’ll give it a go

[hasty stratus]

yeahh theyre helpful

i just cant bring myself to do them lol

you use anki?

[merry cove]

Haha yea I do

I’ve been using it for my lectures so far

It does take discipline to get used to

Once u make a habit

I think it should stick

[hasty stratus]

yeah ill try to make it a habit

itll be helpful for my german course lol

[merry cove]

👍 definitely for languages

Gl

[hasty stratus]

ty u too

[merry cove]

I did use it for French but got bored of it

[hasty stratus]

yeah u need vocab with context for it to stick

[merry cove]

Tbh I just prefer doing math questions even if i have to stress over for a while

[hasty stratus]

samee

[merry cove]

Anki seems like a supplement in some sense

It’s just annoying when u just don’t know what to do after it’s been more than half an hr of just blank

Then I get one small hint and it somehow works out

But then I feel like I was spoon fed into it

So didn’t gain much

Sorry im yapping

Back to work

[hasty stratus]

nah ur good

growth always uncomfortable

[merry cove]

Yea I just want to do very good in the analysis exam

[hasty stratus]

you got this

[mortal iris]

If you're using Zorich then stick with it, especially if you have multi-part courses that use both volumes. It's a lot different from other analysis texts in that it doesn't shy away from applications while still being rigorous. Supplement it with Cummings if it is hard at some points. If you're also using the second volume I recommend supplementing with Hubbard and Hubbard.

If it's just for the first course then Cummings or Abbott is fine.

[trail void]

a person here recommended to me to use zorich with abbott as supplementary for analysis I

[trail void]

great love immortal venerable

[dusky dome]

I fond of number theory,I have grasped some foundational knowledge.
Can you recommend some interesting advanced number theory books?

[remote sparrow]

do you know any abstract algebra or analysis

[strong mortar]

Anybody know any real analysis books

[tender cobalt]

Any book recommendations for doing some measure theory and functional analysis? 😔

[dim pendant]

Lang

[remote sparrow]

https://measure.axler.net

[molten gulch]

https://measure.axler.net/

[molten gulch]

At what level

[strong mortar]

Dw my question got answered already

Ty tho

[tender cobalt]

thanks

[odd cargo]

i think i've finally came up with the most effective way to study anything math related in an 8 hour window

of course after months of trial and error

All you have to do is.... 1 hour of reading material and the remaining 7 hours contemplating what you've just read

[tender cobalt]

facts...

[odd cargo]

Mind you, this is a statement about the lack of effective writing skills plaguing the mathematics community.

a normal ratio would probably sit around 50/50

[mortal iris]

There is plenty of beautiful material. Just hard to find and of course, even harder to find one that is suited to one's tastes.

I found my "type" and how to look for them virtually after 6 years of studying mathematics and physics, not counting high school.

[odd cargo]

bro got a type

in all seriousness though, i agree, but im too much of a cynic to agree too quickly.

[mortal iris]

Everyone does. Not unlike reading fiction or watching tv lol. There's a style of exposition that I prefer to others.

It's hard to strike a balance with my needs tho. I like real world applications or motivations to mathematical ideas. I like rigorous presentations but would like the rigor also to be well motivated. I like meaningful definitions. Moreover I like visual aid. All this while being concise with exercises that teach me as opposed to unnecessarily challenge me (not mutually exclusive).

[odd cargo]

applications of mathematics are genuinely the most important thing to me.

[mortal iris]

The meaningful definitions bit is the most difficult. I hate to say this but I do not find the notion of a vector space to be well motivated at all for instance. There are plenty of reasons I could give to sell the idea that it's useful but I always will be left wondering "but why specifically this"?

And as I teach linear algebra it's become a headache for me. I do have a couple of ad-hoc physically motivated ideas though, courtesy of a very interesting stack exchange answer I came across years ago. Still... Can't scratch that itch.

[odd cargo]

you could write like a toddler for all i care but atleast provide a problem that puts all of the content you provide in perspective, right?

[mortal iris]

You should look for texts by Soviet and Russian authors from Soviet schools then. One of the reasons I like books by the likes of Arnold, Zorich, Shilov, Kolmogorov, etc. They won't all fit the bill but many would.

[odd cargo]

i already do have a ton of those

my fav being the calculus book by piskunov

[odd cargo]

teaching linear algebra is not good for ones mental being

[mortal iris]

Fairly practical book. It's very commonly used in first year Calculus courses at the IITs of India.

[odd cargo]

which linear algebra resources do you use for that though

[mortal iris]

Well, I do work in quantum information so it's kinda my bread and butter.

[mortal iris]

My own notes ofc (WIP). Primarily based on Shilov. Axler has an interesting perspective that is sometimes useful. There's a few comments Grant makes in his videos that capture some points quite elegantly which I quote. Though I have to strike a delicate balance since my course is a bridge course for high school students who have only been introduced to the elementary physics notion of vectors.

[odd cargo]

are you doing a phd or something?

Also, teaching people what vector spaces are is a pretty gruelling task, good luck with that

[mortal iris]

Nah. I presently teach while finishing up old loose ends and working on a paper from my research in grad school. I am still contemplating a PhD. Honestly enjoy teaching a lot more but I'd like to teach and provide commentaries on teaching math and physics more than work on either of them. It's a bit of a dilemma

[mortal iris]

Yeah I was a TA in a linear algebra course a few years ago. That experience stuck with me. Greenhorn me didn't really question the idea much and just went with it because I could. Teaching is legit humbling but honestly opens you up to lines of questioning that might have escaped you.

Probably why professors are required to teach as a part of their job.

[odd cargo]

you're not chasing a professorship?

dont those need a phd?

[mortal iris]

Well I am not quite sure. I used to be, but not anymore.

[mortal iris]

I mean I will probably end up getting a PhD but I am not quite sure whether research science education as a discipline appeals to me and Idk if there is any point to work in quantum foundations or quantum information.

It's a bit of a dilemma. I even rejected a couple PhD offers since I was not sure and walking into a PhD while being unsure is a very stupid idea.

[odd cargo]

well look bro, not that im trying to make it my responsibility to convince you, but the people who I know (my own father included) who do (or did) teach maths at universities, dont really regret it.

[mortal iris]

Yeah but in this day and age there are plenty of other avenues to educate and communicate. I have the background and experience to also use those avenues if I choose to. Having a PhD doesn't offer me much more than some archaic form of credibility in academia. Whether I need that or not is not something I have been able to make a decision for yet and I most definitely am confused about which direction I should go even if I did decide.

[odd cargo]

you know what, im sort of in the same dilemma when it comes to research in medicine

[mortal iris]

I am on downtime mostly to figure that bit out. It's not like I am not actively teaching or learning. I am in fact working on a paper on curriculum structures and pitfalls in physics education as well with a prof here in my home country given the state of it here for decades. And these bridge courses are something I am building with a network of ppl in academia and in teaching.

[odd cargo]

because in reality, its not all cool dissections and what not (what i used to think it was), its literally p-value dependent research that requires you sit through a lot of hypothesis testing (that a lot of students dont really understand)

[mortal iris]

Well medicine is applied statistical biology lol

[odd cargo]

in a way, but it would probably be a lot more accurate to call biological sciences that rather than medicine.

all in all, 17 year old me wasnt really aware of this at all

[mortal iris]

I was joking tbf. I have no clue about medicine research besides what I've seen on House lol

[odd cargo]

i mean, histopathology is pretty cool, so theres that

probably the only lab work i look forward to

[shadow vector]

has anyone here read this book? Is it good? Any thoughts on it? https://link.springer.com/book/10.1007/978-1-4614-7732-7

[tender cobalt]

any (abstract) algebra book with physics applications?

[old elk]

Does anyone have the arxiv paper on how to prove that two groups are isomorphic?

[naive lava]

like lie groups or like C* algebras?

[tender cobalt]

ye, but for someone without algebra background

[tender cobalt]

also rep theory

basically i wanna learn group theory, rep theory and lie stuff but with physics applications and physics focus

[naive lava]

okay which one lol

[naive lava]

usually, you learn these stuff in QFT and QFT textbooks provide a description for these stuff

but if you want a seperate book

[tender cobalt]

group and rep theory stuff mainly

[naive lava]

you can check out gregori's lie algbebras is particle physics, and group theory in a nutshell

[tender cobalt]

sadly idk qm to start a qft book

[tender cobalt]

okay thanks

[naive lava]

well

if your focus isn't on qft or similar

you probably won't understand the applications

[tender cobalt]

right

[naive lava]

why do you wanna learn rep theory?

[tender cobalt]

it seemed pretty interesting

[naive lava]

I see

[tender cobalt]

and i saw some physics applications with particles and stuff but it seems like ill need to learn qft

[naive lava]

Well maybe check out zee

I think it's zees book although I'm not sure

The nutshell

[tender cobalt]

group theory in a nutshell?

[naive lava]

Yeah

[tender cobalt]

alright thanks

[mortal iris]

This should fit your needs. It is not mathematically rigorous but is written by a mathematician so there is plenty of commentary on issues related to rigor wherever necessary. You also get to learn a bit of quantum theory and qft here in a different way cos it's mostly a quantum theory book but with a focus on groups and representation theory.

[mortal iris]

If you are interested in applications related to cryptography and computer science (no background needed) and a preview of things you will find in physics you can check out Judson's Abstract Algebra.

[mortal iris]

A vast majority of the math that is used in physics is seriously heavy stuff post the calculus and linear algebra. The math background for said topics is a steep curve. There are plenty of nice resources that can give you some access to the tools of the trade but not rigor and vice versa. Rare to find both of them together.

Imo you would benefit from reading Spivak's Physics for Mathematicians volume on Mechanics, particularly the initial parts on Newtonian Mechanics (latter parts need a lot of differential geometry). He has these sections iirc titled "why easy physics is hard" in the sense of intuitively obvious but hard to justify rigorously which would give you a good idea about my above statements.

[minor venture]

<@&268886789983436800>

[slow roost]

you may enjoy Penrose, The Road to Reality

[full pike]

rudin RCA is a good book for complex analysis?

I thinking about rudin or conway

to delve deeper into the content

[naive lava]

no

it's not even about being hard or anything

it's a bad book

you can instead try ahlfors, conway or gamelin

these are some of the popular choices

[full pike]

my professor is gonna use stein

but I think it's pretty superficial

I'll go see conway then, I think

thanks

[shadow vector]

Is it actually realistic to learn any math through that book?

[low ginkgo]

Can anyone recommed me a nice geometry book

[naive lava]

geometry as in? high school?

[low ginkgo]

Yeah

[molten gulch]

Cox little and oshea for computational algebraic geometry, lee is quite common for differential and smooth manifold theory

for proper scheme theoretic AG there's hartshorne

[slow roost]

it is admittedly hard to imagine who would get the most from it

but the first few chapters on the history of science/math are accessible and really well done

and it introduces a lot of interesting stuff, but I don't think it's really learnable from there in a serious way

[normal crystal]

Jacobs, or Gelfand, or AOPS

[whole trail]

Hi, any recommendations on textbooks for algebra 2, trigonometry, precalculus and AP physics 1

[grand thistle]

😭

[mortal iris]

For the intuition to some extent yes, but not a whole lot more than that.

[mortal iris]

Flatland

[wheat swan]

i mostly do differential geometry, spectral theory, and functional analysis, and i kind of want to get into number theory. some texts i’ve seen recommended are a classical introduction to modern number theory by ireland & rosen, introduction to analytic number theory by apostol, and multiplicative number theory by montgomery & dickson.

suggestions?

[vital bane]

Do you do spectral geometry?

[wheat swan]

not really

read a little bit on it

[sage python]

@wheat swan what kinda number theory are you thinking of? Those are all a bit different

Actually given your background, you might like a book called "The Spectrum of Hyperbolic Surfaces" by Bergeron

[wheat swan]

thanks, i'll look into it

[tender cobalt]

Thanks. Actually after a lot of searching I was considering that book but I wasn't sure if it's going to be a good idea to read that without knowing quantum theory

[tender cobalt]

Alright

[tender cobalt]

I see

[mortal iris]

It does not presuppose knowledge of quantum theory.

[tender cobalt]

it seems like the book has very few problems and exercises, what should i do about that

[slow roost]

I hadn’t heard of this one before but it looks extremely cool. I’m a big fan of several books in that SUTM series. I might order this myself while it’s on sale

[mortal iris]

Its more than sufficient if you actually work through the book as opposed to plainly reading it which is pretty much impossible for books like these anyways.

[tender cobalt]

Oh okay, i thought working through the book Isn't enough and that id need exercises

[mortal iris]

There are some exercises for each chapter or a couple of them together at the end of the book in case you didn't notice.

[tender cobalt]

Ye that's what i mean by very few exercises. I dont know if they're gonna be sufficient for my understanding and i want to prevent rote learning as well

[mortal iris]

Rote learning only happens if you do not work through the material. There's plenty of theorems that are not proven. Some steps skipped in several non trivial constructions.

It's the type of book that demands you work through it to understand the material. The exercises are a checkpoint to see if you met the bare minimums.

And this is an introductory book. If you like what you see and are interested, there's plenty to do in both physics and math but that requires further background which you do not yet have.

[tender cobalt]

ohh i see

[tender cobalt]

okay I got it

Thanks for the suggestion, I'll try working through this book

[brittle hornet]

I'm trying to study and catch up in terms of Precalcus and algebra. Does anyone know a good study book I can buy and use?

[jovial venture]

sorry i got one question i want to astart a math and ohyscis journey do yall have any google drives link to give me some good books? thanks

[mortal iris]

Stitz and Zeager

[trail void]

pirating aint allowed here

[jovial venture]

Ok can I get book links so I can buy the books then

[trail void]

ur question is too vague

what do u need exactly

[jovial venture]

😕 basically yh I want to know math intuitvely and not just know math by formular memorization and all at si yh

[vital bane]

I think khan academy would be great tbh

it's a website

[jovial venture]

Aight thank you I'll probably pair it with yt and AI and try to find practice papers

🤓 then maybe I'll do some brilliant.org

[glad basin]

have you watched 3blue1brown on youtube? he does the best in providing math intuition

[stark turret]

Texts for after LADR?

[heady ember]

Whatever you like. For instance, multivariate analysis.

[near jewel]

Pretty broad. What do you want to learn after linear algebra?

[split niche]

anyone know any good linear algebra textbooks?

[heady ember]

Look in pinned

[split niche]

cheers boss

[trail void]

mate ngl there are countless just pick any

[sage kelp]

Friedberg Insel

[pine charm]

Sheldon Axelor

Tbh personally haven’t used it yet but I heard if you’re interested in learning proofs it’s really good

[vital bane]

nah

FIS better

[visual delta]

I read Nathaniel Johnston's two books and they were pretty good. I went from having a friend explain to me what a dot product is at the start of last summer to helping him with his linear algebra homework this semester by reading those books over break.

[lusty anvil]

Damnn

[tender cobalt]

LADW better

[vital bane]

I haven't used LADW tbh

[tender cobalt]

try it bro, ive been reading it and it has goated explanations

[vital bane]

Imo Hoffman Kunze and FIS are peak 🗣️

[vital bane]

Doesn't it only work over R or something?

[tender cobalt]

only over R and C

[vital bane]

do you have a link?

[tender cobalt]

but most results generalize to general fields

[tender cobalt]

https://www.math.brown.edu/streil/papers/LADW/LADW_2017-09-04.pdf

[dusty harness]

Can anyone. Help me how like how to learn integration in two days like any specific yt video or channel cuz I have exam coming up!!!

[mortal iris]

A lot of ppl can help. Whether you learn or not is a different issue altogether. What do you think?

[late lantern]

any books about euclidian geometry specifically triangle and dot reflections? Beginner btw (not olympiad geometry too)

[dusty harness]

Then help and we will see if I learn from it or not that's upto the learner

[mortal iris]

I never said I will. I said a lot of ppl can. Good luck to you.

[mortal iris]

Perhaps have a look at Solomonovich's Euclidean Geometry: A First Course, if it fancies you.

[dim delta]

For the kind of help you’re looking for, I’d suggest going to wyzant and hiring a tutor.

[shadow vector]

I don't get his hate for determinants, they are awesome.

[tender cobalt]

I'm talking about linear algebra done wrong

[shadow vector]

OOhhh nvm lol

[tender cobalt]

i dont get his hate for determinants either

[midnight gulch]

https://tutorial.math.lamar.edu/pdf/Calculus_Cheat_Sheet_Integrals.pdf

if you dont understand any specific thing watch a khan academy video

[gray gazelle]

Get an R.D SHARMA

[molten gulch]

For what field of maths is RD Sharma relevant for, though?

[normal crystal]

RD Sharmatics

[rugged fiber]

Are the 'For the Practical Man' series by D.E. Thompson still good nowadays? Although they were considered very prestigious at the time, I’m not sure if the more complex topics in them are still relevant today

[mortal iris]

Very very poor advice.

[mortal iris]

He was referring to the learn integration in 2 days thing.

[still orbit]

i think i'm glad I don't know whatever an r.d. sharma is

[mortal iris]

It's James Stewart but worse in terms of useful exposition and material covered since it also includes discrete math. Does justice to neither that nor Calculus.

[marble swallow]

I think som questions in James Stewart are very good. But the content is somewhat introduction type

[kindred wind]

House of leaves

[mortal iris]

It is somewhat decent but nothing great tbf. RD Sharma is just worse and packs more content in discrete math

[normal crystal]

@mortal iris I remembered someone in another server mentioned Calculus for scientists and engineers : an analytical approach by KD Joshi and it looked somewhat interesting

[remote sparrow]

what books have you gotten recently

[normal crystal]

my last book from Springer arrived today

[remote sparrow]

right but what are the titles

at least some

and they don't have to be springer

[normal crystal]

the springer ones were Algorithm Design Manual, Data Science Design Manual, the two Calc books by Lax, some texts in CS, and A Modern Intro to Prob and Stat by Dekking

oh, I snagged a pristine copy of Simmons Intro to Topology and Modern Analysis off ebay
I lowballed the seller🤡
they have a bunch of old math texts, probably a retired prof or former student

https://tenor.com/view/shrug-gif-12013959660765767621

[marsh arrow]

Real

[pastel wing]

white people mostard topology book?

[normal crystal]

he has multiple semesters of lectures and support materials for the books

[winter skiff]

Its based on CBSE board's syllabus... covers the basics of high school mathematics

But it is not helpful for practicing very high level questions or concepts

Still good tho

[viscid remnant]

I've seen that book. It does too many things in one book and takes a very fast approach. And I think it only does high level concepts, albeit not very nicely. For low level concepts, you need a specialised book. I do not recommend that book. It does a bad job at allowing the reader to explore mathematics, instead it just hands everything raw. Also there is no clearly perceptible motivation in the book.

It's a very good thing that I did not use that book in hs.

[mortal iris]

If you think that RD Sharma and the likes are useful at any level then mathematics would be crying while you would partake in it in the way the book does. Admittedly there are worse books out there but this is up there with them.

And this is coming from someone who used the book and thought it was great until getting humbled when asked to prove the euclidean division lemma.

Thank goodness I did not end my high school with that trash.

[normal crystal]

publisher will contact you soon to provide this ringing endorsement on the back cover

[viscid remnant]

I meant the same thing yeah, I meant to write that it does not have any low level concepts. I did not mean to say that it is good for high level concepts. Mb. I agree with you 100%

[trail void]

stop asking to be spoon fed

[gray gazelle]

From which book uve completed ur high school mathematics

Is it one of the best Indian maths books for high school

I know it is not the best but it is decent

[viscid remnant]

I live in India too. There are better books. Also it is not necessary for someone in a particular country to use books originating there. The math does no lt change from country to country

As Killuminati pointed out, it's down there with some other not great books

[gray gazelle]

I said it is decent bro

Not so much bad

And sorry for that bro my bad if you r hurt

[viscid remnant]

I'm not hurt lol. Why would I be?

[mortal iris]

For what we were covering I used Higher Algebra by Hall & Knight and Piskunov for Calculus. Also for some missing bits, Rosen's Discrete Mathematics. For Co-ordinate Geometry I was using Pogorelov for the most part. I got these books for very cheap so didn't really bother looking for better ones. These were pretty damn good and covered far more than I needed anyways.

[gray gazelle]

Ok-ok fine bro no more discussion about that my bad ok

[mortal iris]

It's not. It's designed to numb your brain to thinking about mathematics by routine trick-based problem solving and unmotivated theory with zero regard for proof. RD Sharma is honestly not too bad for lower grades when you are learning things like constructions in geometry and basic algebra. But at this level it's trash.

Honestly don't mind a text without good proofs but at least the intuition should be delivered properly.

[gray gazelle]

I am saying at max to max grade 10 it is decent book

[mortal iris]

Yeah. It's not bad up until that point. Not ideal but okay. Still kills the joy of learning the subject imo.

[gray gazelle]

Hmm....

So which book u prefer

Upto 10

[tribal vine]

In my opinion, R. D. Sharma is simply a book for people who want to score easy grades in math and wish no more of a quality association with the subject

[tribal vine]

Look, mate, I've studied in the CBSE board my entire life

[mortal iris]

There is no single one. That is the problem. You may have to use more than one, of which there are plenty. AoPS for Geometry for instance, maybe even Kiselev 1. Hall & Knight for Algebra.

[gray gazelle]

Isn't it too much high leveled for a grade 9 student

[tribal vine]

Yeah, though if you're looking for math resources simply for school and nothing else, then it's a different gamble

[mortal iris]

Hall and Knight have 3 grades of Algebra books which work for grades 6-8, 9-10 and 11-12 equivalent in India. It is still heavily used in some old schools.

[tribal vine]

There's always somewhere to start, in my opinion.

[mortal iris]

Kiselev might be a bit hard on the geometry (esp for self study) but that depends on the teacher to a degree. AoPS is not that hard compared to Indian standards.

[tribal vine]

As long as you have the prerequisites, having a rosy gentle introduction won't teach you as much about university math-related fundamentals as slightly challenging yourself

[tribal vine]

Never heard of Kiselev. Is it an olympiad preparation book, similar to EGMO?

I've never done olympiad prep, so

[mortal iris]

Not meant for Olympiads but is used quite often for that purpose. It's a famous old Russian text.

[gray gazelle]

Teacher is TGT in maths

[mortal iris]

That means nothing in the grander scheme of things bud.

[tribal vine]

I don't see the correlation, tbh. Mine were all PGT and still awful. Learning to be self-reliant helps even in uni where you're dumped with autonomy

[gray gazelle]

Hmm.... So I have to study it by myself

[tribal vine]

Interesting. It seems like a standard Euclidean geometry text, no?

[mortal iris]

It is indeed but aimed at a high school level.

So basically a lot of intuitive constructions and less emphasis on rigor.

That said, still very good geometry book for that level, albeit a bit dense.

As someone who is vocally against texts like Rudin, it should tell you that this book does a good job if not anything else lol.

[tribal vine]

Ah, I guess so, sure. Then again, 11th and 12th grade in the Indian board are almost ripped off of Euclidean geometry from what I remember

The math syllabus has been nastily affected by the board

[mortal iris]

Yeah but 9th and 10th has a little bit. 11th and 12th deals more so with analytical geometry of straight lines and conics.

But hastily done lol

[tribal vine]

Interesting. I'd agree that there are better intros to analysis, if that's what your gripe with that is

https://classicalrealanalysis.info/com/documents/TBB-AllChapters-Portrait.pdf
Came across this in the Analysis OCW (MIT) course, and quite well-written imo.

[mortal iris]

There's a bit more. I'm a physicist. I do not like the "this book is too good to apply anywhere" snobbery.

[cursive rivet]

How do people feel about Goertz and Wedhorn's books on AG? I want to learn schemes more thoroughly (I know some already), but dislike Vakil's writing and am moderately scared of Hartshorne (though that's where I learned some from in the past)

[tribal vine]

Oh, alright. I'm a statistics student. I think the Rudin series were considered standard because of the rigour overdrive that the above-average analysis course required, no?

The one in my uni doesn't use Rudin though (or equally known texts like Abbott)

[mortal iris]

That rigor and more can be found in texts like Zorich which includes plenty of applications in physics and some in economics too. Abbott and Cummings are great introductions as well and have the requisite rigor for an analysis text.

[tribal vine]

Yeah, the analytical geometry in 11th and 12th grades was not my strong suit

[tribal vine]

Ah, interesting. Never heard of Zorich, will check it out!

[mortal iris]

Brevity does not mean rigor. Rudin's text is notoriously unmotivated and dry. I mean, if I were to use Lean with Rudin I would probably kill myself. It's a handy reference to have I am told but I have never referred to it once since I did Analysis as opposed to the others I mention.

[molten gulch]

I think @dapper root read them before so I'll CC him here

[dapper root]

They’re good, I like them

Have the errata handy

[molten gulch]

how are the exercises compared to hartshorne?

[cursive rivet]

can you comment on the writing style and what parts you like?

I appreciate it

[dapper root]

Idk what “writing style” really means

It’s pretty German, things are handled with a good amount of category theory but not excessive I don’t know how to describe it other than that it’s German. If you read enough AG you’ll eventually get what I mean

Exercises are more approachable than Hartshorne

I think that overall it has more details which on a first pass you would wish Hartshorne had, but it’s also more modern. It treats things in a more modern way (volume 2 uses the derived category) which is, I think, good

There’s just a lot of typos so the errata is handy to have nearby

I would say it’s like if Hartshorne was more like the stacks project, you’d get Gortz and Wedhorn

[cursive rivet]

I certainly know what German writing means haha, I've read plenty of German DG and complex AG

[molten gulch]

Alex, in your opinion what makes a certain text more "German" in its writing style?

[cursive rivet]

it's hard to describe as a fluent German speaker, since it feels like one just translates German text to English without translating the "standard" writing style

I'll try to think of it and get back to you, have a meeting in a few minutes

[molten gulch]

Sounds good, hope the meeting goes well

[dapper root]

I actually meant that the mathematical style and choice of presentation is German

Like, it reflects what the German algebraic geometers need, they talk about some like more technical finiteness conditions which Hartshorne doesn’t talk about. They aren’t as important for like, geometry over C or over fields, but matters when things are over Z or are not finite type etc and that reflects what the German mathematicians do, since a lot of them are doing arithmetic shit

[molten gulch]

Ahhh that makes sense

[short depot]

Book for Calc 3 ?

I want the best one

[molten gulch]

No such thing as "the best"

But I quite like Hubbard and Hubbard - Vector Calculus, Linear Algebra, and Differential Forms: A Unified Approach

[short depot]

Aaah i see thnx

I'll look into it

[trail void]

i was told to read it as supplementary with analysis II

that works?

[mortal iris]

Buddy, you have been asking about this for like forever. Either stop second guessing or stop asking lol. The whole thing depends on what you want to even call analysis 2, which I have mentioned the last N times with N tending to infinity.

The way Zorich's volumes go, the second one is dedicated to Differential Calculus on Normed Vector Spaces, Integration of Differential Forms, Analysis of Vector Fields, Analysis of Families of Functions, Fourier Analysis and Asymptotic Expansions. Hubbard and Hubbard also covers a sizeable portion of this and very well, as well as things like the Lebesgue Integral which Zorich does not.

If you don't like the suggestion, reject it. Don't play around asking ppl to reiterate over and over again.

[molten gulch]

<@&268886789983436800> user has been asking the exact same questions repeatedly for days and rehashing the same arguments

[split portal]

Sometimes people just want multiple opinions

[remote knoll]

Like maliciously? This doesn't read as malicious to me

[mortal iris]

It's not malicious but it's spam worthy atp

[mortal iris]

I agree but how many multiples is enough?

[remote knoll]

One guy asking one question three times in as many days?

Or am I missing some other context?

[split portal]

They have like 7 messages total

[split portal]

Is your question answered at this point?

We are getting complaints now, so it seems like maybe it's time to just start studying the recs you've gotten rather being stuck in some kind of choice paralysis situation.

Ah wait

Hmmm I am referring to the wrong person lmao

@trail void you instead

[mortal iris]

Not sure about the time frame but repeated requests/discussions have been initiated about recommended analysis texts which all seemed to end in natural conclusions until one more popped up. There have been many recommendations made many times and not only by me.

[split portal]

There are posts on mse for this kind of thing as well.

It's not like there is one single best book in analysis.

[molten gulch]

Also just analysis texts in general have been recommended so many times that almost every angle of almost every major textbook have been covered in some manner or another which proper usage of the Discord search function could reveal without needing to ask again because it seems like inevitably the same people who responded to the question 6 months ago are going to respond today

This is ofourse unless you decide to ask a more pointed question on specific features which may not have been answered before, but even then the nice old adage of CHECK IF THIS WAS ALREADY ASKED should be in enforcement

[split portal]

You pick one and try it. Either you fail or it works. If it doesn't work you try some other thing.

[full cairn]

Is it really spamming? As far as I can tell he asked about an analysis book a week ago, then asked a follow-up question 3 days ago. I can't see where he specifically asked for the same recommendation repeatedly

[split portal]

I don't think it's spam

I think people are getting annoyed at seeing the same q over and over.

I'm assuming the other person is in a choice paralysis situation

Which is also sort of understandable.

[full cairn]

yeah, that's understandable, but that's kinda the nature of this channel. Different people will ask the same questions over and over again

[split portal]

Yeah. I don't think anybody is doing anything explicitly wrong here. I just think the user we've got the complaint about is just at a point where they probably have the info they need and just need to pick a particular book and try it.

Tbh I think in their msg history they mentioned they might start with proofs or something. So they may also just be metagaming too much.

[mortal iris]

Yep. Nearly a month since.

[hallow oriole]

does cambridge press ever have any discounts? springer has a very decent discount rn, but cambridge i am NOT buying ts book for 158 usd

[normal crystal]

they have their own weirdness
a bunch of their textbooks have relatively low prices and can be found cheaper
but rando hardcovers will be overpriced

[slow roost]

anyone know if any good springer ODE books are currently on sale?

and/or PDE

[hallow oriole]

jost and perko are on sale but i don't know how good either of them are

[normal crystal]

it's not on springer, but it's over half off on Amazon new, pretty cheap
ryc said they use this for the NYU classes he TAed/taught
https://www.amazon.com/dp/0387978941/

[slow roost]

oh I might go for Jost.. I have his riemannian geo / geometric analysis book and it's very interesting but also very challenging for me

[slow roost]

I really like this front cover!

[remote sparrow]

maybe save ur money for taylor

or have it printed

[naive lava]

jost is like this huge ass book with a billion topics mostly relevant to physics

and when you originally write a book with 4 chapters and then decide to add 25 more

it gets a bit messy

also quite dense

[slow roost]

I'm thinking it could be good for if I want to get more serious about diff geo

[naive lava]

have you considered nicolasceu

i didn't quite like it but ppl do

[slow roost]

nope, I'm not familiar

this looks pretty nice for undergrad ODE material https://link.springer.com/book/10.1007/978-3-031-11531-8

I like Essential Topology a lot from the same series

the only ODE book I have is Zill, which isn't bad but feels more aimed at general STEM majors

[slow roost]

is it Lectures on the Geometry of Manifolds?

[naive lava]

yeah

[vital bane]

Spivak

[thorn hinge]

What book is the best for this:

Extension theorems for measures and integrals. Basic convergence theorems. Signed measures. Hahn-Jordan decomposition theorem. Absolutely continuous measures. Lebesgue decomposition theorem. Radon-Nikodym theorem. L^p spaces: basic properties, duality. Product spaces. Fubini-Tonelli theorem. Riesz-Markov representation theorem. Convergence in measure. Relationship between differentiation and integration: Vitali theorem, Lebesgue differentiation theorem.

?

[tiny crescent]

which book is best to learn groups and rings and fields theory
im a pre uni and i need a book give everything i need

is there one?

not dummit & foote cuz i find it more advanced and complicated for me

[thorn hinge]

Hungeford

https://link.springer.com/book/10.1007/978-1-4612-6101-8

[mortal iris]

Bruh. He said pre uni and Dummit and Foote is too advanced. This is worse.

[thorn hinge]

I mean, he assumes nothing and starts from set theory

[tiny crescent]

yea

[thorn hinge]

If you find algebra hard, you should start studying basic number theory

[tiny crescent]

what

[thorn hinge]

Things like properties of Z, GCD, etc

[tiny crescent]

no need for that i guess

[tiny crescent]

foundation of mathematics i good for uni algebra?

[mortal iris]

Still moves at a breakneck pace and you don't really need exposure to axiomatic set theory for being introduced to abstract algebra.

[mortal iris]

For an introduction, you can try Judson's AATA. I highly recommend doing the sage math exercises as well.

[thorn hinge]

Sorry

[thorn hinge]

Yeah, I was thinking something like this. Chapter 2 has basic properties of Z, euclidean algorithm etc

[wet sentinel]

lang's algebra

(warning: do not try that)

[tiny crescent]

دز يخوي

[wet sentinel]

لا هوي أصعب من D&F

[chrome wasp]

Maybe you could try some of those book and watch some online lectures going thru them

[wet sentinel]

bsm3 2no kotob mtl fraleigh w gallian 2ashal mn D&F. jrib wa7d mnn 2za bdk

[chrome wasp]

I think there are lectures on yt from some university based on Artin book

[tiny crescent]

3jbni al sarahah

[tiny crescent]

Socratica you mean?

[wet sentinel]

lang?

[tiny crescent]

Aywh

[wet sentinel]

jrbo 2za bdk bs ma bns7k fi, 2za l2yto ktir s3b w2f

l2no btt3b 3l fadi 2za l2yto s3b ktir, w bye5d m3k w2t twil

[tiny crescent]

Awl 3 chapters msh s3bin?

[wet sentinel]

bs fik tjrbo 3adi

[tiny crescent]

Akid ma rah akhls klh abi bs awl 3 chapters

Groups rings fields

[wet sentinel]

blsh b2wl chapter, 2za ma l2yto s3b kml fi

[wet sentinel]

fields chapter 5

2za ma bdk modules fik t2fi chapter 3

[tiny crescent]

Mdre

Bjrb D&F shkle

[chrome wasp]

https://youtu.be/YRdSQtGo73Y?si=RF6AdCkAa1LpN0yJ

[wet sentinel]

mtl ma bdk, 2nti 2lt 2no D&F mle2i s3b shwy. 2za bdk rja3 jrb fi, w 2za bdk 8yro bsm3 2no hodi lkteben 2ashal

lek 5lina n7ki 2nglizi 3shen lkl yfhm 😂

w 3shen ma yjo lyna hl2

[tiny crescent]

Even D&F is hard?

[wet sentinel]

it depends on the person. you said that you found D&F a bit hard right?

it also depends on the background

[tiny crescent]

There are many chapters that I don't think I will need in my university specifically

947 pages is so ahh

[chrome wasp]

Why are you learning it?

[tiny crescent]

Learning groups and preparing for mu final

My

[wet sentinel]

ohhh, you shouldnt read it all

[tiny crescent]

Then what should i read

Learning groups and rings and fields is enough for me tbh

[wet sentinel]

well you can read the chapters about this then

so rn you want to study these for fun right?

[tiny crescent]

For fun and also for my final exam

[wet sentinel]

you have groups, rings and fields for your final exam before uni?

[wet sentinel]

i see

[tiny crescent]

Bro im pre uni

Uni final exam i mean

[wet sentinel]

i see mb

[chrome wasp]

I dont get it... you are not enrolled into uni right?

Anyway

[tiny crescent]

.

[wet sentinel]

ok then go for D&F, honestly i dont like it because it talks alot. Tho other people do like it, and almost all reviews are good about it.
Also here is a list of abstract algebra books:
#book-recommendations message

[tiny crescent]

[wet sentinel]

yea i tried it and tossed it away because i didnt like it ngl

tho that doesnt mean its bad or anything

just that its not aligned with my tastes

[tiny crescent]

• Groups: definitions; subgroups; examples; group homomorphisms; group isomorphisms. Give examples of finite groups \mathbb{Z}/n\mathbb{Z} (n = 1, 2, 3, \ldots) and the permutation group S_3.
• Rings: definition; subrings; rules of computation in a ring; units (invertible elements); zero divisors; ring homomorphisms; ideals.
• Fields: definitions; study the case of a finite field through the example \mathbb{Z}/p\mathbb{Z} where p is prime; the fields \mathbb{R} and \mathbb{C}.

Thats what we study at uni

[chrome wasp]

I think its hard to start on your own reading math book until you get some mathematical maturity and experience. Its a lot of helpful when you follow teacher, having someone to regurgitate information for you, make it easier connect the dots, see theirs thinking process approaching problem. Thats why maybe some recorded lectures can be helpful. I havent tried it for myself tbh.

[tiny crescent]

I want to read the whole book if I can, but I have some other modules

[tiny crescent]

Take courses you mean?

[wet sentinel]

I mean at some point everyone will have to just read books/papers on their own with no instructor/teacher

so imo its better one starts this process early on to not struggle with this later

[tiny crescent]

Our teacher is ass tbh in uni

He explain in french instead of english

[wet sentinel]

tho of course lectures on yt are helpful and i am not saying that one shouldnt watch them

[tiny crescent]

My level of French is not sufficient to study with him.

[wet sentinel]

reminds me of lebanon

specifically lebanese university

[tiny crescent]

The same with algeria

Taking courses in french is so ahh

I mean i dont hate french

But english is better tbh

Anyways

Maybe I'll read D&F

[wet sentinel]

and if you want check the books in this linked message

there is a brief description of each of the books

[dusk patrol]

anyone of trigonometry book suggestions

[molten gulch]

Loney

[dusk patrol]

"Plane Trigonometry By S. L. Loney, M.A."?

[remote sparrow]

pinter and/or judson

[molten gulch]

yes

[tribal vine]

Hi folks, do any of you have suggestions for good combinatorics techniques books? Want to strengthen combinatorics concepts especially for tackling some interesting discrete math problems (which also spill over in probability)

Any thoughts on Principles and Techniques of Combinatorics by Chen Chuan-Chong and Koh Khee-Meng? I hear it's a decent textbook for this purpose

[cloud imp]

Does anyone have any lecture notes/book recommendations for getting into Galois-module theory? For reference, I'm at a PUI and have taken all advanced abstract algebra courses my undergrad has to offer (we primarily used Artin); however, my background in things like categories or algebraic number theory is very sparse. I think I would really like the subject, but I'm slightly lost on what materials are most appropriate for my limited background, loll

[inland tundra]

can you read german?

[hybrid sigil]

I like Miklós Bóna “A Walk through Combinatorics”, I think his explanations are good and there are many interesting problems! (they are not easy, but have solutions right in the book). Also the third part of the book gives a taster for more advanced areas of combinatorics (I haven’t read much from that part though)

[verbal bolt]

Has anyone read Blood Over Bright Haven?

[cloud imp]

Sadly, no. :(

However, I can read Russian, if that helps! :-)

[inland tundra]

yeah, i couldve sent you a script about galois but its sadly written in german

[honest reef]

What is the equivalent of Evan Chen's "Euclidean Geometry in
Mathematical Olympiads" but for other math Olympiad topics, namely, combinatorics, numbertheory, and algebra?

[lucid flicker]

what are some good maths books

[molten gulch]

At what level, in which topics

[lucid flicker]

Calculus I level, doesn't matter what topics, could be a variety

[molten gulch]

abbott understanding analysis

[scenic sequoia]

Apostol

[lucid flicker]

Thanks

[cunning elk]

maybe try "modern olympiad number theory" for NT?

[odd cargo]

calculus 1?

[molten gulch]

<@&268886789983436800> user is requesting pirated materials

[split portal]

Due to discord tos we can't allow this kind of thing.

[mighty pewter]

???

What

[mighty pewter]

Dude the people in the server told me to go in this channel and ask wytb

how is pirated material if someone bought it and is giving me the book?

[split portal]

If it's copyrighted and paid for how is that not literally what piracy refers to?

I do not care what other people told you to do.

I do not care what you do off the server.

I care about not violating tos and having discord have a reason to do something stupid like delete the server.

[molten gulch]

If you request a PDF, because PDFs generally have terms of use rules from the publisher preventing resale or distribution, then it's piracy. Physical books are fine at-least in the US under first sale doctrine

Discord's primary servers are hosted in the US fwiw

[daring wolf]

vro is not able to use noggin

🥀

[mighty pewter]

https://tenor.com/view/staring-not-funny-laughing-memes-meme-gif-20679699

Whatever bud

[mighty pewter]

ok

[mighty pewter]

https://cdn.discordapp.com/attachments/1378091918768083127/1445942028931170436/IMG_6271.gif

[wet sentinel]

lol no one is telling you that pirating is bad, just that it shouldnt be discussed because the server may be forced to shut down if something like this happens