book-recommendations

[trail hemlock]

for elementry math prob not right? cuz single-variable calc has not changed that much since the 1970s

[tawny copper]

Many pre latex books are alright

Even that very ugly typesetting, I think youd get used to it if you had to read it

[trim kayak]

Well, some older math books have black and white images vs. colorful images. The only thing I think may differ is a Financial Math textbook. The tax tables and various cost of items such as a car or a house would be out of date. Otherwise, the math is the same. All 3 angles of a triangle add to 180 degrees 40 years ago and they still do today. 🙂

I know nothing about latex

[hallow pivot]

if I had to choose a rigorous book on formal logic what would you recommend?

just and only one book

[violet shuttle]

the way we taught has

it used to be that calculus classes were just real analysis classes

also, one wants the latex

[hallow oriole]

oh, yeah, the content is fine, don't get me wrong. i'm just spoiled

[violet shuttle]

your last statement is literally false

now, 1970 onwards will be fine

that doesn't count as old to me

note that schemes first came in 1960

along with the zariski topology on the spec of prime ideals

it was Zariski [1952] who introduced a topology on an arbitrary algebraic variety, by taking its algebraic subsets as closed sets; then Grothendieck [1960], exploiting the correspondence between points of an affine variety and maximal ideals of its coordinate ring, transferred Zariski's topology to the set of prime ideals of an arbitrary commutative ring.

https://math.stackexchange.com/questions/55259/did-zariski-really-define-the-zariski-topology-on-the-prime-spectrum-of-a-ring

[golden salmon]

I count anything pre-2005 as old :P

[trail hemlock]

i knew someone was gonna say it 😭

[trail hemlock]

i think throwing a rigerous calc book in there instead of a computational one is just better

but yeah ive heard ppl who just learn analysis before calc (like hyzae)

[crude sage]

On the topic of alg geo, how does one get into the subject starting from basic undergrad groups/rings/fields knowledge?

(of course I am fishing for a booklist)

[violet shuttle]

Most of the math I know was worked out from ~1850-~1950

[golden salmon]

I was first introduced to Alg. Geo. via The Rising Sea by Ravi Vakil, but I didn't really enjoy it and just skipped around it. I recently came across https://stacks.math.columbia.edu/ which seems to be a very slow and robust entry to Stacks (an object in Alg Geo which has lots of useful properties for generalising sheaves). There's also Hartshorne, which I hear is good but haven't tried

Short ver: uhhh try stacks I like it so far

[violet shuttle]

Read the part about Lang that he says is needed for Hartshorne

Then Hartshorne

I haven't done this yet

But it's probably a good idea

[crude sage]

I hear Hartshorne has a reputation

"The student who wants to get through the technical material of algebraic geometry quickly and at full strength should perhaps turn to Hartshorne’s book [37]; however, my experience is that some graduate students (by no means all) can work hard for a year or two on Chapters 2–3 of Hartshorne, and still know more-or-less nothing at the end of it. "

from the preface to Shafarevich's book

[golden salmon]

https://link.springer.com/book/10.1007/978-1-4757-3849-0 Check it out for yourself

its a free download from springerlink, which is the official publisher

[crude sage]

I will check these out, thank you both

[trim kayak]

You think the content of math books have changed over the years?

[remote ginkgo]

triangles don't necessarily have angles adding up to 180

[lusty ermine]

internal ones?

but whatever

[hallow oriole]

they're probably talking abt triangles on a sphere

[lusty ermine]

I think she made the point through

[hallow oriole]

from context it was clearly in r2 so this is just pedantry

[trim kayak]

Did I make sense? I could be wrong but the content hasn't changed over time. There are newer books with better explanations and examples but the content is the same.

[golden salmon]

IDK I think every decade there's really interesting papers and books written. I won't pretend I read them all but I enjoy the contemporary approach whenever I bump into it. It's even more pronounced in physics. Go read e.g. Dirac's QM (1930's) vs e.g. Shankar (1980s) or Townsend (1990s).

[remote sparrow]

for learning or for reference

[hallow pivot]

self study

[remote sparrow]

https://knightscholar.geneseo.edu/cgi/viewcontent.cgi?article=1005&context=geneseo-authors

[hallow pivot]

thx

[violet shuttle]

not just pedantry

it's also memeing

look i'm taking a riemannian geometry class thus i must

[violet shuttle]

it depends what timescale

of course if you are new enough the content will have literally been made yesterday

but I already gave examples of stuff that only came about past 1950

and definitely you should be past 1920s

Let's take examples from "undergraduate" mathematics:

Urysohn metrization is from 1926

Tychonoff's theorem is somehow later, from 1935

generalized stokes in its modern form is due to Cartan from 1945

zariski topology as i mentioned is from 1960

Hewitt Savage's 0-1 law is from 1953

(Kolmogorov's is from 1928)

the first rigorous classification of semisimple lie algebras is from (baby) cartan in 1894, though dynkin diagrams are from 1946

Synge's theorem comes from 1936. I have no idea how this can come before generalized stokes.

[violet shuttle]

if you look at the books the difference is obvious

if they are nice and beautiful like

$R^{j}(F)(\tilde{A} \oplus (B \otimes \bigcup_{i \in I} C_i) \oplus \mathbb{C}$

that's latex

[hasty eagle]

Xela

[violet shuttle]

or $\langle \phi \vert \psi \rangle = \int_{-\infty}^{\infty} \phi^{*}(x) \psi(x) dx$ with $\phi, \psi \in L^2(\mathbb{R})$

[hasty eagle]

Xela

[violet shuttle]

(this should showcase most of what you see)

[violet shuttle]

Now you said "content"

the content changes more than the mathematics

due to what's usually taught

e.g. whether calculus is literally just real analysis or not

[molten mason]

Any calc book written after ~1960 is perfectly fine

[mellow wren]

Hartshorne is a trial by fire from which one emerges knowing quite a bit

In my experience at least

[remote vortex]

Of course one possible outcome of a trial of fire is not emerging at all

[violet shuttle]

which is why i sell fire protectant gear to any community that has a sizable population embarking on trials by fire

[bronze current]

Hey , have anyone of you have read "A School Geometry" ? My teacher gave me a copy of it , and asked me to practice form it but I cant seem to find the answers in it , kindly help 🙂

[flat marten]

Alot of maths books simply don't have answers in them in afraid

[royal gale]

I'm searching for some too

[trim kayak]

Or they will have answers to the odd-numbered problems only.

[vital bane]

is that called matsumura

[molten mason]

I'm laughing out loud that I never considered this as a possibility and I'll be using it from now on

[molten mason]

Quizlet Plus (like $8/mo) has answers to both odd and even of many popular textbooks. For example Stewart's calculus. Not just the answers, but complete walkthrough

[trim kayak]

Oohh thats interesting. I've used Quizlet many times. Didn't know there was a Plus too.

You think Stewart's Calc book is good? I want one to read through and learn from just for fun. Don't laugh.

[molten mason]

They're all the same IMO. And with each author, the editions are mostly all the same.

Literally any book in the last few decades will work.

If you want to stick to a single author for both Calculus and Linear Algebra, I like and recommend Howard Anton for that.

[slender cargo]

Didn't you say you've already taken two Calculus courses? You'll learn far more if you go with something more advanced.

Just pick up a Real Analysis book

[trim kayak]

Yeah I have but it was years ago and I dont remember much.

[kind kayak]

any book recs for math history; things like interesting mathematician biographies or history of certain fields of math

[trail hemlock]

you can make a new account every week and cop the free trial

[trail hemlock]

i used a pdf of “yet another introduction to real analysis” before rudin, there’s no need to relearn the whole of calculus

[viscid comet]

I need a text on fourier analysis

that prefrably also mentions its discretized transforms and w/e

need it for a skool thing

[trail hemlock]

thoughts on this series?

https://www.ams.org/bookpages/simon
the fact that it’s all by 1 author is nice, but so is daddy and grandpa rudin

[gray gazelle]

how do I disable im studying

,im not studying

,done

[stuck zephyr]

,iamnot studying or go to browser channel

[hasty eagle]

No selfroles matching studying or go to browser channel.
See ,selfroles --list for the list of valid selfroles.

Mar 26, 2024, 4:13 PM

[stuck zephyr]

they both work

[gray gazelle]

,iamnot studying

[hasty eagle]

Removed the studying! role from you.

[gray gazelle]

thonks

[stuck zephyr]

np

[storm zinc]

I see a lot of people recommend Friedberg for Linear Algebra. Are there any well known online lectures that also use the book?

[tribal crow]

[tribal crow]

I believe Dr. Peyam on YouTube used FIS

he has quite a few LA playlists

that basically cover the first 5 chapters of the book

[storm zinc]

Awesome, thank you! Hoping I'll be able to figure it out just by reading but nice to have some lectures for confirmation.

[tribal crow]

there are probably lectures from others too, but I don’t know of any

sorry

[storm zinc]

np, ill do some googling too, i just know it gets recommended here a lot so thought id shoot my shot

if i find any good ones ill let the people know lol

[remote sparrow]

i'm pretty sure there's an instructor's solutions manual associated with it. there's also a student solutions manual that's sold with it too.

[dreamy ridge]

Hello, can someone recommend an article or book that will explain to me the concept of Generalized Szasz-Mirakyan Operators?

[sleek python]

How do the solution manuals differ to justify different books

[crude sage]

If I have learned anything from this channel, it is that people who read Rudin, Hartshorne, or Lang enjoy suffering

[native cradle]

any good casual books for an introduction to analysis ?

[crude sage]

Abbott's Understanding Analysis is good

[native cradle]

hmm, thanks

[violet shuttle]

baby rudin

[crude sage]

If baby rudin is casual, what is a "serious" intro analysis book?

[tribal crow]

Folland

[cerulean rain]

guys can someone tells me a good calculus book writen in french

calculus 1

[tribal crow]

I’ve seen Schroeder recommended before too, but I haven’t read it myself

I hear it’s very good though

[molten mason]

I'll rather just pay the $8 lmao

[molten mason]

How was it

[molten mason]

I've seen that posted here before. I forgot who shared it.

Also Lang has an entire degree by one author

[hexed forum]

Has anyone found a good book for general visual review? From maybe prealg to complex or something..

Anything more in depth I can google. Just trying to reboot my mems

[remote sparrow]

what?

the solution manuals have all the answers in one place

no searching necessary

there are probably even some instructor solutions manuals leaked online

they are presumably scrutinized by an editor

[loud cradle]

probably meant, what's the difference between the student solution manual and the instructor solution manual (i also don't know)

[remote sparrow]

the instructor's solutions manual has all problems worked out

the student solutions manual might only have the odd problems worked out

[loud cradle]

ah, sounds valid

[remote vortex]

That was a joke recommendation as intro to analysis, but on the other hand it's genuinely a very decent measure theory textbook, even as intro.

Not as accessible as Axler, but not as actively hostile as Rudin

[tribal crow]

mhm

I might read it one day

[loud cradle]

folland does have a "baby" version (advanced calculus is the title), freely available on his website, physical book out of print

[remote vortex]

Ah, neat, the only Folland I know is his real analysis one.

[tribal crow]

yeah I’m probably going to read this one too

but I was referencing his measure theory one earlier lmao

[loud cradle]

yea, his measure theory one is the main one that people know

[sleek python]

but why is there a need to have an instructor's solutions manual as well as a students solutions manual? I don't see how the answers to the problems would change for a student or an instructor

[remote sparrow]

so that lazy instructors can assign some problems from the book without worrying about students just copying down the instructor's solutions manual?

the instructor's solutions manual is usually not available to the general public; you have to provide some kind of credential (generally a valid institutional email) in order to buy one

[trail hemlock]

pretty good. but it didn’t give me any real advantage, just a refresher.

[trail hemlock]

in lang we trust

[pliant wadi]

Has anybody here heard about Leonard M. Blumenthal? How often have you come across his work? This guy even had an award named after him that was later discontinued.

[sleek python]

But they could just copy from the student's solutions manual

[sleek python]

There is Blumenthal's 0-1 law in probability, likely named after him since I don't know another Blumenthal

Nvm just checked on wikipedia and it's not the same Blumenthal

[violet shuttle]

isn't folland pretty good?

like very good?

[tribal crow]

that’s what I hear yeah

but it’s probably not good as a very first introduction

lmao

[violet shuttle]

baby rudin shouldn't be used past chapter 8

oh i heard that folland was easier than rudin

[tribal crow]

hm?

Folland’s measure theory book?

or you mean his Advanced Calculus?

[remote vortex]

I haven't read grandpa Rudin, but Folland's Real Analysis is reasonably accessible

And I doubt any Rudin book can be described as "reasonably accessible"

[violet shuttle]

I mean this one

or real analysis

I think I meant real analysis

I thought they were the same book

[remote vortex]

Folland's measure theory book is titled "Real analysis"

But it doesn't cover stuff like sequences, derivatives or Riemann integral

It's mostly measure theory, and some functional analysis

[violet shuttle]

oh, okay

[crimson leaf]

Royden is probably the most accessible measure theory book I'd imagine it's so easy to read it's kind of nice

[remote vortex]

Axler is great

and legally downloadable

[trail hemlock]

to be fair, only “downloadable” really matters

[remote vortex]

nevertheless

he's publishing it in open access

measure.axler.net

[trail hemlock]

nice

there’s so many real analysis books i’m tempted to stick with 1 author

[tribal crow]

you can always get a physical copy too

[tribal crow]

everything is free if you run fast enough

[trail hemlock]

parents said no more

[jade sluice]

should read the darkest minds

series

[remote sparrow]

did you miss the part where i said the student's solutions manuals don't have every problem worked out? an instructor could just assign the problems that aren't worked out in the student's solutions manual

[sleek python]

Oh yeah I did miss that message

[remote sparrow]

doesn't the newest edition have a lot of typos?

[gray gazelle]

Math books or any type?

[ashen axle]

Can someone recommend me a book about trigonometry and geometric?

[bright epoch]

I am going to be studying Lie Groups with an applied mathematician who is pretty far from physics this summer, but I barely know anything about Lie Groups. I have some knowledge of rep theory, but not enough. What's a good book for that level

[tender wyvern]

for euclidean geometry you can try evan chen's book but that's more geared towards olympiad maths rather than school/uni maths

[bright epoch]

I really liked Coxeters geometry, though I haven't read it in forever

I think it's something like Revisiting Geometry?

[violet shuttle]

I like Fulton and Harris. At first I was put off by their approach, but, I have come to think it makes sense. I recommend reading the chapter giving the lie group lie algebra correspondence, the example chapters about sl2(C) and sl3(C), and chapter 14 and the other later one (on root systems) to see the general theory. Do those two example chapters first, they are critical and basically teach you the core of what's going on.

You are a physicser first, yes? Then think of a Lie Group acting on a manifold, (e.g. rotation), and the derivative of the action as being an action of the lie algebra (e.g. angular momentum operators). Likewise if G->GL(V) you can take a derivative and get \fraktur{g}->\fraktur{gl}(V). The hard part of the lie group lie algebra correspondence is going backwards.

SO3 acts on 3D space by rotating. If you take the infinitesimal generators, your matrices will literally just be the ones that do a cross product.

In quantum mechanics, rotation by theta is exp(-i \theta L/\hbar)

where L is the angular momentum operator

[bright epoch]

I'm not a physicist, I see why that was confusing; I just saw a lot of texts which were for physicists

but Fulton and Harris looks good, I'll look through that

[violet shuttle]

Oh, oops.

[bright epoch]

nah that's my b

[violet shuttle]

I wasn't sure, then saw a black hole in the pfp and jumped to conclusions 🙂

[bright epoch]

lol fair enough

someone else reccomended Hall to me on this; do you know how it compares to Fulton and Harris?

[violet shuttle]

I didn't like it as much

The biggest selling point to me is that there's a fleshed out section on compact lie groups.

It is easier going than Fulton and Harris.

[bright epoch]

interesting. Thanks!

[crimson leaf]

What's a good book to pair with Davenport's multiplicative number theory?

[lost bobcat]

i am a 9 th grader i know basic algebra some basic trigonometry and precalculus could you recommend me some beginners level books for learning more mathematics
i need to know some more maths concept to get into machine learning

[lusty ermine]

Books to get good at real anal? Undergrad

[remote sparrow]

you can usually find some pamphlets or booklets in sexual health clinics, but not often books

[remote sparrow]

#book-recommendations message

[torn crypt]

@wicked fractal

[wicked fractal]

Davenport has a major focus on Dirichlet's theorem. I'd pair it with Apostol's analytic number theory just in case. In case you want to go deeper into Riemann zeta function, I'd recommend Titchmarsh's book. If you want to learn about sieve methods as a "starter pack" I'd recommend Murty and Cojocaru's book then maybe after try Dimitris' book

[crimson leaf]

Yeah I bought Davenport before knowing it didn't have exercises 😢 I'm not sure what I want to learn about tbh I'm learning complex analysis rn and I just wanted to get a feel for the area and see how I like it

[trim kayak]

My brain is exhausted but I'm always interested in reading and learning math. I don't think I can process information and think about math problems right now though. Let me know your favorite math textbooks for Algebra, Geo, Trig, Calc, or Stats and I will check them out! 🙂

[bright epoch]

Algebra like algebra algebra or like the high school subject

Either way The Symmetry of Things by Conway et Al was a fun read and not super mentally taxing

[trim kayak]

Either one. Algebra Algebra is good and so is the hs subject. Oooh I'll check that out. Thanks

[violet shuttle]

Lang's Algebra. Rudin's Principles of Mathematical Analysis. Hatcher's Algebraic Topology. Fulton and Harris's Representation Theory. Real Analysis for Graduate Students, by some prof (you should probably try Folland or Tao instead). Kallenberg's Foundations of Modern Probability.

Munkres Topology

Lee's Introduction to Smooth Manifolds, and also his one on riemannian manifolds.

[bright epoch]

Another book which is maybe not strictly on any of the topics you mentioned but is similarly less intense than your average textbook is strogatz nonlinear dynamics

[violet shuttle]

those are books I ended up liking

[trim kayak]

Is the Symmetry of Things a scholarly article? I found an article...

Thanks for the recommendations

[bright epoch]

It's a book

Maybe also an article?

[trim kayak]

Ahh. The book is Symmetries of Things. Found it

It looks interesting

[gray gazelle]

Did you read all of Lang?

[violet shuttle]

not yet

have barely read kallenberg

[gray gazelle]

how far in are you?

[violet shuttle]

Well, I read the section on group, the section on rings, most of the section on polynomials, then enough of the Galois theory to get the Abel Ruffini theorem, and then got distracted by Fulton and Harris

[remote sparrow]

https://link.springer.com/book/10.1007/978-3-030-51669-7

try applying the coupon code HLT23 to see if you qualify for a 40% discount

[trim kayak]

Ooohh that looks interesting too. The website shows hardcover for $4.99. Doesn't look like I would need a coupon.

[remote sparrow]

wait what?

it was way more for me

it's $54.99 for me

[trim kayak]

I just logged in with my university (institution) email that I've had since being a student and I was able to down load it. My pdf shows 263 pages.

[remote sparrow]

oh

[gray gazelle]

,imnot studying

iamnot studying

,iamnot studying

[hasty eagle]

Removed the studying! role from you.

[lusty ermine]

bro this is book recommendations 💀

[gray gazelle]

im sorry i wont do again

[trim kayak]

I prefer physical textbooks, but I don't mind reading pdfs sometimes. I REALLY like hardcover textbooks 🙂

[gray gazelle]

but discussion channel was unavailable so i had to do here

even tho i have removed study role, i still cant access #advanced-lounge

?

[lusty ermine]

!redir

[hybrid sparrow]

This channel is only for on-topic discussion. Please take casual conversation to #discussion or #chill.

[quick hornet]

(to answer the question, that channel is only for people with the undergraduate or postgraduate roles.)

[gray gazelle]

ok

[violet shuttle]

#bots

[molten mason]

Download all of Springer now

[trim kayak]

Isn't that a site with a TON of books? I can't download them all!

[tribal crow]

just download all of UTM and GTM like Salagos did

[remote sparrow]

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

[trail hemlock]

alr so if I use these books, will I end up losing any info? is it not worth it to stick to a single author, or are there just generally better books for each of these topics? I dont wanna go down the wrong path 😦

[modest owl]

anyone here got good resources for learning qiskit

[molten mason]

What a Chad

[molten mason]

You literally can though. They're text PDFs, not AAA games, your computer can handle it.

[slender cargo]

hot take but I think people get too concerned about choosing the right book

You just have to learn the material, one way or another

[slender cargo]

I said it before but you should consider just getting a Real Analysis textbook since that's where more serious math tends to start (that and proof-oriented linear algebra). You'll relearn Calculus in a Real Analysis textbook. Maybe try Spivak's Calculus

[vital bane]

same

new emoji/sticker when?

[pine widget]

need a book to prepare for STEP ... any suggestions?

[vital bane]

what is step?

[tribal crow]

I assume the Cambridge entrance exam?

[pine widget]

yeo

sixth term examination papers

any suggestions!?

[novel obsidian]

I've seen this book be recommended

https://www.openbookpublishers.com/books/10.11647/obp.0181

[kind kayak]

any book recs for math history; things like interesting mathematician biographies or history of certain fields of math

[pine widget]

used it?

[karmic thorn]

Stillwell, Mathematics and its History

Some books tend to include biographies, two I recall are Gallian's Contemporary Abstract Algebra and Etingoff's Introduction to Representation Theory

[novel obsidian]

I haven't used it myself, but I know it is used

[chrome yacht]

barry simon's book series- a comprehensive course in analysis also has tons of historical notes on math (mostly analysis) history, lives of mathematicians, historically significant results, their solution strategies, etc. and here is a related video series
https://www.youtube.com/watch?v=DEgn6zG0lX4
https://www.youtube.com/watch?v=6JU0XN2MxCw

[light cedar]

sorry cross posting from #discrete-math since i got no replies, (ill delete if its not allowed)

im looking for a book on logic that rigorously defines the low-level concepts?

[remote sparrow]

#book-recommendations message

[violet shuttle]

GTM is superior

[sullen raptor]

this book was recommended by my teacher for step

I’ve seen other people use it as well

[gray gazelle]

hey do someone recommend a analitical geometry book?

[torn crypt]

I don’t know how rigorously you want, but how about Rautenberg, or the one by Ebbinghaus & Flum?

[pliant wadi]

ah nvm

Thanks anyway

[main hill]

I've read the wiki's article about shadow libraries like Anna's etc. and even visited the site of the library itself but I'm still a bit confused. Do they store books or just metadata for these books?

[tawny copper]

the number of downloads is crazy

[sage python]

Algebraic Topology Book Review:

• Hatcher is probably the most common book nowadays. Leans heavily on the geometry than the algebra: categories are delayed quite a bit (some see this as a virtue, I don't) and a lot of arguments are by picture. Problem is, the (admittedly pretty) pictures are at times underexplained to the point of being unconvincing, so I don't think this is as good as one might hope at teaching visual intuition to those who don't already have a predisposition toward it. Overall I don't like it, but if you are biased away from categorical language and are either willing to accept stuff on faith or are strong at visualizing so as to fill in details yourself, you may enjoy it
• Rotman is probably one of the better books for an absolute beginner. The pace is rather relaxed, and the arguments are often quite careful with details, including continuity of maps. Not sure why covering spaces are done as late as they are.
• Bredon is a "one-stop shopping" book: starts off with most of the point-set topology you'll ever need, followed by an intro to smooth manifolds, then algebraic topology (with cohomology being introduced first via differential forms). I particularly like that it first defines singular homology, sets up the Eilenberg-Steenrod axioms, then uses the axioms to get cellular homology. This is probably my preferred "mid level book".
• tom Dieck is a hard hitter: you're assumed to already know what a category is on page 2, there's a fair bit of homotopy theory (including (co)fibrations and stable homotopy) before even doing homology, and there's also a bunch of material on bundles, manifolds, characteristic classes, and bordism. Probably this book or Concise would be my choice for a more sophisticated audience
• May's "Concise Course in Algebraic Topology" is aptly named: it covers a lot of the same points as tom Dieck but in less than half the space. This comes at the expense of some detail, and there aren't as many examples and exercises as in the others. Also, there is a bias toward homotopy theory, partially due to the author's proclivities and partially because it was written around (what was then) the third quarter of UChicago's topology and geometry sequence, assuming students did differential topology and geometry in the first two quarters.
• Spanier is very old school and very formal. Compared to other books on this list, there is much less emphasis on CW complexes (instead preferring simplicial). The impression I get is that it's quite a dry read. Does cover spectral sequences.
• Massey has three different books. The one titled "Algebraic Topology: An Introduction" is quite leisurely, not discussing (co)homology at all, but spending a fair bit of time talking about classification of surfaces, free groups/products, and graphs. This is followed up by "Singular Homology Theory", and the two are merged (with the exception of the last two chapters of the former) into "A Basic Course in Algebraic Topology". I've heard some praise about the first book in particular.
• Fomenko and Fuchs seems to be quite a hard hitter as well, with a homotopical bias (hence the name "Homotopical Topology"). First half is standard material on homotopy and (co)homology, followed by spectral sequences, cohomology operations, and generalized cohomology.

[bright epoch]

of these I bounced off of hatcher (didn't like how non-algebraic it was) and then loved rotman

[sage python]

I think this is good now

[stuck zephyr]

[heady ember]

When's Dami gonna post a foundations book review?

[sage python]

Okay my thoughts on foundations books are too long to go into a message

I tried this long ago

And it didn't work

[bright epoch]

yeah the early ones were good but they really went off the rails after book 3

/s

[sage python]

But I have a video review: https://www.youtube.com/watch?v=BBJa32lCaaY

[elfin scarab]

Where is it?

[heady ember]

I haven't clicked it, but that's a rick roll ain't it

[elfin scarab]

Yes

[heady ember]

[trim kayak]

Hey guys 📖📚

@sage python Can you post a review for Geometry, Stats, and/or Calc books too? 😃

[uncut zealot]

Sounds like I should give Rotman a try.

[trail hemlock]

I HATE YOU

HOW DID THIS NOT TRIGGER ANTI RICK ROLL

FUCK

[sage python]

Am I just built better?

[blissful pike]

This book for Langurian Mechanics/Control Theory I found pretty helpful: https://math.hawaii.edu/~grw/Classes/2009-2010/2009Fall/Math442_1/439notes.pdf

[remote sparrow]

https://link.springer.com/book/10.1007/978-3-031-24228-1

[lime vessel]

What's anti rickroll

[remote sparrow]

likely a browser extension that catalogs links to rick astley's "Never Gonna Give You Up"

[hallow oriole]

for the record im not a fan of this book

see #book-recommendations message

gordon is like hysterically good at integrals tho, so still worth looking at

[remote vortex]

I'm mostly amazed and impressed people are rickrolling and getting rickrolled in 2024

Few internet phenomena have this kind of longevity

[sudden kindle]

Its just bc dami is a boomer

[remote vortex]

Don't knock it till you've tried it

[torn crypt]

Sheaves, Games, and Model Completions, as I mentioned to @remote sparrow, for covering some aspects of modal or intuistionistic logics in the direction of “your logics have certain nice properties iff these classical conditions hold” https://link.springer.com/book/10.1007/978-94-015-9936-8

Though I haven’t read the whole thing and therefore cannot attest to the quality of later portions

[small ice]

What are the best books you would recommend for Linear Algebra on university level?

[bright epoch]

I liked Axler, but I read it when I already knew linalg idk if it is good as an intro

[tribal crow]

#book-recommendations message

[small ice]

These are 9 books! How would you choose the right one?

[bright epoch]

depends on your background and what you need out of it

[remote vortex]

Read them all

[small ice]

I need it for these topics for example:

• Vector spaces (definition and examples, subvector spaces, linear independence and bases, basis transformation)
• Analytical geometry (vector operations, coordinate systems, straight lines and planes)
• Eigenvalue problems (scalar product, orthonormalisation method, eigenvalues, eigenvectors and principal axis transformation)

[gray gazelle]

Any linear algebra book with cover that

Are you comfortable with proof writing?

[bright epoch]

all of them would work, maybe try axler and tell us how it goes?

[small ice]

Do you mean Linear Algebra Done Right?

[bright epoch]

yeah

[gray gazelle]

I’d also recommend Halmos, my personal favorite

[chrome yacht]

depends on what kind of approach you are looking for. matrix heavy? try reading one of gilbert strang's books (has video lectures from mit ocw associated with the book), an abstract approach with minimal usage of matrices? https://linear.axler.net/ (also has video supplements on youtube) works for most. a more balanced approach? Friedberg, Insel, Spence is probably better for that. want a bit of a challenge? try Peter Lax's book (also very balanced between theory and applications and not as boring as FIS can sometimes be). you hate yourself? try Greub.

[bright epoch]

I read linear algebra and its applications by Strang when I wore a younger man's clothes, and I didn't like it

but it was light on proofs and very straightforward, so if that's what you want then it's probably decent

[graceful moon]

I don’t personally like Axler very much, if you want a more abstract proofs based approach Hoffman Kunze is good. If you want a more concrete approach then Nicholson is good

[small ice]

Thank you all the recommendations, but I feel overwhelmed at the moment. Everyone has a different opinion 😓

Wouldn't it be best to set up a website where you can categorise and rank books about maths? That way, everyone can find books quicker and better!

[dusk tapir]

be the change

[tribal crow]

there’s this ig?

https://www.ocf.berkeley.edu/~abhishek/chicmath.htm

[bright epoch]

the good thing about linear algebra is that most of the books are at least pretty good

so you can't really go wrong

[small ice]

Ah, you guys should definitely hire a CS student, who redesigns and optimizes the websites layout. That looks like 2005 or something...

[tribal crow]

lmao

it’s not mine

[bright epoch]

I like the purity of it

[tender river]

get used to it that's how most uni course websites look like

[remote knoll]

Looks pretty optimized to me

[tender river]

and what's so awful about it anyway? lacking in advertisement? funky javascript ?

[remote knoll]

Hard to get more optimal than just the text you want to read on a page

[small ice]

It does not have to look so modern and edited. However, you should be able to navigate through the page quick and find information about various topics with references if you would like to dive deeper into it

[remote knoll]

To add though, the American Mathematical Society publishes reviews of books.

[small ice]

The website is from 1999.

[tender river]

if only there were a toc with hyperlinks

[remote knoll]

Sorry, not AMS, MAA: https://maa.org/press/maa-reviews/browse

[small ice]

Yes, this is what I'm talking about 👍

[remote knoll]

I prefer the site from 1999 tbqh

But maa reviews are usable

[lusty escarp]

Is Abbott analysis softcover the same as hardcover or does softcover has corrected printing? Does anyone know?

[lusty escarp]

I am thinking of finally buying one.

[remote sparrow]

i'm pretty sure they're the same

[lusty escarp]

I am asking this because softcover was published an year later to hardcover.

[remote sparrow]

for what it's worth, i've seen hardcovers that are the corrected version

[violet shuttle]

I like this better than some modern shitty web design

If a website just needs text, it should have just text. You can put pictures, links and all, a header, but no need for anything super fancy.

[gray gazelle]

I find it charming

[violet shuttle]

The fanciest feature I like (in fact, that I love) is from the best designed website I've seen, the website of Gwern

the feature is that of viewing pages when clicking links within Gwern's website, with arbitrary depth allowed

https://gwern.net/about

[bright epoch]

Oh gosh that's a lot

[violet shuttle]

It's legitimately more pleasant to browse wikipedia from Gwern's website than from https://wikipedia.org

[halcyon ether]

Hi, Whats a good book to cover introductory complex analysis?

[vital bane]

#book-recommendations message

[violet shuttle]

Dami is such a Chad for these recommendations

[molten mason]

Contact Berkeley and let them know.

They might have CS students.

[bright epoch]

does dami have a list for set theory texts

my set theory class is using an absolutely awful text by suppes

[vital bane]

@heady ember

[remote sparrow]

#book-recommendations message

[gray gazelle]

thoughts on book of proof

[remote sparrow]

it's good

[wispy phoenix]

Are there any books covering the "required" fundamentals to start calculus? (assuming I know the bare minimum of algebra, so basically nothing)

Dont want an absurdly large book

[gray gazelle]

r u in HS

[bright epoch]

Most good intro to calc books are readable if you have some elementary algebra and trig

[gray gazelle]

why don't you cover Khan Academy, either the path and use textbook with relevant textbooks or just the khan academy thing in general

[wispy phoenix]

yes

[wispy phoenix]

I am not very fond of using videos to learn

Sure, a good lecture is fun, but I still like to go through a text book.

[gray gazelle]

👍 Yep that's why I mentioned you could use their syllabus as a checklist

I assume you've covered college algebra?

[wispy phoenix]

Which one would you recommend? I am not even very familiar with functions yet, so i doubt i could just start reading one.

[wispy phoenix]

no, not really

[gray gazelle]

fuck

i can't copy paste images here

[wispy phoenix]

use imgur

[gray gazelle]

College Algebra
Linear equations and inequalities: College Algebra
Graphs and forms of linear equations: College Algebra
Functions: College Algebra
Quadratics: Multiplying and factoring: College Algebra
Quadratic functions and equations: College Algebra
Exponents and radicals: College Algebra
Rational expressions and equations: College Algebra
Relating algebra and geometry: College Algebra
Polynomial arithmetic: College Algebra
Advanced function types: College Algebra
Transformations of functions: College Algebra
Rational exponents and radicals: College Algebra
Logarithms

hv u done all that?

[wispy phoenix]

I definitely dont know what quadratic functions are, depends on what polynomial arithmetic is, and definitely none of the last four chapter.

I know a little about most of the topics, but i am not very confident in any.

[gray gazelle]

Do all of them well

Then:

Trigonometry
Right triangles & trigonometry: Trigonometry
Trigonometric functions: Trigonometry
Non-right triangles & trigonometry: Trigonometry
Trigonometric equations and identities

Complete that

[wispy phoenix]

from where, though

[gray gazelle]

r u english speaker?

[wispy phoenix]

I mean, i can understand english just fine

but it isnt my native language

[gray gazelle]

if you don't like the videos, you can perhaps try the questions as a benchmark, and when you struggle, go into the textbook and learn the concept

on khan

[wispy phoenix]

what textbook, though

[gray gazelle]

hmm

let me look i have found one

[gray gazelle]

what hs curriculum are you in?

https://assets.openstax.org/oscms-prodcms/media/documents/College-Algebra-2e-WEB.pdf

This is good

[covert abyss]

what is good books to revise for my gcse which are pretty far away from now

[gray gazelle]

AOPS

if you're a sweat

[covert abyss]

nah im just an average child looking for big improvement

[gray gazelle]

khan academy should be good enough for a perfect grade

[covert abyss]

yea im looking for atleast grade 7-8

[wispy phoenix]

We dont exactly have a set of courses to choose from here, you instead choose the subjects you want to learn. the content is decided by the overlords. (if thats what you are asking)

[covert abyss]

aiming high if you get me

[gray gazelle]

Good, consistent use of Khan Academy will put your avg HS student 99th percentile

I'd recommend textbooks maybe as a means of preparing for university (e.g if you want to study maths/physics, you're going to have to use one at some point) or if you're a sweat

[covert abyss]

can u send a few links of book reccomendations

and also is CGP good

[gray gazelle]

I don't know what is

[wispy phoenix]

I have used KA in the past, and honestly i start to treat it as a game, and forget everything after a while.

[gray gazelle]

Usually your coursebook is good, otherwise you can search through OpenStax

[wispy phoenix]

Never built that muscle memory i do after doing like 60 hard questions in a textbook

[gray gazelle]

Yes one of its weaknesses is that it doesn't incentivize note taking

[gray gazelle]

I don't think that's the most effective way to learn

in my opinion, good notes should minimize it

[wispy phoenix]

It might not be, but i am able to do it rather well after:

1. Understanding the concepts
2. Making quick notes
3. Solving all the questions in the textbook

[gray gazelle]

Your aim after doing a couple hard questions is to try and find some sort of structure

the questions might have different numbers, might be framed in a different way

you have to be on the look out

one way to find this structure more easily is to only plug in numbers at the end

[cinder stirrup]

where does one go to read about zfc + continuum hypothesis as a system?

[remote sparrow]

what does "as a system" mean?

[cinder stirrup]

axiomatic system

so continuum hypothesis taken as an axiom along with the rest.

[quick hornet]

i dont think CH adds much besides obvious corollaries

most mathematicians "basically" work in CH anyway, insofar as its not like we ever deal with counterexamples

you need at least GCH for interesting stuff

[quick hornet]

[this isnt to say there arent legitimate philosophical reasons to reject CH, to be clear; in fact i am sympathetic to that viewpoint]

[quick hornet]

in any case, the best source fo rthis is probably Woodin's essays, such as The Axiom of Determinacy, Forcing Axioms, and the Nonstationary Ideal

[cinder stirrup]

G stand for? goldbach?

[quick hornet]

generalized

i have no clue how goldbach relates

[torn crypt]

Well there’s some definitely some nontrivial implications

[torn crypt]

There’s also additional information about ZFC and CH in both Jech and Kunen’s set theory books, or Halbeisen.

There’s a lot of different ways to go about things, like Schindler’s book, but idk what he’d cover wrt CH in particular so

Halbeisen goes over stuff like how CH (or weaker hypotheses) imply things about some combinatorial aspects

I have no idea what Jech or Kunen say in detail beyond the obvious independent parts

[sick holly]

nice ill look at those books ty!

[torn crypt]

Some books have good content but are hard to read start to finish without aid, and they each do something different in what they cover or focus on

So do remember whatever book you read is a way to do things rather than the way

Though it’s often a reasonably good way

[gray gazelle]

Cn u expand a bit

How would you go about using it?

What did you like and dislike

[violet shuttle]

I struggled with D&F before dropping it, doing Baby Rudin, and then other math, and then using Lang.

[sage python]

Exactly

[trim kayak]

@sage python I asked about recommendations for books on various topics. Did you see that?

[trail hemlock]

Peepo_Ping

[sage python]

Ah I see. Yeah unfortunately I have much less to say about those. Calculus has the divide of the proof-based books (Spivak, Apostol, some analysis books) and the non-proof-based books (Stewart et al)

[trail hemlock]

so after doing rudin is it better to do D&F or lang

without LA

[molten mason]

Why in mathcord's name would you skip LA

[trail hemlock]

im scared of linear algebra

[sage python]

Apostol seems like more boring but more standard Spivak. Spivak is alright but at times tries too hard to be cute for its own good.

The ones like Stewart are largely isomorphic to me

[trail hemlock]

idk

[sage python]

Lang is way scarier than linear algebra lol. This is something you wanna learn asap

[trail hemlock]

uggg

fiiiine

😦

[molten mason]

LA is the thing you need most. It's used everywhere, in everything.

Lang has 2 linear algebra textbooks in you want to use him. Howard Anton has a nice easy LA textbook in you want to get in a hand-holding route.

[trail hemlock]

lang really published a whole major

[violet shuttle]

learn linear algebra

[trim kayak]

Hey Salagos

[violet shuttle]

foundation for most things

[trail hemlock]

i no no wanna 😢

[violet shuttle]

you want to do fucking algebra without linear algebra?

[trail hemlock]

fine

ill read lang's LA this summer

[violet shuttle]

at least your protests would be a bit more understandable if you were really wanting to learn like riemannian geometry or something

still would be incorrect, but, more understandable

[trail hemlock]

k

[molten mason]

If his Linear Algebra is too difficult for you, he has Introduction to Linear Algebra

[trail hemlock]

ok cool

is LA as rigerous as baby rudin

cuz that could be kinda fun

[molten mason]

Idk, Xela would know

I mean, it's Lang

That's why he made Introduction to Linear Algebra

[trail hemlock]

💀

its fine ill suffer through it

masochism is the way 🗣️ 💯

[molten mason]

Linear Algebra has a solutions manual, idk if Intro to LA does

[trail hemlock]

🏴‍☠️

theres literally a legal pdf its fine

[molten mason]

I have the legal PDF

[trail hemlock]

woww

[heady ember]

What sort of set theory are you looking for

Naive? Axiomatic? Ug or grad?

[tribal crow]

LA is awesome, don't be scared of it

[heady ember]

FIS is pretty managable

[tribal crow]

FIS my beloved

[heady ember]

I would recommend not looking at the hints though.

[molten mason]

Yeah my copy of FIS is within arms' reach right now lmao

[heady ember]

It often makes the exercises trivial, even for the simpler ones.

[heady ember]

Its 1m away from me

Wanted to do some exercises yesterday but procrastinated :kekwait:

[molten mason]

real

[slender cargo]

Again, something about this server and Lang

[hallow oriole]

are all of us sitting next to our fis copies

lmfao

[slender cargo]

The only book I've heard from Lang that is regularly used at universities is his Algebra book. Not his... dozens of other books

[bright epoch]

Not entirely sure, but definitely not like the normal ug naive or axiomatic texts I have read some of them and they're not enough. Probably grad, I guess?

[hallow oriole]

ive seen lots of ppl use his ca book

oh

at univerisities

[slender cargo]

Yeah, I'm not sure about self-studying

[molten mason]

I'm managing

[slender cargo]

As in.. managing with Lang?

[molten mason]

Jech is commonly recommended at that level.

[molten mason]

via self-study, yeah. I have all of his textbooks either physical or pdf lol

[slender cargo]

Ah gotcha. Are you not taking classes then?

[molten mason]

That's complicated answer, yes/no depending on the semester.

[slender cargo]

Oh okay, that's fair

[tribal crow]

my FIS pdf, yes

[slender cargo]

I've looked at Lang's Undergraduate Analysis, I think it was, and I noticed that it was written without much exposition

[molten mason]

I have a full-time career and life so I try to take uni classes when I can (for some reason Math is one of the only majors at my school that are 100% in-person with no online options), but I still self-study throughout the year.

[bright epoch]

Noted

[molten mason]

I have that next to me also lmfao

I have his Undergraduate Analysis and Real and Functional Analysis in physical

[slender cargo]

That's totally understandable. I got laid off at my last job and decided to just go for a Math MS full time.

[bright epoch]

Which jech

[molten mason]

Ah yeah! That leads to the rest of my answer complication. I already have a degree in something else, and I want to get into math graduate school. I don't need to do the full math degree, but I have to show I have the knowledge to get into the grad program lol So I technically have to take a lot of the math classes but I don't need to officially worry about all the details in getting the bachelor's degree. So I could potentially get into the masters at my local school and apply for PhD elsewhere, or stop at masters, or just do PhD at local school. Haven't gotten that far yet.

[slender cargo]

Yep, basically the same for me. Well, I've been away from school for some time, so a Math MS made sense for me. It's been a good experience so far.

It is interesting seeing how much better I perform now that I treat classes like a job.

[molten mason]

I can also do the first year of the master's program as a non-degree seeking student, without having to worry about pre-reqs and applying, and if I do good that first year then they'll take me in for the second year.

So self-studying helps me toward that goal, I figure if I can self-study at the level of Lang or other GTM textbooks, I can skip some of the undergraduate classes and just head straight into the graduate classes (Some classes are combined for grad and undergrad students but you pick which credit you're taking it for)

[molten mason]

That's awesome!

[molten mason]

Yeah similar, it's nice to study and treat it as a job/career-progression thing instead of just some class I need to cram and study and pass in a set time

[heady ember]

Kunen's Set Theory is a usual rec I believe

[slender cargo]

Yes. School feels very different with an academic goal in mind. I absord stuff way better now. Kinda weird how that works.

[heady ember]

If you need a higher calibre set theory text than that, then check out Jech's third millenium.

Look at Clerk's recs for more info

[bright epoch]

Oh this one has forcing, cool. Will check it out thanks

Also jech, but that might be a bit above my head 😅

[molten mason]

Oh yeah there's Introduction to Set Theory too.

Grass and Sage and Sour would be the ones who can go into more detail about all of that.

[tribal crow]

sour drop is truly the goat of #book-recommendations

I have no idea how he knows of so many damn books

[molten mason]

Yeah the one thing I like about this freedom and mindset is I can just pivot at any time, I paused my study through Lang so I can go through Set Theory stuff, and then when that's done I can go right back into Lang without stress of deadlines lol

[smoky zephyr]

what if instead of learning math he just learns books

[violet shuttle]

there's dami

[trim kayak]

As an educator, I often support and help students with their math classes. A lot of students are taking Algebra I, Algebra II, Geometry, and some Trig. I've taken all of these classes and remember most of the concepts, but not all of them. I'm looking for a decent textbook that I can reference for any of these topics. I don't mind using older textbooks since the content and info is the same. Any recommendations? Thanks!!

[glad rampart]

Khanacademy is free

[slender cargo]

What's your goal with asking for these recommendations? Is it to help your students? Is it for you to learn?

[trim kayak]

Kind of both. A quick refresher to help me if needed but also to help them with different concepts in each of those math areas.

[slender cargo]

People who are participating in this channel are generally interested in more rigorous, proof-based mathematics. As in, learning why things actually work the way they do and proving stuff themselves. For example, a lot of the stuff we learn in Algebra 1, Algebra 2, Geometry, and Trig are not fully explained. It's just intuitive explanations that are given. You actually learn why all that stuff works in later proof-based math courses.

For those subjects you asked, people here generally just suggest Khan Academy. Lang's Basic Mathematics is often also suggested here, since that book does try to be a bit more rigorous with that material (and the author is basically trying to get the student to become interested in higher level math).
Paul's Online Math Notes are also a good free resource online.

One book that would be interesting to me, if I were a high school math teacher, would be Axler's Precalculus. Simply because the author is notorious for his upper level math books.

[quick hornet]

to be honest i dont think theres much of a quality difference between textbooks at a high school level

or rather like, there are some really bad textbooks

but as long as your book isnt really bad

its probably roughly the same as others modulo exercise quality

and i think exercises are something better constructed by a prof or tutor than by a textbook at that level anyway tbh

to that end, the openstax books are probably a reasonable recommendation just because theyre free

though i do get that often giving students a physical "book" is better than linking them a website

since theyll just get distracted if they need to use technology to access it

[glad rampart]

I’m the opposite, it’s hard for me to put down my online textbook

[quick hornet]

if you have enough motivation to be on a math server, youre probably outside the central band of students here

[glad rampart]

True

[violet shuttle]

i hear good things about Lang's Basic Mathematics

I do like Lang here

[solemn mantle]

I have a question about learning commutative algebra and algebraic geometry. I’ve heard most of the motivation in commutative algebra comes from algebraic geometry, and I’ve also heard that it’s useful to learn commutative algebra prior to learning algebraic geometry. How is this possible? What am I supposed to “learn” first?

[gray gazelle]

Where Can I find a big textbook, black and white, with everything I need to know about math, before doing the 12th year final exam. I woild like to have one that explains everything, and another white and black text book that have exercises.

[wispy phoenix]

While I didn't get any recommendations yesterday, I think its worth giving a shot again. What textbook is recommended for someone who just wants to start calculus? (assuming I know very little about algebra, geometry, and trig)

I dont want a very large book, but it should be rigorous enough.

There are a lot of precalc books out there, i am not sure which one to pick

[gray gazelle]

I am a little confused for my self but, I can tell you a hint: good textbooks are the black and white ones. White background behinde black plain text. Also printing those papers rather than viewing throw your monitor screen is away better. (On my opinion)

[wispy phoenix]

do you have any idea how little that narrows it down?

i think the majority of math books are black and white.

[solemn mantle]

LOL

[gray gazelle]

Yes, but some most related are colorfull.

[molten mason]

Basic Mathematics by Serge Lang is a rigourous Pre-Calc textbook

[solemn mantle]

Color 😍

[molten mason]

Just turn the printer setting to "black and white"

[golden salmon]

@gray gazelle: I have no idea what you mean by black and white - that's how all textbooks are printed. If as Xela said above, Lang's Basic Mathematics is a great intro text but whether it covers whats in your year 12 exam is going to depend on what country and therefore curriculum you follow.

@wispy phoenix: Check out Thomas' Calculus on archive.org and see if you like it. It's pretty accessible and very methods based. There is also Stewart's Calculus which is of a similar flavour.

Oh didn't see the pre-calc comment mb. Then yeah +1 on Lang from me too

[wispy phoenix]

I dont think lang goes into great detail, but i havent read a lot.

the proofs are fun

[golden salmon]

What topics would you like covered then/what did Lang miss that you were hoping for?

[gray gazelle]

Can I dm you a templeate?

[molten mason]

He doesn't, which satisfies the "I don't want a very large book" requirement.

[golden salmon]

no

[gray gazelle]

Okay.

[wispy phoenix]

one would be polynomials, i dont think he goes into much detail about them. (unless i havent read the chapter where he does yet)

[wispy phoenix]

is lang the only recommended textbook, or are there others aswell? i would still like some options

[molten mason]

That would be Chapter 13

[golden salmon]

https://openstax.org/books/prealgebra-2e/pages/10-introduction-to-polynomials <- something like this, or too easy?

[wispy phoenix]

I hate openstax books

for no particular reason

[golden salmon]

That's fine, I can suggest others. In any case, can you self-assess if you feel ok with the content linked?

[glad rampart]

I don’t like how disorganized they are between books, like half of one book will be in another

[wispy phoenix]

that seems too basic

[golden salmon]

All good. Try this then? https://web.mit.edu/wwmath/calculus/differentiation/polynomials.html

[molten mason]

Axler has a pre-calc book.....

There's a list somewhere in this channel, I can't find it right now but I'm also going to bed. I think sour drop has a few recs but you would have to find it in the searchbar or wait until he comes on

[wispy phoenix]

e

[golden salmon]

<@&268886789983436800>

[wispy phoenix]

my eyes

why did i click on them

[golden salmon]

What was it

[wispy phoenix]

just dont

[golden salmon]

I just assumed it was malware

[wispy phoenix]

its a gif

no embed perms though

[wispy phoenix]

i dont know half the shit going on in that article, so cant say anything.

[golden salmon]

gotcha

Check out Stewarts Precalculus then. I think that's probably close to what you're after

[wispy phoenix]

yes, thats what i was about to ask.

also, are gefland's algebra and trignometry a bad choice for calc?

they seem to be pretty short and have a quite a lot of hard problems.

[golden salmon]

no clue on those sorry

[scarlet pumice]

Does anyone know of a book that has full working solutions of calculus 1 and Linear algebra questions?

[molten mason]

If you get Quizlet Plus ($8/mo) It has solutions + walkthroughs for all problems, even and odd, to most popular textbooks including Calc and Linear Algebra

[gray gazelle]

if you don't know what quadratics are don't start calculus

don't start pre calc yet

do College algebra i gave you a textbook, if you don't like that there are others

Calculus is a way of evaluating how good you are at algebra and trig, trying to start calculus without even knowing quadratics is like trying to run before walking

[pulsar pollen]

Book recommendation for starting out on number theory?

[glad rampart]

I just finished AoPS intro to number theory and it was good

[tawny crater]

some book for algo trading? I'd like to see the theory side (if there's any)

[trim kayak]

Well, I didn't get any helpful recommendations 😑

[hallow oriole]

ent by rosen

or friendly introduction to number theory

aops nt books are enjoyable maybe but not really very good if u want to truly learn nt

[molten mason]

Roughly in ascending order of difficulty:

• Popular
• Beiler, Recreations in the Theory of Numbers: The Queen of Mathematics Entertains
• Ogilvy & Anderson, Excursions in Number Theory
• High School
• Dudley, Elementary Number Theory
• Friedberg, An Adventurer's Guide to Number Theory
• LeVeque, Elementary Theory of Numbers
• College Non-Major
• Silverman, A Friendly Introduction to Number Theory
• Andrews, Number Theory
• Math Major
• Stein, Elementary Number Theory: Primes, Congruences, and Secrets
• Jones & Jones, Elementary Number Theory
• LeVeque, Fundamentals of Number Theory
• Niven, Zuckerman, & Montgomery, An Introduction to the Theory of Numbers
• Apostol, Introduction to Analytic Number Theory
• Graduate Student
• LeVeque, Topics in Number Theory, Volumes I and II
• Hardy & Wright, An Introduction to the Theory of Numbers
• Borevich & Shafarevich, Number Theory
• Ireland & Rosen, A Classical Introduction to Modern Number Theory
• Cohn, Advanced Number Theory

[pulsar pollen]

Wow thanks

[molten mason]

Valley's recs are good I don't think they're in the list. I need to add them in

[glad rampart]

I’d say it’s good for learning the basics but it is what the title says, an introduction

[wispy phoenix]

I know what quadratics are, though. also i am pretty sure pre calculus books cover all of what you mentioned.

[solid bloom]

Is there any book that like- breaks down the most fundamental concepts of mathematics, like the stuff that builds up mathematics

A rather more philosophical book kinda

[glad rampart]

Look into set theory perhaps

[remote sparrow]

@dapper root

[dapper root]

Do whichever you can tolerate first. You do AG first then it’s harder because you don’t know comm alg. Do comm alg first and you probably get bored because you don’t know what it’s for. Pick your poison (I recommend comm alg to the level of like Atiyah-MacDonald, then AG, then back to more comm alg)

[remote sparrow]

https://www.youtube.com/watch?v=_o9HtUoQE1A

https://www.amazon.com/Advanced-Algebra-Pal-M/dp/8120347374

@sage python i was made aware of this abstract algebra book that gives a thorough introduction to linear algebra from this video

[remote sparrow]

https://www.youtube.com/watch?v=pm1KPZMEDCk

https://www.youtube.com/watch?v=21jCn-SwRpQ

https://www.youtube.com/watch?v=Cf5Eh1tqo7M

[marble solar]

Older editions are better

[remote sparrow]

how old are we talking

[marble solar]

I have a second or third edition that's pretty good

[remote sparrow]

👍

[marble solar]

These publishers zombify these books

Like Stewarts calculus

They just appendage on parts to keep it going

[earnest blade]

• any good books for studying linear transformation in detail ☝️

[tribal crow]

so... linear algebra?

[earnest blade]

All I know about it is that it has something to do with transformation matrices and reflection, refraction and displacement

[tribal crow]

so linear algebra

are you looking for a proof-based book?

[gray gazelle]

Halmos or Axler if you’re familiar with proof writing, Strang if you just want something computational

[earnest blade]

any kind

[earnest blade]

thanks 👍 😃

[remote sparrow]

https://www.youtube.com/watch?v=15y5unonBgc

https://www.springer.com/gp/authors-editors/book-authors-editors/ebooks-go-in-print-mycopy/19882

[stone lance]

hi

[remote sparrow]

https://www.youtube.com/watch?v=vdMsuZ-8DWU

[gray gazelle]

is Book of Proof meant to be an alternative to Jay Cummings book " Proofs "

[remote sparrow]

they are comparable

cummings is much more chatty however

[earnest blade]

The math sorcerer

[remote sparrow]

correct

[gray gazelle]

ik math sorcerer says that book is great

[dapper inlet]

does anyone know of a hand holdy real analysis book?

[remote sparrow]

cummings

[remote sparrow]

do you prefer your books to be more concise or do you prefer more talky books

[gray gazelle]

concise tbh but i'mma have to use book of proofs since the uni uses it seems

[remote sparrow]

book of proof is more concise than cummings

[lament radish]

thanks baymax

[slender cargo]

I've been going through this book in my Real Analysis class and while it has nice exposition, it's missing small details here and there that I think are important (particularly in the Integration chapter). I recommend pairing it with a book like Abbott or Bartle and Sherbert. I've frequently been referencing Bartle's book.

[torn crypt]

Cassels-Frölich?

[slender cargo]

For example, with regards to Jay Cummings' Real Analysis book:

In the Fundamental Theorem of Calculus, it does not emphasize that f can simply be continuous at a point, which is an important detail. It only gives the case for where f is continuous across the interval (and only proves it for that case).

And for some of the linearity properties of integration, it does not discuss what happens if the integral is negative, where as other books do.

[dapper inlet]

[remote sparrow]

you should email cummings with some of these suggestions

[slender cargo]

imo just go with either Abbott's Understanding Analysis or Bartle and Sherbert's Introduction to Real Analysis. Those two books have a good amount of exposition and are tried and tested.

[slender cargo]

I might actually do that

[remote sparrow]

cummings is kinda like a real analysis for dummies (like calculus for dummies) type of book

[remote sparrow]

abbott is on sale right now, bartle is pretty expensive but used editions might be affordable

[slender cargo]

For the most part it does its job well. He includes challenging problems and it has a lot of exposition. It's just missing some key details which, uh, may be due to him not being Analyst.

[remote sparrow]

also new copies of bartle are generally of inferior construction (which i noticed in the bookstore)

[trail hemlock]

its a good book, but i think for any actual student, understanding analysis is just plain better

because it skips over a lottttt

but the proofs are dumbed down to where even I can understnad them 🤷‍♂️

[karmic tangle]

https://i.imgur.com/kGjjDwh.jpeg

springer what is this

ah images are not allowed in this channel? I was confused why discord wouldn't let me

[karmic tangle]

Book is understanging analysis xD

all the pages are half see through like this

[remote sparrow]

the person above did ask for a hand holdy book, and i gave him the most hand holdy book possible

[trail hemlock]

i wish cummings would hold my hand as i read rudin 😭

[trail hemlock]

springer not trying to be a cheap fucking conpany even though their books are expensive as fuck, hence why people always seem to have pdfs instead of physical copies (impossible challenge)

[remote sparrow]

springers are often medium-priced compared to, say, wiley or mcgrawhill books

[trail hemlock]

🏴‍☠️

[remote sparrow]

for example, brown and churchill's books on complex variables and fourier series are super expensive, and they're mcgrawhills

complex variables comes in for $130

fourier series is like $200

thankfully there's a big used market

[trail hemlock]

used??

[remote sparrow]

new

complex variables is like $60 used

[karmic tangle]

i dont get it man

They've some of the most sold math books don't they? Why can't they just print them proper

[remote sparrow]

do the pages feel smooth in your hand?

[remote sparrow]

because cutting corners saves money

[gray gazelle]

This is why I just print and bind the books myself now (springerlink for the win)

[karmic tangle]

theyre very smooth and asscrack thin

[trail hemlock]

freeeee springerlink

all my friends get the legal pdfs from springer

cuz they have access via instituion

[remote sparrow]

idk i saw a used copy of that and i'm more of a fan of those kinds of pages

[trail hemlock]

thats my only motivatio nto go to colleg

[gray gazelle]

Yup

[remote sparrow]

being see through doesn't super bother me (though it would be better if it weren't) but i like that sort of paper

[karmic tangle]

I like the feel of the pages, if only I didn't have to see what's on the other side of the page

[trail hemlock]

tbh in india when im buying physicsal books the thin pages ones are sooo much cheaper

[karmic tangle]

I got LADR and thst has pages with the same smooth feel but without being see through

i guess i might have been too hardh a judge with the thicknesses, I manly wanted to use the expression asscrack thin

theyre very thin compared to dover book pages for example

but it's not a problem by itself

[gray gazelle]

Dover pages are shockingly good though

[remote sparrow]

it's to accommodate the color printing

[karmic tangle]

and they're all $20 a pop max!

[karmic tangle]

ahh true I totally forgot about that

[gray gazelle]

I’ll be honest, I’ve never paid for a dover book. I keep finding abandoned copies in my department’s closet lmao

[remote sparrow]

roughly average, not maximum

[karmic tangle]

how do I find the abandoned book closet at my uni

[remote sparrow]

you can walk to the math department offices or lounge and ask if anyone is giving away books

or look for anyone that's retiring and clearing out their office

[karmic tangle]

i guess, i don't remember seeing any more expensive I think but I was probably just looking at the main ones that are all cheaper

[remote sparrow]

community college libraries also sometimes dispose of some items in their collection (my state uni doesn't discard books though)

[gray gazelle]

My uni ended up with so many old books in one of the printing closets that they organized it and encouraged students to grab whatever they want

[karmic tangle]

Thw math department is like one floor of a building at my uni

Actually idk if that's considered small or not, but the building is just one 50m? long hallway with a staircase section in the middle

all the classrooms are in the bottom floor and profs are on the first so it's the area we so far only go to to take oral exams

[remote sparrow]

dovers used to be extremely high quality (some paperbacks used to be sewn in signatures, now they're just glued. the advantage is once the paper cover is worn out, you can take it a bookbinder and have it rebound in a nice hard cover.). can't complain about the price, but they once gave even more bang for their buck.

[karmic tangle]

So id have to snoop around there i guess lol

[gray gazelle]

You can rebind glued spines as well

[remote sparrow]

yeah i guess

i should probably get some of my paperback covers laminated tbh but quite a few of my dovers shipped from amazon have their covers slightly bent from being jostled in the package

[karmic tangle]

how much does it cost to get printed and bind a book yourself?

if I want it to look like a book and not a stack of A4s bound together with a spiral binding thing or whatever those are called

[gray gazelle]

It depends on what quality paper you use. Binding a hardcover takes a while (usually a 2 week project), so I tend to print onto higher quality paper. On 70lb text, it can cost similar to just buying from springer, but the quality is way better

If you go on thinner paper, I’m guessing printing costs shouldn’t be more than $20 from a print shop

And the rest of the material (waxed thread, glue, book cloth, etc) is cheap

[karmic tangle]

Noice

[remote sparrow]

if your file is considered "print-ready" for print-on-demand services like lulu or barnes and noble press, it can be pretty cheap

[karmic tangle]

Are they gonna print for me a pieated pdf

[remote sparrow]

i don't think they care

[karmic tangle]

great

[remote sparrow]

it'd be a problem if you tried to sell it and law enforcement caught wind of it

but printing for personal use, no one is gonna go after you unless you're printing a huge amount

[karmic tangle]

are non-print-or-demand-books printed using actual presses with the letters arranged for each page and all that while others are just from printers?

[karmic tangle]

nice, it also sounds like a fun thing to do

[remote sparrow]

idk

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

[gray gazelle]

Yeah it’s a fun process. If you want to do a cover design, I’d recommend heat-transfer vinyl

[karmic tangle]

I was wanting to read some books that don't even have printed versions

[remote sparrow]

they might use this machine?

[karmic tangle]

thats starting to sound more complicated, like youd need some machinery?

[remote sparrow]

this device is extremely expensive though, like $3000+

[remote sparrow]

you should probably read the guides on https://reddit.com/r/bookbinding

[gray gazelle]

You need a cricut (or you can find someone on etsy to cut the vinyl for you), then you can just use an iron to put it on

[karmic tangle]

apparenrly theyve super powerful pronters at the print on demand shops that print for amazon, capable of producing huge amounts of books in small timeframes

i wonder how the ink differs between printing methods also

Ive had documents from some at-home printers make me sneeze

[remote sparrow]

#discussion

[karmic tangle]

thanks for the book binding tips guys, Ill check it out

yeah lol I turned this into a spam thread apologies though I guess it's relevant to anyone looking to buy bokks?

[molten mason]

Isn't that ANT?

[torn crypt]

Yeah?

[molten mason]

That sounds terrifying lol like graduate-level terrifying.

I downloaded it

[torn crypt]

Definitely not super intro-y

[molten mason]

2025 is my number theory arc. I want to be fluent in both ANTs

I think I have about 2 dozen NT pdfs ready to go

[pliant wadi]

Okay so what's a good place to read up on stability theory?

[remote sparrow]

Model Theory: An Introduction by Marker and A Course in Model Theory by Tent and Ziegler

note that marker has a long list of errata

@torn crypt

[torn crypt]

Ok so

Marker is the typo man who makes typos

@pliant wadi how much do you know

And how willing are you to very carefully read things

[torn crypt]

Hodges has section 6.7 and some mentions here and there, but I don’t think it’s great to learn that stability stuff from. Good for the prerequisites and related topics though

Can’t forget Classification Theory also, but it is not a clean read like Hodges, but for different reasons to Marker’s typo land. Marker covers homogeneity and \omega-stability, but I don’t remember him doing much beyond that for stability? So he wouldn’t be great for the stability theory but is good to get to that point, ykwim?

[trim kayak]

Hey Sage

[trim kayak]

Recommendations for Geo and Alg II textbooks?

[remote knoll]

If you have a half price books nearby, I recommend you go there and pick up any geometry or algebra ii book. It will be cheap and certainly cover all of the material needed.

Many used book shops will carry random used math textbooks for super low prices. I have built up quite a collection this way.

[snow valley]

What's the best abstract algebra book

[violet shuttle]

Lang

[serene merlin]

I liked Abstract Algebra theory and applications (Judson)

[buoyant halo]

https://csclub.uwaterloo.ca/~pbarfuss/18093757-Fuckin-Concrete-Contemporary-Abstract-Algebra-Introduction-by-Nicolas-Bourbaki-Junior.pdf

[snow valley]

Lmao

[remote knoll]

Is this just another book sent through a computer program that replaced words with fuck and adds in random interjections, with the settings set to maximum obnoxiousness?

Because if so, I'm here for it

[left cloud]

hahahaha

[daring lake]

I haven't read Lang but going to assume its more terse than D&F and covers more?

[uncut zealot]

"Introducton by Nicolas Bourbaki Junior"
This is amazing

[solemn mantle]

Ahh ok. Damn that’s kind of annoying. My uni offers an undergraduate “Elementary Algebraic Geometry”, whose course description is the following:

The goal of this course is to introduce students to the basic principles of algebraic geometry in a hands on manner. Our study will focus on how algebraic methods can be used to answer geometric questions. Students are encouraged to use computer tools such as Macaulay2 or Sage to explore examples and investigate problems.

The primary object at study will by systems of polynomial equations in n variables. The solutions set of a system of polynomial equations forms a geometric object called a variety; we will see that this corresponds to an ideal in a polynomial ring. We will explore the geometry of varieties both computationally and abstractly using the algebraic structure of polynomial rings.

A major component of this study will be the theory of Gröbner basis, this theory will form the basis for our computational approaches to geometric problems. At the end of the course students will be able to answer such questions as: Does a given system of polynomials have finitely many solutions? Is so what are they? If there are infinitely many solutions, how can can these be described and understood?
Do you think this would be a good class to take before trying commutative algebra?

It might give me the concrete examples which underlie the theory of comm. algebra

Right?

[daring lake]

Do they mention comm-alg as a pre req?

If not, then I would say go ahead

But it wouldn't hurt to do few chapters of Atiyah before you dive in

[solemn mantle]

No, I don’t think so

[violet shuttle]

this seems basic enough to be fine

[solemn mantle]

Wait shit that course was from a while ago

[remote sparrow]

any progress on cox @daring lake?

[solemn mantle]

Last fall it was this:

Introduction to basic commutative algebra, algebraic geometry, and computational techniques. Main focus on curves, surfaces and Grassmannian varieties.

Hm then I guess they develop it hand in hand

[solemn mantle]

What about number theory? Isn’t that where the other examples of commutative rings come from in comm. algebra?

[daring lake]

Unfortunately not, Rudin attracted me once again so I was doing problems from RCA

[violet shuttle]

yes technically sure but like you don't need to come in with number theory knowledge

that's my impression at least

[solemn mantle]

Ah ok

[violet shuttle]

also with the class description, doesn't seem to require number tjoerh

(the old description) sounds like it's the setup of algebraic geometry. which sounds good for you

also, Lang

I dislike Lang the least among the algebra books I've seen.

[daring lake]

Any reason why?

[violet shuttle]

there's a thing where he says something like "now, we'll do enough commutative algebra for you to read hartshorne"

[heady ember]

What do you think of Jacobson

[violet shuttle]

honestly, timing in which i read it plus terseness that isn't so terse that i severely struggle (e.g. it was a bad idea to try to use May's A Concise Course in Algebraic Topology as an introduction)

[heady ember]

A concise introduction

[trail hemlock]

something tells be this group wont pioneer new algebra textbooks

[uncut zealot]

This was just my first reaction after seeing the URL. Clicking on it and reading it was a genuinely amazing experience.

[trail hemlock]

lmao

To my fuckin’ father, Nicolas Bourbaki.

amazing 🫶

[sudden kindle]

From this fuck emerged what is now known as modern fucking algebra or fucked abstract algebra.

[vital bane]

:clopencry:

[round shore]

https://pro.univ-lille.fr/fileadmin/user_upload/pages_pros/lorenzo_ramero/CoursAG.pdf

[vital bane]

this is too good man

[worn gyro]

nope sorry i didnt laugh

[royal lark]

omg this is fuckin amazing

[grand thistle]

fire cover art

what does it represent tho

[rich sun]

Zorn's lemon

[grand thistle]

Lol that was their pfp right i rmb

[round shore]

Satanic commutative algebra

[grand thistle]

the algebraic geometry cult

[safe wyvern]

Seems accurate

[graceful moon]

I have been looking for that book for a long time, no wonder I couldn’t find it if it’s fr*nch

[polar pagoda]

why did you censor it

[vital bane]

because it's fr*nch

[karmic tangle]

I've read good things about Aluffi's books

He's got "Algebra: Notes from the Underground" and "Algebra: Chapter 0"

the former is supposed to be proper introductory undergraduate and the latter assumes you've already seen some stuff in undergrad at least, and it introduces categories at the start and then tries to place the rest in context of them. I'm really enjoying it though haven't gotten very far in at all yet

[loud gust]

I wanna learn about zf theory and continuum hypothesis and how they proved it to be idependent of zfc theory. I know basic naive set theory, and basic logic like definition of or,xor, and, implies, equivalence etc. etc. What source would you recommend?

[round shore]

And that's the best book in commutative algebra, cope

[gray gazelle]

Just learn french lmao

[graceful moon]

Might do it for the memes

[vocal owl]

hi ,so im a first year in university studying a bachelors of engineering in australia and recent developed a keen interest in competitive maths but i have no idea how to start so i was wondering whats a good roadmap or route i should take to kind of work my way up into the levels of imo's and things of that nature

so far ive been recommended a website called art of problem solving

but im not sure on good easy to navigate books for each field

so i would really appreciate if anyone could let me know

[polar pagoda]

I think it's a good starting point, like solving their books for beginners

[glad rampart]

I concur with whoever recommended AoPS

[polar pagoda]

first do their books for each topic they suggest and continue with your uni syllabus?

[novel hound]

AoPS has a book list (useful even in case you don't wanna do their books). If you have specific questions about one vs other you can ask here. Otherwise your question is too general to answer...

[vocal owl]

So Ive looked through the website and the max level is hs

Im trying to look at the university stuff but got no clue😭

im not tech savvy at all..

[glad rampart]

They don’t cover stuff beyond calc I don’t think

[gray gazelle]

You can go through AoPS and continue on from there by going through math books related to your uni syllabus. If you don't know what book to follow for each topic, you can ask here

[restive current]

im doing aops rn

[vital iris]

what’s a not scary alg geo book that goes over things like the correspondence you described yesterday @lapis sundial

[round shore]

#groups-rings-fields message this one?

It's pretty much done in the same way in the first chapter of every AG book

Maybe it's better in Gortz-Wedhorn than in Hartshorne

[mellow wren]

I believe in hartshorne superiority

[gray gazelle]

that's ironic

[vital iris]

Nice, I like how complete the appendix is in GW for algebra

[lapis sundial]

One nice place is Gathmann's notes online

[plucky dragon]

can someone wire resources for learning, preferably pdfs or something, for abstract algebra, number theory and graph theory?

i am bored

[vital iris]

👍

[versed coral]

is james stewart's precalc book great? some ppl say it has got weird questions while others say its a great source

[queen lantern]

Has anyone read both Elementary Mathematics From an Advanced Standpoint: Arithmetic, Algebra, Analysis by Felix Klein, and Basic Mathematics by Serg Lang? If so which one would you recommended?

Or maybe would you recommend Art of Problem Solving from Pre-Algebra to Pre-calc

Right now I'm reading Elementary Geometry from an Advanced Standpoint By Edwin Moise

But I want brush up on my algebra with a deeper dive into the fundamentals and theory

I think I will read Basic Mathematics along Art of Problem Solving up till pre calc

[mystic orbit]

isn't this literally the devil

[worn gyro]

Nah actually looks like it

[novel hound]

oops, I didn't realize you are at first year university level. Well, in that case you can't do IMO as the eligibility criterion is that you have to be pre-university. not sure if they have competitive math in uni in Australia...

I guess there's Putnam in the US, maybe there's equivalent in Australia?

[surreal depot]

theres this website https://www.amt.edu.au/amo not sure for what ages/levels they do tho

[rose geyser]

SMMC is the equivalent

[lusty escarp]

There seems to be 50% off on springer using 50off right now.

[molten mason]

Can confirm, 50off works

[regal solar]

LMAOOOO

[lusty escarp]

I am not able to order from springer. After I enter name, number, address and try to go to payment page, an error occurs saying "there is a problem with your account settings". Has someone else also faced this?

[rigid forge]

Are there any proof-centered precalculus/algebra/trignometry books? I know most books centered on hs mathematics are not rigorous, but still looking for them anyway.

I can only think of serge lang's book.

[left cloud]

hung-hsi wu books

rational numbers to linear equations, algebra and geometry, and pre-calculus, calculus, and beyond

[pearl nimbus]

if you still need, DM me

i've got a bunch of pdf's of books i collected while i was preparing for a competition

not posting them here bc it's not allowed

[terse garnet]

yo

is stitz and zeager precalculus good?

[rigid forge]

thanks, are there any pre requisite to his books(familiar with proofs, etc) or are they like any beginner book on the respective topic?

[left cloud]

i would call them beginner friendly

the intended audience is people who want to learn correct high school level math but don't know any

it's not like it's written for mathematicians to read or anything

[vocal owl]

okay i req u

[rigid forge]

alright, thanks again.

[hardy olive]

if any1 have read proofs long form delibrately (from cummings) , do u think its good for learning from prespective of highschooler

i read first chapter full i think its so gud in explainations

[foggy relic]

im holding out for the $15 like last summer

[solid bloom]

Is there any book that like- breaks down the most fundamental concepts of mathematics, like the stuff that builds up mathematics, a rather more philosophical book kinda

[glad rampart]

Get a book on set theory perhaps

[solid bloom]

no but like

even more basic stuff

even counting numbers or something

I just need the essence of ✨the beauty in mathematics✨ in that book

[slender cargo]

That comes from set theory?

Or you're thinking of combinatorics

[solid bloom]

oh uh

so

[slender cargo]

But I think axiomatic set theory is about as far down as you can go

[solid bloom]

everything comes from set theory right

[daring lake]

sounds like a mix of set theory and analysis to me

pick PMA by rudin ofc

[solid bloom]

I didn't know this before omg😭

that's interesting

[slender cargo]

Maybe try Goldrei's Classic Set Theory, which I intend to work on over time

Although I think it's better to learn this stuff after you've learned some Analysis and Algebra

[tender river]

goldrei constructs reals before naturals, so you might wanna do the chapters in a different order than presented if you want everything built up for you from scratch in order

[solid bloom]

I'm fine with alg but not so sure about analysis

[remote vortex]

Friends don't let friends read PMA

At least not until they know analysis already

[tender river]

definitely not to someone that just posted:

breaks down the most fundamental concepts of mathematics

[daring lake]

I was joking, I thought the 'ofc' would make it obvious

[tender river]

rudin doesn't break down anything

[remote vortex]

I will never miss an opportunity to point out that PMA is an awful introduction to analysis, although it is a great analysis book

[daring lake]

I supplemented it with Bartle

[slender cargo]

imo it's good to just have some motivation for why we need an explicit construction of the Real Numbers before seeing its construction. That's all. It's not strictly necessary. And if you don't care about seeing a construction of the Reals, then yeah, no need

[daring lake]

I think Rudin provides a great problem set

[solid bloom]

then ima look into that book then : )