book-recommendations

[signal canyon]

it rly is

i watxyed it on the toilet

😂😂

[tender river]

theres this other channel that does book reviews https://youtube.com/@mathematicaltoolbox?si=7HuKQw7DSVkPwplP

mostly on analysis and pdes and adjacent things

[frank saffron]

interesting, good to know, thanks!

[gray gazelle]

what would be the recommended trajectory for someone who has finished pst at the level of mendelson?

(all the possible trajectories, rather, since i'm studying out of interest not necessity)

specific reference(s) would be appreciated

this is the ToC

[tiny gulch]

<@&268886789983436800>

[cerulean steppe]

real analysis, like these two books: https://mtaylor.web.unc.edu/notes/math-521-522-basic-undergraduate-analysis-advanced-calculus/

[trim kayak]

Is anyone familiar with Basic Statistical Analysis 7th ed. by Richard Sprinthall?

I came across the book in a donation pile at the library and swiped it. It looks interesting and something fun to read through and learn.

https://www.amazon.com/Basic-Statistical-Analysis-Richard-Sprinthall/dp/0205360661

[gray gazelle]

I have already taken analysis - it’s often a prerequisite for topology

(Prerequisite as a measure of mathematical maturity, not really content)

[gray gazelle]

Please ping me

[cerulean steppe]

so you learned about inverse function theorem, surfaces, differential forms, and differential geometry?

this would be multivariable analysis, which is a second course in analysis

[sturdy shore]

what's your algebra?

[gray gazelle]

ah, i suppose that could be a viable path

[gray gazelle]

i've studied groups, rings and fields

[sturdy shore]

you can go to algebraic topology, measure theory, or smooth manifolds/differential geometry (for which multivariable analysis would be a prereq like the one above)

[gray gazelle]

but i do want to mention that my goal is to have something that would be a smooth transition from mendelson; i have university starting in september, so something that i could read beforehand or in passing that wouldn't require intense dedication

[gray gazelle]

what would you recommend for AT?

[sturdy shore]

I myself am no authority on AT but Hatcher and Rotman are two popular ones

[gray gazelle]

i see

i'll check those out then, i guess

[sturdy shore]

tbh you could look at this categorical topology book I've been looking at recently

it would be another perspective on the topology you've just seen, an intro to category theory if you haven't seen it before, and it also does some AT

[gray gazelle]

that sounds pretty cool

[sturdy shore]

maybe a bit too advanced for your level though

https://jterilla.github.io/TopologyBook/index.html

free

[gray gazelle]

ah okay, i'll check that out too

thank you

[sturdy shore]

[normal crystal]

the Springer flash sale
anyone know exactly when it ends
23:59 est July 4th, I assume

[lime hedge]

Chat are there any chess chat?

[timid lion]

#chess-go-shogi

[sturdy shore]

If discount is not applied automatically, please use this code: FLSH50. The discount is available through July 4, 2025 until 23:59 EST.

any good math books on sale?

https://link.springer.com/book/10.1007/978-3-319-05792-7

mmm

aaaaa

oh wait, a lot of shit is half off

wow

[normal crystal]

I think it's everything after the coupon

[sturdy shore]

sure seems to be

crazy

[remote sparrow]

i'm getting a copy of ideals, varieties, and algorithms by cox

as well as using algebraic geometry and cohn's measure theory book

[sturdy shore]

I've got so many candidates

[remote sparrow]

maybe grafakos?

[sturdy shore]

no, that's not the harmonic analysis I deal with

that's classical

[remote sparrow]

i don't really know anything beyond the basic measure theory and probability books

not my primary interest

[sturdy shore]

https://link.springer.com/book/10.1007/978-0-387-72476-8

wouldn't be interested if this were 45 usd but at this price feels like a steal

https://link.springer.com/book/10.1007/978-1-4612-1007-8

this is a great book, but a bit redundant for me

so conflicted on this as well

[sturdy shore]

this is my no 1 option, I may commit to more

[full cairn]

That's exactly what I was planning too I'm a bit worried that I'm buying too many books, but IVA is a classic, I pretty much have to have it, right?

[mossy flume]

is there a list of books that are on sale

[mossy flume]

huuuge

[mossy flume]

huuuuuuuuuuge

holy fuck 55$ off combinatorial commutative algebra

ugh this other book I want is only a softcover

[remote sparrow]

nah just try the coupon code FLSH50

[vital bane]

Canach Algebras

[humble spire]

every single book ive tested in the utm series is on sale 😭

[sturdy shore]

ughhh do I order now or wait until tomorrow to see if I'll change my mind on what I buy

I'll do it tomorrow morning

[trail hemlock]

i love cohns measure theory book

acc so peak

[remote sparrow]

i'm also gonna get royden from lulu

i like axler but i'm curious about other treatments

they both get recommended here often

your thoughts on royden?

[humble spire]

wait was that not the one with 14 pages of errata?

[remote sparrow]

that's a review of the 4th edition. the 5th edition has been out since 2023

i would assume most of the errors in the 4th edition were fixed since then

[normal crystal]

@remote sparrow @full cairn fyi, there is a new edition in August
but the coupon still applies
https://link.springer.com/book/9783031918407

[vital bane]

What about Folland? Do you like that?

[remote sparrow]

it was ok after reading axler

[remote sparrow]

o shit i better email springer to exchange my order

i already ordered the current version

[normal crystal]

is the coupon one time use?
I would just reorder the new version and cancel old

[vital bane]

I can understand that, since Folland doesn't have cats in his book

[remote sparrow]

i think the coupon is reusable

we want hard copies

[normal crystal]

Chipper in his head
"How do you put the hardback inside your phone screen"

[vital bane]

"Is there a mobile phone sized hardback?"

[normal crystal]

the super max phone screens are bigger than mass market paperbacks
aren't they
or at least one page

[remote sparrow]

we also have foldable smartphones

[normal crystal]

those are pretty rare for now
the super size phone screens are close to the height of a MM PB with less width

[remote sparrow]

@mossy flume

it covers a typically advanced subject in a way accessible to those who only have linear algebra background

[normal crystal]

I unironically want a folding ipad
obviously, one that expands to twice the current size

[remote sparrow]

is that any more terrifying than knowing someone prefers reading textbooks on their phone?

https://tenor.com/view/monka-cross-gif-4035178244594551512

[cunning elk]

[normal crystal]

there will be folding ipads if folding phones become more mainstream
if anything, it makes more sense

[toxic heart]

Would yall recommend openstax for precalc as a good free resource of learning

[trail hemlock]

royden 5e is prob my fav measure theory book. fun problems and a nice presentation as well. some of the problems are fairly difficult but nothing crazy. the proofs are neat but no need to fill in the details like with rudin. some important results are relegated to exercises which some people prob arent big fans of.

on this topic, ive heard a lot of good stuff about Taylor's General Theory of Functions and Integration, has anyone read it

[remote sparrow]

no option for paypal 😔

[normal crystal]

you mean you can use PayPal to order available now books
but not the preorders?

[remote sparrow]

doesn't seem like it

well is paypal bank transfer?

idk

[remote sparrow]

is a bank transfer the same thing as a wire? idk

[normal crystal]

bank transfer probably means entering your banking/checking account number
you can proceed and check without completing

[remote sparrow]

i'll try then

cuz i got no credit card

[normal crystal]

can you fool the system
by ordering an available book at the same time

but also, it looks like they have these flash sales a couple times a year
if you don't need that particular book right away

[remote sparrow]

idk

i already ordered the currently available IVA before u told me

i'll cancel that one if the pre-order works

[vital bane]

What about debit card

oh nvm they say either bank transfer or credit card

[sterile pelican]

My 4th edition is just waiting at the corner

Then I see this 🥲

[mossy flume]

I'm not buying a 5th edition of IVA 5th edition is great

All that'll change is I'll download a new PDF lol

[molten gulch]

Yeah

Same here

Uni access is awesome

[heady ember]

Just bind your own IVA

You are your own quality control

[molten gulch]

Buh

[heady ember]

I'm looking forward to my bookbinding project

I'm gonna try to make the most impeccably bound book I can

[molten gulch]

For what book

[heady ember]

Jeffrey Lee's Manifolds and Differential Geometry

We shall just casually ignore the fact that I'm nowhere close to reading it in terms of prerequesites.

[molten gulch]

Ooooh

Have fun!

[heady ember]

Thanks!

[molten gulch]

How'd you learn to bind?

[heady ember]

I just searched a tutorial on YouTube

My first finished project that was handmade from start to end (barring the printing and the raw materials ofc)
#1059828221887135774 message

[molten gulch]

Thank you!

[heady ember]

Np!

[molten gulch]

How much did all the materials cost? And what country. So I know if I need to convert for US

[heady ember]

Not much

[hollow shore]

I have stopped hoarding books because of the limited space

[cinder magnet]

What are the prereqs?

[heady ember]

So, depending on what you have in your house, it can range from $0.00 to maybe $20-30 max (ofc you can get better materials if you so wish)?

But you can reuse a lot of the stuff like the needle

[molten gulch]

I see

[heady ember]

I got my 300m nylon thread for like 3 SGD (< 3 USD)

If there are any local bookbinders near you, you can probably approach them for scraps at next to no cost, too.

[molten gulch]

I see, thank you! Sadly I know of none around where I live

[heady ember]

Same here, unfortunately.

[molten gulch]

Afaik small binding shops aren't that common here

[heady ember]

Oh boy its an incredibly large tome

Having it on paper really gives a sense of scale

[signal canyon]

any good books to learn the basic integration

u-sub, trig, parts,

[fresh skiff]

binding this book??

[heady ember]

Indeed. Its ridiculously thick lol

[fresh skiff]

about 700 pages

[heady ember]

Yes

[fresh skiff]

grass Diff geo arc when ?

[full cairn]

Thanks for the heads-up! It costs twice as much though, do you think it's worth it? 🤔

[vital bane]

You are close

[heady ember]

Not at all

[vital bane]

you just need to finish anal on R and LA, then finish up R^n anal

[heady ember]

I should have a working understanding of comm alg and general topology, too.

[vital bane]

Comm alg is not at all needed

[heady ember]

Modules and multilinearity (and cat theory)

[vital bane]

the multilinear algebra needed is usually covered in a diff top/diff geo book

But yea you do need some gen top, which you can cover quickly

[heady ember]

That aside, its pretty far up on my reading order:

1. Schroder + Rudin + FIS
2. Algebra + Multivariable derivatives
3. Comm alg + measure theory
4. DG/AT/AG

[vital bane]

I'm just saying, if you want, you can get to it pretty quickly

[heady ember]

Maybe. Even so, there's no reason I wouldn't just read a comm alg book: its something I wanna get to eventually, as well.

[mossy flume]

It seems the main additions would be material on toric varieties

which are a beautiful theory that I should learn more about

However toric varieties are a very rich field in their own right and there are some good texts out there

• Brasselet - Introduction to Toric Varieties (maybe these are course notes idk)
• Fulton - Introduction to Toric Varieties
• Cox, Little, and Schenck - Toric Varieties
• Cox, Little and O'Shea - Using Algebraic Geometry Chapter 7 has some material
• Miller, Sturmfels - Combinatorial Commutative Algebra Part II has some material as well

[full cairn]

Thanks for the suggestions I think maybe I'll stick with the 4th edition, and if I want to read about toric varieties I can look at these other sources (or just look at the 5th edition on pdf)

[runic crater]

Hi guys, I would like to ask for suggestions on what books should I read to have a good grasp on the theorems in Plane and Solid Geometry. These are the topics I need to study and I basically have zero knowledge/intuition in this area.

[humble spire]

Kiselev planimetry

[trim kayak]

How does everyone prefer to read and study math textbooks? Do you take notes as you read and then practice the problems at the end of each chapter? Do you prefer a notebook for notes and a separate one for practice problems or do you keep everything together?

Let me know! I'm curious.

[proud abyss]

ill share the way i learn that works for me: If its a topic that is fundamental then I just analyze, read, try to understand, fully comprehend it a few times over and keep rereading and try to apply what its telling me in my head to get a feel of it then I write my own examples of what I think I understand, read the actual examples and compare my examples and then I repeat the example process like 50-100 times over weeks
If its a topic thats just building on something i already know like i learn logarithms and now im gonna learn a lot of formulas and stuff with logarithms, I just learn what its saying, go through the comprehension phase and just look at given examples and try them out myself and if i feel i got it i just move on

[fresh skiff]

honestly i wanna know this, but the truth is; everyone has their own way. Try various methods and see what works for you.
I am still finding a suitable method for myself. Currently i take notes on latex and write all theorem (prop, lemma and corollaries) and i do write exercise problems as well with proofs (only ones i am interested), it does not mean i skip others i do other problems as well but on rough pages.

[proud abyss]

^ this is true though yeah

[fresh skiff]

Next time i will try to write notes for theory and exercise problems separately.

[proud abyss]

taking notes on latex is next level tho

i got a giant thick callus on the finger i hold my pen 😭

[fresh skiff]

my hand writing isnt super well, nor my phones camera is really good. So i write proofs on latex then do yapping in my thread

[proud abyss]

yeah i started doing this as well recently tho

[fresh skiff]

oh? probably you hold your pen so tightly

[fresh skiff]

cool

[trim kayak]

Is handwriting notes not a good idea?

[proud abyss]

i think it reinforces learning

to write with hand

but i had a theory where wouldnt writing with your keyboard also have the same affect if you memorize the letters on the keyboard?

[fresh skiff]

it is good as well.

[upper estuary]

I think writing by hand is much faster unless you're one of them 200wpm virtuosos

[proud abyss]

also meanwhile im here, is there any short books that summarizes like base concepts for number theory

[ancient creek]

It would depend how you interpret information, for visual memory cognition, writing would make sense, for typing you would have a good cognition with the position of keys and their order. I tried both, it's good to train both, sometimes I find myself doing both(mostly handwriting)

[proud abyss]

with writing i can draw shapes symbols sizes a lot easier though

[ancient creek]

Same with learning how to take notes with the hand that's not predominantly your main in-use hand - right vs left hand. Your brain would have better cognition in terms of how it memorizes the data.

[ancient creek]

Yes! 😎 Doodles all the time

[proud abyss]

yeah 🔥

[ancient creek]

I think what it comes down to is what your brain is used to more so you would naturally have an inclination towards but you can develop the ability to have that inclination towards any way of comprehending information.

[ancient creek]

One suggestion I would give(something that I do 😁)is when I am reading through the pages, I would search online if someone has made some questions about the definitions or the proof, usually you would find a lot of perspectives that aren't covered in the book. I have a big A4 notebook so everything can look nice, for practice problems I just use a small one.

[trim kayak]

That makes sense. I have a few math texts that I want to read through and learn from. I'm just not sure how I want to do it yet.

[calm thorn]

Recommend me something on philosophy ? Ik this for math mainly but if anyone’s got a book rec send it

[remote sparrow]

yeah this is good

lulu increasing their prices soon

[sturdy shore]

ordered this 😌

decided against ordering the commutative banach algebra book or pedersen's book because I knew it was highly unlikely I'd need to use them physically

still... it hurts

[remote sparrow]

https://old.maa.org/press/maa-reviews/general-theory-of-functions-and-integrations

[trim kayak]

I have 3 different texts that I want to read through and learn: Intro to Probability and Stats, Stat Analysis, and Calc. What order should I read through and learn these?

I'm curious because I don't know if calc is needed for either of the other two even though they're inteo books.

[cerulean steppe]

calc, then probability, then statistics. You probably should change the texts accordingly

[trim kayak]

Ohhh. Thats the opposite of what I thought. Calc first even though the other two are intro books? I don't know ow how much Calc I will need for those.

[cerulean steppe]

you need calculus for probability and you need probability for statistics

[molten gulch]

I do not see anything overtly aggressive about it, is it not true what the reviewer has stated about the decline of mathematics education?

[gray gazelle]

hi i am good at math but i had a bad teacher the last year and at my exam of june i had 7/20 .because i don't understand geometry and functions is to go from something visual to equations and how that relates to the concrete. chapters that i really don't understand are plane analytic geometry and functions of the second degree. anyone know how i could find out about these subjects?

I sent this message here because there may be a book about it.

[remote sparrow]

https://fixvx.com/stupidtechtakes/status/1940923805779829058?s=46

stupid tech takes (@stupidtechtakes)

perfect for when i need to bend my phone around my wrist!

QRT: FearedBuck
Motorola revealed a bendable phone that can be worn on your wrist 👀

▶ Play video

vxTwitter / fixvx 💖 3.33K 🔁 76 · Jul 4, 2025, 12:01 AM

for when chipper really needs to read books on the go

@green aurora

[molten gulch]

I hate that so much

[valid dawn]

they always have this song in the background too lmao

[fossil arch]

Any beginning-graduate or upper-level undergraduate texts on thermodynamics and/or fluid mechanics use a strong, rigorous mathematical basis to help guide the physical intuition and results?

[heady ember]

It can be faster and nicer provided that you have an established workflow, where you don't get the urge to mess with (La)TeX too much.

[sand bobcat]

I'm currently learning pre-calculus topics using the OpenStax book, and I'm finding it very easy. Is there another book with more challenging exercises? I'm not focused on math olympiads or anything like that, I'm just learning for fun

[remote sparrow]

just move through it quickly and then hop to calculus

you will then figure out what you need to revise as you go

[trail hemlock]

one paragraph is dedicated to trashing this generation of students and saying it was better in the good ol days

😭😭

[slender wasp]

good stuff

[vital bane]

Bro writes 200 wpm by hand?!? No shot

[vital bane]

Holy crap that's so cool! Damn!

It looks goofy as hell when you wear it on your wrist but look at how much the screen is bending, that's sick!

[edgy hare]

At least add a strap geez also how the heck is a case gonna work on that

[vital bane]

Bendable case

[edgy hare]

Regular case geometry says naw

[vital bane]

use non-euclidean case geometry

[last cipher]

thoughts on nicholson's lin algebra

vs David c lay's lin algebra

[ancient creek]

As long as you start it and keep reading, you will be good don't worry

[steel cloud]

So papa Rudin introduced abstract measure theory?

[last cipher]

i personally write in the textbook in pencil and deconstruct proofs bit by bit

then id do the exercises on a scheduled period since recall is important in the long term

sometimes i rewrite theorems in my own words that is comprehensible to me

[sage python]

At a quick glance, Nicholson seems to cover more theoretical topics

More abstract treatment of inner product spaces (even some chit chat about Fourier approximation, later Jordan form)

Also it mentions applications to linear codes over finite fields

So there might be some talk of linear algebra not just over R/C

(It is also just longer)

Lay seems to go a bit more into Markov chains

[vital bane]

Yes, measure theory and some complex analysis (as the name indicates) and grandpa rudin is functional analysis

[daring wolf]

yep

[heady ember]

You can use custom fonts with LaTeX.

Idk what you mean by fancy paper, but any paper design is possible with the help of TikZ.

[steel cloud]

I see

[steel cloud]

So reading abstract measure theory before Lebesgue measure, is that good?

[remote sparrow]

either way is valid

[last cipher]

Whats the comparison between nicholson and axler's treatment of linear algebra?

[upper estuary]

I don't but I meant that if you're typing latex you have to type a bunch of extra stuff like \frac{}{} instead of just drawing a line by hand

I guess I should've said characters per minute rather than wpm

[cunning elk]

me poring over my thousands of nested brackets trying to find which one i mismatched

I’ve typeset pretty huge documents in latex

solution manuals for the math contest i run

so big that overleaf can’t compile them for free (i use a local editor/compiler)

[vital bane]

https://www.overleaf.com/learn/latex/Learn_LaTeX_in_30_minutes

[signal canyon]

this stweart book everyone talks ab for calculus, is it calculus early trasncendants 7th edition

[remote knoll]

I believe I'm using texlive on my computers, but I'd need to double check. Whatever's the default.

I started reading through Ideals, Varieties, and Algorithms, and it's such a clear book.

[sterile pelican]

I want to finish the remining AA and LA before I touch Cox's IVA

But it is a book I want to do

Ideally after finishing say Bloch's RA, Anderson's AA, and Berberian's LA I want to do Duistermaat's RA 1&2 and Cox's IVA

Then after those two I have no clue where to go :^)

[heady ember]

DG

[sterile pelican]

So...the Lee Trifecta?

[vital bane]

Or the Spivak Pentafecta

[little wave]

Hi everyone, I'm studying for a math competition rn and I need some suggestions on what books/documents I should practice. My test focuses on Solid Geometry without a coordinate system ( that means the questions don't give any points or functions) and question is about distance, volumes , angle, ratio max/min of volumes, angle, expressions,.... And the question is also usually about tetrahedron,quadrilateral pyramid and prism

[heady ember]

Which Lee

Jokes aside, the one by Jeffrey Lee is an option too

[fresh skiff]

Both Lee are well known

[sterile pelican]

I don't know Jeffrey Lee's one :^)

[graceful moon]

It’s so well written, I feel like they could jump into the algebra a little more in the beginning but it is still phenomenal

[sterile pelican]

I uhh am not a masochist thank you, but I do want to try to read at least Lee's topological manifolds...since I own it :^)

[heady ember]

You can also DIY tools yourself

Awl at home

What an awl is supposed to be

[vital bane]

The only awl I know is Outsider

[drowsy thicket]

You do bookbinding?

[fresh skiff]

impressive

how much time do you spend binding your book

[sage python]

Axler will have much fewer computations, no applications, and start with the general vector space material instead of Nicholson starting with linear equations/matrices/determinants

So Axler won't do much (if any) RREF, and determinants are way at the very end and presented more abstractly (it's the conceptually better way to do determinants)

[trim kayak]

How does everyone prefer to read and study math textbooks? Do you take notes as you read and then practice the problems at the end of each chapter? Do you prefer a notebook for notes and a separate one for practice problems or do you keep everything together?

Let me know! I'm curious.

Ahh ok. Im just curious what others do. I have 3 books I want to read through and learn from. Just not sure how to do it. I know its different for everyone but Im curious.

[timid lion]

i take notes as i read. if it’s not for a class then i don’t do the exercises

[sturdy shore]

I've done both methods: writing most of the content down and not doing exercises, or not writing most of the content down but doing exercises

the former works only if there's stuff to be filled in during proofs imo

or if the content is not so difficult that you can actually meaningfully attempt theorems before reading the proofs

at the end of the day, there needs to be some friction in there for you to challenge yourself, that's what exposes gaps

and reinforces learning

esp during undergrad it was essentially unfeasible for me to attempt exercises in any book I was reading

unless there's already a narrow area of math you are focusing on

learning through exercise is the one that will stick the best, but it is also the slowest

depends: if done well imo it can be a good substitute

[analog wraith]

A mathematicians apology

😛

[trim kayak]

You don't practice the problems to apply what you have learned?

[timid lion]

no

[analog wraith]

What level of maths are you doing

[trim kayak]

I have 3 books i want to read through and learn: Intro to Stats, Stats Analysis, and Calc. What order should I read and learn these in?

[timid lion]

what is stats analysis?

[trim kayak]

Statistical analysis

[timid lion]

what is the difference between stats and stats analysis

[trim kayak]

Statistics is the broader field of collecting, analyzing, interpreting, and presenting data, while statistical analysis is the specific process of applying statistical methods to data to discover patterns, trends, and relationships. Essentially, statistics is the foundation, and statistical analysis is the application of that foundation to make sense of data.

[valid dawn]

idk lol

[heady ember]

Depends, but I don't really keep track so I can't give you anything concrete.

[fresh skiff]

No problem

[gray gazelle]

I’m an incoming freshman this a.y, do you guys have any book recommendations for college advanced algebra and mmw?

[cunning elk]

“college algebra” is just high school precalc no?

[gray gazelle]

yeah, but honestly I don't know much about it because we didn't take that subject... that's why I’m asking for a book recommendation if there is any

[daring wolf]

wdym by college algebra

like do you know what you learn there

usually algebra learnt in mathematics department refers to abstract algebra

[gray gazelle]

I'm confused...

[cunning elk]

“college algebra” usually just refers to precalc

[normal crystal]

here's the confusion
"college advanced algebra" is not a standard course that everyone will know
so you have to say more or we have to guess
idk what "mmw" even refers to
it sounds like what you want is a textbook for what's called "college algebra" in many US universities, which is actually just a condensed HS algebra 1 and 2/ half of precalc
if so, Openstax or similar is fine

[cunning elk]

“algebra” by itself in a college context is usually abstract algebra (groups, rings, fields, modules, etc)

[gray gazelle]

Ah I see! Sorry for the confusion 😅 I'm from the Philippines, and here “College and Advanced Algebra” is a subject usually taken in first year. It includes functions, equations, logarithms, etc. Not abstract algebra. And MMW stands for “Mathematics in the Modern World,” which is a gen-ed course focused on real-life applications of math I think? I just wanted to prepare early, so I was looking for beginner-friendly (text)book suggestions. Again, I’m sorry for the confusion (I was nervous...)

[normal crystal]

ok, so the first course is what we said
Openstax has a Algebra and Trig, College Algebra, or Precalc, they overlap

[fresh skiff]

Advanced algebra is usually taken after year 3 or 4.
By advance algebra i assume subjects like : Homological algebra, representation theory, category theory etc

[normal crystal]

the second course sounds like a topics in math for liberal arts type course for people to fulfill gen ed requirements
there are textbooks for thst type of class, even legit free ones
but they are topics dependent, so it matters what's on the syllabus

[gray gazelle]

cool, thanks a lot

[normal crystal]

she just explained, that doesn't help, c'mon

[fresh skiff]

Oh i misunderstood mb

[normal crystal]

Openstax even has this for what I was saying about the second course
https://openstax.org/details/books/contemporary-mathematics

[gray gazelle]

thank you so much, I’ll check it out:)))

[normal crystal]

there are other recommended free books for those and other subjects here
https://textbooks.aimath.org/textbooks/approved-textbooks/

[next storm]

What is the ideal book for learning real analysis on your own?

[fresh skiff]

There is no ideal book. There are good books for learning real Analysis for selfstudy as a first course. I prefer the book by Stephen Abbott namely Understanding analysis.

This book has clear exposition of the subject, with a variety of problems that range from easy to hard.

[upper estuary]

I'm not the OP, but would you say real analysis is something it makes sense to take only after, say, Spivak's Calculus or Apostol's trilogy, or is it largely a different unrelated branch of math that one can reasonably study at the same time as Calc/analysis?

I always get confused in the course naming/terminology

[timid lion]

real analysis is analysis dealing with real numbers. Spivak's Calculus is basically an analysis/real analysis book with emphasis on calculus

[upper estuary]

Ohh so like as opposed to complex analysis?

That clears things up, thank you!

[wintry quartz]

Hey, Im going into my fourth year and I have done a course in topology (covered pretty much all of munkres) and differntial geometry (covered pretty much all of lee) and I am really inetrested in symplectic geometry and mathematical physics. I have seen online that the current research in symplectic geometry seems to be in homology theory, is there any recommendation for texts that cover symplectic + intro homology + some mathematical physics things? I barely remember covering spaces things, so thats around the level of book I am looking for. Hatcher seems a bit too hard, so im kinda lost here

Im going over the munkres chapter on algebraic geometry

[fresh skiff]

Calculus and real Analysis are sometimes interchangeable. Spivak's calculus is actually a real Analysis book, it is of same level as Abbott. In general
Calculus is more about computations and real Analysis is about the analysis of calculus and ofc it involves proofs and rigorous formal stuff.

[daring wolf]

for introduction to homology theory and cohomology theory, you would like to get an algebraic topology book, and you will get some introductory homological algebra book after and also category theory as well.

hatcher is pretty standard for algtop, and for homological algebra i heard rotman is a pretty decent choice

other algtop books i know are bredon, and i heard munkres has algtop book as well
and Lee's intro to topological manifolds covers some homology things afaik, and Lee's smooth manifolds book has de rham cohomology, and dealing with de rham cohomology first will help you in a variety ways in learning algtop since de rham cohomologies are very intuitive.

other algtop books are explained in the pined messages here.

i dont know anything about symplectic geometry and (deep theory of) mathematical physics, maybe some other will help you

[cursive rivet]

da silva's intro to symplectic geometry is a good jumping off point (has the physics too), though I don't remember how much of the baseline homology theory she assumes

[wintry quartz]

from what I have seen she only really talks about the deRham cohomology. Maybe I have the wrong book?

[wintry quartz]

In all this how much algebra is needed? I have gone through most of the groups and rings part of dummit and foote. Do you think that is enough to jump into homological algebra?

[daring wolf]

rings and modules are enough(or more than) to get into algtop. but since usually homalg and cat theory are introduced after you learn sufficiently many topics in algebraic topology, just go learn algtop. you probably like to learn commutative algebra along with those advanced topics after algtop but idk

while you can start with homological algebra with your rings and modules base, but they will require you category theory as well (they are also introduced in homalg books ig), but since you will benefit more homological algebra after doing some algtop, you should learn algtop as well.

learning 100% abstractful thing without proper use is like pointless thing to do(the abstract side of the concepts are developed from intuitive things, and totally applicable things), like just learning homological algebra without learning how they are used.

[wintry quartz]

yeah what I meant was that is my algebra side of knowledge sufficient or is there something from group, rings and fields that I would need to learn on top of algtop to go into homological alg

[daring wolf]

ok

[wintry quartz]

I should've been more careful with how I worded it

[daring wolf]

np that was okay

[proven lantern]

I want a probability book as a preliminary for durrett's or bilingsley's book, any recommendations? How about Bersikas? Or even Shiryaev?

[remote knoll]

@rose parcel please don't unsolicitedly advertise in the chat.

[vestal junco]

Does anyone know how to make your own hardcovers

Not the design but

The actual cover

[molten gulch]

@heady ember

[fresh skiff]

The first person who came in my mind after reading that message

[open solar]

I want to learn number theory but don't know where to start. (let's say I am Total beginner or just decided due to intrest)

[molten gulch]

Rosen elementary number theory; learn some abstract algebra and/or read ireland and rosen

[open solar]

okay thanks for suggestions. I will give it a try.

[potent quest]

highly recommend Weissman's An Illustrated Theory of Numbers, very well-written intro to number theory that doesn't assume much background and puts a lot of emphasis on visual intuition

http://illustratedtheoryofnumbers.com/

[cerulean steppe]

Apostol's Introduction to Analytic Number Theory is highly regarded, if you know analysis

[open solar]

okay sounds good but out of my budget. I live in India and it's has price of 4,000 rupees.

my parents will not agree (I am a 16 year old student right now)

[tender river]

theres a dover book too https://store.doverpublications.com/products/9780486682525 (George Andrews Number Theory) that is probably available for cheaper. i know nekoma recommended this a while ago

[open solar]

yea it is cheap.

well it's not like my parents doesn't purchase high price book for me, they does but that book should be my academic related. it should be related my school but number theory is not related to my school topics (I want to learn it, I am interested in it) that's why price become the problem.

[slender wasp]

Elementary Number Theory by Burton or Friendly Intro to Number Theory by Joseph Silverman (popular and cheap).

[indigo turret]

Hello, does anyone have a good book recommendation for pre-calculus that is easy? (im going into grade 9)

[tender river]

https://openstax.org/details/books/precalculus-2e

[fickle quiver]

hey I'm headed into my senior year of highschool and I'm looking into majoring in math for my undergrad. I've taken algebra I/II and geometry and planning to take pre calc in the fall and I wanted ask what resources should I look into for furthering these foundational levels of math?

[tender river]

theres a bunch here in the "Basics" section https://realnotcomplex.com/

[fickle quiver]

much appreciated

[harsh berry]

Hey, I was considering checking out PDEs as a topic (it seems pretty interesting) now that I did a course on ODE and rather enjoyed using it in random places in physics and ecology. But there's no course on the same in my college till masters, so gotta self-study. Could someone recommend some books/video lectures I could check out?
Also are there any major pre-reqs for the topic however? I have studied analysis in several variables, however haven't done much functional analysis. Is it majorly required or the major results are covered while studying the topic?

[bright epoch]

Usually the latter, but it helps to have a little bit of background

[harsh berry]

Hmm 🤔
Functional analysis I think I can manage to somewhat prep (got batchmates studying that), but any clue about pdes tho, I'm hopelessly confuzzled 💀

[cerulean steppe]

you need measure theory background. Functional analysis can be covered as needed while studying PDE

[harsh berry]

Oh damn, I wasn't aware. Do I need to study it deeply, like as in a course depth, or would a overview of the major concepts be alright?

[glacial spire]

I'd like to study Representation Theory from Fulton and Harris, but the multilinear algebra part is too difficult for me, even though I had the impression I was good at linear algebra. I know Greub should be at the appropriate level, but it's also a difficult book to go through right now. Any book recommendations that will bring my algebra to the right level to study Fulton and Harris?

[remote sparrow]

https://bookstore.ams.org/amstext-54/

you can check this book out for an overview that doesn't require anything beyond linear algebra and real analysis

[cerulean steppe]

You need it deeply. Check out a good PDE book, like the one by Evans, Folland, or Taylor to see what the authors say about prerequisites.

[heady ember]

If you want the budget option, then glue cardboard (non-corrugated) together. When the glue dries, it has a suprising strength.

Just cut your board to the correct size, and then glue your bookcloth/leather/etc onto the hardcover. Done.

https://youtu.be/fvgRQqgXLoA?feature=shared

https://youtu.be/UoUiJ4c1aEw?feature=shared

[vestal junco]

Alright, thanks man!

[toxic heart]

Hello just curious what calculus Stewart book should be recommended to get? There’s like 3 books but I don’t know if the early transcendental or the one that just says calculus should be bought I just want to learn calc 1-3. Also how huge are the differences for each edition I am not trying to pay a lot lol

[lavish orbit]

looking for a differential geometry book with an emphasis on hamiltonians/lagrangians and lie groups/lie algebras
my riemannian geometry foundations are ok, but could do with some revision, specifically in the areas of things like parallel transport, geodesics, subgeometry

[full frost]

book to study calculus

[full frost]

i have used the simple one and people say it is underwhelming

they have recommended apostol

[bright galleon]

My university used Early Transcendentals for Calc 1-3, so that's probably the one you want

[ionic rain]

Thoughts on Calculus by James Stewart?

I've heard mixed reviews

[idle pawn]

Hello! I’m a Comp. Sci. who enjoys maths a little too much.
One of the things that I’ve been trying to get into is Topology And Manifolds. I was recommended a textbook or two, but I found them somewhat difficult to understand.
Any recommendation on a good textbook that’ll give me an overview on what topology is, what manifolds are, and how to do the maths on those? Like I understand the ‘concept’ in a very rudimentary way, but nothing in a manner to manipulate them.

[vital bane]

For general topology Munkres is great

but if you want to learn topology for learning manifolds and for doing math on manifolds

Lee's Introduction to Topological Manifolds is great

[bright galleon]

Lee, as recommended above, is fine. I'd stay away from Munkres because I'm confident that if you think you're interested in topology and manifolds, you're not looking to get a super solid foundation in general topology.

My personal recommendation would be Tu's Introduction to Manifolds. You get enough general topology to get started in an appendix, and then you immediately start developing ideas of calculus on manifolds but on Rn first, along with the multilinear algebra that comes with it. You then go back and develop the theory for general manifolds.

I have a couple other questions for you though.

1. Are you comfortable with proofs? You mention struggling with other books, so I'm wondering what you might be ready for.
2. What do you think would be interesting about manifolds? (just figuring out what your motivation is so that I can make a better rec)

[vital bane]

My question is unrelated to the current discussion but what is your opinion of Spivak's "Comprehensive Introduction to DG"?

[bright galleon]

I'm not familiar with it, unfortunately

[idle pawn]

Proofs are quite in between for me. I can’t really say I’m really comfortable, neither can I say I’m pretty terrible.

My only motivation is to understand how to do math on it. That’s really about it. Working in the Neuroscience lab, I was trying to see if I can, do math on a brain surface, which led me to this rabbit hole.

I will mention:
I have tried primarily two textbooks John M. Lee’s Graduate Texts in Mathematics: Introduction to Topological Manifolds, but I felt like it was just too much, and a lot of it was somewhat unnecessary for me.
I have also tried General Topology by Stephen Willard. I confess that I immediately gave up due to how ‘mathy’ it was and how much focus I required to put into it.
@bright galleon @vital bane

[vital bane]

If you wanna do diff top/diff geo for some other applications, you don't really need to learn it the pure math way

you can learn it how the physicists learn it

[bright galleon]

Alright gotcha, so let's dial back the recommendation then. You definitely don't want a book on general topology, though you'll have to do some to even define a manifold properly. Idk recommendations for that, but maybe try searching things like "calculus on manifolds" and try to make sure it's fairly computational? @vital bane do you know any sources for "how the physicists learn it"?

[vital bane]

Actually iirc Eric does neuroscience stuff, he might know it some resources for this @fallow cypress

[vital bane]

I know nothing beyond GR books and http://www.damtp.cam.ac.uk/user/tong/gr.html

There is also Applied Differential Geometry by William L. Burke, but I haven't gone through it personally and I don't know how it is, but you can check it out if you want

Oh I also know this, it's called Tensor Calculus but it's really DG

but they all approach it from a physics POV

[vital bane]

Have you learnt multivariable calculus?

[remote sparrow]

https://www.damtp.cam.ac.uk/user/tong/books.html

that reminds me, david tong's books have all released

@vital bane

[vital bane]

Oh yea I saw this

[worthy kindle]

they smell nice
ts gotta be the math sorcerer's alt

[vital bane]

Nah math sorcerer is different, lots of people like the new book smell

THIS is math sorcerer's alt

The unkempt appearance might have something to do with that

[normal crystal]

he simultaneously looks right out of the shower
and dirty
hidden talent

[worthy kindle]

he looks tuff fr

[vital bane]

No One is Coming to Save You

[normal crystal]

he should make a Math Sorcerer AI sitcom/procedural
like he interrupts criminals to suggest 13 different prealgebra books, half of which are out of print, the other half random old editions from tag sales
and they just give up instead of accepting his Amazon referral code

[idle pawn]

Yes! Yes I have.

[flat forge]

best basic to olympiad books for polynomials i.e. includes everything from scratch?

?

[bleak slate]

hi folks, i've got 10 days (in total, so only about 5 or 3 days to collect info) to work on a project about the fundamental theorem of algebra - i.e every polynomial of degree n (with complex coefficients) has exactly n complex roots (including roots that appear multiple times)
what ressources should i use? i like videos, articles, or books (but idt i can get my hands on any useful ones)

[molten gulch]

There will be no single text on polynomials at this level

[flat forge]

Do ou know good ones to read for polnomials?

I mean like for intermediate

[molten gulch]

Sadly not at this level

[fallow cypress]

Very well written, at least the first book

[fallow cypress]

Not a textbook but this video might be helpful in getting an overview? https://www.youtube.com/watch?v=QHj9uVmwA_0

[foggy quest]

There are "elementary" and non elementary proofs here: https://mtaylor.web.unc.edu/notes/complex-analysis-course/

[full frost]

Guys calculus book suggestions

I have only done basics of it

A book that takes the application and theory of calculus relatively together and is rigorous

[molten gulch]

Most calculus texts are rigorous though they make subtle assumptions better treated in a text on analysis

[full frost]

Hmmm

So which one should I go for

There's apostle's

And James Stewart's

There is spivok asw I think

I am confuzzled

[molten gulch]

Stewart is fine, Spivak does some of the aforementioned analysis but for anlaysis I woukd.recommend Abbott's book, Rudin, etc... (check pins)

[full frost]

Pins alright

[crystal flame]

Recommend me something for mental maths 🧮

[long stone]

I read Secrets of Mental Math: the Mathemagician's Guide to Lightning Calculation and Amazing Math Tricks by Arthur Benjamin

[crystal flame]

Helpful?

[long stone]

yeah, to some extent, but the most important part is practice

[crystal flame]

What did you use to practice?

[long stone]

just did a lot of simple problems ig

iirc they also have example problems so u can practice w/ those

[crystal flame]

Oh sounds good

[crystal flame]

Also what do you mean by “to some extent”?

Do you need to supplement it with some other book?

[long stone]

it helps a bit, but if you don't practice, it won't work

[crystal flame]

I see, thats the plan - to practice.

[long stone]

mhm, yes

[crystal flame]

Thanks @long stone

[long stone]

No problem!

[crystal flame]

What you learning currently?

[long stone]

We are getting a bit off topic, but I'm currently studying Ehrhart theory

[last cipher]

Kolmogorov's Analysis v. Abbott's Analysis?

[tender river]

apple v orange

[last cipher]

oh makes sense

[tender river]

[idle pawn]

Got it! I’ll 100% look into this. Thank you!

[vital bane]

Orange

[steel cloud]

How is the Tao introduction to measure theory book is good for beginners?

And Tao II has some chapters on calculus on R^n, how is it?

[rotund halo]

book reccomendation

for calculus

self teaching

like from basic (like significan of it , how it was created proof and all with graphs)

[molten gulch]

Yeah so you need to pick, do you want a million proofs and not many images or lots of images and computation practice but unsatisfying proofs

[rotund halo]

one that will help me and make my interst in it

[rotund halo]

i dont have any choice for images

i want some proof but they should make me understand the core concept of it

[upper sigil]

Does anyone know a site or source like paul's notes but instead of calculus it's linear algebra ?

[round roost]

Sadly I dont

Honestly though

Textbooks are the same

Pauls notes are just a textbook if you think about it

[cunning elk]

most intro computational linalg texts are isomorphically bad so

[last cipher]

have you done an introductory proof course

[honest pelican]

I need a book rec for highschool

math

[last cipher]

College Algebra by Carl Stitz and Jeff Zeager

https://www.stitz-zeager.com/

You can get a large print paperback copy for a really cheap price on amazon if you want one

[honest pelican]

i appreciate that

[rotund halo]

no

[worthy kindle]

u could jus read spivak's Calculus

without a course in proof writing

[last cipher]

Pretty sure sets could be used for basic probability

Basic Set Theory is taught in Canadian High Schools esp in my province

but its VERY dumbed down

and its surprisingly for the lower level math course that we offer in my province

[last cipher]

I mean what concepts do you even want to learn about in Calculus

in the "proofs" perspective

[rotund halo]

i m mean the core on how it was created , ( sorry if i m sounding dumb)

a begg. book which covers the core and explains it greatly ( i was refering proof in that way )

[last cipher]

Oh on how it was created

Like how limits snd such work?

[rotund halo]

some what

[rotund halo]

yaya

[last cipher]

It'd be hard if you havent taken a proof course

But yeah I recommend spivak's calculus

[rotund halo]

do u have any course

or prequiste book before

that i do , before start doing spivak's calculus

[last cipher]

Discrete Mathematics by Rosen

but

you can do spivak without any proof course

[arctic bramble]

Are you looking for a proof based book?

[rotund halo]

yes , but i havent done any proof course

[rotund halo]

do u know any proof course

thank you

sir

[arctic bramble]

Of course

I have more things which might be tangentially related, but not a direct 'proof book'

I actually love proof theory so much that I am reading the Cunningham book as well, so we have that in common

[rotund halo]

nice

[arctic bramble]

Hopefully you enjoy them, and they help

[rotund halo]

thank you

do i need any prequite knowledge

for these book

[last cipher]

no

just a curious mind ig!

dont rush things

[rotund halo]

okok

[last cipher]

DO NOT SKIP EXERCISES

[arctic bramble]

Yes

To what whyhello is saying, yes

[last cipher]

a lot of self studyers skip exercises (i was a victim) and it pretty much screwed up my progress

[arctic bramble]

Take your time, annotate and/or take notes, and be very deliberate. There is no clock on your reading, the only thing that should matter is how well you can digest information

[rotund halo]

okok

[arctic bramble]

The Hammock book is actually very descriptive and starts early enough in what you would need to know that I do not think you need a ton of prereq knowledge

[normal crystal]

the first book is not OER
you can't just share it here

[arctic bramble]

Be willing to struggle, and do not worry about asking questions

[arctic bramble]

What is OER?

[normal crystal]

Open education resource

[rotund halo]

i will keep that in mind

[arctic bramble]

Ah

[normal crystal]

no piracy on the server

[arctic bramble]

Apologies, It was sent to me by a friend I believe

This good?

Can I ask how you were able to check that, so that going forward, I am aware

[normal crystal]

it doesn't matter
unless you can verify it's legit free, don't share here
Hammack is fine, but you can share the link to his site too

[rotund halo]

i will be taking my leave now

thank you sire

sir*

[arctic bramble]

Goodnight

[normal crystal]

it's published by a real publisher
springer does do some Open Access books
but they're marked as such

[arctic bramble]

Thanks

[last cipher]

sooo

i have this sudden urge to get baby rudin

i mean i already have abbotts analysis

probably

LOL

is a collection hobby terrible

i might have developed one

[arctic bramble]

Nahhh it happens

[last cipher]

I have 3 linear algebra books 😭😭

[arctic bramble]

I have things that if I read the things I need to be able to read the things, ill read them

[last cipher]

Im getting some now so I dont have to buy some of the textbooks once I get into university

[arctic bramble]

MIT coursewave is a beautiful place

[last cipher]

Now you see, I need an algebra book

charles E pinter is next

[arctic bramble]

Take your pick

[last cipher]

Lang's alg

[arctic bramble]

Honestly, wouldve been my choice

Artins and 'Advanced Algebra' are fun too

[last cipher]

oh

[arctic bramble]

Wait

No bc I did download it legally, I just need to provide proof (lol)

Sorry

[last cipher]

i cant wait to get into university

finally do something i like

[last cipher]

not yet

just entering senior year

[arctic bramble]

Good luck

[last cipher]

yesssh

ive already attended some math conferences hosted at my university

[arctic bramble]

Sufficient proof or is this still not allowed? @green aurora

[last cipher]

so i have at least a general idea of whats coming

[arctic bramble]

What interests you the most from what youve seen?

[last cipher]

Analysis is very very fun

Ive completed chapter one of abbotts analysis

[arctic bramble]

Alr

[last cipher]

algebras also pretty amazing. love the abstraction

[arctic bramble]

I agree with that

Im a fan of abstract algebra because of what it can lead to, like galois theory, category theory, etc.

[last cipher]

yeah

i have to confess though i barely read my discrete maths book

[arctic bramble]

I have.. a couple if you ever find the interest

[amber sand]

hellohello

[last cipher]

I just did logic, methods of proof, sets,

thats pretty kuch it

functions too

[amber sand]

I've been pursuing a discrete maths textbook

[arctic bramble]

Logic is my bread and butter so I feel that

[amber sand]

A pretty particular one

Its not one single book

[arctic bramble]

I do have 'discrete math for comp sci'

[last cipher]

I use rosen's

[amber sand]

but I couldnt like any of the ones that I've already read

[amber sand]

Like the Scheinerman one

anyway

[last cipher]

I mean this is basically all that you need right? The rest can be learned later on or through a higher level subject?

[amber sand]

Any recommendations?

Im an CS undergraduate btw

[amber sand]

Is it the Gersting's one

[arctic bramble]

....Yes. You can develop a more advanced understanding if you know that field interests you, and thus you are either 1) simply interested in learning more about what you love or 2) you know you want to pursue more advanced study and want to familiarize yourself

[arctic bramble]

Small book

[amber sand]

Im into almost any book

[arctic bramble]

Set theory specific books would cover more, and obviously logic textbooks, depending on the specific one, would cover more.

But if you are not specifically interested in them, I would recommend reading an 'algebraic logic' book potentially, because it will, at least in part, help bridge the gap between logic and other fields of math

[amber sand]

if ya know this one, what do you think about it

[last cipher]

so i dont really need to know graphs, relations, discrete prob and trees if im looking to get into just pure math? I mean im not in uni yet so

[arctic bramble]

I dont know it actually, I apologize

[amber sand]

Its think its pretty popular

[amber sand]

thats ok

[last cipher]

ill look into it. Havent heard of it

[arctic bramble]

Proof theory books would help cover trees, since they are a semantic part of logic

Analytic tableaux (semantic trees) are a proof method

[amber sand]

Some of my professors really reccomend it, while others openly roast it

So its natural that im confused about it

[arctic bramble]

That just means you need to make your own impression

[last cipher]

i see

[amber sand]

I really dont trust myself to tell if a maths textbook is good or not

[arctic bramble]

I dont have any other books specifically titled things like 'discrete mathematics', but logic is my specialty so I have a lot of logic textbooks that would cover potential topics in discrete math courses

[last cipher]

shall we spend money on pinters algebra guys

[amber sand]

Its always safer to ask for it to someone more experienced

[arctic bramble]

Being able to learn on your own and grow on your own in your field will become a very valuable skill to have in college and beyond

[amber sand]

thats great, what are they?

[arctic bramble]

That depends, what about logic and/or what logic(s) are you interested in?

[amber sand]

Ok

Thats way more than I expected

I think FOL and set theory will cover everything I need, even though I'd like to learn everything I can about logic

[arctic bramble]

Set theory might help

One minute

I absolutely adore this site, and their textbooks are amazing https://openlogicproject.org/

https://builds.openlogicproject.org/

This would probably be best for you, or their open introduction to set theory

After that, it would likely be their intermediate logic book, if we are going by their stuff

[last cipher]

Calgary mentioned 🔥🔥🔥

[arctic bramble]

Great book

[last cipher]

never knew Dr. Richard Zach was in the project

[arctic bramble]

Mmmm

[amber sand]

its about cantor's set theory, right

[arctic bramble]

I downloaded an unfinished section they have on second order logic as well

[amber sand]

Where could I learn more about ZFC?

I think im going to far

I have too much to do by now, that can wait

[arctic bramble]

Potentially... .

[remote sparrow]

people upload books without regard for copyright all the time; just because it's on the first page of google results doesn't mean it's legal to share

[arctic bramble]

This is a great book, there are annotations in it from my buddy but if that doesnt bother you you are all good

If it bothers you, just download it from Open logic project

[amber sand]

of course not, I'm really glad to have so much new things to study

[arctic bramble]

If you get to this section, and a specific logic here interests you, just let me know and myself or others will likely have texts on it

Modal logic might be helpful for comp sci

[arctic stream]

Can anyone recommend good books for an intro into algebraic topology ?

[molten gulch]

Hatcher, rotman, may, tom dieck are four common authors for this stuff

[arctic bramble]

I have a book on combinatorial set theory

[trail hemlock]

rotman is kinda peak fr

[cunning elk]

graph theory.

huge connections to CS

[livid lintel]

For graph theory, A good first book might be Diestel’s.

But you do need some general mathematical maturity, and it can be quite hard

[remote sparrow]

https://www.amazon.com/Walk-Through-Combinatorics-Introduction-Enumeration/dp/9811277842/

you can probably find a 3rd or 4th edition that costs less

[half arch]

Hi guys

I'm going to learn math from 0 soo is there any book that i should use

[smoky inlet]

"Is Maths Real" - Eugenia Cheng.
Great if you question every answer instead of answering every question

[torn jay]

Hello everyone, can anyone recommend a resource to learn math from start to finish?
I don't know how to add, subtract, divide and multiply.

[upper estuary]

Khan Academy is great, it's 100% free and can take you from addition and subtraction all the way to calculus and linear algebra

[torn jay]

any book recommendations as well?

[upper estuary]

I learned most of the math I know in school so I don't have any specific books for those levels of math, but Khan Academy really can be self-sufficient. It lets you start all the way at Pre-K level if you wish, and slowly builds up to high-school/early college level. You may or may not end up needing a textbook for a while. Once you reach algebra you can try OpenStax Algebra, it's also online and fully free

[humble spire]

Just search elementary school math on amazon ig

[normal crystal]

KA and Openstax both start at the (near) bottom

[humble spire]

But the prek on khan acad is review only iirc

[torn jay]

ty guys

[alpine topaz]

If u need some books of maths I can give a library, some are in Spanish

[torn jay]

I speak Spanish and Portuguese. Please give me this library

[alpine topaz]

https://drive.google.com/drive/folders/1EDPpzhc8xdtfSjjaqI43lOH2TD9NdisJ

[normal crystal]

no piracy

[torn jay]

is not piracy

[alpine topaz]

I took it from scribble

[rotund halo]

Do u have english version of it

[molten gulch]

which rotman

[normal crystal]

not a book per se
but looks cool
https://ocw.mit.edu/courses/res-9-009-introduction-to-computational-neuroscience-with-neuroblox-january-iap-2025/

[vital bane]

Metal logic?? @broken meadow ??

Happy birthday btw Metal

[broken meadow]

thank you

[shrewd talon]

It’s your birthday?

[vital bane]

Yes

[shrewd talon]

https://media.discordapp.net/attachments/934212312921931786/1044744858050498610/971265916040003615.gif

[broken meadow]

Every day is my birthday

[shrewd talon]

Happy birthday ig

[broken meadow]

thanks

[shrewd talon]

I saw ryc

[vital bane]

Partial Differential Pigeon

[shrewd talon]

Indeed

[normal crystal]

busy tier ranking leafs and twigs on the pavement

[shrewd talon]

It’s dirty

[vital bane]

things in the dirt are dirty

[lavish quarry]

Black book

[alpine topaz]

Some of them are in English

[native cradle]

for differential geomerty is tapp sufficent ( I have it), or would Pressley be a better choice fo a first course?

[short meteor]

i only had experience with tapp and do carmo, but tapp ought to be sufficient.

[native cradle]

Awesome!

thanks

[cobalt arch]

Are there any more modern books compared to fikhtengol'ts the fundamentals of mathematical analysis which treats integral calculus as thoroughly as that book does (Indefinite integrals, definite integrals, improper integrals, integrals depending on a parameter, line integrals, surface integrals, double/triple integrals, etc.)? I prefer something theory focused instead of computational approaches.

[hearty pollen]

Does anybody have any textbook recommendations on Differential Geometry, that maybe takes a more historical perspective to its development and really flushes out the concept of Hodge Star Operator?

[remote sparrow]

@remote vortex

[swift imp]

Blood Meridian

[frozen perch]

Calculus and Analysis in Euclidean Space builds the multivariable Riemann integral from scratch, then pivots to differential forms to get a more elegant theory for many of the things you're looking for

[tender pendant]

Does anybody have any good books on calculus 3 as a whole I’m starting it this year

[kindred cove]

literal

"calculus volume 3"

[tender pendant]

By who

[kindred cove]

idk i just searched it up

https://openstax.org/details/books/calculus-volume-3

[tender pendant]

Alt

Alr*

Ty

[kindred cove]

seems like some random math professors

[tender pendant]

Ye

[true sail]

Besides CLRS and Sedgewick, which other Data Structures and Algorithms book could you recommend for a first-year CS student?

[frozen perch]

I like Kleinberg and Tardos - when I taught algorithms I only dipped into CLRS for the master theorem, and otherwise pulled from K+T

[rain apex]

233

[deep moat]

Introduction to Algorithms and if you want something more related towards to solving problems (that's equivalent to an interview) I suggest go with USACO Guide, USACO, Codeforces, CSES, Competitive Programmer's Handbook, etc.

[timid lion]

Goodrich and Tamassia, or https://algorithms.wtf

[sage python]

So, you've already been told that piracy is not allowed on this server (against TOS)

But also do not post requests in multiple channels even if the request is fair game

[proud timber]

Sorry

[sacred crystal]

Ah

[tribal bough]

Do anyone have a mathematics book reading road map?

[sly jolt]

What maths do you already know, and what maths are you interested in learning

because im mostly self taught from books so can send you what I read and when I read it, but it's catered to my interests and where I was when I started

[tribal bough]

A know a little bit of calculus but assume I have no prior knowledge. I am interested in math in general, I was trying to learn linear algebra (you can recommend me another starting point) but every book I try to read I feel that it assumes I have prior knowledge on the subject and the its notation

[sly jolt]

notation is for sure a big thing, i'd recommend just googling unfamiliar notation

I started from more or les the same place as you. I read Stewart's calculus up to integration, then Strang's introductino to linear algebra. that gives you a solid foundation in applied maths (problem solving) but not much theory.
After that I read Rudin's principles of mathematical analysis for more of the theory behind calculus, and Friedberg's linear algebra for more of the theory behind LA, then went back to Stewart for multi-varaible calculus

that's enough for more than a first year of most maths degrees, and I threw Rudin in a bit early so if you follow this format exactly dont bother trying to understand everything. Focus on epsilon-delta limits, and convergence of series

Once you've got those foundations all down, you can basically go onto anything you want. Differential equations is something everyone has to study at some point, abstract algebra is something all pure mathematicians have to study. i'd recommend both, with algebra first. Dummin and Foote is standard algebra text and basically any book works for differentail equations

[timid lion]

i also felt like this and reading Spivak’s Calculus was really nice! it’s an advanced introduction to calculus but assumes only algebra skills

[crystal sedge]

Hi

I just cracked open a book, and it had this in it:

Are there any books that are specifically about learning/practicing counting by sight? Like this?

I realize I want to get better about knowing how much hoozamawatsit I'm looking at in day to day life.

[fiery hamlet]

AAAAAAAAAAAAAA

[timber mesa]

I don't know any specifically but this section seems to be about mental arithmetic? Maybe look up things related to improving that skill

fwiw when counting large sets visually I tend to group things in fives or tens

[last cipher]

what am i looking at

is the book screaming at me

[true sail]

More like
AAAAAAAAAA
AAA
AAAAAAAAAA

[gray gazelle]

it's probably possible to use software to generate these puzzles and then practice, sounds like an interesting puzzle game

what is that book? @crystal sedge

[sturdy eagle]

hey yall

[vital sequoia]

It appears I was using the wrong channel for this before. My apologies. Any recommendations are appreciated

Does anyone have any textbook recommendations for getting a general overview/introduction to modern synthetic mathematics?

[golden salmon]

Are there any 'audio-only' lectures in maths that can be listened to with full comprehension? I mean something like Michael Sugrue for maths. This rules out stuff like 3b1b and khan for what I'm thinking of.

Especially if they cover topics at an early graduate level

Pretty agnostic to what topic, I'm more interested in the speaker clarity and ease-of-understanding

[gray gazelle]

huh this looks kind of interesting http://streetfightingmath.com/

anyone here else a fan of dan friedman's books? i recommend them https://mitpress.mit.edu/little-books-on-big-topics-in-computer-science/

[slender wasp]

https://www.susanrigetti.com/math can also look up curriculums on any university website.

[gray gazelle]

Go search up Aops follow their curriculum

[quartz venture]

anyone here know some hard precalculus problem book? thx

[signal canyon]

so i saw this book called Calculus by Hugh Niell

and this is what it says for definite integrals explained using summation

but isnt this wrong? its not infinite number of rectangles tho?

its js a rly rly large number of rly rly narrow rectangles?

it does explain the rest quite well tho

[civic python]

Imagine using more and more rectangles. For each n(number of rectangles) we have an associated approximation to the definite integral. In fact, by considering n=1,2,3,… and so on we generate a sequence. The claim is then that this sequence converge(becomes closer and closer one specific real number).

But yes you are right

[signal canyon]

yeha i understand it

[civic python]

You do have correct intuition here. Using the terminology ”infinitely many rectangles” is sort of a handwavy descriptional thing people use. It’s not rigorous.

[signal canyon]

makes no sense for it to be infinite tho

cuz then ud be having to divide by infinity

no sorry

[civic python]

Ye

[signal canyon]

acc yeah

im right

[signal canyon]

trye

its js a way to understand it sorta

[civic python]

Ye. But in some sense it’s true.

The point is, we are considering a sequence of numbers, and each number was generated by approximating the area using a finite number of rectangles.

[signal canyon]

is there any functions where this tiny tiny offset approximation becomes dire

or rather

any situations

maybe something to do w particles given their size

im not versed on this at all

js spouting my brain

[civic python]

The integral exist and is well defined as long as we have convergence. As long as the offset -> 0 we have convergence.

[signal canyon]

oh true

forgot limits existed for a second

makes sense

[civic python]

One thing people do is they try to numerically approximate integrals with computers.

[signal canyon]

fair enough

thank you

[civic python]

I think chaos theory deals with situations where even very small perturbations lead to wildly varying results.

[frozen perch]

The double pendulum is the classic example

[crystal sedge]

Quick Arithmetic, A self-teaching guide, by Robert A. And Marilyn J. Carman.

[past siren]

does anyone know any books to study set theory?

[still panther]

whats your target audience?

[quiet pike]

Good books for:

Measure theory
Functional analysis
Topology

I'll be using them to tackle PDEs and their numerical solutions posedness

[molten gulch]

Jech

[fluid violet]

Folland is good for measure theory

[foggy quest]

Folland's book covers all 3 of those topics

[sturdy shore]

looking for a book that covers tensor products of hilbert spaces in reasonable depth, any ideas?

seems like kadison ringrose has some stuff, but man their notation hurts to look at

[cursive rivet]

brezis's functional analysis is good for the FA part, folland is a good precursor

[digital onyx]

Folland’s good for measure theory for sure. Though it’s quite painful. For even one sentence of it, sometimes but it’s actually self contained and quite nice you’re patient enough

Every part is actually workable, but introduction to functional analysis is a bit hard in many ways since functional analysis requires a more in depth background in mathematics than just measure theory.

[gray jungle]

Yosida is great ref for FA if you can follow it

Peter lax is also good

[digital onyx]

Though personally speaking, Folland is really hard I followed a course for it. And without the functional analysis, though not a necessity to study the part L^p space it becomes extra hard compared to peers with solid background (so you basically apply different inequalities to problems without deeper understanding) since we actually skipped the chapter of introduction to functional analysis. But the chapter 1-4 are pretty much very self contained and nice in many ways

[gray jungle]

Though ile say depending on what type of PDEs you're tackling, the books on the topic will usually include appendixes or chapters on the relevant results you'll need

you can ommit the MT framework buildup if you wanna be efficient (if you are not learning a proper course on it)

for example blackboxing caratheodry

[digital onyx]

Just personal advices, one can try to find different lecture notes for measure theory or functional analysis they are often nicer and less blackboxing for example this one which is a great source for measure theory

This has been the life saving lecture note for me overcoming almost nonsensical content for folland’s

[bleak pier]

Hello guys, I'm new here and I'm just starting to study abstract algebra at my college, does anyone have any book recommendations?

[timid lion]

fraleigh

[heady ember]

abstract algebra

[digital onyx]

Abstract algebra?

[tender river]

he said he's looking for an algebra book and not a linear algebra book specifically

[digital onyx]

🫣🫣I’m so sorry

[golden salmon]

i like gallian

[remote sparrow]

#book-recommendations message

[tidal summit]

does anyone know if the calc essentials book by dr. sood has partial derivatives practice

[quartz venture]

Anyone here know some good book on polynomial? Thx

[stray cosmos]

Guys i have SL Loney for trigonometry
Someone please tell what examples I should do to practice trigonometric functions and equations for JEE.

Im in high-school

[elder atlas]

hi guys I wanna learn calculus for my uni study, any guys can give me some pdf.

• I need single variable and multivariable calculus

[coarse estuary]

I self study math, and in the future, I plan to study algebraic or geometric topology. Soon, I will be studying real analysis (particularly through Abbott’s “Understanding Analysis” which was recommended by a friend); after finishing Abbott’s, should I go back and study from something like Rudin’s book to get a more rigorous understanding of analysis, or should I move on to linear algebra?

[vital bane]

You can use Rudin along side Abbott

Doing problems from both Abbott and Rudin

[coarse estuary]

My understanding is that rudin has a lot more work on topological stuff

I’m not sure tho I skimmed over it on an online pdf

Should I read the topological stuff and use Rudin when the topics in there are not included in Abbott’s?

[vital bane]

I think Abbott and Rudin have the same topology stuff, connectedness, compactness etc. (it's just that Abbott works on R in chapter 3, but all his proofs generalize to a general metric space)

But Rudin does have more about metric spaces than Abbott

[trail hemlock]

might be worth just using rudin for problems

id argue theres no skill rudin teaches that u cant get from abbott

[slender cargo]

Rudin proves some stuff in more generality using metric spaces, and some theorems are presented through complex numbers and not simply real numbers. It’s stuff you can learn in other books though

[coarse estuary]

Alr

Based on ur guys advice I’ll probably just use Abbott’s mainly and then use Rudin’s for additional problems

Or at least that’s what I got

[trail hemlock]

rudin's proof are also very clever and nice to read on a second pass, pretty difficult to get a grasp on a first pass

well at least for me.

[slender cargo]

I feel like Abbott’s got good problems. imo just stick to Abbott primarily for now

[past siren]

ty!!!

[fresh skiff]

true, abbott has pretty good problems from easy to hard

[still panther]

painfully crawling through terse texts is a useful skill

[vital bane]

10% luck, 20% skill, 15% concentrated power will, 5% pleasure, 50% pain and a 100% reason to remember the name

[trail hemlock]

unironically yeah

[vital bane]

It is but it doesn't need to be your first exposure to analysis🗿

[trail hemlock]

was for me and i turned out ok

[topaz silo]

His alter ego knows the truth and it reacts

[sly jolt]

https://www.apexcalculus.com/downloads

[digital onyx]

Though a bit sarcastic but the last point is reasonably important. Skimming through concepts won’t lead to firm understanding

[digital onyx]

Abbott’s book is very nice but if you want to build foundation then book from Kenneth Ross “elementary analysis” is even better for intuition building. Rudin prepares you skills to understand terse proof and unbox layered abstraction (which other books don’t have). Though concepts are the same, the difficulty is completely different, though it’s painful but it’s helpful and sometimes often necessary to build up all the proofs from the book yourself and to complete every exercises since they are standard in more advanced settings and expected.

Rudin’s book has very little disadvantages, it’s more a matter of patience and practice. Abbott’s book itself is wonderful but it doesn’t give you nearly equivalent skill for solving more abstract problems (those techniques usually hide within exercises of Rudin’s exercises rather than just the theorem lemma or corollaries which is why exercise is important)

However if you only aim for efficiency for advancing to higher level, you really should try Ross’ book plus rudin, because Ross’ book is more elementary than Abbott yet it covers all concepts required for introductory analysis. So it really depends, Abbott’s book alone in my opinion is actually sufficient without rudin if we assume you’re studying mathematics continuously for the upcoming 2 or 3 years. Otherwise you can go with Rudin+Ross by repeating the study you can pull it to high level.

It depends whether you are in a math department or you study something else. One often should not ignore if you study yourself your environment might not be as mathematically centered as those dedicated to study mathematics as majors.

An alternative route is to replace Abbott’s book or Ross’ book by calculus written by Spivak, it’s a decent book enough to serve as an introductory material for real analysis. Plus rudin you will have both procedural skills and conceptual pictures.

[cerulean steppe]

Abbott's is rigorous. The one variable book here is good too, covering metric spaces, which you will need later: https://mtaylor.web.unc.edu/notes/math-521-522-basic-undergraduate-analysis-advanced-calculus/

[willow merlin]

which book explains order relations?

and symmetric difference of sets?

[tender river]

discrete math books, set theory books, intro to proofs books, most introductory analysis/algebra books

[willow merlin]

by symmetric difference I mean

[tender river]

yes

what is there to explain

[ocean marsh]

Hello, may I get a recc of a book on first order logic

[willow merlin]

i dont understand it

[tender river]

read some intro to proofs book like velleman then

[willow merlin]

does this book cover order relations, symmetric difference and equivalence relations?

[tender river]

im only guessing it does and id be surprised if it didn't cause thats what intro to proofs books do

[willow merlin]

interesting

[willow merlin]

i will check it out and come back if i need more material, thanks

[last cipher]

thoughts on this boi

[still panther]

open a random book

[last cipher]

cant seem to find a sample from it

[still panther]

chances are it will cover order relations and set difference and quotient by an equivalence relation

[old elk]

I think most abstract algebra books are fine.

I haven this

[lapis lantern]

I am currently reading this book. It was first published in 2001. It doesn't seem overly emotionally charged but I've only read 40 pages of the book so far

[ocean marsh]

speak spanish?

[lapis lantern]

The contents of the book are not about actual mathematics topics but about Robert Moses' work on voter registration etc in the 60s in Mississippi. The second part of the book (starting far back as the 80s) is about his work on teaching students disadvantaged students algebra, but my understanding is that this part is also devoid of math subject discussion. I enjoy the book right now.

[narrow gull]

Ig I'll ask this here cause this is probably the closest place to ask, but what's everyone's go-to notebook/writing utensil combo here

[ocean marsh]

I use nebo in my tablet

[trim kayak]

I have a few math textbooks that I want to read through and practice the problems but I'm having a hard time getting started. Suggestions or tips?

[mossy flume]

pick only one text and then read through it and do problems

doing multiple texts may be too much to tackle at once

[desert oriole]

https://arxiv.org/pdf/2008.13244

thoughts?

[trim kayak]

I figured just one book at a time. Should I take notes on each chapter?

[mossy flume]

up to you

this kind of comes down to how you best study

I personally don't take notes, I just annotate the PDF as needed, maybe keep some extra notes clarifying confusions, and write up solutions

but some people take notes to write the content in their own words

[vital bane]

Yea I just read the book

procrastinate for 2 weeks, do problems, then procrastinate for 2 more weeks and do more problems

[steady eagle]

Pretty much known but why post in this channel 🤔

[narrow gull]

For self study I like to just quote Axler in his preface to Linear Algebra Done Right

[daring wolf]

I just pick one book

I dont write notes, but rather write a solution book with some remarks in PDF (vscode+texlive)

[vital bane]

And Alaine Connes https://youtu.be/9qlqVEUgdgo

[narrow gull]

This is amazing, haven't seen this

[lapis lantern]

I use a spiral notebook and mechanical pencil. (I've only been back at math a few weeks but it does the job).

Often i find a whiteboard is available or handheld whiteboard and i enjoy that

[rigid trail]

nvim with typst

[trim kayak]

I'm going to read hard copies of textbooks, not pdfs.

I know everyone is different. Just curious what everyone prefers.

[narrow gull]

Literally me

[rigid trail]

Obviously hard copies are nicer

[narrow gull]

Down to the "only been back at math a few weeks"

[rigid trail]

But I pretty much read everything from PDFs

I can't afford those books man

[trim kayak]

Do you take notes too?

[rigid trail]

And I often want to reference many books on the same topic

Not just one

Ctrl F is really nice

[trim kayak]

I got an older edition from Amazon. $7.00. Im reading and learning for fun so I don't have to have the newest edition or anything.

[trim kayak]

That's true. That's one feature I don't have with hard copies.

[lapis lantern]

BRB 5 minutes

[rigid trail]

$7 for what book

[cerulean steppe]

I use a spiral notebook (mead five star) and mechanical pencil and eraser for most things. For really neat things, I type them into texmacs.

[lapis lantern]

I'm not in a class but yes i do take notes off the textbook a friend loaned me last week. I'll have it for another few weeks it's precalculus with limits by by Ron Larson and Robert Hostetler

I'm trying to figure out how to take notes consistently because that's grave a problem for me. It's a good textbook ig just starting at the beginning looking at the algebra fundamentals appendix first

[lapis lantern]

I'll check it out

[trim kayak]

Ahh okay. That makes sense. I think notes on every chapter will help you stay consistent.

[trim kayak]

Intro to Probability and Statistics 13th ed by Mendenhall. Seems like a good book to me. I want to review some basics and then more advanced topics/books.

[steady eagle]

Do you really need this? There are free very respectable probability books

[trim kayak]

@lapis lantern You're studying math just for fun too?

[trim kayak]

I'm sure there are. Somebody recommended it to me. It's an intro to probability and stats. I just want to review it. 🤷🏽‍♀️

[steady eagle]

Ah ok, well I was wondering if the USD7 would even be too expensive

[trim kayak]

Ohhh. Where are you from?

[steady eagle]

Sorry, I'm not answering that 🙏

[lapis lantern]

It started out that way but I need a direction in life and I think I'd like to go back to college and get some kind of math degree

[brisk crypt]

such as?

[steady eagle]

https://stat110.hsites.harvard.edu/
For Prob/Stats I think the openintro books could do

And if you're looking for something slightly harder, I think Evans Rosenthal will work more than sufficiently

[trim kayak]

Oh that's cool. I would like to do that too but I have enough degrees and don't really need to go back.

Do you already have a degree?

[light fern]

hey, what is a good book to use to self-learn abstract algebra and also one for real analysis

[bright galleon]

Do you have any experience with proofs?

[light fern]

yeah

[bright galleon]

Like have you done any analysis or algebra before? What have you done with proofs?

[light fern]

yeah covered bits of algebra and analysis

also did quite of proofs when learning for olympiads and stuff

[bright galleon]

Okay cool. I'd say given that you're comfortable with proofs, Aluffi's Algebra: Chapter 0 should be approachable for algebra, and then for analysis you could use Abbott's Understanding Analysis or Rudin's Principles of Mathematical Analysis. Abbott is probably fine, but some people say the added rigor of Rudin is worth it.

[lapis lantern]

No I originally planned to get a degree in computer science but I had no experience really some tech knowledge. And then a certificate in hardware and networking or something like that but that fell off too. My focus really not the subject. But then I realized a few weeks ago Math is pretty appealing to me and my focus is better now

Do any of your degrees involve mathematics, musicmeg?

[trim kayak]

Ahhh okay. As much as I love math, no they don't. I do teach math but it's a basic level. I used to teach higher level math in another state. I'm trying to obtain a different certificate so I can teach higher level math where I'm at now.

I just love math and enjoy studying and learning it on my own time.

I'm a nerd 🤓🤓

[old elk]

yes

[lapis lantern]

I speak some spanish but I'm still learning

Actually what's cool is that the textbook that was mentioned earlier by me was one of two that the person loaned me

The other one was an algebra textbook. The cool part is that the this algebra textbook* had a full glossary of algebra definitions in english and under it it was translated into spanish

[old elk]

[light fern]

alr thank you

[foggy quest]

The books here are good for analysis: https://mtaylor.web.unc.edu/notes/math-521-522-basic-undergraduate-analysis-advanced-calculus/

[desert oriole]

which channel would have been better

[sullen wren]

Sorry if this has been asked allot, but does anyone have some recommendations for books to teach myself some trig, linear algebra or calculus?

[cunning elk]

openstax, KA, etc.

at a level this low almost all the online resources are basically isomorphic

[tiny gulch]

I would also like to ask - does anyone have recommendations for books that cover complex geometry? Stuff like Riemann surfaces

For context I’ve taken a course in complex analysis, but nothing with complex numbers beyond that

[sullen wren]

So just anything i can get my hands on?

[cunning elk]

yea

[sullen wren]

Thanks

[cunning elk]

content/presentation wise precollege mathematics is essentially a solved game?

• early uni

[sullen wren]

Sorry what?

[sly jolt]

https://www-fourier.ujf-grenoble.fr/~demailly/manuscripts/agbook.pdf legal pdf btw

[ebon whale]

?? linear algebra done wrong disproves