Mathematics

[Anonymous No.14943412]

Please recommend some books on mathematics. If possible in progressing order (from the most basic algebra and geometry, to the most complex fields in mathematics).

[Anonymous No.14943431]

Math was retroactively refuted by uncle Ted.

[Anonymous No.14943437]

>>14943412
>Mathematics
>Please recommend some books on mathematics. If possible in progressing order (from the most basic algebra and geometry, to the most complex fields in mathematics).
>Pythagoras.jpg

[Anonymous No.14943518]

bump

[Anonymous No.14943521]

>>14943431
He writes legibly, clearly, to the point, without any crossings-out. I like Uncle Ted.

[Anonymous No.14943601]

>>14943521
yea he cool

[Anonymous No.14943648]

Well, I guess /lit/ wasn't the right place to ask.

[Anonymous No.14943672]

>>14943412
Here's some basic geo for you.

[Anonymous No.14943708]

>>14943672
Thanks!

[Anonymous No.14943734]

>>14943412
Nigga just get a textbook

[Anonymous No.14943750]

>>14943412
Pic related should be required reading before you're even allowed to post on this board. Would save us from a lot of faggotry that we have to endure daily.

[Anonymous No.14943760]

>>14943412
Spivak Calculus is the foundational/beginner text that everyone uses. It also includes a recommended reading that is quite comprehensive. The is the first-year textbook for undergrads who intend on doing "serious math".
Abbot's Understanding Analysis is very fun and pretty but you would need some more knowledge than just high school pre-calc to begin because it starts off quick.
Pretty much every intro to linear algebra is the same, but Linear Algebra Done Right is pretty good. It's also the easiest of the texts mentioned here.
Dummit and Foote's Abstract Algebra is the gold standard for algebra (not the same as linear algebra). Just read the group theory bit unless you want to seriously challenge urself.

All these texts can be read independently, you can also go to stackexchange and search for "[math topic] reference request"

[Anonymous No.14943839]

>>14943760
oh and I would add A Readable Introduction to Real Mathematics as your go-to introduction if you actually intend to do this, but you are still hesitant. its probably the easiest and fastest taste of what "proper" math feels like without going through too much pedantics. Just read chapters 1. 2. 4. 8. 10. 12. and 13. 14. if you want something harder

>>14943750
if you recommend this as an introduction to math, you probably haven't done much "real math"

>"hey /lit/ i want to learn some beginners/foundational math, what should i read?"
>"how about you read Halmos Naive Set Theory, that assumes no pre-requisites and is certainly foundational"

[Anonymous No.14944023]

>>14943839
What do you mean by this comment? Mathematics is defined by the method and not the subject matter, as far as I'm concerned. The material in the book is what you would normally learn in the first course in a maths degree in my country, Why would I not recommend this as an introduction? Replace it with other similar books if you so please but the content has to be understood one way or another.

[Anonymous No.14944130]

>>14944023
its not to say that the content of that book is unimportant for math students, but to treat logic/set theory in such a rigour manner is a bit of an overkill for an introductory textbook.

perhaps its just my bias, but IMHO the logic of things/math is already implicit, and only needs to be skimmed over in the first/zeroth chapter as an obligatory acknowledgement, and perhaps as a friendly reminder of several ideas (demorgan's law, double negation = true, proof by contradiction = proof by contrapositive)

[Anonymous No.14944148]

>>14944130
....and indeed you will find that such material is already covered as such in most of the texts i mentioned above

[Anonymous No.14944314]

>>14944130
Ok I think I understand now. I don't think I agree with this idea of "real math"s that you were putting forward. Certainly, someone who can be said to "know" about math needs to be familiar with those subjects that are dealt with in those books you recommended, but I don't think these things are more real.

The "how to prove it" book is very beginner friendly in my opinion, and from what I've been able to gather it seems far less extensive than the Halmos book you mentioned. In my country some students won't hear about ZFC until sometimes their second year even, but this stuff is not brought up in that book at all.

[Anonymous No.14944398]

>>14944314
me mentioning Halmos was a joke: its the standard text for set theory.

point being was just that i think anyone who introduces themselves to math via logical syntax first will find it much more dry and pedantic then it needs to be.

i think a better approach to math will start with something intuitive and easily understandable, and then quickly show important results (integers, prime numbers, euclid's proof of infinity primes), instead of starting with the pedantics first; and if you look at the historical development of math, i think you'll find that the intuitives began first, and then the pedantics

[a No.14944428]

https://discord.gg/qtgT9je What's this cult? it seems very interesting LIGH TLIG HTLI GHTL IGHT LIGHT TIME!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

[Anonymous No.14944886]

>>14943412

[Anonymous No.14945016]

>>14944886
either you've never done any math before and don't recognize this is a joke, or you are a troll: no high school student will do Galois theory unless they plan to go to an ivy-leauge tier school to do their math-55 equivalent. also around sophmore/junior the difficulty of the content becomes such that you'd be a specialist to read it (read as; you don't need some random anon giving you a list of books to read)

[Anonymous No.14945044]

>>14945016
lol not the anon you're responding too but I'm pretty sure this is a screencap from a thread where autists on /sci/ were trying to engineer from the scratch their own version of mathematical education from high school up, they do that sometimes and picrel is an obvious overkill

[Anonymous No.14945129]

>>14943412
I never really had a basic analysis textbook (learnt from lecture notes) so you'll have to have someone recommend one for you. I used Stein and Shakarchi for measure theory and you could conceivably use that for everything I think. Don't bother with more than very basic pointset topology, it's a waste of time and you should just learn it as you need it.

Linear Algebra Done Right (Axler)
Algebra (Artin)
Fields and Galois Theory (Milne)
Gathmann algebraic geometry notes (https://www.mathematik.uni-kl.de/~gathmann/class/alggeom-2002/alggeom-2002.pdf))
Algebraic Topology (Hatcher)

For a complete education I would add something on differential geometry and something on complex analysis, but I don't have any books because neither subject interested me.

If you get through all those (which I doubt you will desu, self studying maths is hard) then you should have the mathematical maturity to find good textbooks.

[Anonymous No.14945200]

>>14945044
ty 4 de clarification i was pretty triggerd

[Anonymous No.14945230]

>>14943412
Gowers is THE book.

[Anonymous No.14945258]

>>14943412
Euclid's Elements(any edition would do fine), Coxeter's Projective Geometry, and Heath's history of Greek Geometry are what I believe you're looking for given the Pythagoras picture.

[Anonymous No.14945995]

>>14943412
watch some 3blue1brown videos first