/sci/ - Science & Math

>>8039163
the typical books are

>>7944255

>>7914570
>I need to get more used to these universal properties, probably skim through Leinster/Aluffi some more.
implying these books are not the best

>>7761844
get the book on the left: you will learn baby set theory done in category theory in passing.

>>7745970

>>7738246
yes, only borceux is worth it. and the other one in the pic.

>>7542774
constructive predicative maths through topology [predicative locale theory] HOTT, stacks [commutative and non-commutative] and the book of lawere to begin. Also, finite mathematics Feng Ye (auth.)-Strict Finitism and the Logic of Mathematical Applications-Springer Netherlands (2011) to see what you can do with minimal mathematics

plus all the writing of Grothendiek

also, history AND philosophy of mathematics to put all this into perspective.

>>7440373
well typically category theory and everything touching the curry howard transformation, the constructive logic, type theory, lambda calculus, hott for the meme. these will be words that you will encounter.

You can check Hott really, since it is math/topology and there are computer programs to show you the proofs.

watch all the courses here

http://www.cs.uoregon.edu/research/summerschool/summer12/curriculum.html

https://www.youtube.com/playlist?list=PL8Ky8lYL8-Oh7awp0sqa82o7Ggt4AGhyf

the two books in the attached image are good introductory books in category theory

reminder that constructive algebra remains in infancy, it would be quite a subject for a pHD to have an equivalence of Hott/topology in algebra

>>/sci/thread/S7419087#p7419277

>>7419087
>babbling about R
because topology matters

in fact, the construction of R is topological in constructive math, then you add your multiplication and addition WHICH MUST BE CONTINUOUS.,
You claim that

for abstract algebra, I do not know much on this, but you are right on the noetherian rings for instance.

if you want to go constructive abstract algebras, know that
-everybody will laugh at you
-nobody will care about you
-there is hardly any references
-Coquand is the one doing a few things, along with some other french math guy, Lombardi, Henri.

http://www.cse.chalmers.se/~coquand/algebra.html

thus far, the field is essentially classical, and it will be a lifetime nightmare to get it straight. Perhaps jump directly to category theory, stacks and all this, where more constructive math are involved. [or at lest, you know when classical math is used]

Reminder that algerbas and topology are connected. For instance, lately, the work of Coquand has been on constructive gelfand duality. More generally, the work is on the stone dualities

>>7408916

>>7404105