Constructing maths

hi there.

i want to construct(*) maths (not everything but quite a bit) from ground up. i learned so much in lectures but this is worth nothing if i can't do it myself. so, what is the correct/best order to do this? i guess at the beginning there is logic, then set theory and then what? algebra? calculus? or something else?
i'm favouring algebra though because i want to leave out infinity for quite a while.

yeah i know this is stupid but i'm in the mood for _really learning something_, not just what the professor tells me and i pretend to understand.

help much appreciated, thanks.

(*) construct not as in constructivism. :P

Logic, set theory, then metric and topological spaces.

>>2
Then algebra and calculus. And from there it's pretty much whatever interests you.

Don't you need set theory before logic?  Like how can you talk about models and satisfaction without some notion of sets?

I'd call the set theory the addition and container for said models... Which is more important to have first? The jar, or the butterfly? Hmm....

>>1
infinity plays a pretty huge role in set theory, gl avoiding it.

>>6

well that's of course true. didn't think about it. i rather meant convergence, continuity, derivatives and integrals. i lack basics so hard... i just want to ignore them for a while.

>>2

isn't algebra necessary for metric and topological spaces? afaik i need a vector space first. :?

thanks for replies!

>>7


Nope topological space is a structure on sets, Metric space is structure on sets defined by a distance function.

Structure it like a tree from the ground up and start from the absolute ground level, counting.

>>9
Right, but we're supposed to be the ones adding nodes, parents, and  basically just an algorithm for searching them.

Construct maths eh?  Well damn, start with the ZFC axioms and have at it.

To construct a math you must first have your basics covered.
1. You must be able to observe recurrences.
2. You must be able to define the recurrences.
3. You must be able to measure the recurrences.

once these are done, then you will be able to unite the recurrences with mathematics, but, now you also get into the harry parts.

1. Observing recurrent reactions of unification.
2. Define recurrent reactions of unification.
3. Measure recurrent reactions of unification.

Finally, from this you will have greater potential to easily define mathematical process for whatever your constructed math is for. Taylor-made. :)

>>12
Might I add that the analysis of this process shows a fundamental difference between two main types of mathematicians, namely; those who solve problems, and those who create problems. Though that was not entirely necessary, your future as a mathematician will follow one of those paths indefinitely, and it is up to you to decide which will be yours.

could you post a number of existing forms of mathematics? that way Evin idiots and English meager can figure it out!  

>>9

then from counting use equivalence classes to obtain the integers and rationals and irrationals, then one of many (?) methods to construct the reals. reals may not be absolutely necessary until much later into the project, since i would imagine a rigorous exploration of calculus might not require anything other than Z,Q, and N.

this is a pretty neat idea.

why would you construct everything that already exists in math? why dont you start on your own and see where it gets you.
then poast pics.

>>14
Group theory, game theory, infinitesimal analysis, analytic geometry, linear algebra, abstract algebra, differential geometry, topology, complex analysis...

>>16
I tried that when I was high. It sucked terribly and left me wondering why I attempted it at all. Oh, yeah, it's because I got high, because I got high, because I got high, la de da da da da.