Is there a math website to study math from a mathematician point of view (ie proof oriented?)

Question

I´m a student of the University of Puebla, Mexico, and I think that we lack of exigence there so I want to study math on internet to improve my education. I have already looked sites like edX, but I can´t find a source for pure mathematicians. Can somebody bring me a high quality resource for pure mathematicians? I will appreciate a lot.

Answer 1

http://maths.kisogo.com

Sorry this should be a comment but not enough rep

This site is good because it explains the motivation for things, for example:

http://www.maths.kisogo.com/index.php?title=Measure_Theory (incomplete page)

You can see it talks about why you'd care about sets on a ring, an obvious measure (rular/Lebesgue measure) for a motivating example, saying "great we can measure on a ring", and fully developing the idea intuitivly, before going into the formal.

Another example:

http://www.maths.kisogo.com/index.php?title=Basis_and_coordinates This page discusses and motivates coordinates with respect to a basis , how to write linear transforms, which provides a great way to use existing knowledge with intuition which links directly to the actual things (eg change of basis matrix)

http://www.maths.kisogo.com/index.php?title=Set_theory_axioms list of set theory axioms, great, http://www.maths.kisogo.com/index.php?title=Motivation_for_set_theory_axioms why we would want these axioms, what we can do, all done in a logical order

http://www.maths.kisogo.com/index.php?title=Compactness compactness defined properly, and then a subset being compact is given as a lemma and proved

http://www.maths.kisogo.com/index.php?title=Group

http://www.maths.kisogo.com/index.php?title=Coset <--notice the nice theorems

It addresses commonly seen notations, which one is preferable (with reasons, rather than saying "Trust me") - I call that good.

Each definition page often has "first theorems" which prove those trivial properties intuition tells us we have.

Note the http://www.maths.kisogo.com/index.php?title=Metric_space mathematicians are lazy bit, which explains why we write $(X,d)$ rather than $(X,d:X\times X\rightarrow\mathbb{R}_{\ge}$)

Index of notation http://www.maths.kisogo.com/index.php?title=Index_of_notation

It's less than 2 weeks old (so far) and is being actively worked on (evidently)

Answer 2

I have been searching for similar courses but I have not found many. The only link I have saved while searching is the following one: https://www.pinterest.com/mathematicsprof/

I had the same problem (and still do most of the time). In this situations I search the ideas on the internet and in different references. Many teachers giving undergraduate courses have their notes on the internet and they usually are very well explained. Doing those things made me learn different equivalent ways to define mathematical objects and different approaches to solve the same problems.