Just how rigorous should a math textbook, tutorial, or other kind of reference be? How much can be taken without proof, how many steps can be skipped, how precise must the definitions be? How paranoid about "rigor" must you be yourself? All the smart kids took those "rigorous" math classes, so you should, too, right? The answers lie in understanding the concept of rigor properly and then determining what it is you're really after.
The first section on integrals is alive! A section on sums has been separated out into the beginning area for ease of understanding. It's easier to read up on sums and then learn how they're used in integrals, rather than to learn about them both at once. The two sections on Riemann sums have the same practice problems to make it easy to compare the results of the two methods. The definite integral is defined in the last section, and its problem set provides some practice with the rarely used method of computing definite integrals directly from the definition.
More sections soon to come!
With all of the countless math resources out there, why on earth would someone bother making another? Students all have their textbooks, and usually some kind of access to either teachers, tutors, professors, TAs, or some other kind of knowledgable person. Khan Academy is a household name, YouTube has no shortage of videos explaining all kinds of topics, and Google turns up plenty of content for many a topic. Anyone willing to pay even a few dollars a month can access the step-by-step functionality on WolframAlpha. So again, why bother making yet another math website?
The first reason is price. I remember being a student, and the idea of spending money didn't even cross my mind. It was free or nothing. So while anyone can charge for help, my goal is to send the direct cost to the student to exactly zero. The more content that can be made permanently and freely available, the better.
It's happening! Mathmatique has been redesigned and relaunched with a brand new site. Now with a proper home page, it's no longer a *total* dumpster fire. Here's a short list of improvements: