"The set theory formalism presented here differs from the traditional ZF system"
Do not, I repeat, DO NOT study nonstandard theories before familiarizing yourself with the standard theory. The standard set theory (ZFC) survived for over a century for very, very good reasons. Without an exposure to the accepted standards, you will not be able to tell what is reasonable and what is not in this set of notes.
It should also be noted that the author's field of concentration (geometric analysis) has nothing to do with set theory. A typical mathematician knows very little about axiomatic set theory and is prone to making imprecise statements about it.
Yes, the "universal" complex-conjugate operator cannot be unitary. And yes, you can conjugate a vector or two using a unitary operator. Coming up with an algorithm to conjugate a specific configuration of qubits is just linear algebra.
I am not a physicist, and so I don't have a good grasp of the physical significance of the size and existential probability of supersystems mentioned in the paper. But I have to say I'm just a bit skeptical about the main claim of the paper.
The problem isn't unique to software engineering, though. So long as there are lucrative, exclusive jobs whose qualifications include passing an exam, there will be a massive test-prep industry. Princeton Review, Kaplan, etc., etc.
The research mathematics community on the internet is fairly small, and a lot of them are over at MathOverflow, math.SE, and personal blogs. What does this site offer that would lure people away from them?
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Don't study "math." Find a topic or a problem you'd like to understand, look up the prerequisite knowledge for it, and start there.
You need to know what you want to do before you go looking for resources. There is no set agreement on what should constitute an undergraduate applied mathematics curriculum, and you are likely to get lost in the deluge of conflicting information. On the other hand, the undergraduate pure mathematics curriculum has been more or less stable for half a century. Any college curriculum will do at this point, and many are freely accessible online.
Either way, there is no shortage of information and resources available. Any topic you'd choose as a layperson likely already has a course or a seminar covering it, and the corresponding syllabus should give you what you need.
Just go to college and study what you like. Contrary to the popular belief, mathematics and computer science aren't solitary pursuits. You'll meet people who share your interests and ways of being.
Besides, a lot of introductory math textbooks are thinly veiled introductions to subjects the authors think are important.