markkm
Besides, a lot of introductory math textbooks are thinly veiled introductions to subjects the authors think are important.
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.
For those who aren't already familiar with Vim, Kile 3.0 beta is a fine substitute. It does most of what's described in the post in a GUI environment.
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.
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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.