The difference is k means has literally nothing to do with linear algebra. Might as well sneak in a chapter on finite state machines, or zebras, either would be just as relevant to linear algebra, which is to say that at a certain point the topics in a linear algebra course should be somehow related to linear algebra.
"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.
While I agree that one could take caution when studying proposed alternative foundations of mathematics (there are a lot of dysfunctional theories out there, and the link may be one of them for all I know), I think it is unfair to presume incompetence based on the fact that the author has another field as his specialisation. ZFC is also not the one true way, there are many sensible ways to formulate set theory, and even valid criticisms of ZFC.
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.
Funny enough I was thinking the same thing. This really isn't any different than the test prep industry for other types of standardized tests. The only real difference is that we have to constantly be doing these tests as people working on software, whereas people in other professions tend to only need to prove they have basic knowledge once.
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?
I imagine the main differentiator would be open-ended discussion that's not necessarily trying to answer a well-defined question (or any question at all for that matter). Stack Exchange and MathOverflow are both fairly bad at supporting this at best and openly hostile towards it at worst.
That's a separate issue. The content here appears far too specialized and restricted even for math PhDs (while I don't have a PhD, I do have an extensive background in math and have published research).
Yeah but the /r/math subreddit is already very good for that, and is well moderated. There are plenty of tenured professors from excellent math departments around the world contributing to discussion there.
Sure, but then "open-ended discussions" don't provide much value to academics with many more pressing things to do. On the other hand, crowd-sourcing answers to specific research question is extremely valuable to them.
For a point of reference, I've been thinking lately about the value a mathematician in a research career gets from blogging (I am thinking specifically about researchers and /not/ people focused on primarily education or popularization oriented careers). My conclusion is that the answer is "not much." Apart from a few small blogging communities and very famous mathematicians' websites, most math blogs get very little or no engagement that would be valuable to their career. Time is much more efficiently spent working closely with the people in your immediate spheres or focusing on making connections with specific researchers you want to collaborate with in the future.
With a HN site, it's easier to see what's "hip" this month, which can be entertaining, educational, and makes good "casual" conversations. Mathematics has trends just like any other field, and unfortunately if you're not actively working at a university and going to conferences multiple times a year, you'll never get exposed to that.
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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.