daffodil2

I'm actually very interested, which is why I bothered to comment in the first place. I had to download the HTML of the article and search and replace all exclamation points with periods to be able to read it.

I wish this didn't have so many exclamation points in it! There are literally 41 (!!!) exclamation points in this short blog post! It is exhausting to read! Please consider not using so many! There should be ways to convey enthusiasm about a topic without peppering your writing with exclamation points!

For a function f and a value x,

    foldr f x [a,b,c]

gets turned into

    f(a, f(b, f(c, x)))

'(:)' is list concatenation, so the result is

    1 : (2 : (3 : []))

(Here we are writing list concatenation in infix notation, rather than the customary prefix notation). '[1,2,3]' is shorthand for 1 : (2 : (3: [])) in Haskell.

A "well actually" occurs when a person is splitting hairs. This can be desirable, for example when you're trying to obtain a complete understanding of something. But in normal conversation, such pedanticism is often annoying. The "well actually" policy, as I understand it, is an attempt to make such hair splitting "opt-in" rather than "opt-out".

I didn't mean to imply it was trivial to understand, but it's no more difficult than the formal definition of, say, a derivative (which involves a limit, and hence an epsilon-delta construction, which in my experience are not so easy to fit in your head at first). Understanding what a multigraph is should be doable.

The article argues against overly formal approaches, but I actually think it errs too much in that direction. When I'm studying a math thing, at some point I need you to shut up with the English words and simply describe the object in terms of sets, functions, relations and properties. Categories stopped being mysterious for me once I realized they were just multigraphs with a certain algebraic operation defined on edges (composition) such that edges with certain properties (identities) were stipulated to exist.

Just as it would be unreasonable to require that anyone who drives a car roughly understands how an engine works, it would be similarly unreasonable to require that anyone who uses the internet roughly understands how addressing works. It is of course true that your car ownership experience will be greatly enriched by understanding roughly how an engine works, and that your internet experience will be greatly enriched by understanding how addressing works. But neither should be a prerequisite.

You underestimate how subtle the concepts underlying addressing are, probably because, like many technical people, you have understood how URLs work for so long that you can no longer remember what it is like to not understand them.

Wait, it's not clear to me from the blog post. Did they make a system that obsoletes reCAPTCHA? If so, it's just a matter of time before the spam systems catch up, correct? If so, what's the successor to CAPTCHA? Or is the web just going to be full of spam in the future?

I'm not sure what "fit to be a developer" means. People (with very few exceptions) are not born with labels that say "able to write software professionally" or "not able to write software professionally". Try to understand what has prevented you from landing jobs so far. Go through http://sijinjoseph.com/programmer-competency-matrix/ to determine what you lack, and then work on improving those. (Not saying that that link is the ultimate criteria for determining one's suitability as a programmer, just that if you really don't know what you're missing, it will give you some ideas)

I've tried reading Rudin a couple times, but it's a bit of a slog. There are easier analysis texts. Abbott's Understanding Analysis is good, though a bit basic. I'm currently reading Terence Tao's Analysis I, which is very good if you're in the right frame of mind for it. The first 150 pages are spent building the real numbers from scratch, starting with set theory and the Peano axioms. You successively construct the naturals, the integers, the rationals, and then the reals (as equivalence classes of Cauchy sequences of rationals). It's fun to see how the sausage is made, but I can also admit that when I was just starting out in math I might have found this book unbearably tedious.

Find a book about C++. Read as much of it as you can. Write some code. (solving a few Project Euler problems might be worth it as long as you focus on writing dumb brute force solutions). Prioritize the parts of the book that cover things you think will be on the test.

I have no idea if this is good, but its free: http://rooksguide.org/

60 pages before defining vector spaces seems like a not so good approach to linear algebra. Since Linear Algebra Done Right has already been recommended, I will suggest Linear Algebra Done Wrong: http://www.math.brown.edu/~treil/papers/LADW/LADW.html