I am very interested in AI that can teach itself(sounds too great). Where can I learn up about such AI(related concepts and the whole 9 yards) to start reading papers in the field? I am just looking for comprehensive sources(preferably textbooks).

AI by Russell and Norvig. Machine learning by Murphy, Elements of Statistical Learning by Hastie et al. Just a few good ones out of many!

AI by Russell and Norvig is one of my favorite textbooks of all time.

To start from absolute zero, check out Suzanna Epp's Discrete Math[0]. I believe even a motivated high school student could get started with it and even finish it. If your proof-writing is shaky, the book provides a very good workout. From there it will be easy to choose the areas of discrete math to specialize.

[0] http://www.amazon.com/gp/product/0495391328?keywords=susanna...

Thanks, I'll check it out. My proof-writing is definitely shaky. I can clearly see the relationship between programming on writing proofs, but I can't get immediate feedback on the validity of my mathematical proofs like I can with code.

Questions in Epp are by no means unique. If you search MSE, you'll see that every question in Epp has probably been asked and reasked about a thousand times each. That goes for subjects like Real Analysis, Abstract Algebra, Topology as well.

Any one know any books or resources that concentrate on invariant programming? Translating recursive code into properly tail recursive or iterative code can be pretty difficult.

`Pearls of Algorithmic Design` by Bird - Beautiful little book. It's a series of problems that are solved by first writing the naive program and then transforming it rigorously to make it more efficient.

`Algebra of Programming` by Bird and De Moor - This a treatment of the theory that is implicit in the methods of the previous book.

I recall that Concrete Mathematics has a pretty section on solving recurrence relations. That's probably as close as I can get you to this.

I am reading CTM by Van Roy/Haridi and watching Van Roy's edx vids. Very nice explanations that require a lot of filling in the holes.

If someone else is familiar with Oz/Van Roy stuff, I have a question.

I am, but I read it many years ago, so I might not be able to help

In this video[0] Van Roy claims that the function Three "resolves" to 3. It's at around 8:45 minute. I tried working that out, but can't seem to get it correct. What I tried

   {Inc {Inc {Inc Zero}}}
   {Inc {Inc 1}}
   {Inc {1} + 1}
   {{{1} + 1} + 1}

Can we consider {{{1} + 1} + 1} to be 3 or what are my mistakes? Thanks.

[0] https://youtu.be/Arh_6J5_fWU?t=8m46s