Reddit mentions of Thinking Functionally with Haskell

Conceptual Mathematics by Lawvere and Schanuel is a good low level introduction to category theory (and a bit of set theory) if you are feeling shaky on those grounds. From there lots of books open up to you.

The best books I know on how to "think" like a functional programmer are all written by Richard Bird. http://www.amazon.com/gp/product/1107452643/ref=pd_lpo_sbs_dp_ss_1?pf_rd_p=1944579842&pf_rd_s=lpo-top-stripe-1&pf_rd_t=201&pf_rd_i=0134843460&pf_rd_m=ATVPDKIKX0DER&pf_rd_r=090NKMWKY6078Z0WPCTW http://www.amazon.com/Pearls-Functional-Algorithm-Design-Richard/dp/0521513383

Not much is available in book form, especially that I can recommend on the FRP front.

Dependent types is a broad area, you're going to find yourself reading a lot of research papers. You might be able to get by with something more practical like Chlipala's Certified Programming with Dependent Types, but if you want a more theoretical treatment then perhaps Zhaohui Luo's Computation and Reasoning might be a better starting point.

My personal favorite is: https://www.amazon.com/Thinking-Functionally-Haskell-Richard-Bird/dp/1107452643

Thinking Functionally with Haskell by Richard Bird.

I really liked the 2nd edition, though I found myself growing impatient, having already read LYAH by the time I found that book. Pre-ordered, regardless. Happy birthday to me! Kindle edition was immediately available, so I didn't have to wait for my birthday.

PS - available for pre-order on amazon.com Didn't realize the reddit entry linked to amazon already. Whoops... << walks out quietly >>

http://www.amazon.com/Thinking-Functionally-Haskell-Richard-Bird/dp/1107452643/