In a similar, but different, vein, I also recommend Alan Turing: The Enigma, by Andrew Hodges. Do not be turned off by the useless film adaptation. The book is intelligent and fascinating, and more aimed at someone with an undergraduate level understanding of math and logic, rather than a general layperson.
After finishing it (I read it after watching the movie) I was rather shocked at just how many liberties the film had taken. I'm not against a historical movie tweaking things here and there for the sake of drama, but The Imitation Game totally mischaracterised almost everything about Turing and his work in my opinion. I guess, to the movie's credit, it did make me want to learn more about Turing.