I found this book to be a godsend. I never took statistics and always wanted to better understand the deep conceptual ideas in the field. I had so many frustrating experiences with books that came highly recommend to me, and turned out to be not what I wanted at all. They spend chapters and chapters beating around the bush, conversationally talking about general ideas around data management and measurement bias and research design and different ways of charting data sets.

I cannot tell you how frustrating this was for me. I wanted just the meat: the core mathematical concepts on which statistical models and inferences are built. Don't tell me a folksy story about gathering soil samples, show me the tools and what they can do, both their power and their limitations. I can think for myself about how to apply those concepts.

I loved this book for being exceptionally clear and terse. I was hooked from the first sentence: "Probability is a mathematical language for quantifying uncertainty." That one sentence makes the concept clear in a way that the entire chapter on probability from "Statistics in a Nutshell" (http://www.amazon.com/Statistics-Nutshell-Sarah-Boslaugh/dp/...) did not.

I'm not someone who thrives on theorems and proofs, I thrive on concepts. And I found this book dense with clear explanations of the key concepts.

Project Euler is a fun way to motivate yourself to learn some algorithms, number theory, and a few other math topics, by solving programming puzzles: http://projecteuler.net/

O'Reilly's Statistics in a Nutshell is a good stats textbook and reference, has some good exercises to be done in R (or S or Matlab), and is generally more programming-oriented than most statistics treatments. http://oreilly.com/catalog/9780596510497/

Two important classics are Knuth's The Art of Computer Programming (more algorithms/programming-focused; very steep learning curve) and Concrete Mathematics (with Ron Graham and Oren Patashnik; more math-focused; may be easier for self-study). Both have exercises you can work through, though many of the exercises are proofs (not easily translatable to programming).