I am currently trying to get through Pattern Classification by Duda et al (for a course). However, the book seems too dense for me. Pattern recognition seems like a topic that could be better learned through guided discovery. That made me think... There is a a thread over at mathematics SE about books that teach math by guiding you from exercise to exercise; So, essentially you prove every result yourself.
Are there any similar books on the mathematics used in computational science? It seems to me that computational science is something that can be learned by doing.