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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.

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I learn computation science through Practical Numerical Methods with Python.

https://github.com/numerical-mooc/numerical-mooc/wiki

It covers finite differencing and many other numerical algorithms. For me the most interesting part is that it shows how various factors impact the stability, accuracy, and performance through small working examples.

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How about Numerical Recipes: The Art of Scientific Computing, Third Edition (2007); Cambridge University Press (ISBN-10: 0521880688, or ISBN-13: 978-0521880688).

It does not contain exercises but it will give you insight in a lot of valuable topics. Important algorithms are presented, discussed in detail theoretically. In addition written C++ code is presented. You can also download the code with a single user lisense as far as I know.

There is a second book similar containing pseudocode instead of working C++ code. Similar topics are discussed. I need to look for the name and add tomorrow.

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