Applied mathematics Books (graduate level) What are some good graduate level books on applied mathematics which explain in-depth the general modern problem-solving methods of the real-world typical hard problems? 
There is a lot of books on numerical methods, engineering math, but I do not know any good modern book, which emphasizes algorithmic complexity of the discussed problems.
 A: Modern Computer Algebra by von zur Gathen
http://www.amazon.com/Modern-Computer-Algebra-Joachim-Gathen/dp/0521641764
Topology for Computing by Zomorodian
http://www.amazon.com/Computing-Cambridge-Monographs-Computational-Mathematics/dp/0521836662/ref=sr_1_2?ie=UTF8&s=books&qid=1259939528&sr=1-2
A: Geometric Fundamentals of Robotics by Selig  applies algebraic and differential geometry to problems in robotics.
Computational Homology by Kaczynski et al  has applications of homology to image processing and nonlinear dynamics.
Robert Ghrist, http://www.math.uiuc.edu/~ghrist/, applies topology to problems in engineering, including robotics and sensor networks.
A: This book by Erica Flapan relating chemistry and algebraic topology was of use to my wife when she has writing her undergrad thesis.  It seems like it might qualify.
A: Since the question was tagged with "algorithms", I will give an algorithms recommendation. (You don't say specifically what type of problems you want to solve, but you do mention "algorithmic complexity.") For a book that was written to motivate the theory of algorithms from real-world problems, I would recommend Algorithm Design by Kleinberg and Tardos. It discusses many problem-solving methods. From the website for the book:

Algorithm Design introduces algorithms by looking at the real-world problems that motivate them. In a clear, straight-forward style, Kleinberg and Tardos teaches students to analyze and define problems for themselves and from this, to recognize which design principles are appropriate for a given situation. The text encourages a greater understanding of the algorithm design process and an appreciation of the role of algorithms in the broader field of computer science. 

Amazon link: http://www.amazon.com/Algorithm-Design-Jon-Kleinberg/dp/0321295358
A: Derivations of Applied Mathematicsis a book of applied mathematical proofs. If you have seen a mathematical result, if you want to know why the result is so, you can look for the proof here
