I need a textbook suitable for teaching dynamic programming and its applications for undergraduate applied mathematics students. The textbook should cover most aspects of DP specially its applications in optimization.
Your suggestions will be appreciated.
From the algorithmic perspective it is probably best to read "Introduction To Algorithms" by Cormen, Leiserson, Rivest and Stein. The perspective is from the point of view of algorithms, more than from the perspective of mathematical optimization. So
if you need a more mathematical one try the book by Bellman on dynamic programming - nowadays found cheaply on Dover, or, if you are quite mature, get the two-volume text by Dimitri Bertsekas:
http://www.amazon.com/Dynamic-Programming-Optimal-Control-Vol/dp/1886529086
Good luck!
Hi Ehsan. I think some chapters of the book by Puterman can be taught.
http://books.google.com/books?hl=en&lr=&id=VvBjBAAAQBAJ&oi=fnd&pg=PT9&ots=rqhCzKTYRN&sig=CGBpWRk1hQ-HmVcc4PJDKlhcmJs#v=onepage&q&f=false
Is this lower or upper end undergraduate course level? (i.e., 4th year? 2nd year?) This will make a huge difference on what book I'd recommend personally.
Dynamic Programming and Optimal Control by Dimitri Bertsekas is a good one!!
Thank you very much for your suggestions.
@Daniel Page: I'm not sure! I know the students have some light backgrounds in algorithm design, linear and nonlinear optimization; and, they pass some computer science courses such as "programming in C++" and "data structure".
The book Algorithms of S. Dasgupta, C. H. Papadimitriou, and U. V. Vazirani 2006 can help you to improve the course. You can find a lot of interesting exercises here.
If that is the case, I'd go with Michael Patriksson's suggestions personally. There have been some good suggestions made here. Also, you'll find that most texts in Combinatorial Optimization will do a decent job of covering Dynamic Programming as well.
It really depends on which aspects of optimization you want to cover. For example, some will talk about dynamic programming in order to discuss polynomial-time approximation schemes (if they are interested in approximation algorithms as an application of the technique) such as Combinatorial Optimization by Papidimitriou and Steiglitz does. If its only the technique you want from an algorithmic perspective a couple books like Introduction to Algorithms or Foundations of Algorithms (by Neapolitan and Naimipour) focus on them as techniques (but don't get their hands too dirty). You'll find there is a spectrum of how texts will treat dynamic programming on how geared it is towards computer science students, engineering students, or maths students.
Another book: Approximate dynamic programming from W. Powell.
And if the focus is more on modeling of (stochastic) problems: Modeling with stochastic programming from Alan King and Stein Wallace.
I would like to recommend "Dynamic Programming and Optimal Control volumn 1" by Dimitri Bertsekas.
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