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Mathematics of Optimization: How to Do Things Faster

Steven J. Miller
American Mathematical Society
Publication Date: 
Number of Pages: 
Pure and Applied Undergraduate Texts 30
BLL Rating: 

The Basic Library List Committee suggests that undergraduate mathematics libraries consider this book for acquisition.

[Reviewed by
Jason M. Graham
, on

I started reading Mathematics of Optimization: How to do Things Faster without a significant background in optimization, linear programming, or operations research. Hence, I really did not know what to expect from the book. I was pleasantly surprised to find the book to be so much fun to work through. The writing is upbeat, entertaining and enlightening and the mathematics is varied, interesting, and inspiring.

In this one book, the reader is exposed to ideas from algorithms, elementary number theory, combinatorics, linear algebra, fractals, differential equations, and analysis. If someone were to have told me before reading it that there was a book that touched on all of these topics, I would have assumed that this was just a book that surveyed a number of largely disconnected topics in mathematics. What I find in Mathematics of Optimization is that this is not necessarily true. All of these topics and more share a common thread. That thread is optimization.

Of course, as Miller’s book shows, there are different types of optimization, or perhaps different contexts for optimization. But even here there is a common thread: real world problems. Thus, not only does Miller combine topics from many different areas of mathematics in an interesting and coherent manner, he also mixes pure and applied mathematics within one single book.

I am really impressed by Mathematics of Optimization and I would love to teach a course based on this book just in order to spend more time going through it myself. In fact, the book is based on courses on operations research taught by the author. Furthermore, there are a few different tracks through the text emphasizing various degrees of theory and applications. This makes the book useful for a variety of different courses on optimization, linear programming and related areas.

One of my favorite features of this book are the exercises. There are more than 600 varied exercises. Some exercises are straightforward yet interesting checks of understanding, while many other exercises either introduce or make use of results not strictly covered in the main text. I actually think it would be interesting to implement an inquiry-based or problem-based course using the exercises from this book as a foundation.

In summary, Mathematics of Optimization is a well-written, interesting book on optimization, operations research and some closely related mathematics. I think that the book is unique and should be relevant and of interest to advanced undergraduate and beginning graduate students in pure and applied mathematics and some closely related areas.


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Jason M. Graham is an assistant professor in the department of mathematics at the University of Scranton, Scranton, Pennsylvania. His current professional interests are in teaching applied mathematics and mathematical biology, and collaborating with biologists specializing in the collective behavior of groups of organisms.

See the table of contents in the publisher's webpage.