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I am looking for survey-books on open math (esp. probability) problems from engineering fields but phrased in mathematical language.

There are hundreds of specialized math-engineering books out there, but I haven't found an introductory survey of math-engineering problems.

Given the diversity of problems in engineering, feel free to post survey books of specific engineering fields eg. "survey of math problems in civil engineering".

The main fields are: chemical engineering, civil engineering, electrical engineering, mechanical engineering and systems engineering. So a survey book from each, will be nice.

One excellent related post is Computer Science for Mathematicians .

Thank you

PS Even though engineering is diverse, there are certain mathematical problems that keep repeating such as removing noise, estimating integrals etc. This is the kind of list I had in mind.

Math people are usually far removed from engineering problems so at least having a sense of the themes will be highly beneficial to both math and engineering.

If there is no such survey, then at least list of big open math problems from various engineering fields is good enough. Mathoverflow is a great place to have this list since many people visit it and can add their suggestions. Who knows maybe someone will get inspired to compile a list of the themes in mathematical-engineering problems.

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    $\begingroup$ does financial engineering count? $\endgroup$
    – Tyler
    Commented Feb 20, 2015 at 0:59
  • $\begingroup$ actually, I am happy with the answers I received so far. $\endgroup$
    – Thomas Kojar
    Commented Feb 21, 2015 at 23:04

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There is a (perhaps somewhat dated) nice little book devoted to open problems in communications (coding and information theory), system and control theory, and computer science where open problems are motivated. Some of these problems were actually solved by the participants at the 3 workshops in the 1980s, on which this book was based.

Open Problems in Communication and Computation, edited by Thomas M. Cover, B. Gopinath.

http://www.amazon.com/Problems-Communication-Computation-Thomas-Cover/dp/1461291623

If your institutions subscribes to Springerlink, you may be able to access this title in softcopy.

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I do not know of any survey books of this sort (perhaps it is impossible to write because "engineering" is too large and diverse) but I have two outstanding mathematical problems arising from engineering (more precisely, control theory) on my web site:

http://www.math.purdue.edu/~eremenko/uns1.html

Problems under the title "POLYNOMIAL MATRICES".

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A book that covers a broad range of subjects of open problems (as of 2004) in control and systems theory is Unsolved Problems in Mathematical Systems and Control Theory.

As its review already says,

The book consists of ten parts representing various problem areas, and each chapter sets forth a different problem presented by a researcher in the particular area and in the same way: description of the problem, motivation and history, available results, and bibliography. It aims not only to encourage work on the included problems but also to suggest new ones and generate fresh research. The reader will be able to submit solutions for possible inclusion on an online version of the book to be updated quarterly on the Princeton University Press website, and thus also be able to access solutions, updated information, and partial solutions as they are developed.

The updates on the status of the problems are posted in this link.

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