New Mexico Tech Mathematics Faculty

Dr. Brian Borchers


BS (Computer Science), Rensselaer
MS (Mathematics), Rensselaer
PhD (Mathematics), Rensselaer


My primary research and teaching interests are in optimization and inverse problems. I teach a number of undergraduate and graduate courses at NMT in linear programming, nonlinear programming, time series analysis, and geophysical inverse problems. My research has focused on interior point methods for linear and semidefinite programming and applications of these techniques to combinatorial optimization problems. I've also done work on inverse problems in geophysics and hydrology using linear and nonlinear least squares and Tikhonov regularization.

I am the editor of MAA Reviews, the website of the Mathematical Association of America for reviews of mathematics books.

Together with Rick Aster (NMT, Geophysics) and Cliff Thurber (geophysics at the University of Wisconsin), I've coauthored a textbook on inverse problems aimed at graduate students in the earth sciences. This textbook is based on a course that Rick Aster and I started teaching in the late 1990's. The third edition of the book was published in November of 2018. You can buy it direct from Elsevier or from Amazon

I've edited the conference proceedings volume from the INFORMS Computing Society 2015 Conference, Operations Research and Computing: Algorithms and Software for Analytics. The individual papers from this volume are available in open access under the CC-BY license, or you can purchase a copy of the printed volume from INFORMS.

If you're an undergraduate or graduate student looking for a project, please see my list of projects. In some cases there is even funding available to pay you for work on these projects. If you're looking for a directed study course, I am also willing to teach directed studies related to optimization and inverse problems, including Data Assimilation, Convex Optimization, and Compressive Sensing.

I am available as a consultant to industry on numerical analysis, optimization, and inverse problems.


Contact Information

Fall 2020 Office Hours: M 12-1, T 2-3, W 1-2, F 11-12, at

Office: Weir Hall 210
Telephone: 575-322-2592
Fax: 575-835-5366

Note: 575-322-2592 is a Google voice number that will ring my home, office, and mobile phones. It's the surest way of reaching me or at least getting to my voice mail. 835-5813 is the actual number in my office- it doesn't lead to a useful voice mail.

I don't normally use text messages or chat clients. I will use Skype for long distance communication if I have scheduled a call in advance, but I'm not usually online with Skype. My Skype username is brian.borchers1.

If you need to physically mail something to me, my postal address is:

Brian Borchers
Department of Mathematics
New Mexico Tech
Socorro, NM 87801

Do not use this address to send books for review by MAA Reviews. Unsolicited books sent to me will be disposed of by donation. Rather, send books for review to:

MAA Reviews Editor
Mathematical Association of America
1529 18th St NW
Washington, DC 20036-1358

Contact Information in .vcf format

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