Benford Applied Mathematics


Although in my mid fifties, I found myself taking online classes to obtain my bachelor’s degree. Because of conflicts, I found myself talking RES/342 RESEARCH AND EVALUATION II, three years after talking RES/341. As a business person, I realized that I was in trouble and would require a tutor to help me with this course. I contacted Frank Benford and fortunately, with the additional materials and coaching, I was able to obtain a “B” in this difficult class. I believe that without Frank’s assistance, I would not have passed this class. I highly recommend Frank to others who are attempting to learn college statistics.

Lyle Schellenberg, President

Armadillo Underground, Inc.

Salem, OR


Frank is a pleasure to work with. He is prompt, extremely helpful, very efficient, considerate to your needs and affordable. Even though a distance of thousands of miles separates him from us, we consider Frank to be part of our team.

We first found out about Dr. Benford through LinkedIn.  We contacted him to assist us in solving a mathematical problem in order to apply its algorithm in our software. In a very reasonable amount of time we had our solutions and were able to apply them. We are so pleased with his work that we contract him on a regular basis. We highly recommend Dr. Benford without any reservations.

Panos Economou, Founder and Director

Mediterranean Acoustics Research & Development Ltd



By way of background to this endorsement for Dr. Frank Benford, I had the opportunity in the late 1990s to revisit the entire portfolio of red pine (Pinus resinosa) growth and yield studies maintained by the US Forest Service and its cooperators in the Lake States. This was a follow-up to similar research I did at the beginning of my career nearly 40 years earlier. At this time the information from more than 30 separate experiments and data sets was 10 times larger than previously available. The 3700 individual growth estimates were of high mensurational quality but with serious statistical shortcomings. I understand the ecology and silviculture of red pine reasonably well, but needed assistance with the statistical and mathematical characterization of this large and complex data set. It was here that Frank Benford provided invaluable assistance.

Largely through the skills that Dr. Benford brought to this research, we were able to create and estimate a mathematical model that characterizes red pine stand growth and mortality in relation to age, density, site quality, stand structure, and several other key variables. In turn, Dr. Benford collaborated with Dr. Tom Hanson to embody this mathematical model into the computer program RP 2005 that permits a forest user to simulate stand behavior over time in relation to an almost infinite combination of forest management strategies. As a check, growth and yield forecasts from RP2005 were compared with independent growth observations and found to be consistent. All of this workand its methodology are contained in the publication NC 271, available here. The red pine mathematical model is described in detail in Appendix III.

Please contact me ( if I can provide additional information.

Robert E. Buckman

Professor (retired), Oregon State University


It is with pleasure and ease that I recommend Dr. Frank Benford. I have known Dr. Benford for over ten years now. In fact, I recruited him to WOU in an effort to bring greater strength to our Department of Mathematics. During his time with us, he made major changes and improvements in the math curriculum here that are still in place and working well.

I personally regard Frank Benford as one of the best three or four academic mathematical minds I have encountered anywhere. He has special strength as a teacher and researcher in the field of applied mathematics where he can bring his abilities as a math theorist to bear on complex empirical problems.

I recommend Dr. Benford highly and without qualification. If I may be of further help beyond this letter, please contact me at

John Minahan, Ph.D.

President, Western Oregon University


It is a pleasure for me to write a letter of recommendation for Frank Benford. Dr. Benford was a colleague of mine in the Department of Mathematics as Western Oregon University from 1989 until 1996.

Frank’s unusually strong and diverse academic background gives him a broad perspective that is invaluable for showing the usefulness of mathematics as a tool for tackling real-world problems.  We had hoped to take full advantage of Frank’s unique strengths by developing interdisciplinary courses in mathematics/economics, but due to severe budget constraints we were not able to add such courses to our curriculum.

During the winter term of 1993, I sat in on Dr. Benford’s Elementary Discrete Mathematics class in order to evaluate his methods of instruction. My credentials as an evaluator include twenty-five years of teaching experience in mathematics at Western Oregon University, and I base my comments on observing about ten class periods that were fifty minutes in length.

I was quite favorably impressed with Dr. Benford’s style of teaching. He shows an obvious mastery of his subject and is effective in helping students better understand the utility as well as the aesthetic aspects of mathematics. His lectures are carefully organized and clearly presented, and Frank allows students ample opportunity to ask questions about material that may be unclear to them.

Dr. Benford communicates ideas in a clear and succinct manner. I believe that he is especially effective in teaching capable students who are highly motivated, although he is very patient in interacting with students who are struggling to learn mathematics. As interested in achieving excellence in teaching as in pursuing his research interests, Frank is apt to engage one in a conversation about what constitutes good teaching as he is to talk about mathematics.

Dr. Benford’s academic credentials are impressive, and in talking with him one is quickly aware of his intellectual prowess. However, Frank is such a mild-mannered and considerate person that his intellect is stimulating rather than intimidating. This is no small factor, I think, when a person of Frank’s ability is engaged in teaching undergraduate classes. Frank’s amiability makes him a pleasure to work with, and he interacts smoothly with his colleagues.

Dr. Benford treats his students with respect, prepares carefully for each class, and does his best to help students master the mathematics that he teaches. In my opinion he is a highly qualified mathematics instructor. He is an excellent teacher and an enthusiastic scholar, and has my respect and adviration for the work he did at WOU.

Dennis D. Williams

Assistant Professor of Mathematics (retired), Western Oregon University


Benford Applied Mathematics

About Frank Benford

I hold two Ph.D.s: one in Applied Mathematics and the second in Economics. I've worked as a computer programmer (at the Harvard Center for Population Studies), a professor of math, statistics, and econometrics (at several universities), and as an economist (at the Pacific Northwest Research Station of the Forest Service). I enjoy working with people with subject matter expertise to convert their intuitions into mathematical models.

More information about me is available on my LinkedIn public profile:Frank Benford