Maurer's research has been in combinatorics, with forays (sometimes continuous) into mathematical biology, economics and anthropology. As for expository and curricular activities, he has written and spoken widely on discrete mathematics and was involved with calculus reform as well.
Maurer won the Allendorfer Award of the MAA in 1980 for his article "The King Chicken Theorems" in Mathematics Magazine. From 1981 to 1987, he chaired the MAA committee on high school contests, producing the AHSME (now called the AMC10 and AMC12), the AIME, and the USAMO. Later he published "Contest Problem Book V" (with George Berzsenyi), which compiles and augments the problems and solutions of the AHSME and AIME from those years. His freshman-sophomore text, Discrete Algorithmic Mathematics (with Anthony Ralston) appeared in Fall 1990. A substantially revised third edition was published in 2004.
Maurer is interested in the special nature of writing in mathematics. He has published articles on this subject and has prepared a Short Guide to Writing Mathematics for undergraduates.
In recent years he has taught primarily linear algebra, discrete math, and analysis, the last of these ranging from a gentle multivariate calculus course through an honors seminar on calculus on manifolds.
Maurer is interested in mathematics education from childhood through undergraduate studies. He has served on the MAA's Committee on the Undergraduate Program, its editorial Board for the Classroom Resources series, and is currently the Editor through 2013 for the MAA Notes series. He served on and sometimes chaired the Dimensions in Math committee of his local elementary school when his kids were there, where he acted as a "Math Parent" and ran the computers and software in the "math room". He was a consultant to the second edition of the CorePlus program, a "reform" national high school math curriculum, and the lead writer of the matrix algebra chapter for the CME Project, another new high school math curriculum developed by the Educational Development Center (EDC). Currently he is a consultant to a followup CorePlus project on an alternative transition course to college.
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