Dr. Royer joined IWU in 2001. He has taught mathematics at community and technical colleges as well as at the university level and occasionally does volunteer English teaching in Asia. His professional interests include mathematical analysis, dynamical systems, applied mathematics, and post-secondary mathematics education. He and his wife, Barb, enjoy travel, music, church activities, and reading.

INTERESTS

Dynamical Systems: Useful Beauty 
Dr. Royer's favorite research topic is dynamical systems. Consider a sequence starting with first term x(0)=0.6 and with successive terms given by x(n+1)=ax(n)*(1-x(n)). If a=2.8, the sequence values soon approach a number around 0.64. If a=3.2, the sequence values eventually oscillate between numbers approximately 0.51 and 0.80. Finally, if a=3.6, the sequence values never have a clear pattern at all.

It is not at all obvious why small changes to the value of a result in such different sequences. The incredible structures of some fractals, such as the Mandelbrot Set, are due to very different sequence behaviors resulting from slightly different dynamical systems. Dr. Royer sees the beauty of such fractals as a creation of God in the same way He can be seen in the patterns of a sunset or a mountain view. Dynamical systems are not just beautiful but are also frequently used to model biological populations, including of germs and cancer cells. By adjusting values in these mathematical models, scientists can help predict ways to effectively control the spread of diseases.

SCHOLARSHIP - PROJECTS

Dr. Royer's background in electrical engineering and interest in teaching have led him to be most interested in applied mathematics and student projects. View some of his projects, or projects he supervised, below.

PERSONAL

I have spent five summers in China, one in Mongolia, and one in Laos teaching conversational English mainly to high school teachers.   The experience gives me the opportunity to work the right half of my brain and to make friends with teachers from from a very different culture.