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Abstract
We will discuss introducing ideas from experimental mathematics into a Computing for Mathematicians class. We will focus on how the class can be led to rediscover some facts about the Newton–Raphson (or the Babylonian) method for approximating square roots. We apply these ideas to describe the behavior of this algorithm for both real and complex square roots.
Additional information
Notes on contributors
Neil J. Calkin
NEIL J. CALKIN studied Mathematics as an undergraduate at Trinity College, Cambridge, and received his Ph.D. in Combinatorics and Optimization from the University of Waterloo. In 1994, he co-founded the Electronic Journal of Combinatorics with Herbert S. Wilf. This is his fourth contribution to this Monthly, including one article coauthored with Jonathan M. Borwein.
School of Mathematical and Statistical Sciences, Clemson University, Clemson, SC 29634, USA
Killian Davis
KILLIAN DAVIS is an undergraduate student at Clemson University and is set to graduate in 2022. His mathematical interests vary broadly, and he is still exploring the subject to see what fields interest him the most.
School of Mathematical and Statistical Sciences, Clemson University, Clemson, SC 29634, USA
Evan Haithcock
EVAN HAITHCOCK is an undergraduate student in Mathematical Sciences at Clemson University. He graduated in spring 2021 and afterwards plans to pursue a Ph.D. in mathematics. While his research interests are not yet clear, he is very intrigued by problems in graph theory, algebra, and combinatorics.
School of Mathematical and Statistical Sciences, Clemson University, Clemson, SC 29634, USA
Catherine M. Kenyon
CATHERINE M. KENYON received her bachelor’s and master’s degrees in Mathematical Sciences from Clemson University and is currently working toward her Ph.D. in Engineering and Science Education to become a triple tiger. Her research interests lie in the realms of combinatorics, graph theory, student motivation, and future time perspective theory.
Engineering and Science Education Department, Clemson University, Clemson, SC 29634, USA
Sylvia Wu
SYLVIA WU is an undergraduate student in Mathematics and Philosophy at Clemson University. She has long been interested in areas of math ranging from algebra to statistics. After graduating in 2021, her plans include law school and possibly the Peace Corps.
School of Mathematical and Statistical Sciences, Clemson University, Clemson, SC 29634, USA