A Random Walk Through Experimental Mathematics
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We describe our adventures in creating a new first-year course in Experimental Mathematics that uses active learning. We used a state-of-the-art facility, called The Western Active Learning Space, and got the students to “drive the spaceship” (at least a little bit). This paper describes some of our techniques for pedagogy, some of the vignettes of experimental mathematics that we used, and some of the outcomes. EYSC was a student in the simultaneously-taught senior sister course “Open Problems in Experimental Mathematics” the first time it was taught and an unofficial co-instructor the second time. Jon Borwein attended the Project Presentation Day (the second time) and gave thoughtful feedback to each student. This paper is dedicated to his memory.
KeywordsExperimental mathematics Continued fractions Chaos game representation Dynamical systems Backward error
We thank David Jeffrey for his early encouragement, Steven Thornton and Torin Viger for their help with the course material, and the membership of USAM: Julia Jankowski, Andy Wilmot, and Anna Zhu. Gavan Watson, Stephanie Oliver, and Wendy Crocker were very helpful with active learning and the use of WALS. We thank Lila Kari for introducing us to the chaos game representation. We also thank the Rotman Institute of Philosophy and the Fields Institute for Research in the Mathematical Sciences for their sponsorship of the Computational Discovery conference (www.acmes.org), at which some of these ideas presented here were refined. We also thank the Center for Teaching and Learning for a Fellowship in Teaching Innovation Award 2018–2019.
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