Rotate and Fan Out Your Hand to Unlock the Geometry of Complex Analysis

Embodiment, specifically gesture, in conjunction with metaphors can unveil one’s reasoning about mathematics. In this talk, I will share what my colleagues and I have learned regarding visualization of complex analysis concepts. A pivotal finding is that understanding the geometry behind complex multiplication can unlock the geometry behind other inscriptions such as $$ f'(z)=dw/dz , ∫_C f(z)dz $$ and the Cauchy-Riemann equations. In concluding remarks, I will offer implications for teaching complex analysis and the role of embodiment.

Bio
Hortensia Soto was born in Belén del Refujio, Jalisco, Mexico and raised on a farm in western Nebraska. She is the second of nine children and although her parents only have a third-grade education, all her siblings have a college education.

Hortensia has published in various areas of mathematics education including assessment, mathematical preparation of elementary teachers, outreach efforts for high school girls, and especially in the area of teaching and learning of undergraduate mathematics. Her current research efforts are dedicated to investigating the teaching and learning complex analysis, where she adopts an embodied cognition perspective and is part of the Embodied Mathematics Imagination and Cognition community. Since her days as an undergraduate student, Hortensia has mentored young women and promoted mathematics via summer outreach programs.

Hortensia is a Professor of Mathematics at Colorado State University and the President of the Mathematical Association of America.