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The Art of Mathematical Induction

Karen S. Adams, Assistant Professor of Mathematics

Monday, February 12th, 2018 at 4:00 pm
Byrd Center for Legislative Studies Auditorium

Mathematical Induction (MI) is a method of mathematical proof typically used to establish that a given statement is true of all natural numbers n,  or otherwise is true of all members of an infinite sequence. The simplest and most common form of MI consists of two steps. The ‘basic’ step shows that the statement holds for n = 1 and is followed by the ‘inductive’ step showing that if the statement holds for n = k for some k ≥ 1, then the statement also holds for n = k + 1.  However, this does not mean that proof by MI is purely procedural as will be demonstrated in this talk.  Two original proofs using MI will be presented.

Dr. Adams is an Assistant Professor of Mathematics at Shepherd University. She has taught undergraduate mathematics for over 20 years.  In addition to teaching, Dr. Adams supervises student teachers in the field, has written a number of federal and private grants that support student research activities and scholarships.  She has served as an outside evaluator for numerous projects on subjects ranging from nutrition to school bullying. Her mathematical interests are primarily rooted in analysis.