#CALCULUS OF VARIATIONS ARBITRARY DELTA SERIES#

We will not give a substantial history of Calculus here, since that subject has been examined in great detail elsewhere. We will see, as we have in each article of the series, that many competing notations were proposed and used, and that no true consensus was reached-even today, many ways of representing mathematical change coexist (however tenuously) in textbooks and classrooms around the world.

#CALCULUS OF VARIATIONS ARBITRARY DELTA SERIES#

It is fitting, then, that this series end with a reflection on the mathematics of change: those symbols from differential calculus that are often a student’s first exposure to a deeper, more creative mathematics. My hope is that seeing the explicit changes in both symbols and concepts illuminates our own role in the ongoing story of mathematics-as the readers and writers of the present, we have the power to build upon and modify the concepts of the past.

In each of these articles, the original meaning of a symbol or concept has evolved through the centuries before landing in today’s undergraduate textbooks. Thus far in the Math Origins series, we have explored number theory in The Totient Function, asymptotic notations in Orders of Growth, linear algebra in Eigenvectors and Eigenvalues, and mathematical logic in The Logical Ideas and The Logical Symbols. Over the course of the past five articles, it has become something more than that: a testament to tumult and confusion, and to the complexity of that very human endeavor of mathematical inquiry. As originally conceived, this series of articles was meant to explore the often-labyrinthine process by which notations in the undergraduate mathematical curriculum came about.

Calculus of variations arbitrary delta