Description
This monograph is the fourth in a series devoted to special topics in
Mathematics; in particular those topics not covered in a standard High School mathematics core curriculum. As such, the target audience would be mathematically motivated and/or intellectually curious High School students and recreational mathematicians. No mathematics beyond introductory Calculus is required to understand the technical material covered in this monogram.
The first monograph - A Finite Introduction to Infinity - explores transfinite arithmetic, the infinite levels of infinity, and the (seemingly) paradoxical nature of infinite sets.
The second monograph explores advanced techniques used
to count in the context of analyzing poker hands, tennis matches, discrete sequences (e.g., the Fibonacci series), and Stochastic Processes. As well as having a firm theoretical basis, these techniques are used extensively in diverse engineering applications; thus they are of significant practical importance.
The third monograph - Variations on Curves - pays homage to one of the crowning intellectual achievements of Western Civilization: The Calculus. In particular, this volume explores the Calculus of Variations and explores solutions to select problems and phenomena that intrigued 17th and 18th century mathematicians and physicists.
This volume explores the historical and mathematical underpinnings of Galois Theory and investigates its application to the solution polynomial equations. This work is a tribute to the genius and tragedy of Evariste Galois who laid the foundation of this most important body of work that bears his name in homage.