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Books & Other Works

Mathematical Techniques for Biology and Medicine (MIT Press Classics)
Mathematical Techniques for Biology and Medicine, 3rd Edition (Dover)
Mathematical Techniques for Biology and Medicine, 4thEdition (Dover, eBook)
Copyright © William Simon, 1972, 1977, 1987, 2015

Useful at both the graduate and undergraduate level, this volume recalls basic concepts of calculus and shows how physiological problems can be formulated in terms of differential equations. Techniques for solving differential equations are applied to often-encountered problems.

Variance: An Alternative Definition
Copyright © William Simon, 2015
Best Hotel, Largest Dowry
Copyright © William Simon, 2012

This problem, known as the best hotel or the largest dowry, is one of the great classics of probability fun.

What Is This Thing Called e?
Copyright © William Simon, 2011

One of the most frequently asked and poorly answered questions in the mathematics of physics (or chemistry or even physiology) is, What is this thing called e? The usual classroom answer is that e is the base of the natural logarithms which is no answer at all.

The more informative but lengthy answer given in the typical advanced calculus course requires explanations of series convergence and assumptions with regard to the validity of series expansions for complex arguments.

This document provides a clear answer requiring at most the first two weeks of an elementary calculus course. Euler's formula is then derived without the use of series expansions.

Mathematics of Spin
Copyright © William Simon, 2005

Spin was one of the earliest recognized cases of quantum weirdness for which there was no explanation in classical mechanics. It was first proposed by Wolfgang Pauli in 1924 as a simple but ad hoc two valued forth quantum number of the electron apparently needed to account for the anomalous Zeeman effect.

Shortly thereafter a number of people identified it, erroneously it turns out, with a spinning ball of charge. In 1928 Paul Dirac published a more satisfactory but extraordinarily abstruse ( Like much of Dirac’s work.) explanation.

The above book chapter offers a slightly unrealistic but highly simplified version which allows one to follow Dirac's logic.

Na+ Channel Reorganization in Demyelinated Axons, In Multiple Sclerosis as a Neuronal Disease
Copyright © Shrager P, Simon W, Kazarinova-Noyes K, 2005

Edited by Stephen G. Waxman; Elsevier Academic Press.

Semi-automatic Tracking of Neuronal Processes, In Computer Analysis of Neuronal Structures
Copyright © Coleman PD, Garvey CF, Young JH, Simon W, 1977
Edited by Dr. George Moore; Plenum Publishing Corporation
Advanced techniques for the small computer, Chapter 11 of Digital Computers in the Behavioral Laboratory
Copyright © Simon W, 1973
Edited by Bernard Weiss; Appleton-Century-Crofts