Books & Other Works
- Best Hotel, Largest Dowry (300 KB)
- 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? (1 MB)
- 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 (7 MB)
- 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.
- Mathematical Techniques for Biology and Medicine, 3rd Edition
- Copyright © William Simon, 1986
- Dover Publications
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.
- 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
- Cytokine production associated with smallpox vaccine responses. Immunotherapy. 6, 1097-112. (2014 Jan 01).
- Should we still be focused on red cell hemoglobin F as the principal explanation for the salutary effect of hydroxyurea in sickle cell disease? Pediatr Blood Cancer. 57, 8-9. (2011 Jul 15).
- (2009 Mar 17). Should Aspirin be Discontinued at Age 80? Annals of Internal Medicine.