Things of Interest ?

by Siegfried "Zig" Herzog

started August 2013

Introducing myself

I obtained my PhD in Mechanical and Aerospace Engineering from Cornell University in 1985. After a post-doc at Leheigh University and Penn State University I started my teaching career at the Mont Alto campus of the The Pennsylvania State University

After some 24 years of teaching courses in statics, dynamics, strength of materials and thermodynamics I decided to retire on a high note (Excellence in teaching award from the College of Engineering at PSU in 2012) and co-authoring a paper in prime number theory (accepted but not published yet) in July of 2013.

Below you find links to material which are partially related to my past work and partially to my present hobbies. You may contact me on any of the subjects listed below. Comments, questions and suggestions are most welcome, feel free to use either the "Send a Note to Zig" link or my email address.

Courses I taught which have some type of web presence


On the Gaps of adjacent Prime Numbers

Although prime numbers have - as far as I know - no application in engineering they are by themselves a fascinating subject area, at least to me. Get a list of all prime numbers up to 10,000 here

Although there are some equations available which produce a large number of prime numbers these equations cannot be used to predict prime numbers in general. A classical example, dating back to Euler, is the equation :

f(n)=n2 + n + 41

which produces prime numbers for each n between 0 and 39 (inclusive) but mingles primes and composite numbers for larger n in seemingly random fashion.

Already a casual observation of the first, let's say hundred, prime numbers reveals that they seem to thin out. Still, it can be proven easily that there are infinitely many of them, see here for a proof due to Euclid (300 B.C.).

Related to that is the question as to how many prime numbers exists below a chosen value x. This is called the prime counting function, most often denoted by π(x) or pi(x). An excellent and short treatise of π(x) can be found at Chris K. Caldwell, How many primes are there, table, Values of pi(x) and analytical functions which approximate π(x) at Chris K. Caldwell, How many primes are there,approximations.

Having access to some computational resouces I participated in a research project on prime numbers which resulted in an article EMPIRICAL VERIFICATION OF THE EVEN GOLDBACH CONJECTURE AND COMPUTATION OF PRIME GAPS UP TO 4*1018 by Tomás Oliveira e Silva, Siegfried Herzog and Silvio Pard published in Math. Comp. 83 (2014), 2033-2060

Click here for more on prime numbers and gaps between adjacent prime numbers

Linear Equation Systems Solver

Linear equations appear in all types of mathematical problems and general solvers for them are frequently needed. Of course, mine cannot cover everything particularily when it comes to efficiency. But the following has served me well on numerous occasions.

A linear equation system solver (up to 20 unknowns)

Stirling Engines

Stirling Engines have fascinated me for a long time but I never found enough time for this hobby. Follow the link below to find out what I have done sofar which is mostly theoretical stuff. But some of it might be of interest to the practioner as well.

Stuff on Stirling Engine


Send a Note to Zig

Zig Herzog © 2014
hgnherzog@yahoo.com
Last revised: 10/24/14
Visits to this pages : 3393