The Physics of Generating Electricity

 The basic ideas underlying how electricity is generated are two fundamental laws of electromagnetism that were discovered by experiment in the early 19th century. Before this time, the concepts of electricity and magnetism were considered separate topics of study. The laws that changed all that said that a changing magnetic field can produce a current and that a current can produce a magnetic field. These two phenomena were incorporated into Maxwell's equation and given mathematical rigor later in the 19th century. 

After their discovery came the inventions of the electric motor and the electric generator and the world was never the same. 

In the paper Generating Electricity , the physics behind the electric motor and the electric generator are reviewed and these applications are described. The paper is a synopsis of the engaging presentation of these ideas at Khan High School Physics Unit 6.

The Monty Hall Problem

 The Monty Hall Problem is a game show type strategy problem that has been well known in the general public for many years. Many people who first hear the problem, use their intuition and come up with the wrong solution to the problem. Some, having heard the correct solution, have still argued vociferously against it because their intuition is so strong and feels so right. There are many discussions on the internet of the history and histrionics related to the problem.

Some explanations of the correct solution seem to be a little bit hand-wavy to me. I wanted to write a solution myself that allowed my hands to do less waving and hopefully contain the fervor of the intuitionists. For your enjoyment (comments welcome), I have written it down at the following link Monty Hall Problem .

The Euclidean, Extended Euclidean, and RSA Algorithms

The Euclidean Algorithm is a methodical process for calculating the greatest common divisor of two integers. It does not require the factorization of the integers which is an advantage for large integers. The Extended Euclidean Algorithm is a methodical process for finding the integer coefficients in the linear representation of the gcd in terms of the original two integers. The RSA Algorithm is a public key cryptographic system in wide use in computer systems all over the world. The system's security rests on the mathematical fact that there is no known easy way to factor sufficiciently large integers. (If a way was discovered, there would be hell to pay in the world of secure data.) The system includes a so-called public key pair by which messages are encrypted and private key pair by which they are decrypted. When the public key pair is established and published, the privacy key of the private key pair is computed using the Extended Euclidean Algorithm. The paper The Euclidean and RSA Algorithms, gives a detailed description and drivation of the Euclidean Algorithms as well as a description and worked example of the RSA Algorithm.