Email filters classify new messages as either spam or not spam based on word frequency, syntax, and metadata. A "classifier" is an algorithm that maps input data into categories based on distinguishing characteristics, or "features." Features can be raw data or attributes derived from that data. "Feature engineering"…

The Miller-Rabin test is a useful probabilistic method for finding large primes. In this paper, we explain the method in detail and give three variations on this test. These variations were originally developed as student projects to supplement a course in error correcting codes and cryptography.

When the new programming language Pascal was developed in the 1970's, Walter Gander did not like it because because many features which he appreciated in prior programming languages were missing in Pascal. For example the block structure was gone, there were no dynamical arrays, no functions or procedures were allowed as parameters of a procedure,…

In our investigation of university students' knowledge about real numbers in relation to computer algebra systems (CAS) and how it could be developed in view of their future activity as teachers, we used a computer algorithm as a case to explore the relationship between CAS and the knowledge of real numbers as decimal representations. Our work was…

Reviewing addition through the use of palindromes is discussed. A rule for converting any number into a palindrome is presented. (MP)

Algorithms for generating random numbers are discussed along with disadvantages. A program for a programable calculator is given that overcomes those disadvantages. (MP)

Discusses the fraction system developed by the ancient Egyptians. Includes puzzles and number-theory problems. (MA)

The author redefines basic numeracy as the ability to use a four-function calculator sensibly. He then defines "sensibly" and considers the place of algorithms in the scheme of mathematical calculations. (MN)

The evolution of Archimedes' method is traced from its geometrical beginning as a means to approximate pi to its modern version as an analytical technique for evaluating inverse circular and hyperbolic functions. It is felt the web of old and new algorithms provides considerable instructional material, and ideas are offered. (MP)

A computer program in BASIC is presented, with the underlying algorithm explained, for multiplying any two multi-digit numbers and obtaining an exact answer. (MP)

Suggests a moving pictorial tool to help teach principles in the bubble sort algorithm. Develops such a tool applied to an unsorted list of numbers and describes a method to derive the run time of the algorithm. The method can be modified to run the times of various other algorithms. (JN)

Describes a pattern which emerged from an examination of the digits of the squares of numbers. Provides eight examples having the pattern at the units or tens digit of the number. (YP)

Describes examples of rational representation as a guide for translating terminology and information encountered in manuals for computers. Discusses four limitations of the representation. (YP)

The trick focuses on a theorem that the sum of the digits of the difference between any natural number and the sum of its digits is divisible by nine. Two conditions of using the trick are noted. The reason that the theorem works is established through a proof. (MP)