The author describes an introduction to, and development of, the complex number field. (SD)

The operation of rounding is shown to lead into an investigation of an abstract mathematical system. Properties of the system are discussed and graphs of the rounding function are drawn. Some questions for discussion are given. (MP)

The topics discussed are, "Helping Students Understand the Distributive Property,""Converting from Base 10: Nonintegral Bases?,""Rapid Mental Squaring of Mixed Numbers," and "Some Nonstandard Binary Operations and their Properties." (JT)

Presents techniques and materials for instruction at secondary school and upper elementary grades in mathematical concepts of number systems structure. Grouping is used as a simple algebraic system to illustrate structure. Closure, inverse, identity, commutative and associative properties are examines relative to manipulation of geometric figureS.…

This is part two of a three-part manual for teachers using SMSG high school text materials. Each chapter contains a commentary on the text, answers to exercises, and suggested test questions. Chapter topics include quadratic equations, the complex number system, equations of the second degree, and systems of first degree equations. (MP)

Born in 1707, Leonhard Euler was the son of a Protestant minister from the vicinity of Basel, Switzerland. With the aim of pursuing a career in theology, Euler entered the University of Basel at the age of thirteen, where he was tutored in mathematics by Johann Bernoulli (of the famous Bernoulli family of mathematicians). He developed an interest…

This is Part 1 of the first course in a series which focuses on building fundamental mathematical structures. The arithmetic studied in elementary school along with modular arithmetic is examined and set notation and mappings of sets are presented. Mathematical group structures are introduced. Points and numbers are related both on a line and in a…

Described is mathematics used by the ancient Babylonians and recorded on tablets which have been dated 3000-2000 B.C., and 700-500 B.C. (SD)

Several hierarchical classes models can be considered for the modeling of three-way three-mode binary data, including the INDCLAS model (Leenen, Van Mechelen, De Boeck, and Rosenberg, 1999), the Tucker3-HICLAS model (Ceulemans,VanMechelen, and Leenen, 2003), the Tucker2-HICLAS model (Ceulemans and Van Mechelen, 2004), and the Tucker1-HICLAS model…

This article extends number bases to negative integers, then to positive rationals and finally to negative rationals. Methods and rules for operations in positive and negative rational bases greater than one or less than negative one are summarized in tables. Sample problems are explained and illustrated. (KM)

This is one in a series of SMSG supplementary and enrichment pamphlets for high school students. This series is designed to make material for the study of topics of special interest to students readily accessible in classroom quantity. Topics covered include operations, standard form, equations, graphs, and conjugates. (MP)

This is one in a series of manuals for teachers using SMSG high school supplementary materials. The pamphlet includes commentaries on the sections of the student's booklet, answers to the exercises, and sample test questions. Topics covered include complex numbers, operations, standard form, equations, graphs and conjugates. (MP)