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Luciano, Dennis; Prichett, Gordon – College Mathematics Journal, 1987
Linear ciphers, substitution ciphers, public-key cryptosystems, and trapdoor knapsacks are each discussed. (MNS)
Descriptors: Algebra, Algorithms, College Mathematics, Cryptography

Perso, Thelma – Australian Mathematics Teacher, 1996
Presents a method for solving linear equations involving the use of inverses instead of memorizing rules. (MKR)
Descriptors: Algebra, Algorithms, Equations (Mathematics), Mathematics Instruction

Bidwell, James K. – College Mathematics Journal, 1986
A possible method of derivation of prescriptions for solving problems, found in Babylonian cuneiform texts, is presented. It is a kind of "geometric algebra" based mainly on one figure and the manipulation of or within various areas and segments. (MNS)
Descriptors: Algebra, Algorithms, College Mathematics, Geometric Concepts

Reimann, Kurt W. – Mathematics Teacher, 1980
A generalized method of synthetic division where the divisor polynomial may be of any degree equal to or larger than 1, and the dividend polynomial may be of equal or larger degree than the divisor polynomial and a generalization of the familiar remainder theorem, are presented. (Author/MK)
Descriptors: Algebra, Algorithms, Division, Mathematics Curriculum

Olson, Alton T. – Journal of Computers in Mathematics and Science Teaching, 1986
Presents an example of mathematics from an algorithmic point of view, with emphasis on the design and verification of this algorithm. The program involves finding roots for algebraic equations using the half-interval search algorithm. The program listing is included. (JN)
Descriptors: Algebra, Algorithms, Computer Software, Equations (Mathematics)

Maurer, Stephen B. – Mathematics Teacher, 1984
Two mathematical topics are interpreted from the viewpoints of traditional (performing algorithms) and contemporary (creating algorithms and thinking in terms of them for solving problems and developing theory) algorithmic mathematics. The two topics are Horner's method for evaluating polynomials and Gauss's method for solving systems of linear…
Descriptors: Algebra, Algorithms, Equations (Mathematics), High Schools

Fay, Temple H.; Miller, H. Vincent – Mathematics and Computer Education, 1990
Discusses a numerical technique called the method of adjoints, turning a linear two-point boundary value problem into an initial value problem. Described are steps for using the method in linear or nonlinear systems. Applies the technique to solve a simple pendulum problem. Lists 15 references. (YP)
Descriptors: Algebra, Algorithms, College Mathematics, Higher Education

Staib, John – Mathematics Teacher, 1982
An approach to using the method of least squares, a scheme for computing the best-fitting line directly from a set of points, is detailed. The material first looks at fitting a numerical value to a set of numbers. This provides tools for solving the line-fitting problem. (MP)
Descriptors: Algebra, Algorithms, Mathematical Applications, Mathematical Models

Book, Ronald V. – American Mathematical Monthly, 1988
The "word problem" is stated for a given collection. Facts regarding Dehn's Algorithm, definition of Thue systems, a rewriting system, lemmas and corollaries are provided. The situation is examined where the monoid presented by a finite Thue system is a group. (DC)
Descriptors: Abstract Reasoning, Algebra, Algorithms, College Mathematics

Gantner, T. E. – College Mathematics Journal, 1984
An efficient division algorithm is developed, using a computer program, to convert any positive fraction to its decimal representation. The computer program listing is included. (MNS)
Descriptors: Algebra, Algorithms, College Mathematics, Computer Software

Carmony, Lowell – Mathematics Teacher, 1981
An unusual algorithm for approximating square roots is presented and investigated using techniques common in algebra. The material is presented as a tool to interest high school students in the logic behind mathematics. (MP)
Descriptors: Algebra, Algorithms, Instructional Materials, Mathematical Concepts

Mathematics Teacher, 1979
Topics covered include alternate methods for finding LCM and GCF, imaginative word problems, and a primes-breakdown method of factoring quadratics. (MP)
Descriptors: Algebra, Algorithms, Instruction, Learning Activities

Mathematics Teacher, 1981
Three teaching ideas are presented: how to present changes between scientific notation and decimal form that eliminate some student confusion; an analysis of an incorrect algebra equation that produced a correct answer; and aspects of a standard calculus problem dealing with minimum and maximum values. (MP)
Descriptors: Algebra, Algorithms, Calculus, College Mathematics

Markowitz, Lee M. – Mathematics Teacher, 1983
Variations on a card trick are noted, with a formula for generalizing them. Another trick which can be proved with algebraic principles is then presented. (MNS)
Descriptors: Algebra, Algorithms, Games, Learning Activities

Thwaites, G. N. – Mathematics in School, 1982
An attempt is made to show that algebra is rarely obvious, and merely expecting children to learn rules is an oversimplification. Sections cover: (1) The Non-visual Nature of Algebra; (2) The Apparently Arbitrary Nature of Algebra; (3) The Relationship Between Symbolism, System and Question; (4) The Complex Nature of Algebra; and (5) Some…
Descriptors: Algebra, Algorithms, Equations (Mathematics), Instruction
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