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Samuel B. Allan; Peter K. Dunn; Robert G. McDougall – International Journal of Mathematical Education in Science and Technology, 2024
In this note we demonstrate two instances where matrix multiplication can be easily verified. In the first setting, the matrix product appears as matrix element concatenation, and in the second, the product coincides with matrix addition. General proofs for some results are provided with a more complete description for 2×2 matrices. Suggested for…
Descriptors: Mathematics Instruction, Teaching Methods, Multiplication, Addition
Lou, Hongwei – International Journal of Mathematical Education in Science and Technology, 2023
In current teaching materials, when using Dedekind cuts to construct real numbers, the definition of a Dedekind cut is always involved in defining addition and multiplication. In this paper, as it is done in many current textbooks, Dedekind cuts are used to construct the set of real numbers. Then the order in it is defined, and the…
Descriptors: Mathematics Instruction, Addition, Multiplication, Arithmetic
Hamdan, May – International Journal of Mathematical Education in Science and Technology, 2019
The literature dealing with student understanding of integration in general and the Fundamental Theorem of Calculus in particular suggests that although students can integrate properly, they understand little about the process that leads to the definite integral. The definite integral is naturally connected to the antiderivative, the area under…
Descriptors: Calculus, Mathematics Instruction, Teaching Methods, Mathematical Logic
Dobbs, David E. – International Journal of Mathematical Education in Science and Technology, 2017
Let R be a ring with identity. Then {0} and R are the only additive subgroups of R if and only if R is isomorphic (as a ring with identity) to (exactly) one of {0}, Z/pZ for a prime number p. Also, each additive subgroup of R is a one-sided ideal of R if and only if R is isomorphic to (exactly) one of {0}, Z, Z/nZ for an integer n = 2. This note…
Descriptors: Numbers, Mathematics Instruction, Mathematics, Algebra
Csenki, Attila – International Journal of Mathematical Education in Science and Technology, 2011
In Probability and Statistics taught to mathematicians as a first introduction or to a non-mathematical audience, joint independence of events is introduced by requiring that the multiplication rule is satisfied. The following statement is usually tacitly assumed to hold (and, at best, intuitively motivated): If the n events E[subscript 1],…
Descriptors: Probability, Mathematics, Professional Personnel, Multiplication
Lynch, Mark A. M. – International Journal of Mathematical Education in Science and Technology, 2011
A procedure for generating quasigroups from groups is described, and the properties of these derived quasigroups are investigated. Some practical examples of the procedure and related results are presented.
Descriptors: Algebra, Mathematics, Mathematics Instruction, Mathematics Education
Torres-Jimenez, Jose; Rangel-Valdez, Nelson; Gonzalez-Hernandez, Ana Loreto; Avila-George, Himer – International Journal of Mathematical Education in Science and Technology, 2011
A branch of mathematics commonly used in cryptography is Galois Fields GF(p[superscript n]). Two basic operations performed in GF(p[superscript n]) are the addition and the multiplication. While the addition is generally easy to compute, the multiplication requires a special treatment. A well-known method to compute the multiplication is based on…
Descriptors: Numbers, Mathematics Instruction, Tables (Data), Arithmetic
Stuart, Jeffrey – International Journal of Mathematical Education in Science and Technology, 2010
Most students complete their first and only course in linear algebra with the understanding that a real, square matrix "A" has an inverse if and only if "rref"("A"), the reduced row echelon form of "A", is the identity matrix I[subscript n]. That is, if they apply elementary row operations via the Gauss-Jordan algorithm to the partitioned matrix…
Descriptors: Geometric Concepts, Matrices, Algebra, Mathematics
Kachapova, Farida; Kachapov, Ilias – International Journal of Mathematical Education in Science and Technology, 2012
Research on teaching high school mathematics shows that the topic of percentages often causes learning difficulties. This article describes a method of teaching percentages that the authors used in university bridging courses. In this method, the information from a word problem about percentages is presented in a two-way table. Such a table gives…
Descriptors: Logical Thinking, Learning Problems, Word Problems (Mathematics), Mathematics
Gierdien, Faaiz – International Journal of Mathematical Education in Science and Technology, 2009
This note presents demonstrations of mathematics that emerges when problems are posed with respect to a combined 12 x 12 multiplication table showing multiplier and multiplicand. Through processes such as recognizing and extending patterns, specializing and generalizing particular functional relationships between the diagonal and row sequences are…
Descriptors: Arithmetic, Multiplication, Mathematics Instruction, Mathematical Concepts
Sani, B. – International Journal of Mathematical Education in Science and Technology, 2007
This paper presents the row-column multiplication of rhotrices that are of high dimension. This is an extension of the same multiplication carried out on rhotrices of dimension three, considered to be the base rhotrices.
Descriptors: Matrices, Multiplication, Algebra, Validity
Barabe, Samuel; Dubeau, Franc – International Journal of Mathematical Education in Science and Technology, 2007
Synthetic division is viewed as a change of basis for polynomials written under the Newton form. Then, the transition matrices obtained from a sequence of changes of basis are used to factorize the inverse of a bidiagonal matrix or a block bidiagonal matrix.
Descriptors: Equations (Mathematics), Validity, Mathematical Logic, Arithmetic
Chen, Hongwei – International Journal of Mathematical Education in Science and Technology, 2002
In this note, using the method of undetermined coefficients, we obtain the power series for exp ( f ( x )) and ln ( f ( x )) by means of a simple recursion. As applications, we show how those power series can be used to reproduce and improve some well-known results in analysis. These results may be used as enrichment material in an advanced…
Descriptors: Calculus, Mathematical Formulas, Mathematics, Multiplication