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Articles 1 - 7 of 7
Full-Text Articles in Algebra
Mat-Rix-Toe: Improving Writing Through A Game-Based Project In Linear Algebra, Adam Graham-Squire, Elin Farnell, Julianna Stockton
Mat-Rix-Toe: Improving Writing Through A Game-Based Project In Linear Algebra, Adam Graham-Squire, Elin Farnell, Julianna Stockton
Elin R Farnell
The Mat-Rix-Toe project utilizes a matrix-based game to deepen students’ understanding of linear algebra concepts and strengthen students’ ability to express themselves mathematically. The project was administered in three classes using slightly different approaches, each of which included some editing component to encourage the improvement of the students’ mathematical thinking and writing. Differences in the implementation of the project illustrate the benefits and drawbacks of various methods of editing in the mathematics classroom and highlight recommendations for improvements in future implementations of the project.
Randomized Detection Of Extraneous Factors, Manfred Minimair
Randomized Detection Of Extraneous Factors, Manfred Minimair
Manfred Minimair
A projection operator of a system of parametric polynomials is a polynomial in the coefficients of the system that vanishes if the system has a common root. The projection operator is a multiple of the resultant of the system, and the factors of the projection operator that are not contained in the resultant are called extraneous factors. The main contribution of this work is to provide a randomized algorithm to check whether a factor is extraneous, which is an important task in applications. A lower bound for the success probability is determined which can be set arbitrarily close to one. …
Revisiting Fibonacci And Related Sequences, Arthur Benjamin, Jennifer Quinn
Revisiting Fibonacci And Related Sequences, Arthur Benjamin, Jennifer Quinn
Jennifer J. Quinn
This issue focuses on proving several interesting facts about the Fibonacci Sequence using a combinatorial proof. The aim of Delving Deeper is for teachers to pose and solve novel math problems, expand on mathematical connections, or offer new insights into familiar math concepts. Delving Deeper focuses on mathematics content appealing to secondary school teachers. It provides a forum that allows classroom teachers to share their mathematics from their work with students, their classroom investigations and products, and their other experiences. Delving Deeper is a regular department of Mathematics Teacher.
Circular Units Of Function Fields, Frederick Harrop
Circular Units Of Function Fields, Frederick Harrop
Frederick F Harrop
A unit index-class number formula is proved for subfields of cyclotomic function fields in analogy with similar results for subfields of cyclotomic number fields.
A Construction Technique For Generalized Complex Orthogonal Designs And Applications To Wireless Communications, Jennifer Seberry, Sarah Spence Adams, Tadeusz Wysocki
A Construction Technique For Generalized Complex Orthogonal Designs And Applications To Wireless Communications, Jennifer Seberry, Sarah Spence Adams, Tadeusz Wysocki
Sarah Spence Adams
We introduce a construction technique for generalized complex linear processing orthogonal designs, which are p × n matrices X satisfying XHX = fI, where f is a complex quadratic form, I is the identity matrix, and Xhas complex entries. These matrices generalize the familiar notions of orthogonal designs and generalized complex orthogonal designs. We explain the application of these matrices to space–time block coding for multiple-antenna wireless communications. In particular, we discuss the practical strengths of the space–time block codes constructed via our proposed technique.
Linear Algebra By Analogy, Scott H. Hochwald
Solution Of Systems With Toeplitz Matrices Generated By Rational Functions, William F. Trench
Solution Of Systems With Toeplitz Matrices Generated By Rational Functions, William F. Trench
William F. Trench
No abstract provided.