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The effect of algebra of sets instruction as an introductory technique on basic concepts comprehension and mathematics attitude of algebra students

Description: The problem with which this study was concerned was to seek mathematics attitude changes, mathematics self-concept changes, and compare comprehension of concepts in college students enrolled in freshman algebra, when introduced to basic algebraic properties by way of algebra of sets as opposed to an axiomatic introduction.
Date: August 1976
Creator: Floyd, James Russell
Partner: UNT Libraries

The Effects of the Use of the Calculator in Algebra I Classes on Basic Skills Maintenance and Algebra Achievement

Description: The purpose of this study was to determine whether there were any differences in basic skills maintenance between Algebra I students who used calculators during classroom mathematics instruction and Algebra I students who did not use calculators during classroom mathematics instruction. Another purpose of this study was to determine whether there were any differences in algebra achievement between Algebra I students who used calculators during classroom mathematics instruction and Algebra I students who did not use calculators during classroom mathematics instruction. This study also investigated the effects of the use of the calculator in Algebra I classes on students' attitudes toward mathematics.
Date: December 1989
Creator: Whisenant, Martha A. (Martha Ann)
Partner: UNT Libraries

Quantum Drinfeld Hecke Algebras

Description: Quantum Drinfeld Hecke algebras extend both Lusztig's graded Hecke algebras and the symplectic reflection algebras of Etingof and Ginzburg to the quantum setting. A quantum (or skew) polynomial ring is generated by variables which commute only up to a set of quantum parameters. Certain finite groups may act by graded automorphisms on a quantum polynomial ring and quantum Drinfeld Hecke algebras deform the natural semi-direct product. We classify these algebras for the infinite family of complex reflection groups acting in arbitrary dimension. We also classify quantum Drinfeld Hecke algebras in arbitrary dimension for the infinite family of mystic reflection groups of Kirkman, Kuzmanovich, and Zhang, who showed they satisfy a Shephard-Todd-Chevalley theorem in the quantum setting. Using a classification of automorphisms of quantum polynomial rings in low dimension, we develop tools for studying quantum Drinfeld Hecke algebras in 3 dimensions. We describe the parameter space of such algebras using special properties of the quantum determinant in low dimension; although the quantum determinant is not a homomorphism in general, it is a homomorphism on the finite linear groups acting in dimension 3.
Date: August 2016
Creator: Uhl, Christine
Partner: UNT Libraries

Constraints and Superspin for SuperPoincare Algebras in Diverse Dimensions

Description: We generalize to arbitrary dimension the construction of a covariant and supersymmetric constraint for the massless superPoincare algebra, which was given for the eleven-dimensional case in a previous work. We also contrast it with a similar construction appropriate to the massive case. Finally we show that the constraint uniquely fixes the representation of the algebra.
Date: April 27, 2004
Creator: Pasqua, Andrea & Zumino, Bruno
Partner: UNT Libraries Government Documents Department

Twining characters and orbit Lie algebras

Description: We associate to outer automorphisms of generalized Kac-Moody algebras generalized character-valued indices, the twining characters. A character formula for twining characters is derived which shows that they coincide with the ordinary characters of some other generalized Kac-Moody algebra, the so-called orbit Lie algebra. Some applications to problems in conformal field theory, algebraic geometry and the theory of sporadic simple groups are sketched.
Date: December 5, 1996
Creator: Fuchs, Jurgen; Ray, Urmie; Schellekens, Bert & Schweigert, Christoph
Partner: UNT Libraries Government Documents Department

Semigroups

Description: The purpose of this paper is to present some fundamental properties of algebraic semigroups. The development of the theory of semigroups has appeared for the most part in the past few years of this century. A semigroup is the result of a weakening of the axioms for a group. Thus all groups are semigroups. That the study of semigroups is very closely related to the abstract study of general transformations is, perhaps, one of the reasons for the rapid development of semigroup theory.
Date: August 1966
Creator: Jeter, Melvyn W.
Partner: UNT Libraries

The application of matrix methods to coordinate transformations occurring in systems studies involving large motions of aircraft

Description: Report presenting the method and advantages of matrix algebra in setting up the geometric aspects of problems of airplane motion. The paper is divided into two parts. The first is about the aspects of matrix algebra required for use in orthogonal transformations and the other shows how to use orthogonal transformations in matrix form by applying them in several examples.
Date: May 1957
Creator: Doolin, Brian F.
Partner: UNT Libraries Government Documents Department

A Decomposition of the Group Algebra of a Hyperoctahedral Group

Description: The descent algebra of a Coxeter group is a subalgebra of the group algebra with interesting representation theoretic properties. For instance, the natural map from the descent algebra of the symmetric group to the character ring is a surjective algebra homomorphism, so the descent algebra implicitly encodes information about the representations of the symmetric group. However, this property does not hold for other Coxeter groups. Moreover, a complete set of primitive idempotents in the descent algebra of the symmetric group leads to a decomposition of the group algebra as a direct sum of induced linear characters of centralizers of conjugacy class representatives. In this dissertation, I consider the hyperoctahedral group. When the descent algebra of a hyperoctahedral group is replaced with a generalization called the Mantaci-Reutenauer algebra, the natural map to the character ring is surjective. In 2008, Bonnafé asked whether a complete set of idempotents in the Mantaci-Reutenauer algebra could lead to a decomposition of the group algebra of the hyperoctahedral group as a direct sum of induced linear characters of centralizers. In this dissertation, I will answer this question positively and go through the construction of the idempotents, conjugacy class representatives, and linear characters required to do so.
Date: December 2016
Creator: Tomlin, Drew E
Partner: UNT Libraries

Properties of R-Modules

Description: This thesis investigates some of the properties of R-modules. The material is presented in three chapters. Definitions and theorems which are assumed are stated in Chapter I. Proofs of these theorems may be found in Zariski and Samuel, Commutative Algebra, Vol. I, 1958. It is assumed that the reader is familiar with the basic properties of commutative rings and ideals in rings. Properties of R-modules are developed in Chapter II. The most important results presented in this chapter include existence theorems for R-modules and properties of submodules in R-modules. The third and final chapter presents an example which illustrates how a ring R, may be regarded as an R-module and speaks of the direct sum of ideals of a ring as a direct sum of submodules.
Date: August 1989
Creator: Granger, Ginger Thibodeaux
Partner: UNT Libraries

The effect of teacher training in the use of computer graphing software on the achievement of Algebra II students

Description: The purpose of this study was to investigate the effectiveness of carefully designed teacher training in the use of the computer to teach graphing skills associated with Algebra II conic sections. Three areas were studied: the teachers' attitude toward mathematics, and the effect on students' achievement in the area of graphing skills.
Date: August 1991
Creator: Loop, Sallie Bell Jackson
Partner: UNT Libraries

Math Anxiety in Fundamentals of Algebra Students

Description: This paper describes the current state of research and understanding of math anxiety, expounds upon this information with independent research conducted at UNT, evaluates this research, and suggests a plan for improved results in mathematics education.
Date: April 3, 2008
Creator: Draznin, Sara & Brand, Neal E.
Partner: UNT Honors College

A Comparison of the Attitude and Achievement in Mathematics of Algebra I Students Using Computer-based Instruction and Traditional Instructional Methods

Description: This study investigated the use of computer-based instruction as a means of teaching Algebra I, compared to the teaching of the same topics using traditional methodologies. The achievement level of the two groups, and three aspects of attitude toward mathematics were considered. Achievement and attitude differences by gender were also analyzed.
Date: December 1992
Creator: Wohlgehagen, Kathleen Shannon
Partner: UNT Libraries

Effects of Instructional Methods on Student Performance in Postsecondary Developmental Mathematics

Description: This study examined success rates and end-of-semester grades for three instructional methods used in developmental algebra and college algebra. The methods investigated were traditional lecture, laboratory, and computer mediated learning. The population included the 10,095 students who had enrolled in developmental algebra and college algebra at Richland College in Dallas, Texas, for five semesters. Success was defined as earning a grade of A, B, C, or D in a course.
Date: May 1999
Creator: Hernandez, Celeste Peyton
Partner: UNT Libraries

The Use of Technology in the Delivery of Instruction in Algebra II in Texas Public Secondary Schools

Description: The purpose of this study was to survey Algebra II teachers in the State of Texas to determine the extent to which they use technology for the delivery of instruction. Additionally, the study attempted to determine reasons why teachers do or do not use technology when they have a choice.
Date: August 1993
Creator: Clay, James H. (James Hamilton)
Partner: UNT Libraries

Wakimoto realizations of current algebras: an explicit construction

Description: A generalized Wakimoto realization of $\widehat\cal G_K$ can be associated with each parabolic subalgebra $\cal P=(\cal G_0 +\cal G_+)$ of a simple Lie algebra $\cal G$ according to an earlier proposal by Feigin and Frenkel. In this paper the proposal is made explicit by developing the construction of Wakimoto realizations from a simple but unconventional viewpoint. An explicit formula is derived for the Wakimoto current first at the Poisson bracket level by Hamiltonian symmetry reduction of the WZNW model. The quantization is then performed by normal ordering the classical formula and determining the required quantum correction for it to generate $\widehat\cal G_K$ by means of commutators. The affine-Sugawara stress-energy tensor is verified to have the expected quadratic form in the constituents, which are symplectic bosons belonging to $\cal G_+$ and a current belonging to $\cal G_0$. The quantization requires a choice of special polynomial coordinates on the big cell of the flag manifold $P\backslash G$. The effect of this choice is investigated in detail by constructing quantum coordinate transformations. Finally, the explicit form of the screening charges for each generalized Wakimoto realization is determined, and some applications are briefly discussed.
Date: November 12, 1996
Creator: de Boer, Jan & Feher, Laszlo
Partner: UNT Libraries Government Documents Department

Design, Development, and Implementation of a Computer-Based Graphics Presentation for the Undergraduate Teaching of Functions and Graphing

Description: The problems with which this study was concerned were threefold: (a) to design a computer-based graphics presentation on the topics of functions and graphing, (b) to develop the presentation, and (c) to determine the instructional effectiveness of this computer-based graphics instruction. The computerized presentation was written in Authorware for the Macintosh computer. The population of this study consisted of three intermediate algebra classes at Collin County Community College (n = 51). A standardized examination, the Descriptive Tests of Mathematics Skills for Functions and Graphs, was used for pretest and posttest purposes. Means were calculated on these scores and compared using a t-test for correlated means. The level of significance was set at .01. The results of the data analysis indicated: 1. There was a significant difference between the pretest and posttest performance after exposure to the computer-based graphics presentation. 2. There was no significant gender difference between the pretest and posttest performance after exposure to the computer-based graphics presentation. 3. There was no significant difference between the pretest and posttest performance of the traditional and nontraditional age students after exposure to the computer-based graphics presentation. Females had a lower posttest score than the mean male posttest score, but an analysis of the differences showed no significance. Traditional age students had a higher posttest performance score than the mean traditional age student posttest score, but their pretest performance scores were higher as well. An analysis of the differences showed no significance. In summary, this computer-based graphics presentation was an effective teaching technique for increasing mathematics performance.
Date: December 1996
Creator: Karr, Rosemary McCroskey
Partner: UNT Libraries

Mapping the geometry of the E6 group

Description: In this paper we present a construction for the compact form of the exceptional Lie group E{sub 6} by exponentiating the corresponding Lie algebra e{sub 6}, which we realize as the sum of f{sub 4}, the derivations of the exceptional Jordan algebra J{sub 3} of dimension 3 with octonionic entries, and the right multiplication by the elements of J{sub 3} with vanishing trace. Our parameterization is a generalization of the Euler angles for SU(2) and it is based on the fibration of E{sub 6} via a F{sub 4} subgroup as the fiber. It makes use of a similar construction we have performed in a previous article for F{sub 4}. An interesting first application of these results lies in the fact that we are able to determine an explicit expression for the Haar invariant measure on the E{sub 6} group manifold.
Date: October 1, 2007
Creator: Cerchiai , Bianca; Bernardoni, Fabio; Cacciatori, Sergio L.; Cerchiai, Bianca L. & Scotti, Antonio
Partner: UNT Libraries Government Documents Department