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The aims of this paper is to prove that every semisimple Jordan algebra bundle is locally trivial and establish the decomposition theorem for locally trivial Jordan algebra bundles using the decomposition theorem of Lie algebra bundles.

Using the decomposition theorem of Lie algebra bundles, this paper proves the decomposition theorem for locally trivial Jordan algebra bundles.

Findings of this paper establish the decomposition theorem for locally trivial Jordan algebra bundles.

To the best of the author’s knowledge, all the results are new and interesting to the field of Mathematics and Theoretical Physics community.

The purpose of this paper is to determine the structure of nilpotent (n+6)-dimensional n-Lie algebras of class 2 when n≥4.

By dividing a nilpotent (n+6)-dimensional n-Lie algebra of class 2 by a central element, the authors arrive to a nilpotent (n+5) dimensional n-Lie algebra of class 2. Given that the authors have the structure of nilpotent (n+5)-dimensional n-Lie algebras of class 2, the authors have access to the structure of the desired algebras.

In this paper, for each n≥4, the authors have found 24 nilpotent (n+6) dimensional n-Lie algebras of class 2. Of these, 15 are non-split algebras and the nine remaining algebras are written as direct additions of n-Lie algebras of low-dimension and abelian n-Lie algebras.

This classification of n-Lie algebras provides a complete understanding of these algebras that are used in algebraic studies.

This study was intended to determine the effects of self-instructional training on algebra problem solving performance of students with learning disabilities, students for whom English is a second language and students who were at risk of failing algebra. Four high school algebra classes consisting of 74 students, of whom 17 were classified as having learning disabilities, 37 had English as a second language, and 20 were considered at-risk for math failure, were assigned randomly to either a self-instructional training condition or a traditional instructional condition. All students were administered pretests, immediate posttests, and delayed posttests of algebra problem solving, pre and post strategy usage questionnaires, and attitude measures. After training, results indicated that both groups’ performance increased from pretest to immediate posttest and pretest to delayed posttest, but no statistical difference was found between groups. The self-instruction group significantly outperformed the traditional instruction group on independent strategy use. Significant correlations were obtained between strategy usage and immediate and delayed posttest scores, indicating that students who successfully learned the strategy had better performance on the math problem solving tests. No significant differences were found across groups in attitude change. Future research issues are discussed with respect to strategy instruction for at risk learners.

Before 2011, student performance rates in college algebra and trigonometry at North Carolina A&T State University (NCA&TSU) were consistently below 50%. To remedy this situation, the Mathematics Department implemented the math emporium model (MEM) instructional method. The underlying principle behind MEM is that students learn math by doing math (Twigg, 2011). The MEM requires students to work on math problems and spend more time on material that they do not understand while allowing them to spend less time on material that they do understand. Also, students receive immediate feedback on problems from teaching assistants as they work through their online assignments. After implementing the MEM, student pass rates improved for both the MEM and traditional sections. Data to date also show that female students outperform male students in both instructional models. Further study is needed to determine the factors that have caused improvement in pass rates in addition to the implementation of the MEM. Some important lessons learned by the NCA&TSU math faculty from implementing the MEM into the college algebra and trigonometry courses are that successful implementation requires a long-term commitment, internal and external collaborations, and the collective ability to determine what works for the local setting.

Discusses the relationship between computer proof and human proof. These issues are discussed both in general and specifically regarding the recent solution of the Robbins problem via a proof generated by computer. The Robbins problem was a long‐standing open problem about axioms for Boolean algebra. One point of this paper is to show that the proof of the Robbins conjecture, generated by a computer, can be filled in and understood by human beings. We accomplish this aim in the present paper by presenting a notational reformulation of Boolean algebra and the Robbins problem. The notational/linguistic issue developed here is of cybernetic, linguistic and semiotic interest. It is our contention that mathematics can behave non‐trivially under change of notation. Change of notation can be as significant as change of language. In the present case the change of language afforded by an appropriate change of notation makes a mathematical domain accessible to human beings that has heretofore been only accessible to computers.

This chapter explores the alignment of teacher leadership and student learning in a professional development school (PDS) by reporting on a successful teacher-initiated PDS project at a southeastern United States high school. De-tracking efforts using teacher collaboration and efficacy in ninth grade Algebra I College Prep courses were examined for effectiveness to improve the achievement in mathematics of students who enter high school without pre-algebra skills. The chapter critiques the lack of democracy inherent in educational tracking as a default system of student grouping because it perpetuates inequities, particularly for students most likely to experience challenges with academic achievement.

A project was undertaken to determine the appropriateness of providing subject‐based courseware in an academic library's software center or microcomputer lab. The courseware was intended to provide remedial instructional support to re‐entry students in selected subjects. For this project, college algebra became the chosen subject because there appeared to be widespread local agreement that a number of adult students needed remedial instruction in college algebra. The question of the appropriateness of CAI in the library remains open. This service seems to be a viable one for academic libraries to offer. Success would be dependent on wide ranging cooperation involving the library, teaching faculty, computing staff, and instructional technologists.

This paper is a survey and classification of a number of factors that relate directly to cost in the computer engineering design of arithmetic units. The general factors considered are inputs, gates, thresholds, algebras, inputs versus gates, values, reliability, implementability, and complexity. The paper contains some recent logic calculations by the author on gate versus input counts and reduction of complexity in the case of ternary logic.

The purpose of this paper is to illustrate how to examine the effectiveness of a pilot summer bridge program for elementary algebra using propensity scores. Typically, selection into treatment programs, such as summer bridge programs, is based on self-selection. Self-selection makes it very difficult to estimate the true treatment effect because the selection process itself often introduces a source of bias.

By using propensity scores, the authors can match students who participated in the summer bridge program with equivalent students who did not participate in the summer bridge program. By matching students in the treatment group to equivalent students who do not participate in the treatment, the authors can obtain an unbiased estimate of the treatment effect. The authors also describe a method to conduct a sensitivity analysis to estimate the amount of hidden bias generated from unobserved factors that would be needed to alter the inferences made from a propensity score matching analysis.

Findings suggest there is no significant difference in the pass rates of the subsequent intermediate algebra course for students who participated in the summer bridge program when compared to matched students who did not participate in the summer bridge program. Thus, students who participate in the summer bridge program fared no better or worse when compared to similar students who do not participate in the program. These findings also appear to be robust to hidden bias.

This study describes a unique way to estimate the causal effect of participating in a treatment program when there is self-selection into the treatment program.