About Nonassociativity in Mathematics and Physics

A short review about nonassociative algebraic systems (mainly nonassociative algebras) and their physical applications is presented. We begin with some motivations, then we give a brief historical overview about the formation and development of the concept of hypercomplex number system and about some earlier applications. The main directions discussed are the octonionic, Lie-admissible, and quasigroup approaches. Also, some problems investigated in Tartu, the octonionic approach, Moufang–Mal'tsev symmetry, and associator quantization are discussed. This review does not pretend to be complete as the accent is placed on ideas and not on the techniques, also the references are quite sporadic (there are many authors and results mentioned in the text without references).     

How to Use the First FTC

<正>At the last time,we’ve learned the First Part of the Fundamental Theorem of Calculus.It shows how indefinite integration and definite integration are related.In the other words,it shows how anti-derivative and the area are related.Today,you’ll deeply understand the First FTC by using it.     

在微积分教学中如何处理好数学与物理相互渗透

通过一些具体例子,讨论在微积分教学过程中如何体现物理与数学的相互渗透.从而促进学生对微积分基本思想的深入理解.     

引导学生从掌握本质中提高学习兴趣

在工科数学分析课程的教学中,对一些经典内容进行了针对性处理,加强了课程知识的前后联系,提高了学生的学习兴趣和效果.     

Students Talk About Prime: What We Heard About Definitions

This study examines data from college students who worked in pairs to make decisions about a list of potential definitions of prime number. Analysis focused on the evidence each student pair cited when they decided whether or not a statement could be used as a definition for prime number. The purpose of this paper is to describe patterns in the ways students used the evidence they cited. Findings suggest that students attend to important features of mathematical definitions, with some students giving preference to usability and others giving preference to definitions that are unambiguous.     

如何利用单纯形表上的信息

本文分析了求解线性规划的基本方法－－单纯形法所使用的单纯形表，将表中所提供的信息分为直接信息和间接信息两类，论述了如何充分利用这些信息的方法。例如如何由最终表求原问题、如何利用表中的数据互相推演和校正等。这是一篇教学经验的总结，对初学者可能有一定的帮助。     

Listening to Students: How I Came to Love My Low-Residency Program

High-profile technology-transfer success stories are especially seductive to institutional leaders in today's economic climate, creating the impression that tomorrow's Gatorade, Taxol, and Google will occur on “my” campus. But longitudinal research of technology-transfer revenue and cost patterns, presented in the form of odds ratios for profitability (i.e., excess revenues available for reinvestment), provides new evidence that this belief is largely unsubstantiated. Universities that engage in less than about $200 million in research and development (R&;D) activity per year, develop fewer than 20 licenses per year, and/or employ fewer than five licensing professionals, confront substantially lower chances for financial success than do those above these output points. For those with a scale of operation above these levels, the marginal returns on higher R&;D investment, licensing, and staffing falls substantially, reaching an odds-for-financial-success maximum of 65 percent. Combined with data indicating that at least five years are required to realize financial success and that the odds for success fall substantially after that point, we argue that a shift in emphasis from revenue generation to the development of university/industry relationships and cost-containment efforts are both needed to meet higher education's social contract to contribute to the public good.     

Single-sex Classes: Female Physics Students State Their Case

Since the passage of Title IX in 1972, gender equity has been addressed through means that reflect inclusion and integration by gender. Recent Supreme Court decisions such as the one deeming the Virginia Military Institute's admission policies to be unlawfully discriminatory against women suggest a reinforced and perhaps narrowed interpretation of appropriate means for attaining gender equity in public schools. This case and others also suggest that publicly funded single-sex programs may be in jeopardy. This study examines data collected from a girls-only physics class in a public coeducational high school. Interview and observation data from this class, as well as from a coeducational physics class taught by the same teacher, illustrate that the girls in the single-sex class made substantial gains in both academic achievement and in perceptions of themselves as competent learners of science.     

哑运算的概率解释

利用随机变量的矩以及期望运算,给出了哑运算一种简单、自然的概率解释,并且得到了Abel恒等式的一个广泛哑运算证明.     

A White-Noise Approach to Stochastic Calculus

During the past 15 years a new technique, called the stochastic limit of quantum theory, has been applied to deduce new, unexpected results in a variety of traditional problems of quantum physics, such as quantum electrodynamics, bosonization in higher dimensions, the emergence of the noncrossing diagrams in the Anderson model, and in the large-N-limit in QCD, interacting commutation relations, new photon statistics in strong magnetic fields, etc. These achievements required the development of a new approach to classical and quantum stochastic calculus based on white noise which has suggested a natural nonlinear extension of this calculus. The natural theoretical framework of this new approach is the white-noise calculus initiated by T. Hida as a theory of infinite-dimensional generalized functions. In this paper, we describe the main ideas of the white-noise approach to stochastic calculus and we show that, even if we limit ourselves to the first-order case (i.e. neglecting the recent developments concerning higher powers of white noise and renormalization), some nontrivial extensions of known results in classical and quantum stochastic calculus can be obtained.     

Understanding How Students Develop Mathematical Models

in this article, we discuss findings from a research study designed to characterize students' development of significant mathematical models by examining the shifts in their thinking that occur during problem investigations. These problem investigations were designed to elicit the development of mathematical models that can be used to describe and explain the relations, patterns, and structure found in data from experienced situations. We were particularly interested in a close examination of the student interactions that appear to foster the development of such mathematical models. This classroom-based qualitative case study was conducted with precalculus students enrolled in a moderate-sized private research university. We observed several groups of 3 students each as they worked together on 5 different modeling tasks. In each task, the students were asked to create a quantitative system that could describe and explain the patterns and structures in an experienced situation and that could be used to make predictions about the situation. Our analysis of the data revealed 4 sources of mismatches that were significant in bringing about the occurrence of shifts in student thinking: conjecturing, questioning, impasses to progress, and the use of technology-based representations. The shifts in thinking in turn led to the development of mathematical models. These results suggest that students would benefit from learning environments that provide them with ample opportunity to express their ideas, ask questions, make reasoned guesses, and work with technology while engaging in problem situations that elicit the development of significant mathematical models.     

Understanding How Students Develop Mathematical Models

in this article, we discuss findings from a research study designed to characterize students' development of significant mathematical models by examining the shifts in their thinking that occur during problem investigations. These problem investigations were designed to elicit the development of mathematical models that can be used to describe and explain the relations, patterns, and structure found in data from experienced situations. We were particularly interested in a close examination of the student interactions that appear to foster the development of such mathematical models. This classroom-based qualitative case study was conducted with precalculus students enrolled in a moderate-sized private research university. We observed several groups of 3 students each as they worked together on 5 different modeling tasks. In each task, the students were asked to create a quantitative system that could describe and explain the patterns and structures in an experienced situation and that could be used to make predictions about the situation. Our analysis of the data revealed 4 sources of mismatches that were significant in bringing about the occurrence of shifts in student thinking: conjecturing, questioning, impasses to progress, and the use of technology-based representations. The shifts in thinking in turn led to the development of mathematical models. These results suggest that students would benefit from learning environments that provide them with ample opportunity to express their ideas, ask questions, make reasoned guesses, and work with technology while engaging in problem situations that elicit the development of significant mathematical models.     

学查字典

本文利用层次分析法对查字典的三种方式进行了综合排序 ,此外还从查找时间的长短进行了定量的比较 .