一道高等数学题的多种解法

高等数学是理工科院校一门十分重要的公共基础课,在培养和训练学生的创新能力方面起着重要的作用.在高等数学的教学中应注重学生数学思维能力的培养和发散思维的训练.发散思维是创新思维的主要形式之一,而一题多解是发散思维的具体表现.利用导数求极值法,变量代换法,等价变换法,不等式法等给出一道高等数学题的九种解法,以此引导学生去深入探索问题,培养学生的创新思维能力.     

Social constructivism,individual constructivism and the role of computers in mathematics education

By asking the question: “Can computers do mathematics?” this paper investigates the relationship between computers and views of mathematics from both individual and social constructivist perspectives. Although these two perspectives ask many of the same questions, they frame these questions in quite different ways of viewing the interaction between individual, subject matter, culture, and cultural tools (e.g. computers). I argue that whereas social constructivist are more likely to take the position that computers alter the way we do mathematics, individual constructivists would more likely say that computers changes the mathematics that we do. Individual constructivists, by placing mathematics itself within the actions carried out by an individual, provide a theoretical framework that allows for the richness and diversity of student constructions that can expand our understanding of mathematics beyond the bounds of any one particular culture.     

Algebraic structure of association schemes of prime order

Finite groups of prime order must be cyclic. It is natural to ask what about association schemes of prime order. In this paper, we will give an answer to this question. An association scheme of prime order is commutative, and its valencies of nontrivial relations and multiplicities of nontrivial irreducible characters are constant. Moreover, if we suppose that the minimal splitting field is an abelian extension of the field of rational numbers, then the character table is the same as that of a Schurian scheme.     

Decision analysis as a replacement for cost/benefit analysis

Decision analysis has recently been employed to analyse public policy issues, and in contexts where cost/benefit analysis might equally well have been applied. In this paper we examine whether these two techniques are in competition, and if so, which is most fitted for public policy analysis. The intellectual origins of the two techniques are outlined, and different modes of interpretation are identified. The two techniques are compared on several different issues, including their handling of uncertainty, equity and conflicting objectives. It is argued that as an aid to decision-making the approach of decision analysis has advantages over cost/benefit analysis.     

A new rating system for duplicate bridge

We propose a new way to rate individual duplicate bridge players, which we believe is superior to the masterpoint system currently used by the American Contract Bridge League. This method measures only a player’s current skill level, and not how long or how frequently he has played. It is based on simple ideas from the theory of statistics and from linear algebra, and should be easy to implement.One particular issue which can occur within any system proposing to rate individual players using results earned by partnerships is what we call the “nonuniqueness problem”. This refers to the occasional inability for data to distinguish who is the “good player” and who is the “bad player” within particular partnerships. We prove that under our system this problem disappears if either (a) a certain “partnership graph” has no bipartite components, or if (b) every player is required to participate in at least one individual game.Finally, we present some data from a bridge club in Reno, NV. They show that even if (a) and (b) do not hold, our system will provide (unique) ratings for most players.     

Student teachers’ types of probing questions in inquiry-based mathematics teaching with and without GeoGebra

Previous studies have produced several typologies of teacher questions in mathematics. Probing questions that ask students to explain are often included in the types of questions. However, only rare studies have created subtypes for probing questions or investigated how questioning differs depending on whether technology is used or not. The aims of this study are to elaborate on different ways of asking students to give explanations in inquiry-based mathematics teaching and to investigate whether questioning in GeoGebra lessons differs from questioning in other lessons. Data was collected by video recording 29 Finnish mathematics student teachers’ lessons in secondary and upper secondary schools. The lesson videos were coded for the student teachers’ probing questions. After this, categories for the types of probing questions were created, which is elaborated in this paper. It was found that the student teachers who used GeoGebra emphasized conceptual probing questions during the explore phase of a lesson slightly more than the other student teachers.     

Operational Research in Organizations: a Metaphorical Analysis

The range of possible ways in which OR influences and is influenced by the organization in which it takes place is great. These influences will be due in part to the nature of the organization involved and such factors cannot be considered in general. However, other factors will have their roots in the generic processes and character found in OR and organizations. A potentially useful way of investigating these factors is to ask what part OR plays in an organization. The particular view held of organizations and of the behaviour of people within them will determine how this aspect of OR is understood. In this paper Morgan's method of organizational analysis based upon the idea of metaphor is adopted to explore the place of OR in organizations. This approach explicitly uses a multi-faceted style of analysis, which is seen to be preferable to one which is more partial in its treatment of organization.     

两个矩阵分布的信息特征

熵是一个分布的重要信息特征，通过对矩阵变量积分的一些技巧，利用矩阵r分布的特征，本文获得了矩阵F分布和矩阵Beta分布的熵．     

哲学视域下的高等数学“课程思政”

数学作为一门学校教育中历时较长的课程,在培养逻辑思维、规则意识、意志品格等科学素质方面发挥着积极的作用,是其他课程所无法比拟的.多年来,我国的数学教学常常忽视教学体系中蕴藏的丰富的哲学思想,哲学元素没有获得足够的挖掘和应有的重视.在“课程思政”理念的引领下,注重哲学视域下的高等数学“课程思政”教学,对于大学的数学教育工作者为国家培养优秀人才,意义深远.     

Internalist Virtues and Knowledge

What role can intellectual virtues play in an account of knowledge when we interpret those virtues internalistically, i.e., as depending only on internal states of the cognizer? Though it has been argued that internalist virtues are ill suited to play any role in an account of knowledge, I will show that, on the contrary, internalist virtues can play an important role in recent accounts of knowledge developed to utilize externalist virtues. The virtue account of knowledge developed by Linda Zagzebski is intended to be supplemented by her version of the intellectual virtues which require an external success component. John Greco and Wayne Riggs both develop credit accounts of knowledge on which the abilities we use when we get credit for a true belief must be reliable. I examine the similarities between these three accounts of knowledge and demonstrate that internalist virtues fit into these accounts just as well as externalist virtues. Thus, although internalist virtues do not require a reliable connection to truth, they can still play an important role in defining the truth-requiring concept of knowledge.     

A new population seeding technique for permutation-coded Genetic Algorithm: Service transfer approach

Genetic Algorithm (GA) is a popular heuristic method for dealing complex problems with very large search space. Among various phases of GA, the initial phase of population seeding plays an important role in deciding the span of GA to achieve the best fit w.r.t. the time. In other words, the quality of individual solutions generated in the initial population phase plays a critical role in determining the quality of final optimal solution. The traditional GA with random population seeding technique is quite simple and of course efficient to some extent; however, the population may contain poor quality individuals which take long time to converge with optimal solution. On the other hand, the hybrid population seeding techniques which have the benefit of good quality individuals and fast convergence lacks in terms of randomness, individual diversity and ability to converge with global optimal solution. This motivates to design a population seeding technique with multifaceted features of randomness, individual diversity and good quality. In this paper, an efficient Ordered Distance Vector (ODV) based population seeding technique has been proposed for permutation-coded GA using an elitist service transfer approach. One of the famous combinatorial hard problems of Traveling Salesman Problem (TSP) is being chosen as the testbed and the experiments are performed on different sized benchmark TSP instances obtained from standard TSPLIB [54]. The experimental results advocate that the proposed technique outperforms the existing popular initialization methods in terms of convergence rate, error rate and convergence time.     

课堂提问在大学数学教学中的意义

课堂提问是一种有效的教学组织形式,它既是重要的教学手段,又是完美的教学艺术.这篇文章以高等代数的教学为例,阐述了大学数学教学中课堂提问的重要意义.希望对年轻的教师能有所启迪和帮助.     

基于迭代自适应随机决策树的个人信用评估模型研究

信用评估是商业银行控制和防范信贷风险的关键途径.决策树模型较好的直观解释性使其成为当前个人信用评估中的常用模型,但决策树模型存在容易导致过拟合且预测精度有限的问题.通过在决策树模型算法中引入类随机森林随机有放回的抽样模式,运用机器自动循环迭代寻求最优树的建模思想,建立了自适应最优C5.0决策树个人信用评估模型.该模型具有快速收敛特征变量、较好的泛化能力和高预测精度的特点,在实证分析中对商业银行个人信用评估模型质量提升带来比较明显的改进效果.     

C3I系统知识库的类特征模式

在Ｃ３Ｉ系统知识库中引入了条件事件推理规则以及类与特征的概念，并给出了进行动态管理知识库的有效方法。     

Dynamics of knowledge-intensive production: An agency-structure framework

In the vast majority of modern technological and knowledge-intensive production systems, human agency and the structure of social interactions among the human individuals are implicated in each other. While the force of agency drives an individual’s urge to introduce innovation and novelty into production, the force of the structuring interactions demands shared expectations and mutual adaptation for co-creation. In an organizational context, when the objective is to manage production work that is governed by the concurrent interplay of both these forces, one might ask whether the cumulative output of each could be reconciled through the emergence of a stable balance between them over time. In this article, I introduce a framework to study the conditions under which this balance can be attained. Based on a real-life application, I show, in particular, that, while a direct realization of the condition is unlikely in practice, it is possible, nevertheless, to establish indirectly the condition through adjustments of certain parameters relevant to the dynamics of a networked system. The work contributes to the growing body of literature that explores the role of coordination between self-driven activities of individuals and their structure-mediated interactions in an underlying social context.     

不可约特征标和B_π-特征标的对应关系

首先给出 Isaacs著名引理的一个推广 .把其中关于θ和φ分别为 G -不变的和 K -不变的特征标的条件减弱为更为一般的和常见的惯性群关系 IK(θ) =IK(φ) .其次 ,我们证明了当θ为 N的一个 Bπ特征标而φ恰为一个与θ相伴的 Fong特征标时 ,相应的对应关系自动成为 Bπ-特征标和 Fong特征标的对应 .     

Deep Reinforcement Learning for Market Making in Corporate Bonds: Beating the Curse of Dimensionality

ABSTRACT

In corporate bond markets, which are mainly OTC markets, market makers play a central role by providing bid and ask prices for bonds to asset managers. Determining the optimal bid and ask quotes that a market maker should set for a given universe of bonds is a complex task. The existing models, mostly inspired by the Avellaneda-Stoikov model, describe the complex optimization problem faced by market makers: proposing bid and ask prices for making money out of the difference between them while mitigating the market risk associated with holding inventory. While most of the models only tackle one-asset market making, they can often be generalized to a multi-asset framework. However, the problem of solving the equations characterizing the optimal bid and ask quotes numerically is seldom tackled in the literature, especially in high dimension. In this paper, we propose a numerical method for approximating the optimal bid and ask quotes over a large universe of bonds in a model à la Avellaneda–Stoikov. As classical finite difference methods cannot be used in high dimension, we present a discrete-time method inspired by reinforcement learning techniques, namely, a model-based deep actor-critic algorithm.     

Collaborative Curriculum Investigation as a Vehicle for Teacher Enhancement and Mathematics Curriculum Reform

The Missouri Middle Mathematics (M³) Project is an NSF-funded 3-year professional development project involving teacher/administrator teams from districts statewide. Project activities focus on collaborative investigation of emerging reform-based middle school mathematics curricula to support individual and systemic reform. Collaborative review and field-testing of material facilitates awareness and exploration of alternative instructional and assessment strategies and informed decision making. Early indicators of the model's success are reflected in participants’ enthusiasm and professional growth. Project activities stimulate discussions of critical topics including questioning appropriateness of various teaching practices, research about teaching and learning, tracking policies, appropriate assessment models for gauging student learning and the importance of calculators and manipulatives as teaching and learning tools. These discussions transcend curriculum materials being reviewed and serve as a powerful vehicle for professional growth and development for individual teachers and districts.     

Developing mathematical modelling skills: The role of CAS

Mathematical modelling as one component of problem solving is an important part of the mathematics curriculum and problem solving skills are often the most quoted generic skills that should be developed as an outcome of a programme of mathematics in school, college and university. Often there is a tension between mathematics seen at all levels as ‘a body of knowledge’ to be delivered at all costs and mathematics seen as a set of critical thinking and questioning skills. In this era of powerful software on hand-held and computer technologies there is an opportunity to review the procedures and rules that form the ‘body of knowledge’ that have been the central focus of the mathematics curriculum for over one hundred years. With technology we can spend less time on the traditional skills and create time for problem solving skills. We propose that mathematics software in general and CAS in particular provides opportunities for students to focus on the formulation and interpretation phases of the mathematical modelling process. Exploring the effect of parameters in a mathematical model is an important skill in mathematics and students often have difficulties in identifying the different role of variables and parameters This is an important part of validating a mathematical model formulated to describe, a real world situation. We illustrate how learning these skills can be enhanced by presenting and analysing the solution of two optimisation problems.     

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Solar cell is the basic component of satellite photovoltaic panels with complicated redundant system structure. Its reliability plays an important role in the system, and its performance shows a degradation trend over time. In this paper, study is conducted for the solar cell degradation modeling and reliability analysis based on practical testing results. Specifically, we illustrate an accelerated test for the attenuation ratio character test under different accumulative irradiation levels, focusing on the heteroscedasticity of the collected testing data. A heteroscedastic linear model is proposed, and the life distribution of the photovoltaic panel is obtained by using Fiducial method. A numerical example is shown for the purpose of illustration.