以培养创新型人才为目标 大力推进大学数学教学方法改革

分析了我国大学数学教学方法改革的现状,介绍了我们在两个试点班上以培养创新型人才为目标,进行教学方法(含考核方法)改革的理念和采取的具体措施,包括将教学方法改革与传授数学中的重要思想方法、按层次分流培养、教学内容改革(含实验教学),考核方法改革等结合起来,并将课堂讲授、习题课、讨论课以及撰写小论文(或读书报告)多种环节相结合.     

“应用数学基础”课程改革的思考

本探讨了“应用数学基础”课程改革的必要性，从教师队伍建设、教学内容改革、教学手段与教学方法改革、课程教材建设和教学实战等五个方面提出了我们的想法。     

工科线性代数教学改革方案的研究与实践

我校对工科线性代数教学内容体系和教学方法的改革开始于1990年，近三年在国家教委面向21世纪工科数学内容体系改革精神指导下，我们的改革方案得到进一步的完善，在深入实践的基础上已形成了切实可用的新教材，CAI软件和教学辅导书。     

高等代数课程的教学改革

讨论高等代数的教学内容以及教学方法的改革问题,介绍我们在实践中创立的立体教学法,着重阐述俯察解析几何、仰观近世代数、联系数学分析以及半双语教学法四个基本方法.     

高等代数课程的教学改革

讨论高等代数的教学内容以及教学方法的改革问题,介绍我们在实践中创立的立体教学法,着重阐述俯察解析几何、仰观近世代数、联系数学分析以及半双语教学法四个基本方法．     

《数学实验》课程建设及分层次教学与实践

主要介绍在本科一年级讲授《高等数学》课程时同步分层次开展《数学实验》课程教学的教学模式、教学内容、教学方法与改革、课程考核办法,以及我们对《数学实验》课程的认识和建设过程.     

工科线性代数教学改革方案的研究与实践

工科线性代数教学改革方案的研究与实践张新育王锦玲王树生刘江国（郑州工业大学数理力学系，郑州４５０００２）一、引言我校对工科线性代数教学内容体系和教学方法的改革开始于１９９０年，近三年在国家教委面向２１世纪工科数学内容体系改革精神指导下，我们的改革方案...     

贯彻教学基本要求 改革高等数学教学

贯彻教学基本要求　改革高等数学教学丁文有（牡丹江大学，牡丹江市１５７０１１）由国家教委颁布的＂高等学校工程专科高等数学课程教学基本要求＂是我们进行高等数学教学的指导性文件，是修订教学大纲、确定教学内容、改革教学方法、进行教学质量检查与评估的基本依据。...     

高中数学新课标下立体几何教学的研究

立体几何是高中数学的重要内容之一,在新课程改革中,立体几何这部分课程的改革力度很大.如何顺应新课程改革,适应新教学内容、教学方法、教学手段等对于我们提高教学质量是很重要的.教师能否适应新课程改革并主动参与实施新课程是改革能否成功的关键.本文从由生活到抽象、动手实践获得直接经验、空间想象力的培养这三个方面来谈谈新课程改革中立体几何的教学的认识与实施.     

数学分析课程教学改革探讨

本初步讨论了数学分析课程教学内容改革，问题的合理设计，教学方法及手段改革，考核形式改革等方面的内容。     

General procedures leading to correlated equilibria

Hart and Mas-Colell [2000] show that if all players play regret-matching strategies, i.e., they play with probabilities proportional to the regrets, then the empirical distribution of play converges to the set of correlated equilibria, and the regrets of every player converge to zero. Here we show that if only one player, say player i, plays with these probabilities, while the other players are not too sophisticated, then the result that player is regrets converge to zero continues to hold. The condition of not too sophisticated essentially says that the effect of one change of action of player i on the future actions of the other players decreases to zero as the horizon goes to infinity. Furthermore, we generalize all these results to a whole class of regret-based strategies introduced in Hart and Mas-Colell [2001]. In particular, these simplify the conditional smooth fictitious play of Fudenberg and Levine [1999].Received: May 2004This is a revision of the authors M.Sc. thesis, May 2000.The author thanks Professor Sergiu Hart for his help and guidance, and the Associate Editor and an anonymous referee for their comments. I am grateful to my parents and wife for everything.     

Mutational equations in metric spaces

This paper summarizes an extension of differential calculus to a mutational calculus for maps from one metric space to another. The simple idea is to replace half-lines allowing to define difference quotients of maps and their various limits in the case of vector space by transitions with which we can also define differential quotients of a map. Their various limits are called mutations of a map. Many results of differential calculus and set-valued analysis, including the Inverse Function Theorem, do not really rely on the linear structure and can be adapted to the nonlinear case of metric spaces and exploited. Furthermore, the concept of differential equation can be extended tomutational equation governing the evolution in metric spaces. Basic Theorems as the Nagumo Theorem, the Cauchy-Lipschitz Theorem, the Center Manifold Theorem and the second Lyapunov Method hold true for mutational equations.This work was motivated by evolution equations of tubes in visual servoing on one hand, mathematical morphology on the other, when the metric spaces are power spaces. This paper begins by listing some consequences of general theorems concerning mutational equations for tubes.     

Some remarks on indestructibility and Hamkins’ lottery preparation

In this paper, we first prove several general theorems about strongness, supercompactness, and indestructibility, along the way giving some new applications of Hamkins lottery preparation forcing to indestructibility. We then show that it is consistent, relative to the existence of cardinals < so that is supercompact and is inaccessible, for the least strongly compact cardinal to be the least strong cardinal and to have its strongness, but not its strong compactness, indestructible under -strategically closed forcing. Mathematics Subject Classification (2000):03E35, 03E55     

特征选择方法在信用评估指标选取中的应用

在信用评分模型中所运用的指标变量对模型的表现有重要的影响,指标选取方法的科学化规范化水平有待于进一步提高。本文研究了机器学习领域的特征选择方法在定量确定信用评分模型指标体系上的应用。以实际信用评估问题为例,对四种特征选择方法(ReliefF方法、基于相关性的方法、基于一致性的方法和包裹性)进行了比较试验,验证了特征选择方法可以在精简性、速度和准确率三个方面提高信用评分模型的表现。其中基于一致性的方法和包裹法表现优于Reli-efF方法和基于相关性的方法。     

Maximal Effective Bandwidth of Constrained Traffic

We investigate the worst possible behavior of a stationary traffic source when the traffic emanating from it is required to meet certain constraints. Specifically, the peak rate of the source is required not to exceed a level and realizations must obey a leaky bucket constraint with bucket size and leak rate . The worst case source is considered to be the one with the largest effective bandwidth, a concept which arises in the large deviation theory of queueing networks and governs the asymptotic loss rate when a large number of sources send traffic to a single server queue. We conjecture the form of the worst case traffic in general and prove the conjecture for the special case when T, the time-scale parameter of the effective bandwidth, is less than both /(–) and /, the times taken respectively to fill and empty the leaky bucket.     

Types in a mixed language system

As a support for writing software, a comprehensive set of problem oriented languages appears preferable to any so-called universal language, as soon as static checking is sufficient to ensure type correctness of the mixed language program. We lay the basis for a mixed language system where this requirement is fulfilled. The general outline of the system is first sketched. Detailed consideration is then given to our basic constructs for establishing communication between languages, namely standard types and foreign types. Abstract types, such as defined in CLU, are finally shown to be a particular class of foreign types.     

van Kampen theorems for toposes

In this paper we introduce the notion of an extensive 2-category, to be thought of as a “2-category of generalized spaces”. We consider an extensive 2-category equipped with a binary-product-preserving pseudofunctor , which we think of as specifying the “coverings” of our generalized spaces. We prove, in this context, a van Kampen theorem which generalizes and refines one of Brown and Janelidze. The local properties required in this theorem are stated in terms of morphisms of effective descent for the pseudofunctor . We specialize the general van Kampen theorem to the 2-category of toposes bounded over an elementary topos , and to its full sub 2-category determined by the locally connected toposes, after showing both of these 2-categories to be extensive. We then consider three particular notions of coverings on toposes corresponding, respectively, to local homeomorphisms, covering projections, and unramified morphisms; in each case we deduce a suitable version of a van Kampen theorem in terms of coverings and, under further hypotheses, also one in terms of fundamental groupoids. An application is also given to knot groupoids and branched coverings. Along the way we are led to investigate locally constant objects in a topos bounded over an arbitrary base topos and to establish some new facts about them.     

Special Varieties and Classification Theory: An Overview

Lang's conjectures link the geometric, hyperbolic, and arithmetic properties of projective complex varieties of general type. We propose here an extension of these conjectures to arbitrary projective varieties X. This extension rests on the notion of special variety. This class contains manifolds either rationally connected or with vanishing Kodaira dimension. We further construct for any X its core, which is a fibration c _X : XC(X) with general fibre special and orbifold base of general type. This fibration seems to permit us to decompose X according to the dichotomy special vs general type, and not only leads to the above-mentioned extension of Lang's conjectures but also to a simple global view of classification theory.     

Quadratic prediction problems in multivariate linear models

Linear and quadratic prediction problems in finite populations have become of great interest to many authors recently. In the present paper, we mainly aim to extend the problem of quadratic prediction from a general linear model, of form , to a multivariate linear model, denoted by with . Firstly, the optimal invariant quadratic unbiased (OIQU) predictor and the optimal invariant quadratic (potentially) biased (OIQB) predictor of for any particular symmetric nonnegative definite matrix satisfying are derived. Secondly, we consider predicting and . The corresponding restricted OIQU predictor and restricted OIQB predictor for them are given. In addition, we also offer four concluding remarks. One concerns the generalization of predicting and , and the others are concerned with three possible extensions from multivariate linear models to growth curve models, to restricted multivariate linear models, and to matrix elliptical linear models.     

Langevin-Type Models II: Self-Targeting Candidates for MCMC Algorithms*

The Metropolis-Hastings algorithm for estimating a distribution is based on choosing a candidate Markov chain and then accepting or rejecting moves of the candidate to produce a chain known to have as the invariant measure. The traditional methods use candidates essentially unconnected to . We show that the class of candidate distributions, developed in Part I (Stramer and Tweedie 1999), which self-target towards the high density areas of , produce Metropolis-Hastings algorithms with convergence rates that appear to be considerably better than those known for the traditional candidate choices, such as random walk. We illustrate this behavior for examples with exponential and polynomial tails, and for a logistic regression model using a Gibbs sampling algorithm. The detailed results are given in one dimension but we indicate how they may extend successfully to higher dimensions.