从技击走向审美:中国武术套路特征分析

解题是学好数学基础知识、培养和提高思维能力的重要手段,中学生思维的片面性与表面性影响他们对数学对象理解的真度和深度,通过解题错误可见一斑．研究表明,错误是把新方法与已有知识统一起来的尝试的必然结果,因此,辨认出学生知识联系上的特殊缺陷从而进行针对性引导是研究错解教学的根本目的．有限的考试时间使学生的思维高度紧张,虽然会造成较多失误,但从认知心理学的角度考虑,这种低反应时状态更利于反映考生知识技能的掌握情况和思维倾向,笔者以江苏高三高考模拟题（理）为例加以说明．     

Solving the quadratic assignment problem by means of general purpose mixed integer linear programming solvers

The Quadratic Assignment Problem (QAP) can be solved by linearization, where one formulates the QAP as a mixed integer linear programming (MILP) problem. On the one hand, most of these linearizations are tight, but rarely exploited within a reasonable computing time because of their size. On the other hand, Kaufman and Broeckx formulation (Eur. J. Oper. Res. 2(3):204–211, 1978) is the smallest of these linearizations, but very weak. In this paper, we analyze how the Kaufman and Broeckx formulation can be tightened to obtain better QAP-MILP formulations. As shown in our numerical experiments, these tightened formulations remain small but computationally effective to solve the QAP by means of general purpose MILP solvers.     

ODE solvers and the method of lines

Factors influencing the choice of ODE solver for the numerical solution of PDEs by the method of lines are investigated. The advection—diffusion equation is used to gain insight that is generalized to some classes of nonlinear PDEs. Numerical results for several nonlinear PDEs illustrate the theoretical developments. © 1994 John Wiley & Sons, Inc.     

Learning to be an opportunistic word problem solver: going beyond informal solving strategies

Informal strategies reflecting the representation of a situation described in an arithmetic word problem mediate students’ solving processes. When the informal strategies are inefficient, teaching students to make way for more efficient ways to find the solution is an important educational issue in mathematics. The current paper presents a pedagogical design for arithmetic word problem solving, which is part of a first-grade arithmetic intervention (ACE). The curriculum was designed to promote adaptive expertise among students through semantic analysis and recoding, which would lead students to favor the more adequate solving strategy when several options are available. We describe the ways in which students were taught to engage in a semantic analysis of the problem, and the representational tools used to favor this conceptual change. Within the word problem solving curriculum, informal and formal solving strategies corresponding to the different formats of the same arithmetic operation, were comparatively studied. The performance and strategies used by students were assessed, revealing a greater use of formal arithmetic strategies among ACE classes. Our findings illustrate a promising path for going past informal strategies on arithmetic word problem solving.

     

The honors class: hilbert’s problems and their solvers

Feel like writing a review for The Mathematical Intelligencer? You are welcome to submit an unsolicited review of a book of your choice; or, if you would welcome being assigned a book to review, please write us, telling us your expertise and your predilections.     

Inertial methods for finding minimum-norm solutions of the split variational inequality problem beyond monotonicity

Numerical Algorithms - In solving the split variational inequality problems, very few methods have been considered in the literature and most of these few methods require the underlying operators...     

Parameterized complexity of the weighted independent set problem beyond graphs of bounded clique number

The maximum independent set problem is known to be NP-hard for graphs in general, but is solvable in polynomial time for graphs in many special classes. It is also known that the problem is generally intractable from a parameterized point of view. A simple Ramsey argument implies the fixed-parameter tractability of the maximum independent set problem in classes of graphs of bounded clique number. Beyond this observation very little is known about the parameterized complexity of the problem in restricted graph families. In the present paper we develop fpt-algorithms for graphs in some classes extending graphs of bounded clique number.     

Comparison of two Eulerian solvers for the four-dimensional Vlasov equation: Part I

This paper presents two methods for solving the four-dimensional Vlasov equation on a grid of the phase space. The two methods are based on the semi-Lagrangian method which consists in computing the distribution function at each grid point by following the characteristic curves ending there. The first method reconstructs the distribution function using local splines which are well suited for a parallel implementation. The second method is adaptive using wavelets interpolation: only a subset of the grid points are conserved to manage data locality. Numerical results are presented in the second part.     

Symplectic boundaries: creating and destroying closed characteristics

((Without abstract.)) Submitted: February 1996     

Comparison of two Eulerian solvers for the four-dimensional Vlasov equation: Part II

In this second part, we carry out a numerical comparison between two Vlasov solvers, which solve directly the Vlasov equation on a grid of the phase space. The two methods are based on the semi-Lagrangian method as presented in Part I: the first one (LOSS, local splines simulator) uses a uniform mesh of the phase space whereas the second one (OBI, ondelets based interpolation) is an adaptive method. The numerical comparisons are performed by solving the four-dimensional Vlasov equation for some classical problems of plasma and beam physics. We shall also investigate the speedup and the CPU time as well as the compression rate of the adaptive method which are important features because of the size of the problems.     

A continuation principle for Fredholm maps I: theory and basics

We prove an abstract and flexible continuation theorem for zeros of parametrized Fredholm maps between Banach spaces. It guarantees not only the existence of zeros to corresponding equations, but also that they form a continuum for parameters from a connected manifold. Our basic tools are transfer maps and a specific topological degree. The main result is tailor-made to solve boundary value problems over infinite time-intervals and for the (global) continuation of homoclinic solutions.     

Going in Circles: Variations on the Money-Coutts Theorem

Given a polygon A ₁,...,A _n, consider the chain of circles: S ₁ inscribed in the angle A ₁, S ₂ inscribed in the angle A ₂ and tangent to S ₁, S ₃ inscribed in the angle A ₃ and tangent to S ₂, etc. We describe a class of n-gons for which this process is 2n-periodic. We extend the result to the case when the sides of a polygon are arcs of circles. The case of triangles is known as the Money-Coutts theorem.     

Computational thinking and constructionism: creating difference equations in spreadsheets

The invention of the computer has led to the establishment of a new research paradigm, computation, which has recently become more and more popular in scientific exploration. However, computation is not well represented in high school and university curricula in science and engineering, although it applies to a wide range of disciplines beyond computer science and software engineering. In light of the increasing need to provide students with computational education, this paper presents a novel way to develop computational thinking among students. The proposed approach is based on the implementation of Papert's theory of constructionism in electronic spreadsheets. In this approach, students build their knowledge while constructing the difference equation that describes a physical (or engineering) phenomenon, based on specific cases investigated in the spreadsheet. The method does not require the students to write code or perform complex calculations in the spreadsheet and makes it possible to teach advanced subjects at a relatively early stage. The method is demonstrated through contents taken from the secondary and tertiary curricula in mechanics and electromagnetism.