Modeling eating disorders in young people

A mathematical model is proposed to simulate the eating disorders of bulimia or anorexia. Earlier models are extended to incorporate the body mass index, which plays a key role in the eating attitude of self thinners. The global existence and ultimate boundedness of solutions of the nonlocal model are proved by using estimates of solutions. The basic reproduction number of eating disorder contagion is shown to be the invasion threshold. The testable linear and nonlinear stability conditions are established by Lyapunov functions. Further numerical simulations are given to reveal how self-forces and peer pressures to be thinner affect the emergence and distributions of eating disorders.     

The Mathematics Writer's Checklist: The Development of a Preliminary Assessment Tool for Writing in Mathematics

The use of writing as a pedagogical tool to help students learn mathematics is receiving increased attention at the college level ( Meier & Rishel, 1998 ), and the Principles and Standards for School Mathematics (NCTM, 2000) built a strong case for including writing in school mathematics, suggesting that writing enhances students' mathematical thinking. Yet, classroom experience indicates that not all students are able to write well about mathematics. This study examines the writing of a two groups of students in a college‐level calculus class in order to identify criteria that discriminate “;successful” vs. “;unsuccessful” writers in mathematics. Results indicate that “;successful” writers are more likely than “;unsuccessful” writers to use appropriate mathematical language, build a context for their writing, use a variety of examples for elaboration, include multiple modes of representation (algebraic, graphical, numeric) for their ideas, use appropriate mathematical notation, and address all topics specified in the assignment. These six criteria result in The Mathematics Writer's Checklist, and methods for its use as an instructional and assessment tool in the mathematics classroom are discussed.     

The optimal runner on the royal road

Assuming a simple biophysical model and using the Carathéodory method, we find the optimal strategy to run or swim a race.     

The royal couple conceals their mutual relationship: A noncoalescent toeplitz flow

There exists a regular Toeplitz sequence over a finite alphabet, such that its orbit-closure in the shift system is not topologically coalescent. The notion of a Toeplitz array is introduced. Supported by KBN grant 2 P 03A07608.     

高等数学教学方法的改革实践与回顾

高等数学在高校的课程体系中占有十分特殊的地位.高等数学的知识和方法,业已成为当代大学生知识、能力结构中不可或缺的重要组成部分.开展高等数学的教学改革,特别是开展教学内容、教学方法与学习方法的整合研究,是提高高等数学教学质量,实现高校人才培养战略目标的需要.     

基金使用的数学模型

对 2 0 0 1年全国大学生数学建模竞赛 C题作了详细的分析 ,给出了第 i( i=1 ,2 ,… ,n-1 )年末发放的奖金额需存的金额为 Mxi 和 Mxn( Mxn 到第 n年末的本息用于发放第 n年末的奖金后剩余原本金 M)的最佳投资方案 ,用线性代数和概率论的基础知识建立了数学模型 ,并给出了用于求解的 MATLAB程序 .     

Chinese and English Mathematics Language: The Relation Between Linguistic Clarity and Mathematics Performance

In Study 1, 48 judges rated the clarity of Chinese, English, and "Chinglish" (Chinese words translated into English) mathematical words-for example, the Chinglish version of the Chinese word for quadrilateral is "four-side-shape." Native Chinese-speaking judges achieve greater agreement on the relative clarity of Chinese words than do native English-speaking judges on the relative clarity of English words. More Chinese words are rated clear than are English. Chinglish mathematical words tend to be rated more clear than English. The inherent compound word structure of the Chinese language seems well suited to portray mathematical ideas.

In Study 2, we examined the relations among the clarity of Chinese mathematical terms, U.S. urban junior high school students' Chinese reading ability, and their mathematics performance. There is a strong correlation between Chinese reading ability and performance on test items with mathematics words rated clear by Chinese judges. The relative clarity of mathematical terms in the Chinese language may contribute to Chinese-speaking students' understanding of mathematics and to superior mathematics performance.     

Chinese and English Mathematics Language: The Relation Between Linguistic Clarity and Mathematics Performance

In Study 1, 48 judges rated the clarity of Chinese, English, and “Chinglish” (Chinese words translated into English) mathematical words-for example, the Chinglish version of the Chinese word for quadrilateral is “four-side-shape.” Native Chinese-speaking judges achieve greater agreement on the relative clarity of Chinese words than do native English-speaking judges on the relative clarity of English words. More Chinese words are rated clear than are English. Chinglish mathematical words tend to be rated more clear than English. The inherent compound word structure of the Chinese language seems well suited to portray mathematical ideas.

In Study 2, we examined the relations among the clarity of Chinese mathematical terms, U.S. urban junior high school students' Chinese reading ability, and their mathematics performance. There is a strong correlation between Chinese reading ability and performance on test items with mathematics words rated clear by Chinese judges. The relative clarity of mathematical terms in the Chinese language may contribute to Chinese-speaking students' understanding of mathematics and to superior mathematics performance.     

数学通报启事

改革开放以来,我国的教育工作者走出国门,国外的老师和教育研究人员也不断地来我国访问,国际间的交往日趋频繁.