A Research on "Imaging" of Basic Mathematical Terms

我们仔细选择了每个领域的数学术语，并从各种来源收集了有关这些术语的信息。从基本数学概念中选择的术语是：“角度”，“重心”，“面积”，“体积”，“集合”，“基数”，“地图”，“等价关系”，“毕达哥拉斯定理”和“同余/相似性”;从分析中选择的术语：“数列”、“等差数列”、“等比数列”、“极限（ε-δ）"、“微分系数”、“导函数”、“切线”、“极值”、“凸性”、“偏微分”、“积分”、“微积分基本定理”;来自几何：“拓扑学”、“不动点定理”、“欧拉特征”、“曲率”、“切平面”和“流形”;以及从代数：“组/环/场”，“代数基本定理”与“同态/同构”从分析领域选择的术语比从其他领域选择的术语多，因为许多接受调查的教授认为，数学术语的成像，特别是分析方面，对于人文社会科学系的大学生是有用的。我们的目标是描述这些术语，而不扭曲其概念轮廓，即使是初中生认为只有基础知识的人也会感兴趣并能理解它们。我们的部分研究成果已经作为品川女子初中的讲座记录在《数学》中介绍，其中使用了我们合作的教材，其中“拓扑学”、“角度”、“重心”、“算术级数”、“几何级数”和“勾股定理”是其主要主题。我们还完成了一个以“微分”、“导函数”、“切线”和“积分”为主题的动画原型。

We made a careful choice of mathematical terms in each field to be imaged and compiled information concerning those terms from various sources.The chosen terms from elementary mathematical concepts are : "angle", "center of gravity", "area", "volume", "set", "cardinality" , "map" , "equivalence relation", "Pythagorean theorem" and "congruence/similarity" ; from analysis : "sequence" , "arithmetic progression", "geometric progression", "limit(ε-δ)", "differential coefficient", "derived function", "tangent line", "extreme value", "convexity", "partial differential", "integral" and "fundamental theorem of calculus" ; from geometry : "topology", "fixed point theorem", "Euler characteristic", "curvature", "tangent plane" and "manifold" ; and from algebra : "group/ring/field", "fundamental theorem of algebra" and "homomorphism/isomorphism".A larger number of terms have been chosen from the field of analysis more than from the other fields because many of the professors surveyed suggested that the imaging of the mathematical terms, especially of analysis, would be useful for those university students who belong to departments of humanities and social sciences.We set our goal at describing those terms, without distorting their conceptual contours, so that even those with only basic knowledge junior high school students are thought to have will be interested in and can understand them. Part of the production of our research has been introduced in Worldly Mathematics as a record of lecture at Shinagawa Women' s Junior High School in which was used the teaching material we collaborated with "topology", "angle", "center of gravity", "arithmetic progression", "geometric progression" and "Pythagorean theorem", as its main topics. We have also completed a prototype of an animation cartoon featuring "differential coefficient", "derived function", "tangent line" and "integral".