A Research on "Imaging" of Basic Mathematical Terms

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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".