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61.
Meroquinene (1), a key degradation product of quinine and an important intermediate in the preparation of the cinchona and other alkaloids,1 has only recently been synthesized 2 even though attempts were made at its preparation for over thirty years. These early attempts were frustrated primarily by the difficulty encountered in the introduction of a potential vinyl group onto a piperidine ring. Alkylation of 3-car-bethoxy-N-benzoyl-4-piperidone (2) with either phenoxyethyl chloride3 or dimethylaminoethyl chloride (3)4 resulted in exclusive formation of the O-alkylated product, even though alkylation of the presumably analogous 2-carbethoxycyclohexanone with 3 gave nearly equal amounts of C- and O- alkylated materials.4 The use of other piperidone derivatives in this reaction was precluded by the report that attempts to alkylate 3-car-bethoxy-N-alkyl-4-piperidones gave only the quaternary nitrogen product.5  相似文献   
62.
A special topics course dealing with perturbation methods in applied mathematics which was recently taught at Stevens Institute of Technology is described. Since the course enrolment was comprised of undergraduate and graduate mathematics students as well as graduate students in engineering, an unusual course philosophy had to be developed and implemented. The approach taken to achieve this in both teaching techniques and selection of subject matter is discussed in detail. Finally, conclusions are drawn from the students’ and the instructor's experiences with the course which hopefully will be of value to those considering offering special topics courses in the future.  相似文献   
63.
The multinomial theorem and a basic property of multinomial coefficients yield a way of counting the number of chains of coloured beads of a fixed length where each colour can be used repeatedly. This coupled with a simple counting argument forms a concise proof of Fermat's theorem.  相似文献   
64.
During the fifties and sixties in Chile many mathematics graduates of Pedagogical Institutes became university instructors rather than high school teachers as intended. In the late sixties Masters level programmes began giving more advanced training for university mathematics instructors. A ‘modern’ mathematics curriculum including computer science was introduced in the high schools. The first significant attempt to adapt the training of Chilean high school mathematics teachers to the new academic and social realities was begun in 1976 at the State Technical University with the cooperation of Teachers College, Columbia University, and the support of the Organization of American States.

The four‐year programme leads to Licenciatura (Bachelors) in Mathematics and Computer Education. All courses are taught by faculty members of the Department of Mathematics and Computer Science. The three basic areas of instruction are mathematics, computer science, and mathematics education. Funds provided by the O.A.S. have helped to make possible the development of curricular materials in Spanish, and the acquisition of computing and video tape equipment.  相似文献   
65.
An attempt has been made to present an overview of various learning theories keeping in view the psychological aspect of problem solving behaviours of children and to explain the processes by which problem solving skills are acquired and applied. The four important research variables—as described by Lester (task, subject, process and instructional variables)—have been discussed and some research questions have been formulated for further research investigations in the area of problem solving.  相似文献   
66.
The purpose of this article is to delineate procedures for viewing education software intended for use in a mathematics classroom. These procedures are applicable at all levels.  相似文献   
67.
Unlike the case of finite matrices, the product of two infinite matrices may not exist in general. Moreover, for infinite matrices A, B, C the product A(BC) may exist whereas (AB)C may not and, if it exists, A(BC) may not be equal to (AB)C. In this paper some significant instances of associativity and commutativity of products of infinite matrices are presented and some of their useful consequences are derived.  相似文献   
68.
Results of mathematics testing of 14‐year‐olds and college freshmen in the West Bank indicate more substantial variation on the basis of cultural factors than on the basis of gender. In particular, no significant difference in the mathematical abilities of men and women appeared in the college group.  相似文献   
69.
70.
Whereas the Diels-Alder reaction has been in vogue as a facile method of six-membered ring construction for many years, its application to a one-step cis-octalone synthesis was precluded by discouraging, early reports on the conditions required for the interaction of dienes with 2-cyclohexenones and on the yields of the resultant adducts.1,2 It is quite conceivable that these observations were responsible in part for the minimization of use of an otherwise attractive route toward angularly alkylated six-membered polycycles in the field of steroid total synthesis. The discovery of Lewis acid catalysis of the cycloaddition of α, β-unsaturated carbonyl compounds3 has rekindled interest in the above reactions.4 The following discussion illustrates octalone  相似文献   
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