The world of academia: culture & education
Мир университетской науки: культура, образование

BackMagazines

01/01/2015 №1
DEVELOPMENT OF SYMBOLICAL LANGUAGE OF LINEAR ALGEBRA

Ерусалимский Яков Михайлович

Annotation

The paper presents a new system of notation in linear algebra which enables to describe transformations of coordinates of a vector at transition from basis to basis briefly and efficiently. According to the author, advantages of the offered notation system are clearly revealed while writing formulas that establish connection between matrixes of the linear operator at different bases. Experience of using the offered system has shown that students understand linear algebra, this complex section of mathematics, much better and make fewer mistakes while doing tasks. The offered system of notation is used by the author of the article for writing textbooks and teaching manuals.

Key words

symbolical language of mathematics, basis, transition matrix, matrix of the linear operator.

Bibliography

1. Khinchin, A.Yiа., 2001. About educational effect of lessons in mathematics. In: Gleizer, G.D. (Ed.). Mathematics: reader on history, methodology, didactics (рр. 243-263). Moscow: published by Publishing house URAO. (rus) 2. Khinchin, AУа. Op. cit. 3. Markin, J.B. and G.R. Rising, 1973. Some Psychological and Pedagogical Aspects of Mathematical Symbolism. Educational Studies in Mathematics, 5 (1): 255-260. 4. Ainley, J. et al., 2009. Algebraic Thinking and Mathematics. In: Proceedings of CERME 6, January 28th -February 1st 2009. Lyon: 415-419. 5. Kostin, S.V., 2009. Notation system for the basic multiple-valued functions of a complex variable and for their significances. Mathematics in higher education, 7: 39-80. (rus) 6. Khinchin, A.Ya. Op. cit. 7. Prokopchuk, Yu.Yu., A.I. Shirokov and V.V. Umrikhin, 2000. Computer science. Moscow: published by MISIS. (rus) 8. Erusalimsky, Ya.M., 2010. Modern mathematics textbook and requirement to it. Ne

полный текст