The educational materials for EGCPM consist of five books and assignments written for the program by I. Gelfand and his colleagues.
These books are :
- Method of Coordinates
- Functions and Graphs
- Algebra
- Trigonometry
- Geometry
Two of these books, Functions and Graphs and Method of Coordinates, were written for the Moscow School by Correspondence. They were and remain popular not only among students of this School. It is common to find these books in the home library of parents who want to enhance their children’s curiosity and intellectual interest. These books present basic mathematical concepts to students in a clear and simple form. For this reason they are well suited for independent study allowing children to work on them without their parents’ guidance.
These books have been translated into many languages and are used in schools throughout the world. The English translations, published in 1990 in Birkhauser, are now used in E-GCPM.
The third book, Algebra (published in Birkhauser in 1993), was written in English by I. Gelfand and A. Shen specially for use in EGCPM.
Two additional books Trigonometry (by I. Gelfand, M. Saul) and Geometry (by T. Alekseyevskaya (Gelfand), I. Gelfand) was published in January 2020.
The essential part of the participation in the E-GCPM is the work with the assignments. For each of three levels of E-GCPM there are 5 or 6 assignments, written by T. Alekseyevskaya and I. Gelfand. The assignments consist of detailed explanations on important topics. Some of these topics are chosen from the books; others supplement the books. The assignments also contain samples of important problems together with their solutions, problems for students to solve and instructions for how to proceed. Material from Geometry is already included in assignments.
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The Method of Coordinates is the method of transferring a geometrical image into formulas, a method for describing pictures by numbers and letters denoting constants and variables. It is fundamental to the study of calculus and other mathematical topics. |
The systematic development of this method was proposed by the outstanding French philosopher and mathematician Rene Descartes about 350 years ago. It was a great discovery and very much influenced the development not only of mathematics but of other sciences as well. Even today you cannot avoid the method of coordinates. Any image on the computer or TV, every transmission of the picture from one place to the other uses the transformation of the visual information into numbers – and vice versa.
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Functions and Graphs provides instruction in transferring formulas and data into geometrical form. Thus, drawing graphs is one of the ways to “see” formulas and functions and to observe the way in which the function changes. This skill, to see simultaneously the formula and its geometrical representation, is very important not only for studies in mathematics but in studies of other subjects as well. It will be a skill that will remain with you for the rest of your life, like riding a bicycle, typing, or driving a car. Graphs are widely used in economics, engineering, physics, biology, applied mathematics, and of course, in business. |
