In this post, we will see the book Methods Of Solving Problems In High School Mathematics by A. G. Tsypkin; A. I. Pinsky ; V. I. Blagodatskikh (Editor).

About the book

In this educational aid, intended for high-school students, an attempt has been made to classify the problems encountered in high-school mathematics by their solution methods.

It was rather difficult to attain the aim the authors set for them­ selves. On one hand, a detailed classification of problems by methods of solution would require the consideration of a large number of con­ crete problems and, on the other hand, a schematic classification would not yield a useful aid for solving different kinds of problems. There­ fore, alongside a large number of worked problems, the book includes many problems (about 2500) for the reader to solve.

In addition to the traditional problems from the course of high- school mathematics, the book includes methods for solving simple differential and integral calculus problems as well as problems which require the use of coordinates and vector algebra. These sections only include problems whose solutions require knowledge that is beyond the scope of high-school mathematics.

Some problems in the book can only be solved by a combined application of the knowledge from the traditional and new divisions of mathematics. These include, for instance, problems connected with the calculation of limits, derivatives and antiderivatives of functions which must first be simplified by means of identity transformations.

The authors consider all the most frequent methods of solving problems from the high-school course of mathematics. The fact that many problems are not followed by their solutions makes it possible to use the book for preparing for the entrance examinations to higher
educational establishments.

Translated from the Russian by Irene Aleksanova

You can get the book here.

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