I remember myself when 5-6 years old. It was a sultry summer and I was with the village boys. We were hiding in the thickets of the Kusak River, which flows into the Tokrau. The Karshyga valley stretched under the Karashoky mountain. With its water, my father and other villagers irrigated small fields where Akbidai wheat and several varieties of millet were grown. We spent the winter on the banks of the Balkhash. At one time we lived on the Tagyrshik peninsula, and then they built a winter quarters in the populous Deresin region. They ate fish, which they caught with a special fishing rod.

My uncle took me to the village of Karabulak, to the teacher Khatim Nigmatullin, but he didn't want to take me into school since we were three months late. While negotiations were going on, I was in the classroom and listened as the teacher gave the students a problem about three metres of chintz. By this time, I already knew that "a metre is a forty-millionth part of the earth's meridian passing through Paris." Having asked permission to speak, I explained how to solve the problem. Nigmatullin was surprised ... and accepted me as a pupil.

It has been a long time since Kazakh departments were opened in the pedagogical institutes of Kazakhstan and in the physics and mathematics faculties of the Kazakh University. Thousands of students in these departments, including part-time students, listen to lectures on higher mathematics in the Kazakh language.

Despite the fact that these departments have been around for a long time, there is still no textbook or manual on mathematics in Kazakh. That is why students studying in Kazakh departments face serious difficulties.

Of course, thousands of Kazakh students demand that textbooks on mathematics be in their mother tongue. In order to meet at least some of these requirements, the author offers one of the branches of higher mathematics - a course of mathematical analysis. This book is based on the author's work for many years at the Kazakh Pedagogical Institute named after Abai and his lectures on mathematical analysis at the faculties of physics and mathematics of the Kazakh University named after S M Kirov.

Topics covered in the book: introduction to analysis, differential calculus, integral calculus, theory of series, functions of polynomials, theory of multiple integrals and curvilinear integrals. This course differs significantly from Russian textbooks in terms of layout and presentation. First of all, the amount of mathematical training of young people from secondary schools in the country and the amount of time allocated for analysis of the curriculum were taken into account. In addition, the interests of part-time students, secondary school teachers, students of technical universities with mathematical analysis are also considered. In writing the book, the author draws on his many years of experience in teaching mathematical analysis.

This clearly written text is entirely in the Kazak language. It is at about the level of Courant's 'Calculus'. The style and pace of development appear to be suitable for undergraduate university study. The six principal divisions are: Introduction to analysis; Differential, integral calculus of functions of one variable; Theory of series; Differential, integral calculus of functions of several variables. Exercises are given at the end of most chapters and a list of errata is included.

The book deals with a relatively new branch of the theory of differential equations. A starting point for the investigation of systems of countably many ordinary differential equations was the work "On Infinite Systems of Differential Equations" by A N Tikhonov, in which existence and uniqueness theorems for such systems have already been proved. Works by K P Persidskii, M A Krasnoselskii, M G Krein and investigations by the two authors of the present monograph contributed significantly to further development. The content is divided into 10 chapters. Chapters 6-10 contain numerous original results from both authors, many of which are published here for the first time. The first two chapters are introductory. They contain some fundamentals from functional analysis that will be needed later and some information about infinite systems of algebraic equations.

This is an elementary text concerning the mathematical modelling of physical phenomena. The problems considered by the author are either in classical mechanics, electromagnetic theory, or control of systems. In the introduction the author expresses his viewpoint concerning the interplay between physics and mathematics which is close to that expressed by Freeman J Dyson in his lecture to the American Mathematical Society (1972). The format of the book is fairly uniform. First a problem is discussed, a simple mathematical model follows, and shortcomings of that model are discussed. The mass-spring system expressed by Newton's law $m\ddot x + b\dot x +cx=0$ is later replaced by a nonlinear system containing a cubic term, as the Krylov correction is inserted (for a real spring). The problem of a flight trajectory is discussed in detail, with the physical assumptions clearly underlying the derivation of the basic equations of motion. Problems of acoustics, Maxwell's equations, Pontryagin's principle are all introduced in a fairly informal manner. This inexpensive paperback is written for undergraduates in various areas of technology or science as a broad first introduction to the art of mathematical modelling.

In addition to huge scientific research activity, Academician O A Zhautykov always paid constant attention to the training of personnel in mathematics and mechanics. Under his leadership, fifteen candidate dissertations were defended. For more than fifty years he has been continuously teaching. His interesting, deeply informative and skilfully delivered lectures were listened to in the student auditoriums of the Kazakh Pedagogical Institute, the Kazakh State University, the Kazakh Polytechnic, and the Kazakh Women's Pedagogical Institute. Based on many years of experience in teaching various topics of mathematics in universities, he wrote the first most complete textbook on mathematical analysis in the Kazakh language, published in 1958. At one time, this was an event in the life of the higher education system in Kazakhstan. As a result, thousands of Kazakh boys and girls had the opportunity to learn and study in their own language from the inexhaustible treasures of mathematics. His experience in creating a textbook in the Kazakh language contributed to the emergence of similar textbooks in national languages in a number of Union republics. At the same time O A Zhautykov was known as a specialist in the history and methodology of mathematics and a consistent populariser of mathematical knowledge.