Such military schools were established during the war, in 1943, in order to revive the old traditions of the former Russian Cadet Corps. A cadet, training to be an army officer in future, was supposed to get a thorough education and a proper up-bringing. In addition to the usual high school curriculum, the Suvorov School offered such subjects as the history of diplomacy, dancing, and higher mathematics.

Here is an example of how we studied higher mathematics. Lieutenant Georgii Ivanovich Bobylev taught mathematics to our platoon. I see now that he was an excellent teacher. His lessons were fascinating and joyful. Once we were not able to differentiate an intricate expression. Calling us slackers, he started explaining the rules of differentiation once again. While he was writing on the blackboard and we were listening to him quietly, our platoon joker, Gena Emel'yanov, purposely whispered so that everyone in the class was able to hear: "Engels said that even a monkey can be trained to differentiate." "But I also can integrate," replied the teacher, thus accepting the joke. By the end of the semester, announcing the grades, he recalled this monkey. While reading out Gena's grades he said: "Emel'yanov - four, four, four," then with a smile he counted the grades: "One, two, three, hence Emel'yanov gets 'three'." Of course, the genuine grade was "four."

In my first year at Moscow State University I was fortunate to attend an unusual seminar. It was an optional beginners' seminar on function theory - "Circle of Freshmen," managed by Aleksandr Semenovich Kronrod, then a young Doctor of Science, witty and friendly. He at once became our favourite and we called him simply Sasha as he requested. ... At that time, seminars for younger students were supplementary to the curriculum: students were reporting on the topics of basic courses. Kronrod's seminar had a different style. It was a training seminar: during the first year no reports were presented, instead all material was offered in the form of exercises - we had to prove even the principal theorems ourselves. We met once a week, but the preparations required several hours every day. Therefore, the number of participants soon reduced very significantly. However, the seminar turned out to be very helpful for those who participated in it. After a year the circle grew into a full scale research seminar. ... At the beginning of my first year at the university I became acquainted with Lev Semenovich Pontryagin. I had learned about him from the tales by Georgii Ivanovich who had attended the university during the same years as Pontryagin and knew him well. Lev Semenovich was an interesting interlocutor. Once I asked him how to study mathematics. He answered that it was very easy, one should just study it (mathematics) incessantly, while the choice of the particular subject was not of much importance to start with. This supported my decision to attend Kronrod's seminar. Such reassurance was necessary because the seminar was leaving little time for other studies, and there was a certain risk of failing the semester exams.

In the fifth year at the university, having listened to Pontryagin's course on continuous groups, I was attracted to topology. For a year I attended the Seminar of Pavel Sergeevich Aleksandrov.

The central theme of this tract, a theme with which students of convex figures have long been familiar, is the desirability of attaching to a subset of Euclidean $n$-space, and also to a function of $n$ real variables, a string of $n + 1$ quantities $v_{k} (k = 0, 1, ... , n)$, whose values provide suitably independent items of useful information about the set, or about the function. The classical notions of $k$-dimensional measure of a set, and of $k$-dimensional total variation of a function, are inadequate in this respect ... In regard to the main theme of the tract, the particular definitions of the $v_{k}$ adopted by the author are natural and interesting, and they are reasonably motivated by their applications. ...

Vitushkin's interest in similar themes [to his 1955 book] did not only have an intrinsically mathematical basis. He was enthusiastically and quite professionally concerned with problems of electrical engineering .... His household musical apparatus was for many years an object constantly in a state of being perfected and an object of pride. This gave rise to an interest in problems of sound recording. During his university years he took piano lessons and achieved moderate success. Electrical engineering, sound recording, and a passion for music all contributed to an interest in the problem of coding and transmission of signals. This interest was useful to him when, in 1957, after completing his graduate course work, Vitushkin began to work in the Institute of Applied Mathematics of the Academy of Sciences, where he was concerned not only with pure science but also with technological developments.

One of the central results of the doctoral dissertation and the monograph is a lower bound for the complexity of an algorithm of a general form that realizes an approximation to the elements of a compact function space ...

Andrei Nikolaevich [Kolmogorov] advised me to take a post-graduate course at the Steklov Mathematical Institute so that later on I would be able to get a research position there. On Kolmogorov's recommendation, Ivan Matveevich Vinogradov invited me for an interview. The interview was going smoothly until Vinogradov learned that I was Kronrod's student. The conversation then took an undesirable turn. Serge Mikhalovich Nikolski, who was also present there, tried to support me. However, Ivan Matveevich cut short my visit, giving his toothache as an excuse. When I left the room he said to Nikolski: "Never mind. He has nowhere else to go if not to us." [And] it did turn out his way. I became a post-graduate at the university and got a position at the Institute only eleven years later. This example shows that Vinogradov's position towards Jews left much to be desired. In other aspects he was an adequate head of the Institute and much respected, especially for his straightforwardness and consistency.

We will discuss one well-known problem of information theory, the problem which at present arises in various branches of radio engineering. We mean the problem of coding signals with finite spectrum. By way of an example, we consider how such problems arise, what comprises their mathematical content, and what conclusions can be drawn from results obtained. We will present an estimate of the length of codes for signals with finite spectrum and discuss it in connection with the problems of sound recording.

Raising of the question.
Of the sound recording techniques the most widely used method is the so-called analogue method. When using this method a signal to be retained is recorded in its natural form without any preceding transformations. This system of recording is remarkable for its simplicity. The system's disadvantage is the impossibility of defending signals from interference. All defects of recording and reproducing devices, the inhomogeneity and ageing of materials and the like lead to distortions in reproducing.

Another method of recording in which we are interested, the digital one, consists of the following: The signal is transformed into a discrete code, the code of the signal is recorded and, in order to be reproduced, it is again transformed into its natural continuous form. As far as this system is concerned, there are many ways of protecting signals from various sorts of noises. But in sound reproduction this system is not used because the existing schemes of coding still remain unacceptably complex.

Successful development of a digital recording system requires the construction of a handy mathematical model of sound signals and the discovery of simple schemes of coding. The first question arising is: How long must the codes be for the signals to be reproduced with a desirable accuracy? The qualitative estimate obtained seems encouraging.

On 9 May 2004, at the age of 72, the outstanding mathematician, the acknowledged leader in complex analysis, member of the Editorial Board of our journal [Matematicheskie Zametki], Full Member of the Russian Academy of Sciences Anatolii Georgievich Vitushkin died suddenly and unexpectedly.

To A G Vitushkin we owe deep and fundamental results in various branches of contemporary real and complex analysis, approximation theory, and complex geometry. He obtained theorems on the impossibility of expressing smooth functions of several variables in terms of superpositions of smooth functions of a smaller number of variables, which is one of the most prominent achievements toward the solution of the 13th Hilbert problem, while his estimates of the complexity of algorithms for calculating and approximating functions of various classes have been incorporated into textbooks on computational methods and mathematical modelling. The Vitushkin criterion for the uniform approximation of holomorphic functions by rational functions has rounded off a century of the development of classical approximation theory in the complex domain and initiated a new period of its development. Vitushkin's results concerning the geometry of real hypersurfaces of multidimensional complex space and the theory of holomorphic mappings between them have led to the creation of new approaches and the development of new methods in multidimensional complex analysis.

A G Vitushkin was the founder and head of a leading scientific school in complex analysis and approximation theory. Fundamental research in multidimensional complex analysis in our country is inseparably linked with his name. A G Vitushkin's deep original ideas and his inspiring personality have exerted influence on practically all scientists who have been working in complex analysis during the past forty years. In addition to numerous courses of lectures brilliantly delivered at the Mechanics and Mathematics Department of Moscow University, his extensive and many-sided pedagogical activity encompassed his well-known research seminar on complex analysis and the creation of a remarkable system of math circles and seminars for junior students.

A G Vitushkin's remarkable research results and the scientific school created by him have played, and will continue to play, a crucial role in the development of complex analysis and geometry in the whole world.

The bright image of Anatolii Georgievich Vitushkin will remain in our hearts for ever.