ON THE PEDAGOGICAL AND SCIENTIFIC ACTIVITIES OF THE DEPARTMENT OF HIGHER MATHEMATICS AT TOMSK POLYTECHNIC INSTITUTE

S. P. KUZNETSOV, G. L. KALINICHENKO

(Presented by the Department of Higher Mathematics)

The birthday of the Department of Higher Mathematics should be considered October 22, 1900, when Vladimir Leonidovich Nekrasov delivered the first lecture in mathematics, with which academic life began at the Tomsk Technological Institute. The institute’s first director, E. L. Zubashev, taking into account the major role of the department in the training of engineering personnel in Siberia, invited to work in the department the prominent mathematician of that time Fedor Eduardovich Molin and the professors V. P. Alekseevsky and N. N. Saltykov. As a teacher of higher mathematics, privat-docent of Kazan University V. L. Nekrasov was invited; in the early period he also directed the pedagogical process in mathematics and theoretical mechanics at the institute, since F. E. Molin arrived in Tomsk at the end of January 1901, and Alekseevsky and Saltykov considerably later.

In the first years of the institute’s existence, a course system of instruction was in place. In order to pass into the second year, a student was required to pass examinations in analytic geometry and infinitesimal calculus, Part I, so that he could go on to study general engineering disciplines. For the purpose of better assimilation of the material, the department introduced practical classes in higher mathematics, which at that time was a pedagogical innovation. To conduct the practical classes, in addition to Molin and Nekrasov, young engineers and teachers from other departments were brought in, who were preparing to occupy professorial positions in technical disciplines. In order to coordinate the conduct of practical classes, at the beginning of 1903 lithographed collections of problems in infinitesimal calculus, compiled by F. E. Molin, and in analytic geometry, compiled by V. L. Nekrasov, were issued. At first these collections consisted of sets of problems for practical classes without any indications as to their solution. Then, beginning in 1907, they began to be issued with detailed solutions, which enabled students to penetrate more deeply into the theoretical material. A substantial shortcoming of these collections was the absence in them of problems with technical content. The impracticality of assigning the conduct of practical classes to persons who did not have special mathematical education became apparent quickly. The engineer-teachers had little interest in mathematics and taught it unwillingly. Professors Molin and Nekrasov believed that the teaching of mathematics could be carried out successfully only when the teacher himself was sufficiently prepared and possessed a solid ma—

mathematical development, and that engineers, even if working under the supervision of professors, present in classes only what has been indicated to them and, when necessary, are unable to go beyond these instructions; by this they restrain the mathematical development of the students. In order to improve the organization of instruction in higher mathematics, in 1903 Mikhail Nikolaevich Ivanov, who had completed the course at Kazan University and was preparing for the master’s examination, was invited to conduct practical classes. In 1909 a second teacher, V. I. Shumilov, was invited to the teaching staff. After passing the master’s examination in applied mathematics at Kazan University, M. N. Ivanov, on September 1, 1910, was sent on a two-year scientific mission to Germany to improve his mathematical education and to become acquainted with the organization of instruction in foreign higher educational institutions. In connection with M. N. Ivanov’s departure, the institute administration raised the question of adding V. P. Zylev to the staff of the department; he was recommended for his professional qualities by Professor A. P. Kotelnikov of Kazan University and by Privatdozent Perfil’ev. However, many members of the Council opposed inviting a specialist mathematician, believing that his duties could be performed by young engineers who needed to broaden their knowledge of mathematics. After a lengthy discussion at the council, V. P. Zylev was nevertheless approved as a regular teacher of the department.

Let us briefly consider the lectures on higher mathematics in the pre-revolutionary period. The lecture courses were entrusted to highly qualified professors: F. E. Molin—the course in infinitesimal calculus, parts 1 and 2—and V. L. Nekrasov—the course in analytic geometry, which was taught according to a single program for all specialties of the institute. Infinitesimal calculus was taught according to two programs: the first, more extensive, for students of the mechanical and civil-engineering departments; the second, an abbreviated program, for students of the mining and chemical departments.

Analytic geometry was taught during the first two semesters in a volume of 60 lecture hours and 30 hours of practical classes. The presentation of analytic geometry proceeded without the use of vector algebra. For the study of the course in infinitesimal calculus according to the expanded program, 300 hours were allotted, of which 180 were lecture hours and 120 hours were practical classes. In addition to the basic course in infinitesimal calculus, supplementary chapters were taught. Thus, the Institute Council, on January 22, 1904, resolved to introduce probability theory as a compulsory subject in the second year for students of the mining and construction departments, and as an optional subject for students of the mechanical department (Minutes of the meeting of the TPI Council for 1904, p. 130). Attendance at lectures in mathematics by students was optional. The students, regarding mathematics as a general-education subject and, in lectures, becoming convinced that mathematics was taught in isolation from its applications, attended mathematics lectures poorly. In examinations the students showed weak knowledge. Here are data taken from the minutes of the mining department of January 27, 1904. In the mining department, those who passed the examinations were:

In the other divisions the situation was approximately the same. Forty to fifty percent of the students passed into the second year in mathematics; the rest remained for a repeat year or were expelled from the institute.

Let us dwell on the scientific and public activities of the department’s first professors. F. E. Molin graduated in 1883 from the Faculty of Physics and Mathematics of Yuriev University with the title of Candidate of Astronomical Sciences. In the same year he entered Leipzig University to broaden his specialized knowledge of mathematics. In 1885 he passed the master’s examination in mathematics and soon received the degree of master. During this period F. E. Molin was engaged in the theory of elliptic functions and higher algebra, and somewhat later in the theory of hypercomplex numbers and group theory. He published the following works:

1. Determination of the trajectories of comets, 1880.
2. On linear transformations of elliptic functions. Dissertation, 1885.
3. On systems of higher complex numbers. Dissertation, 1892.
4. Corrections to the article on higher complex numbers.
5. A note on the theory of homogeneous stepwise groups of transformations, 1897.
6. On the number of variables of a homogeneous irreducible stepwise group of transformations, 1897.
7. On invariants of linear stepwise transformation groups, 1897.

Thanks to his published works, F. E. Molin became a scholar of world renown and the recognized founder of the theory of hypercomplex numbers.

As we have already mentioned, F. E. Molin arrived in Tomsk in 1901 and devoted his knowledge and energies to teaching at the Tomsk Technological Institute. He prepared and published his course in mathematical analysis. He devoted much energy to creating the library for the mathematics section at TTI. F. E. Molin also did not stand aside from the country’s public life. For his solidarity with the revolutionary student body he was dismissed from the institute in 1911 and until 1917 worked only privately. In 1918 Molin transferred to work at Tomsk State University, where he continued to work until 1941. In 1934 the Soviet government awarded him the high title of Honored Worker of Science.

Another prominent teacher and remarkable lecturer was Professor V. L. Nekrasov. In 1887 he graduated from the Faculty of Physics and Mathematics of Kazan University, being awarded the degree of Candidate of Sciences for his work “On the Second Variation.” Having passed the examination for the degree of master of pure mathematics and delivered two trial lectures, in 1895 he received the title of privatdozent. In August 1900 he was appointed first as a full-time instructor and then as extraordinary professor at TTI. In order to raise his scientific qualifications, the institute administration sent him in 1902 on a one-year scholarly trip abroad. During this time he worked in the libraries of Berlin, Vienna, and Zurich and familiarized himself with the organization of mathematics teaching in the higher technical schools of Germany, Austria, and Switzerland. After defending, on October 5, 1908, his dissertation for the degree of master of pure mathematics on the topic “The Structure and Measure of Linear and Point Domains,” he was elected by the institute council as acting ordinary professor.

V. L. Nekrasov published the following works:

1. On the second variation, Kazan, 1889.

1. On the Theory of Functions of Real Variables, Kiev, 1888.
2. A Course in Analytic Geometry, Tomsk, 1905.
3. The Structure and Measure of Linear Point Domains, Tomsk, 1908.
4. Construction of a Triangle on the Sphere, Tomsk, 1911.
5. On One Property of Related Determinants, Tomsk, 1914.
6. Foundations of Spherical Trigonometry, 1914.
7. Determination of the Foci and Directrices of a Curve of the Second Order from Its General Equation, Tomsk, 1916.

With the establishment of Soviet power in Tomsk, intensive work began at the Department of Higher Mathematics to reorganize teaching. In the first years of Soviet power, the country’s educational institutions were transferred to a 3.5-year and then to a 4-year term of study; a new student body entered the institute, requiring different methods of instruction. The country had to train Soviet engineers in the shortest possible time, and this affected the organization of teaching.

The formal-logical basis of instruction was reorganized according to new methodological principles. During the 1920s and 1930s, the department moved away from the formal-logical principles of teaching, and a tendency developed toward presenting the mathematics course in the most accessible possible way. Two basic principles were placed at the foundation of the pedagogical process: to bring the theoretical material of the higher mathematics course closer to the needs of technical disciplines, and to direct students’ independent work toward solving typical examples and problems with technical content applicable to the profile of the faculty. In this connection, the textbooks on mathematical analysis by Granville and Phillips became widely used among students. Granville’s textbook contained only the most minimal information from the theoretical propositions of the higher mathematics course and mainly pursued the goal of instilling in students formal skills in solving typical examples. Phillips’s textbook essentially presented only those topics that found application in technical disciplines and developed in students the skills needed to solve elementary problems of an applied nature.

To coordinate all methodological and methodical questions that arose in connection with the restructuring of instruction, a commission was organized under the chairmanship of Prof. V. I. Shumilov, consisting of the deputy chair, Prof. M. N. Ivanov, Professor S. K. Konyukhov, and instructors V. N. Belyaev, V. S. Bogoslovskaya, and M. A. Dunina. The commission drew up new programs in higher mathematics for the individual faculties. In 1930, the Department of Higher Mathematics of the Technological Institute was divided into several departments in connection with the separation from TTI of branch institutes (SMI, SGI, SKhTI, SGRI), and then, in 1932, it was again united and became the Department of the Tomsk Industrial Institute.

From 1928 to 1932, the teaching of mathematics was conducted according to the principle of the brigade-laboratory method. Under the brigade-laboratory method of instruction, the lecture as the main form of teaching was expelled from the walls of the higher educational institution. The essence of instruction by the brigade-laboratory method consisted in the following: the mathematics course was divided into a series of assignments, compiled by the instructor or by a group of instructors of the department. Before the assignment was worked through, the instructor, in an introductory discussion, posed to the group a series of questions that defined the aim of the assignment. Then the brigade proceeded to the independent study of the material, consulting among themselves and receiving consultation from the instructor. At the end of the period allotted for studying the assignment, the brigade as a whole reported to the instructor. Private sessions were not pre-

was envisaged; supervision of the work and assessment of students’ knowledge were carried out in the course of the work and during the final interview on the assignment. Instruction by the brigade-laboratory method did not produce positive results. The resolution of the Central Executive Committee and the Council of People’s Commissars of 19/IX-1932 stated: “In the practice of educational institutions a number of major shortcomings have become apparent: a decrease in the student’s individual responsibility for his work, depersonalization in academic work, orientation toward the weak and lagging behind, and, in a number of cases, the establishment of a procedure in which direct communication between the student and the professor was replaced by classes with a low-qualified supervisor or brigade leader.” After this resolution, lectures and group classes were restored, and examination sessions were introduced after each semester.

After the branch institutes were united into the Tomsk Industrial Institute, the Department of Higher Mathematics from 1932 to 1938 was headed by Professor Vsevolod Aleksandrovich Maleev. He was an outstanding lecturer, enjoying great authority among the students and instructors of the department. He was the author of works published by him even before 1932:

1. Theory of cubic curves.
2. On an indeterminate equation. Izv. TGU, vol. 24, 1924.
3. On the theory of equations of the third degree. Kazan, Izv. Phys.-Math. Society, vol. 2, 1927.
4. On groups of solutions of a congruence. Kazan, Izv. Phys.-Math. Society, vol. 1, 1926.
5. On compositions of solutions of congruences. Izv. TGU, vol. 79, 1928, and other works.

During his tenure as head of the department, he wrote the following works:

1. Maleev and Stepanov. On determining the order of a function in congruences modulo a double modulus. 1935.
2. Maleev and Prokhorovskaya. On general conditions for the reducibility of congruences of higher degrees. 1935.
3. Maleev and Kaplun. On cases of reducibility of congruences of higher degrees. 1936.
4. Maleev and Chistyakov. On the computation of derived sums of equal powers of roots from the coefficients of algebraic equations. 1936.

In the period from 1938 to 1942, the Department of Higher Mathematics was headed by Professor M. N. Ivanov.

In 1916 his work “On Small Oscillations of a Material System about a Position of Equilibrium” was published, in which an exposition was given of Lagrange’s theory of small oscillations, taking into account later studies and extending Lagrange’s theory to nonholonomic systems. Being a man of great erudition, M. N. Ivanov rendered great assistance to young instructors of technical departments in preparing their Candidate dissertations.

After the Great Patriotic War, rapid growth was observed in the department, now already that of a polytechnic institute. In 1932 the staff of the department consisted of 6 persons: V. A. Maleev, M. G. Ermakova, E. I. Smirnov, A. Kh. Pinsky, S. P. Kuznetsov, and A. P. Arkhangelsky; and in 1962 it consisted of 50 members of the teaching staff.

In 1962 the department was divided into two: the Department of General Higher Mathematics, headed by Prof. S. P. Kuznetsov, and the Department of Engineering and Computational Mathematics, headed by Docent B. F. Krutoi. The Department of Higher Mathematics provides instruction

of the general course in the amount of 400 hours, while the Department of Engineering and Computational Mathematics [was assigned] computational methods, supplementary chapters of mathematics, and disciplines connected with machine mathematics. The volume of the pedagogical work of the Department of Higher Mathematics for the 1965–66 academic year amounted to 40,427 hours. Of these:

To carry out the indicated volume of work, the staff of the department was approved as follows:

Head of department—1, associate professors of the department—5, senior lecturers—6, assistants—35.

In the fall semester the department provided lectures in 39 streams of first- and second-year students. The large amount of pedagogical work of the instructors, carried out in two shifts, has a negative effect on the development of the department’s research work.

In 1949, Senior Lecturer Yu. P. Vinogradov defended his candidate’s dissertation. In 1952, S. P. Kuznetsov defended a candidate’s dissertation in the field of the analytical theory of thermal conductivity. The works published by S. P. Kuznetsov, in their content, belong to mathematical thermophysics and set as their task the investigation, mainly analytically, of the processes of moisture transfer in bodies when temperature fields are present in them. Until recently such questions were considered without taking into account temperature fields in the material, approximately regarding them as isothermal. With the intensification of processes and the application of new technology (removal of moisture by high-frequency currents, etc.), the development of a new theory taking into account the interrelation of the fields of moisture and temperature became an urgent necessity, since at high intensities the temperature field significantly influences the moisture field and, conversely, at large temperature gradients thermal moisture conductivity cannot be neglected in comparison with moisture conductivity. In his works the question is posed of finding analytical solutions for nonstationary fields of moisture and temperature under boundary conditions of the first kind for classical bodies, with uniform initial distribution of temperature and moisture. On the basis of an analysis of the solutions obtained, a new method is advanced for the experimental determination of thermo–moisture coefficients.

In the paper “Investigation of Nonstationary Temperature and Moisture Fields in an Unbounded Plate without Evaporation of Moisture” (Izv. TPI, vol. 89, 1957), the principal shortcomings of existing solutions concerning the heating of moist materials, connected with failure to take into account the effect of thermal moisture conductivity, are indicated, and a new theory of nonstationary temperature and moisture fields in moist materials is developed.

The paper “Nonstationary Fields of Moisture and Temperature with Evaporation of Moisture inside a Body under a Boundary Condition of the First Kind” (Izv. TPI, vol. 97, 1959) belongs to the theory of heat-and-mass exchange in porous materials. Here a system of differential equations of the transfer of heat and of the bound substance (moisture) is solved in the case of constant mean integral moisture content; an analysis of the solutions obtained is given by means of the criteria of Lykov, Kossovich, and others.

In the work “Application of the Theory of Nonstationary Fields of Temperature and Moisture to the Determination of Thermal-Moisture Conductivity Coefficients” (Izv. TPI, vol. 89, 1957), a new method is proposed for determining thermal-moisture coefficients.

The works “On the Theory of Heat and Mass Transfer in an Infinite Cylinder” (Izv. TPI, vol. 119, 1963) and “Investigation of Temperature and Moisture Fields in a Sphere with Evaporation Taken into Account” are a further development of the analytical theory of heat conduction in moist materials.

Over the course of many years of pedagogical work at the department, S. P. Kuznetsov delivered courses in mathematical analysis, vector analysis, selected questions of the equations of mathematical physics, the theory of functions of a complex variable, and operational calculus. On additional chapters of higher mathematics he wrote several teaching-methodological manuals; among them the following were published: “Fundamentals of Vector Calculus” and a teaching manual on algebra for preparation for admission to the institute.

In 1965, in the journal Izv. TPI, vol. 131, articles by senior lecturer V. E. Kornilov were printed, in which questions of the application of the theory of continued fractions to the calculation of certain types of integrals were analyzed. In the article “Extraction of the Algebraic Part of Integrals of Binomial Differentials,” formulas were obtained for transforming integrals

\[ \int z^p (a + bz^r)^q\, dz \tag{1} \]

with arbitrary parameters \(p\) and \(q\) to integrals with parameters \(p\) and \(q\) minimal in absolute value. The six formulas obtained by him, together with four formulas included in the monograph by I. S. Gradshtein, Tables of Integrals, Sums, Series, and Products, pp. 78–79, 1962 edition, give expressions in elementary functions for any integrals (1), in accordance with the conditions of P. L. Chebyshev.

In the article “Application of Continued Fractions to the Calculation of Integrals of Binomial Differentials,” the general form of suitable fractions is given for integrals (1) with a variable upper limit and minimal parameters \(p\) and \(q\), and an estimate of the remainder term in modulus is obtained, which is valid in a certain domain of the complex variable \(z\). The rational approximations of integrals obtained in the article may be applied to the calculation of special functions—the incomplete and complete beta functions. In all, he published 22 articles on various applications of the theory of continued fractions.

The scientific research activity of Associate Professor N. K. Vitvitsky is reflected in the following published works:

1. Generalization of Cauchy’s theorem in finite-difference calculus. Scientific Notes of TSU No. 6, 1948.

2. An approximate method for determining the frequencies of natural bending, torsional, and coupled vibrations of beams of variable cross-section. Collection of Works of TEMIIT, vol. 25, 1958.

3. Determination of the natural frequencies of torsional vibrations of beams of variable cross-section. Collection of Works of TEMIIT, vol. 28, 1959.

4. Determination of the frequencies of natural bending vibrations of beams beyond the elastic limit in the presence of plastic zones. Collection of Works of TEMIIT, vol. 34, 1962.

5. Calculation of the frequencies of natural bending vibrations of beams beyond the elastic limit in the presence of plastic zones. Izv. TPI, 1966.

6. Calculation of the frequencies of natural bending vibrations of a cantilever beam beyond the elastic limit in the presence of plastic zones.

In 1963 V. I. Sadchikov defended his Candidate’s dissertation on the topic: “On the theory of the formation of continuous chips.” V. I. Sadchikov’s dissertation belongs to the field of the analytical theory of metal cutting. It considers the problem of the process of continuous-chip formation under conditions of plane deformation of a rigid-plastic isotropically hardening material. Mathematically, the problem is described by a system of differential equations for steady plastic flow. He was the first to obtain an analytical solution of the cutting problem for the case of chip-formation deformation in one plane, and he investigated separate stages in the solution of this problem in the case when the deformation zone has finite width. The work studies the kinematics of continuous-chip formation and obtains relations among the cutting speed, the speed of chip motion, and the geometric characteristics of the problem. The dependence of the type of chip texture on the form of the deformation zone and on the fields of stresses and velocities in this zone is established. The concept of simple inhomogeneous shear in chip formation is introduced, and necessary and sufficient conditions for this type of deformation in the process of chip formation are established. The main results of the study were formulated by him in 9 theorems, the texts of which we do not reproduce. During the period from 1962 to 1967 V. I. Sadchikov published 9 articles.

Assistant V. S. Kovalenko, in coauthorship with others, took part in writing the following works:

1. On the theory of a diaphragmed waveguide of rectangular cross-section, Radiotekhnika, No. 1, 1961.
2. On the calculation of the amplitudes of spatial harmonics in diaphragmed waveguides, Izv. TPI, vol. 123, 1961.
3. On the theory of the slowing system of a quantum amplifier.
4. On the calculation of spatial harmonics of a diaphragmed waveguide of rectangular cross-section, Izv. TPI, vol. 122, 1962.

At present a group of instructors of the Department of Higher Mathematics is working successfully in the field of differential geometry. In his works—“A multiparametric family of curves of the second order in three-dimensional projective space,” reported at the 25th Scientific-Pedagogical Conference of the Ural Zone (Abstracts of Reports and Communications, Sverdlovsk, 1967), and “Differential geometry of a six-parametric family of nondegenerate conics whose planes form a two-parametric family” (Third Baltic Geometrical Conference. Abstracts of Reports. Palanga, 1968)—V. I. Matveenko investigated the \(m\)-parametric properties of \(V_m\) conics in \(P_3\) for \(m = 3, 4, 5, 6, 7\), constructed and geometrically characterized conic frames, and studied subclasses with special properties of associated geometric images (Proceedings of the Geometrical Seminar, vol. 2, Moscow, 1969). In all he has published 11 articles.

M. R. Vaintrub, in the work “Differential geometry of manifolds of circles in three-dimensional Euclidean space” (Geometricheskii sbornik, issue 7, Tomsk University, 1968), investigated \(m\)-parametric manifolds \(W\) of circles in three-dimensional Euclidean space \(E_3\), for \(m = 1, 2, 3, 4, 5\). He gave an invariant construction of the differential geometry of the manifold \(W_m\), found a geometric characterization of the basic tensors and invariants, and thoroughly studied, in a canonical frame, separate subclasses of the manifold \(W_m\), involving various invariant adjoint and \(W_m\) geometric images and nonholonomic submanifolds of circles (Proceedings of the Geometrical Seminar, vol. 2, Moscow, 1969). In all he has published 15 articles.

The scientific direction of M. S. Bukhtyak is characterized by his works:

1. On one class of four-parameter vector fields. (Fourth All-Union Conference on Geometry, Tbilisi, 1969.)

2. On submanifolds of a line-element space (Proceedings of the Scientific Conference, 1970, Tomsk).

3. On parabolic submanifolds \(\Psi_2\) of a four-parameter vector field (ibid.) and other works.

V. K. Struts defended his Candidate dissertation in 1971 on the topic: “Channeling of Heavy Charged Particles at Various Temperatures.”

The results of his research are presented in 11 articles. Among them are “Channeling of Protons in Silicon at Various Temperatures” (Izvestiya Vuzov, “Physics,” no. 6, 1970), “Channeling of Fast Protons in Single Crystals of Silicon and Germanium at Various Temperatures” (Applied Nuclear Spectroscopy, issue 2, Leningrad, 1971).

A. P. Privezentsev defended his Candidate dissertation in 1972 on the topic: “Problems of the Interaction of Charged Particles with Their Own Radiation Field in a Cyclic Accelerator.” On questions related to the topic of the dissertation, he wrote 11 articles. The following instructors took part in the research and methodological work: R. G. Lazarev, G. G. Pestov, T. A. Lukovskaya, I. O. Davydenko, V. I. Anzhina, L. E. Portnov, and others.

A tremendous contribution to the teaching of the course in higher mathematics is made by senior instructors A. P. Filippova, I. K. Batrakov, G. P. Sergeeva, G. S. Sidorovich, E. V. Shenk, E. M. Smetankina, and many other members of the department.

In 1965, at the institute, on the basis of specialty 0608 (mathematical and computing devices and systems), specialization 0608-a (application of computing technology) was opened, with an admission of 25 students; the training and graduation of students in this specialization was entrusted to the Department of Engineering and Computational Mathematics. Let us note that at Tomsk Polytechnic Institute, one of the first in the Soviet Union, the courses “Computing Technology in Engineering and Economic Calculations” and “Programming” were taught with the direct use of the Minsk-1 digital computer and other continuous-action machines, that is, with students accessing these machines to solve problems. A certain amount of experience was accumulated in the application of electronic computing technology in student instruction.

The inter-institutional conference on the use of electronic computing machines for teaching students in 1969 was held at Tomsk Polytechnic Institute. Members of the department presented five reports at this conference and introduced several teaching aids. The interpretive program for the Minsk-1 digital computer (D. D. Del, G. L. Kalinichenko, V. A. Maltsev), developed in the educational computing laboratory and at the Department of Engineering and Computational Mathematics for teaching students, was adopted by higher educational institutions using the Minsk-1 computer.

Let us note that the recommended curriculum for specialization 0608-a at that time practically did not differ from the curriculum for specialty 0608. At Tomsk Polytechnic Institute, the head of the department, Associate Professor B. F. Krutoi, believed that an engineer-mathematician should have much broader mathematical training than other graduates of the institute. A separate curriculum was developed in which the number of hours for numerical methods, programming, mathematical programming, probability theory, mathematical statistics, and other mathematical disciplines was increased, while reducing the hours in descriptive—

descriptive geometry, drafting, theoretical and applied mechanics, and other engineering disciplines. It should be noted that at that time such curricula existed only in a few higher educational institutions and were subject to criticism. Incidentally, the curriculum approved by the Ministry of Higher Education and Secondary Specialized Education of the USSR in 1972 for specialty 0647 (applied mathematics) almost coincides with the curriculum then in force at the institute.

In 1970 the department graduated its first class of mathematical engineers, who were assigned to the cities of Severo-Donetsk, Omsk, Novosibirsk, Khabarovsk, Irkutsk, and other cities.

In 1970, Associate Professor V. A. Kochegurov was elected, by competition, head of the department. The admission plan for the specialty was increased to 50 persons, and in 1971—to 75 persons.

Great credit for the first and subsequent graduations belongs to the former head of the Department of Engineering and Computational Mathematics, Associate Professor B. F. Krutoi; to Associate Professor G. G. Pestov; Associate Professor G. L. Kalinichenko; and to senior lecturers M. V. Samoilova, M. I. Monarkh, P. F. Pestova, G. I. Stanevko, L. V. Baklanova, and others.

In the Department of Engineering and Computational Mathematics, Associate Professors B. F. Krutoi, G. G. Pestov, G. L. Kalinichenko, V. A. Kochegurov, G. I. Stanevko, G. P. Tarasov, L. I. Minenko, and others successfully carried out research work, publishing more than one hundred articles.

In 1972 the Department of Applied Mathematics was separated from this department, with V. A. Kochegurov as head of the department. In the same year he transferred to a research position in order to complete his doctoral dissertation, and Associate Professor A. A. Tereshchenko was appointed acting head of the department. Associate Professor V. M. Osipov was appointed head of the Department of Engineering and Computational Mathematics.