For the pupils in the science-modern languages section who specialize in mathematics there is a special publication Gazeta matematica, which has appeared since 1895. It is somewhat similar to the Revue de mathématiques spéciales prominent in the French lycées. Quite apart from the obligations connected with their courses of study, the mathematical pupils of the section not only solve the problems in pure and applied mathematics in the Gazeta, but also propose others and contribute notes and articles. The progress of mathematical science in Roumania stands in intimate relation to this review. Such then is the nature of the work which the mathematical professor has to conduct. There remains the consideration of his preparation for the work. The directors and professors in the secondary schools are university men and receive their appointments from the Government. Since the law of 1898 the mathematical professors are appointed from among those who have passed the "examination of capacity,' which is held every three years. To register for this examination it is necessary to have (1) the diploma of licence ès sciences mathématiques of a university; (2) the certificate of a pedagogic seminar. "The students who have passed the examination of licence ès sciences mathématiques have sufficient, theoretical preparation to become good professors in secondary education," as it is modestly expressed by Prof. Tzitzéica. The examinations for the licence are in higher algebra, analytic geometry, descriptive geometry, differential and integral calculus, theory of functions, mechanics, and astronomy. These examinations require at least three years of preparation. During his university studies and afterwards the future mathematical teacher takes a course in pedagogy at the university. He also commences at the same time his practical training at a pedagogic seminar. The pedagogic seminarien in connection with the universities were created by the law of 1898. The examination of capacity consists of (1) three written examinations on the elementary material of secondary education and on the more advanced material of the licence; (2) two oral examinations, one on mathematical questions proposed by the jury, the other on pedagogy; and (3) two practical examinations-that is to say, two lessons such as the candidate might deliver to pupils in a lycée. In order to claim a teaching position as a right, one must have passed an examination of capacity for a secondary specialty. For example, physics or geography may be offered with mathematics. BIBLIOGRAPHY. G. TZITZÉICA, L'Enseignement Mathématique en Roumanie. Enseignement secondaire. Bucarest, Imprimerie, "Gutenberg" Joseph Gobl S-seurs, 1912. 16 pp. 101179°-18- -11 XIV. RUSSIA. It has been estimated that the Empire of Russia contains more than 182,000,000 people. Since the treaty of Portsmouth its area, exclusive of inland waters, is about 8,400,000 square miles. Finland (q. v.) has a separate system of public schools much more highly developed than that of the remainder of Russia, where the general education of the people has been of a very low order. Except in certain parishes of the Baltic provinces, education is not compulsory. The numerous central authorities in connection with Russian education include the ministry of public instruction and the Holy Synod. The former controls the universities and the great majority of the secondary schools of all classes. 2 The secondary or middle schools include: 1 (1) Seminaries for teachers, of which the ministry established 63 in 1891 for the preparation of teachers for certain primary schools; (2) institutes for teachers (33 in number in 1914) which prepare teachers for another class of primary schools; and (3) establishments such as the progymnasia (of which there were 29 in 1914), gymnasia (441), "real schools" (284), and technical schools (68 in 1910), under the control of the ministry of public instruction and providing general instruction for the youth. 3 The progymnasia are incomplete gymnasia with four or six classes instead of eight classes (I-VIII), one for each year of the course. Among secondary schools, only the gymnasia and real schools are considered here. Bobynin has given the mathematical programs of the seminaries and institutes for teachers. GYMNASIA. Pupils normally enter the gymnasia at the age of 10 years. In the explanatory remarks prefatory to the program of the course of mathematics in the gymnasia for boys, the ministry of public instruction sets forth the object of the course: Mathematics as an exact and abstract science furnishing a simple, and consequently appropriate, means of assuring suitable development of the mind constitutes one of the foundations of general instruction. The essential object of study at the gymnasium being the intellectual development of the pupil, the mathematical instruction should be characterized, before all else, by the thoroughness and systematic rigor of a theo 1 Bobynin, 1903 (see bibliography); and A. T. Smith in Cyclopedia of Education, edited by Monroe, in article on Russia. Since increased, according to a report of Jan. 1, 1914, to 122 (Statesman's Year-Book, 1917). retic course; practical applications should be introduced, first, as illustrations of the theory, and then, to habituate in computations. The gymnasia of the ministry of public instruction are of two types: (1) Those in which only one ancient language, Latin, is taught; and (2) those in which two ancient languages are taught. There were only five of these latter gymnasia in 1910. While the whole number of hours devoted to mathematics in these two types of gymnasia is not the same, the programs are identical. The subjects taught are arithmetic, algebra, geometry, trigonometry, physics, mathematical geography (cosmography), and notions of mechanics. Arithmetic is taught in Classes I-III and reviewed in Class VIII, where certain parts, omitted earlier on account of their difficulty, are taken up. In the third year topics of discussion are: Ratio and proportion, problems relating to the so-called rule of three; interest and proportional parts. Algebra (III-VIII). Some of the matters taken up in Classes VI-VIII are: Progressions and logarithms; calculation of compound interest; indeterminate equations of the first degree in two unknowns; continued fractions; binomial theorem; resolution of a system of equations by the method of Bézout. Geometry (IV-VI), with review in VIII.-In V-VI the student is instructed in the measurement of lines and angles; proportionality of segments; similitude of triangles and polygons; regular polygons; notion of a limit; length of the circumference; notions on the calculation of ; area of rectilinear figures, of the circle and of its parts; simple problems of instruction, and numerical applications for each article of the program; regular polyhedra; evaluations of area and volumes of prisms and pyramids; cylinder, cone, and sphere, evaluation of their areas and volumes. Trigonometry (VII-VIII).—Elements of plane trigonometry, including the use of tables, solutions of triangles, calculation of areas and applications to problems in surveying. Trigonometric equations and inverse trigonometric functions are not discussed. Cosmography (VIII).—Rotary motion of the celestial sphere; rotary motion of the earth; true shape and size of the earth; apparent annual movement of the sun; annual movement of the earth round the sun; measurement of time; constitution and dimensions of the sun; moon; eclipses; planets; comets; law of gravitation; tides. Mechanics (VI, VIII).-Motion and force-laws of motion, law of inertia, law of relative motion, equality of action and reaction; force as a cause of motion and of pressure; resistance of motion (friction); equilibrium of forces; composition and decomposition of forces; levers. Theory of gravitation. Theory of motion-uniform motion; velocity; acceleration; uniformly accelerated and retarded motion; motion of a projectile; notions regarding curvilinear motion and centrifugal force; pendulum. Theory of energy-work; lever; pulley; inclined plane; toothed wheels; kinetic and potential energy; transformation of mechanical work into heat and inversely; principle of conservation of energy. In most gymnasia the pupils have the same teacher of mathematics in all of their courses. This arrangement seems to cause the pupil to think of the bonds uniting one course to another. As to the connection between mathematics and physics and mechanics, the courses in physics and mechanics (as well as in cosmography) are conceived in such a way as constantly to give the pupil occasion to apply his knowledge and his experience of mathematics. About one-third of the pupil's time in the ordinary gymnasium is devoted to the study of Latin and Greek, and about one-fifth to mathematics and physics. At various stages in his course the pupil is required to pass written and oral examinations. In the final examination the written portion in mathematics lasts five hours and requires the solution, with detailed explanations, of two problems, one in algebra and the other in trigonometry applied to geometry. The mathematical portion of the oral examination is in arithmetic, algebra, solid geometry, and trigonometry. The student who has successfully passed this examination receives a certificate of maturity (attestat zrelosti). The bond between secondary and higher education is formed by the requirement of this certificate for admission to the universities and that of either the gymnasium or the real school for admission to the higher technical colleges. "REAL SCHOOLS." The normal age of entrance into these schools is 10 years. Most schools now possess, in addition to the former regular six classes (I–VI), a seventh class (VII). Each class lasts for a full year. The subjects common to all real schools are: Russian, with Slavonic; modern languages-German, French; geography; history; mathematics and geometric drawing; natural history; physics; drawing; calligraphy. In a comparison of Real schools with the gymnasia, it is to be noted that logic and the classical languages have disappeared to make room for more of science and of modern languages. The students of the real school cover in six years about the same amount of mathematics as those in the gymnasia cover in eight. Special reference may be made, however, to the five-hour course of mathematics given at many real schools in the supplementary seventh year. The subjects taught are arithmetic, algebra, trigonometry, elements of analytic geometry, and infinitesimal calculus. The leading topics taken up are: Arithmetic: Principal propositions on factoring of numbers; the highest common divisor of two numbers; solution in positive integers of indeterminate equations of the first degree in two unknowns. Algebra: Complex numbers; fundamental properties of an integral function and its roots; special cases, the functions x1-a" and ax2+bxP+c; discussion of equations of the first degree with one unknown and of a system of two equations of the first degree with two unknowns-indeterminate case, contradictory equations. Geometry: Relative positions of lines and planes in space; principal properties of dihedral and polyhedral angles; regular polyhedra; measurement of the surface and volume of the right cylinder, the right cone, and the sphere and its parts; examples leading to computation and construction problems. Trigonometry: Inverse circular functions; trigonometric equations; etc. Analytic geometry: Rectangular and polar coordinates; transformation of coordinates; circle, parabola, ellipse, hyperbola; equation of ellipse and hyperbola in bipolar coordinates; loci; diameters. Calculus: Fundamental theorems in limits; application to the measurement of circumference and area of circles, of the surface and volume of cylinders, cones, and spheres; limit sin z; limit (1+1)"; differentials of algebraic and transcendental func z=0 Z tions; geometric explanation of Rolle's theorem; Lagrange's theorem; increasing and decreasing functions; equations of tangents and normals of the conic sections; definite integrals. Since 1911, students who have satisfactorily completed the seven years' course of the real school are admitted to the universities without examination. Teachers in the real schools are, for the most part, graduates of a university in the subject which they teach. To form a true conception of secondary education in Russia, one should bear in mind that, taken as a whole, the boys attending the secondary day schools are drawn from a lower social stratum than are those attending such schools in England or France. As a rule neither. the children of the aristocracy nor those of the higher officials attend the gymnasia; the former are educated for the most part by private tutors, the latter in special schools open only to the nobility.' THE UNIVERSITIES. In Russia, exclusive of Finland, there are 10 universities. The largest and oldest is at Moscow; The others, in order of foundation, are at Yuriev (formerly Dorpat), Khazan, Kharkof, Petrograd, Kief, Odessa, Warsaw, Tomsk, and Saratov. The last was founded in 1909, and neither there nor at the University of Tomsk has a faculty of physics and mathematics been established. While secondary education in Russia still leaves much to be desired, the standard of teaching in the universities is, on the whole, very high, and may be compared to that of the German universities.3 The scholastic year consists of about 27 weeks of lectures, and the course of study at the university covers four years. The Russian faculty of physics and mathematics is composed of two sections: The section of mathematical sciences and the section of This paragraph is equivalent to what Darlington states in this connection on pp. 347-348 of his report (which sought to represent actual conditions at the end of 1904). The Bureau of Education at Washington has, however, kindly volunteered the information that "about 50 per cent of Russian gymnasium students are sons of nobility and merchants. 'Aristocracy' is represented by at least 20 per cent of the students. The special schools for aristocracy have long ago become insufficient and now are discarded." The bureau states that the authority it quotes is: Russia, Ministry of Public Instruction, Report for 1912, [in Russian], Petrograd, 1915, pp. 50 and 51. 2" A Popular University bearing the name of Gen. Alphonse Shaniavsky, who has given the funds necessary for its creation, has existed at Moscow since autumn, 1908. In 1916 a Woman's University was created at Petrograd with the power of conferring the degree of doctor."-Statesman's Yearbook, 1917. * Encyclopaedia Britannica, 11th edition, 1911, Article "Russia." W. S. Jesien has recently reported great improvement in Russian secondary education during the past decade. |