COURSE OF STUDY IN MATHEMATICS.1 Algebra. The course includes imaginaries, inequalities, permutations and combinations, maxima and minima, indeterminate forms, convergence and divergence of series, determinants, and the binomial theorem with any index. Geometry. This takes up the computation of areas and volumes. Trigonometry. This course includes the solution of trigonometrical equations and inverse trigonometrical functions. Plane analytics. A study is made of conics, including the general equation of the second degree. Solid analytics. This course extends through surfaces of the second degree. Calculus. This is a fairly extended course in differential and integral calculus Differential equations. Elementary course. The remarks made concerning the nature of the instruction, examinations, and preparation of teachers under Technical Schools of Middle Grade apply here. TRAINING SCHOOLS FOR LAND SURVEYORS.2 LOWER COUrse. This is a course of one year. The preparation for admission seems to be completion of the middle school. These are State schools and aim to prepare practical surveyors. The average age of the students is 25 years. COURSE OF STUDY IN MATHEMATICS. Algebra. (Thirty-five hours.) The principal topics are series, binomial theorem, partial fractions, logarithms, differential coefficient, maxima and minima. Solid geometry. (Forty hours). The course includes the usual material of elementary solid geometry, through spherical triangles. Plane trigonometry. (Forty-five hours.) This is a course in elementary plane trigonometry. Spherical trigonometry. (Twenty-five hours.) This course includes the solution of spherical triangles. Analytics. (Forty hours.) This course extends through the equation of the second degree in the plane. Method of least squares. (Forty hours.) The instruction is given mainly by lectures. No textbooks are used. 1 Art. XII, pp. 32-34. This program is recommended in the report, but it is not said to be in use. 2 Art. XIII, pp. 44-48. Examinations are given in some subjects. The teachers are selected from the best land surveyors, graduates of the Imperial University, and specialists in mathematics. HIGHER COURSE. This is a two-year course. The students are selected from the best practical surveyors. The average age of the students is 33 years. The aim is to train specialists "to guide common surveyors." 1 COURSE OF STUDY IN MATHEMATICS.2 Algebra. (Sixty hours.) Series, determinants, probability, and theory of equations are studied. Plane and solid analytics. (One hundred ten hours.) Differential calculus. (One hundred hours.) This course extends through expansion of functions and maxima and minima. Integral calculus. (One hundred forty hours.) Differential equations. (One hundred twenty hours.) This is a course in ordinary and partial differential equations. Dynamics. (Ninety hours.) This is a course in statics and dynamics of rigid bodies. Method of least squares. (Two hundred hours.) RUSSIA. INDUSTRIAL SCHOOLS.3 SCHOOLS FOR APPRENTICES.4 Organization. The course is three years in length. The age of entrance is from 12 to 15 years. The purpose of the schools is to give technical instruction during apprenticeship. In 1909 there were 28 of these schools. COURSE OF STUDY IN MATHEMATICS. Arithmetic. (Four hours a week the first year, two hours the second year, and one hour the third year.) The principal topics studied are fractions, ratio, proportion, and interest. Geometry. This course gives the geometry needed in practice. No attempt is made to give rigorous proofs. This course is followed by geometric drawing. ELEMENTARY TRADE SCHOOLS.5 Organization. The length of the course is four years, but the last year is given to practice. The students enter from the primary schools at the age of 12 to 15 years. The aim of the schools is to educate for a trade. In 1909 there were 131 of these schools. 1 Art. XIII, p. 44. * Ibid., p. 47. 3 Rapports présentés a la Délegation Russe: Sur l'organization de l'enseignement des mathématiques dans les écoles industrielles du ressort du Ministère de l'Instruction Publique, par P. Kolournitzski et A. Hartzouck. Referred to hereafter as Rapport. 4 Rapport, pp. 29–31. 5 Ibid., pp. 29, 30. COURSE OF STUDY IN MATHEMATICS. Arithmetic. (Two hours a week the first year, one hour a week the second year.) This course includes integers, common and decimal fractions, the metric system, and applied problems. TRADE SCHOOLS. Organization. The length of the course is three years. In order to enter, the students must present the certificate of studies from an école préparatoire primaire. There were 30 such schools in 1909. Their purpose is to prepare their students for the trades. COURSE OF STUDY IN MATHEMATICS.2 Arithmetic. (The course extends through two years.) The principal subjects studied are divisibility of numbers, common and decimal fractions, ratio and proportion, interest, and the extraction of roots. Geometry. (Three hours a week the first year, two hours the second year, and one hour the third year.) The object of this course is to teach the geometry necessary for the trades. Geometrical drawing. (Two hours a week the first year and three hours the second year.) Industrial drawing. (Two hours a week the second year and five hours a week the third year.) LOWER TECHNICAL SCHOOLS.3 Organization. These schools require for entrance the completion of the four-year course in the municipal schools. (This is preceded by a three-year course in an elementary school.) The course of study covers three years. There were 19 of these schools in 1909. Their object is to prepare master workmen and foremen. COURSE OF STUDY IN MATHEMATICS.4 Arithmetic. (Three hours a week the first year, three hours with algebra and geometry the second year.) In the first year the subjects studied are fractions, and ratio and proportion; in the second year the rule of three, interest, and exchange. Algebra. Two hours a week are given to this course in the first year, and the fundamental operations are studied; in the second year, through quadratics. Geometry. Plane geometry is studied the first year; the second year, the theory of proportion, some parts of solid geometry, and the trigonometrical ratios. Mechanics. This course includes the mechanics of a point, the mechanics of solids, applications of mechanics to simple machines, and resistance of materials. Projection drawing. (One hour a week the first year, two hours the second year, and six hours the third year.) SECONDARY TECHNICAL SCHOOLS. Organization. The entrance requirements are the completion of the five lower classes of the Realschule. The course is four years or less. There were 32 of these schools in 1909. Their aim is to give an industrial education directed toward the special calling of the student, and in particular to educate engineers' assistants. * Ibid., p. 27. 1 Rapport, pp. 27-32. 6 Ibid., pp. 27, 28. 4 Ibid., pp. 33, 34. COURSE OF STUDY IN MATHEMATICS.1 Algebra. (One hour a week the first year.) This is mainly a study of logarithms in preparation for trigonometry. Geometry. (One and one-half hours a week the first year and one hour the second year.) Plane and solid geometry. Trigonometry. (One and one-half hours a week the first year.) Plane trigonometry. Analytics. (Two hours a week the second year.) The fundamental notions of plane and solid analytics. Drawing. Geometrical drawing, six hours a week the first year; machine design second and third years. Mechanics. First year, general mechanics and simple machines; second year, graphical statics and resistance of materials. SPAIN.2 COMMERCIAL SCHOOLS. The course of study in the commercial schools is divided into three parts-preparatory, elementary, and higher. In order to be admitted to the preparatory division a student must be at least 10 years of age and must pass an examination in grammar, arithmetic, geometry, geography, religion, and writing. The age of admission into the elementary department is 14 years. These schools prepare their students to be merchants, skilled accountants, and commercial teachers. In 1907 there were 14 of these schools, with 3,242 students. The course for merchants includes the study of the elements of arithmetic and algebra, bookkeeping, commercial practice, and industrial technology. The course for commercial teachers includes algebra, advanced commercial calculation, bookkeeping, and public administration. SCHOOLS OF ARTS, INDUSTRIES, AND TRADES. There are many institutions of an elementary grade, some of which prepare for the fine arts or the arts in general and others for the industries. The aim of the schools of arts and industries is: (a) To prepare skilled mechanics, who study arithmetic, algebra, geometry, descriptive geometry, trigonometry, physics, general and applied mechanics, and machines; (b) to prepare skilled electricians, chemists, and workers in various other industries. The schools of arts and trades are night schools and are open to workers. There are 26 of these schools. In order to enter, the students must have an elementary education. 1 Rapport, p. 36. "L'Enseignement Mathématique en Espagne, 2éme rapport de la S-commission espagnole, par le délégué Dr. Zoel G. de Galdeano, pp. 3, 4. NAVIGATION SCHOOLS. Navigation is taught in five general technical schools and in two navigation schools. The number of students is about 300. The students obtain the pilot's certificate. The subjects studied are arithmetic, algebra, geometry, trigonometry, topography, geography, physics, design, astronomy, and piloting. SWEDEN. INDUSTRIAL SCHOOLS.1 ELEMENTARY INDUSTRIAL SCHOOLS. Organization. There were at the time that the report was written (1911) about 60 elementary industrial schools in Sweden, 54 of which had State support. These schools began with private foundations, but have gradually come under State or community control. The school year has two semesters-13 weeks in the fall and 20 weeks in the spring. The instruction is usually given from 7 to 9 in the evening, on weekdays, and from 8 to 10 on Sunday mornings. The course is two or three years in length. The entrance requirements are an age of at least 14 years and the certificate of dismissal from the Volksschule. A small fee of from 1 to 2 crowns (27 cents to 54 cents) is charged. These schools are not compulsory, but a commission is working over the plan of instruction, and it is hoped that attendance will be required between the ages of 14 and 18. In schools where the numbers justify it the students are divided into classes according to occupation, and the instruction in mathematics is adapted to the needs of the different trades. Aim of the instruction.-The aim of these schools is to give practical industrial training. COURSE OF STUDY IN MATHEMATICS. Arithmetic. The course in arithmetic usually extends through three semesters, two hours a week. "In arithmetic, where the object of the teaching is to give the students skill in the computations that they will meet in their special trades, the course given includes whole numbers, common and decimal fractions with applications, percentage, interest, stocks and bonds, discount, and general problems that can be solved by the aid of equations of the first degree.” Algebra. This is a course of two hours a week, but the number of semesters is not given. The topics studied include integral and fractional expressions and equations of the first and second degree. 1 Der mathematische Unterricht in Schweden: Der mathematische Unterricht an den elementartechnischen Gewerbeschulen Schwedens, by Dr. K. L. Hagström. 2 Ibid., p. 3. |