Bulletin of the American Mathematical SocietySociety, 1903 |
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algebraic American Mathematical Society analysis analytic geometry angle applications Auflage axioms B.Sc BULLETIN calculus of variations Chicago Cloth College congruence conic conjugate coördinates corresponding curves defined derived determined Deutsche Mathematiker-Vereinigung differential equations Diss EDWARD KASNER elementary elements F. N. COLE fessor finite number four hours fundamental G. A. BLISS géométrie given Göttingen group of order infinite Instructor in Mathematics integral calculus intersection invariant L. E. DICKSON Leipzig London Mathematical Society mathématiques mechanics meeting Member method paper Paris Ph.D plane plates points problem Professor G Professor Hilbert Professor of Mathe Professor of Mathematics projective geometry rational Read ruled surface segments Seminar solution space sphere straight line subgroups of order surface Synthetic geometry Teil Teubner theorem Theory of functions Theory of numbers three hours tions transformation Ueber University values variable vector volume W. H. YOUNG York
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Page 76 - The four fundamental operations for rational algebraic expressions. Factoring, determination of highest common factor and lowest common multiple by factoring; fractions, including complex fractions, and ratio and proportion; linear equations, both numerical and literal, containing one or more unknown quantities; problems depending on linear equations; radicals, including the extraction of the square root of polynomials and of numbers; exponents, including the fractional and the negative.
Page 76 - The usual theorems and constructions of good text-books, including the relations of planes and lines in space; the properties and measurement of prisms, pyramids, cylinders and cones; the sphere and the spherical triangle. The solution of numerous original exercises, including loci problems. Applications to the mensuration of surfaces and solids.
Page 76 - Quadratic equations, both numerical and literal. Simple cases of equations with one or more unknown quantities, that can be solved by the methods of linear or quadratic equations. Problems depending on quadratic equations. The binomial theorem for positive integral exponents. The formulas for the nth term and the sum of the terms of arithmetical and geometric progressions, with applications.
Page 77 - Definitions and relations of the six trigonometric functions as ratios; circular measurement of angles. Proofs of principal formulas, in particular for the sine, cosine, and tangent of the sum and the difference of two angles, of the double angle and the half angle, the product expressions for the sum or the difference of two sines or of two cosines, etc.; the transformation of trigonometric expressions by means of these formulas. Solution of trigonometric equations of a simple character. Theory...
Page 1 - Lobachevski succeeded in building a logical edifice as coherent as the geometry of Euclid, but in which the famous postulate is assumed false, and in which the sum of the angles of a triangle is always less than two right angles.
Page 77 - ADVANCED ALGEBRA. Permutations and combinations, limited to simple cases; complex numbers with graphical representation of sums and differences ; determinants, chiefly of the second, third, and fourth orders, including the use of minors and the solution of linear equations; numerical equations of higher degree, and so much of the theory of equations with graphical methods, as is necessary for their treatment, including Descartes's rule of signs and Horner's method, but not Sturm's functions or multiple...
Page 76 - GEOMETRY: The usual theorems and constructions of good text-books, including the general properties of plane rectilinear figures; the circle and the measurement of angles; similar polygons; areas; regular polygons and the measurement of the circle. The solution of numerous original exercises, including loci problems. Applications to the mensuration of lines and plane surfaces.
Page 10 - Dean of the College of Science, Literature and the Arts, University of Minnesota. The Century Co., NY, 1930, pp.
Page 83 - Space," it is possible to replace Newton's enunciations by much more simple, methodically better arranged, and more satisfactory propositions. Such, in our estimation, would be the following: a. Experimental Proposition. Bodies set opposite each other induce in each other, under certain circumstances to be specified by experimental physics, contrary accelerations in the direction of their line of junction.
Page 84 - The mass-ratios of bodies are independent of the character of the physical states (of the bodies) that condition the mutual accelerations produced, be those states electrical, magnetic, or what not ; and they remain, moreover the same whether they are mediately or immediately arrived at.