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Image 40 of Catalogue of the Officers, Studies, and Students of the State College of Kentucky, Lexington, Volume 7 (Session ending 1913 June 6)

Part of University of Kentucky course catalogs, 1865-

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42 THE STATE UNIVERSITY. Mathematics. The basis for the determination of units in mathematics must be the quantity and quality of the work done rather than the time ele- 2 · ment. For the average student, however, four years time will be required to do ¤ the work here outlined. Two years should be devoted to algebra, a year to I plain geometry and a half year each to solid geometry and plain trigonometry. i These subjects may very well be taken in the order named. Some prefer to . give one year in algebra, followed by a year in plane geometry; this followed 1 by a return to algebra for a year, the solid geometry and trigonometry coming e _ in the order above indicated. In either plan the use of algebra should be < · emphasized in the work in geometry. The outline work for the four years l follows: 2 (I) /llgrbra-—One and one-half units. The four fundamental operations _ for rational algebraic expressions; factoring, determination of highest com- mon factor and lowest common multiple by factoring; fractions, including z complex fractions, ratio and porportion; linear equations both numerical and ( literal, containing one or more unknown quantities; problems depending on linear equations; radicals, including extraction of the square root of polyno- I mials and of numbers; exponents, including the fractional and negative; quad- y ratic equations, both numerical and literal containing one unknown; simultane- ous quadratic equations; problems depending upon quadratic equations; the . binomial theorem for positive integral exponents, the formulas for the nth E term and the sum of the terms of arithmetical and geometrical progressions, ; with applications. c (2) Plane Gzom:zry—Onc unit. The usual theorems and constructions of good text-books, including the general properties of plane rectilinear figures; r the circle and the measurement of angles; similar polygons; areas; regular poly- a gons and measurement of the circle. The solution of numerous original ex- ercises, including loci problems; application to the mensuration of line and 4 plane surfaces. v (3) Solid Ge0metry—One-half un-it. The usual theorems and construe- t tions of good text-books including the relations of planes and lines in space; l the properties and measurement of prisms, pyramids, cylinders, and cones; the sphere and the spherical triangle; the solution of numerous original exer~ p cises including loci problems; application to the mensuration of surfaces and G solids. t (4) T1·ig02i0metry—One-lzalf unit. Plane trigonometry should include g the definitions and relations of the six trigonometic functions as ratios, the 11 theory of logarithms and use of tables, the proof of important formulas and P considerable practice in trigonometric transformations; the solution of right V and oblique triangles. fl D `

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