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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
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