ISBN: 9781130728934

RareBooksClub.com. Paperback. New. This item is printed on demand. Paperback. 184 pages. Dimensions: 9.7in. x 7.4in. x 0.4in.This historic book may have numerous typos and missing text.… More...

RareBooksClub.com. Paperback. New. This item is printed on demand. Paperback. 184 pages. Dimensions: 9.7in. x 7.4in. x 0.4in.This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1910 Excerpt: . . . with complex coefficients can be transformed into one with real coefficients. In a recent paper Professor J. W. Young has considered these two problems for the complex line from the point of view of projective geometry, the notion of a linear chain being fundamental. In a subsequent paper, f by making use of the idea of a two-dimensional chain, Professor Young considered these problems for the complex plane. Miss MacGregor applies the same principle of classification to the non-singular collineations in a complex space of three dimensions and considers the corresponding problems. She gives the classification of the collineations in space into nineteen distinct types, eacb of which leaves a three-dimensional chain invariant. Any such collineation may be represented with real coefficients. The necessary and sufficient conditions that a collineation be of this type are derived and the corresponding systems of invariant chains are determined. 4. The first paper by Mr. Escott completes the one read by him in April, 1904, before the Chicago Section. In the ordinary logarithmic series X d V d 1 d y 1 lx-d2xAx) J the problem is to express Ain the form of polynomials in a; so that both X d and X--d shall have rational linear factors. The solution of this problem gives interesting applications of the elementary theory of numbers. A number of series of this kind have been developed by others, but there has been no systematic attempt to solve the problem. Mr. Escott shows how an indefinite number of series may be obtained where X is of degree 1 to 7, and gives four examples where X is of degree 10, some of the factors in the latter case being quadratic. 5. In his second paper Mr. Escott shows the application of the series in the preceding paper to the comput. . . This item ships from La Vergne,TN., RareBooksClub.com, RareBooksClub.com. Paperback. New. This item is printed on demand. Paperback. 194 pages. Dimensions: 9.7in. x 7.4in. x 0.4in.This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1897 Excerpt: . . . complete quadratic equations; solution by factoring; by completing the square; roots of affected quadratic equations; solutions of problems involving quadratic equations; equations of higher degree which may be solved as quadratic equations; quadratic equations involving two unknown quantities; homogeneous quadratics, symmetric quadratics. Advanced algebra. The following is a summary of important points to which the attention of the candidate should be directed: 1 Definitions. Of the terms used in advanced algebra. 2 Radical quantities. Reducing radicals to their simplest form; adding and subtracting radicals; multiplying and dividing radicals; involution and evolution of radicals; general theory of exponents; multiplying and dividing imaginary quantities; the square root of binomial surds; rationalization of radical expressions; solution of equations containing radicals. 3 Quadratic equations. General laws; higher equations which can be solved by completing the square; problems involving quadratics; theory of quadratic equations. 4 Inequalities. Fundamental proposition; an inequality reversed by changing the signs. 5 Limits. Theory of limits; interpretation of the forms----J Ooo o 6 Ratio and proportion and variation. Mean proportional, continned proportion; proportion taken by inversion, by alternation, by composition, by division; problems in proportion. 7 Permutations and combinations. The number of permutations of n quantities taken r at a time; the number of combinations of n quantities taken rata time. 8 Arithmetic progression. Deductions of formulas; any three of the quantities, a, I, n, d, s, being given to find the other two; problems in arithmetic progression. 9 Geometric progression. Deduction of formulas; any three of the quantities, a, I, n, . . . This item ships from La Vergne,TN., RareBooksClub.com<