32 Mathematics 



No. 78. SHAW, JAMES BYRNIE. Synopsis of Linear Associative Algebra: A 



Report on its Natural Development and the Results Reached up to the 



Present Time. Quarto, 145 pages. Published 1907. Price $1.50. 



This synopsis aims to present in a synthetic way the results, up to the date of 



publication, of various methods of studying linearly distributive and associative 



operation. The abstract theory of such operations is the intent of the book. 



Under this head are included matrices, linear substitutions, bilinear forms, vector 



algebras, quaternions, and the general theory of operations. The main results of 



numerous memoirs on these subjects are put into organic relationship and some 



further results are deduced. 



No. 120. DECKER, FLOYD F. The Symmetric Function Tables of the Fifteenthic. 

 Quarto, 21 pages. Published 1910. Price $1.25. 



This publication presents the table of symmetric functions of the equation of 

 the fifteenth degree. Similar tables of equations of lower degrees have previously 

 been published, references to which are given, together with a list of corrections of 

 misprints found in some of them. The use of the tables is exhibited by the solution 

 of a numerical equation and by the calculation of a resultant of two equations. 



The publication contains also an historical sketch, compiled from original sources, 

 of the formulas connected with the calculation of symmetric function tables, 

 which may not only give an appreciation of the development of the subject, but 

 which will be useful in calculating tables of higher orders. 



No. 151. STAGER, HENRY W. A Sylow Factor Table of the First Twelve 

 Thousand Numbers, giving the possible number of Sylow sub-groups 

 of a group of given order between the limits of o and 12000. Quarto, 

 x+120 pages, 1 plate. Published 1916. Price $4.50. 



The main purpose of this table is to furnish direct information as to the possible 

 number of sub-groups of a group of given order under Sylow's Theorem, "If p a is 

 the highest power of a prime, p, which divides the order of a group, G, the number 

 of sub-groups, H, of order p a is congruent to unity, modulo p." These sub- 

 groups of order p a are called Sylow sub-groups. Each number is expressed 

 as the product of powers of primes, and for each prime factor greater than 2 the 

 values of k, other than zero, of all divisors of the number of the form p (kp-\-l) 

 are given. Those values of k, other than zero, such that the number is identically 

 equal to p(kp-{-\), are indicated by a star. In addition, a list of those numbers 

 which contain no factors of the form p (&/>-f-l), k >0 is given, so arranged that 

 the number of such numbers between any two limits less than 12230 is easily ob- 

 tained. The table was constructed independently by two different methods, and 

 the results compared for errors. 



No. 245. HEDRICK, HENRY B. Interpolation Tables or Tables of Proportional 

 Parts, containing the products to the nearest unit of all numbers from 

 I to 100 by each hundredth from o.oi to 0.99 and of all numbers from 

 I to 1000 by each thousandth from o.oo/ to 0.999. Folio, 149 pages. 

 Published 1918. Price $5.00. 



These are essentially tables of proportional parts to hundredths and to thou- 

 sandths, or multiplication tables of decimal fractions to two and to three places. 

 They give the products to the nearest unit of all numbers from 1 to 99 by each 

 hundredth from 0.01 to 0.99 and of all numbers from 1 to 1000 by each thousandth 

 from 0.001 to 0.999. They arc intended for use in multiplication where the product 

 is required to no more significant figures than the smaller factor contains, as is 

 usually the case in interpolation or in the multiplication of decimal fractions which 

 are given to three significant figures only. 



They give what is contained in Crelle's . Multiplication Tables, but in a more 

 compact and convenient form when the product is not required to more places than 

 the factors. The advantages over Crelle's tables are that the products are given only 

 as far as needed and so the computer does not have to "point off," nor cut off part 

 of the product. He does not have to notice if the omitted part is more or less than 

 0.500 in order to adjust the last figure of the result. 



