ALGEBRA AND THEORY OF NUMBERS. 



Elements of Algebra. 



1600 General. 



1610 Rational polynomials ; divisibility; reducibility. 

 1620 Permutations, combinations, |3artitions, distributions. 

 1630 Probabilities (including' combination of observations). 



1630a Insurance. 

 1640 Calculus of differences; interpolation. 



Linear Substitutions. 



2000 General. 



2010 Determinants. 



2020 Discriminants and resultants. 



2030 Characteristic properties of linear substitutions : types 



of linear substitutions, 

 2040 General theory of quantics. 

 2050 Binary forms. 

 2060 Tei'nary forms. 

 2070 Special developments associated with forms in more 



than three variables. 



Theory of Algebraic Equations. 



2400 General. 



2410 Elements of the theory ; existence of roots ; symmetric 



functions ; rational fractions. 

 2420 Reality, multiplicity, separation, of roots. 

 2430 Equations of the third and the fourth orders : other 



particular equations. 

 2440 Numerical solution of equations. 

 2450 General resolution of equations ; theory of Galois. {See 



also 1210.) 

 2460 Simultaneous equations. 



Theory of Numbers. 



2800 General. 



2810 Divisibility ; linear congruences. 



2820 Quadratic residues. 



2830 Quadratic binary forms, 



2840 Quadratic forms of three or more variables ; bilinear 



forms. 

 2850 Congruences other than linear ; cubic and higher 



residues. 

 2860 Forms of higher degree which cannot be considered 



as products of linear factors. 

 2870 Forms of higher degree whic'h can be considered as 



products of linear factors; algebraic numbers; 



ideals. 

 2880 Application of trigonometrical functions to arithmetic ; 



cyclotomy. 



