Schedule of Classification 



Partitions 

 Permutations 



PAGE 



86-87 

 87-88 



Fiqurate numbers ... 89 



Special series 91-92 



Probabilities (including com- 

 bination of observations). 

 Theory of errors ... 92 

 Least Squares Method 97-98 

 Probabilities ... 100-103 

 Problems ... 101-102 

 Theory of statistics. Actu- 

 arial mathematics ... 104 

 Mortality ... 114-116 

 Population ... 117-118 

 Calculus of differences; inter- 

 polation 121 



Interpolation ... 1 23-1 25 



Linear Substitutions. 



General 126 



Determinants ... ... 127 



Discriminants and resultants 136 

 Elimination ... 137-139 



Characteristic properties of 

 linear substitutions ; types 

 of linear substitutions. 



(See also 1210.) 



General theory of quantics 

 Binary forms 

 Ternary forms 

 Special developments asso- 

 ciated with forms in more 

 than three variables 



1625 Finite Summation. Recurring 



1630 



1635 



1640 



2000 

 2010 

 2020 



2030 



2040 

 2050 

 2060 

 2070 



2400 

 2410 



2420 

 2430 



140 

 142 

 146 

 153 



lf> 5 



2440 



Theory of Equations. 



General 



Elements of the theory of 

 algebraicequations; exis- 

 tence of roots, symmetric 

 functions; rational frac- 

 tions ; partial fractions 

 Existence of roots 

 Symmetric functions 162-163 

 Reality, multiplicity, separa- 

 tion, of roots 163 



Equations of the second, third 

 and fourth orders : other 

 particular equations 



Equations, 2nd order ... 

 Equations, 2nd, 3rd and 



4th orders 170 



Equations, 3rd order 170-171 

 Irreducible case ... 171 



Equations, 3rd and 4th 



orders 171-172 



Equations, 4th order 172-173 

 Trinomial Equations 173-174 

 Numerical solution of equa- 

 tions (including graphical 

 methods) 174 



156 



158 

 1 59 



169 



169 



PAGE 



Numerical solution of 



equations in general 174 



Approximate determina- 

 tion of roots 174-175 

 Graphical methods 177-178 

 2450 General resolution of equa- 

 tions ; theory of Galois. 



(See also 1210.) 178 



Equations, 5th order 180-181 

 Equations, 6th order ... 181 

 2460 Simultaneous equations ; in- 

 cluding linear equations 184 

 Linear equations ... 185-186 



2470 Transcendental equations ... 187 



Theory of Numbers. 



2800 General 188 



2810 Divisibility ; linear con- 

 gruences ... ... 193 



Divisibility ... 193-194 



2815 Continued fractions and in- 

 determinate equations 197 

 Continued fractions 197-201 

 Indeterminate equations 201-204 

 1st order ... 202-203 

 2nd order, 3rd order, 4th 



order, 5th order ... 203 



2820 Quadratic residues 204 



2830 Quadratic binary forms ... 205 

 2840 Quadratic forms of three or 

 more variables ; bilinear 

 forms. (See also 2060, 



2070.) 209 



Decomposition of numbers 



into sums of squares 209-2 1 

 Bilinear forms ... 21 3-2 1 4 



2850 Congruences other than 

 linear ; cubic and higher 



residues 214 



2860 Forms of higher degree which 



cannot be considered as 



products of linear factors. 



(See also 2060, 2070.) ... 218 



Fermafs theorem on 



z n +y n =z n ... 218-219 



2870 Forms of higher degree which 

 can be considered as pro- 

 ducts of linear factors ; 

 algebraic numbers ; ideals. 



(See also 0820.) 220 



2880 Application of trigonometri- 

 cal functions to arithmetic ; 



cyclotomy 222 



Binomial equations ... 222 

 2890 Application of other trans- 

 cendental functions to 



arithmetic 224 



2900 Distribution of prime num- 

 bers 225 



2910 Special numbers and numeri- 

 cal functions 



Bernoulli's numbers 



228 

 228-229 



