Quote: development of math notation: variable names, functions, symbol lists, numeric rep, vectors/etc. as entities, quantity vs. representation [»falkAD8_1978, OK]

Quote: use 'x, y, z' for unknown lengths and 'a, b, c' for known lengths

Quote: an algebra in math characterizes behavior like types in computer science

Quote: algebraic structures in math include semigroups, groups, rings, fields, and universal algebras [»wegnP10_1986]

Quote: relational algebra expresses queries as operations on a relation; relational calculi as predicates that tuples must satisfy [»wegnP10_1986]

Quote: calculi are concrete (syntactic) algebras while algebras are abstract (semantic) calculi [»wegnP10_1986]

Quote: Viete introduced "analytics" and the use of letters in the theory of equations; e.g., x^2+ax+b=0 [»vietF_1591]

Quote: mathematical analysis uses the art and rules of logic to obtain equations of species (e.g., 'x') instead of numbers [»vietF_1591]

Quote: rules of arithmetic for calculation by species or forms of things, as, for instance, the letters of the alphabet [»vietF_1591]

Quote: there is a geometrical line through every finite set of points

Quote: reduction in lambda calculus is like eliminating differentiation in the differential calculus [»wegnP10_1986]

Quote: the calculus of variations determines the path in space which minimizes the path's action

Quote: efficient, incremental algorithm for solving user interface, constraint systems of linear equations and inequalities; based dual simplex method [»bardGJ12_2001]

Quote: use exponential functions to solve linear differential equations with constant coefficients [»feynRP_1965]

Quote: the EDSAC subroutine library included the Runge-Kutta-Gill process for solving differential equations [»wilkMV_1951]

Quote: if Tx = c x then x is an eigenvector and c is an eigenvalue [»simmGF_1963]

Quote: complex imaginary powers are the same as sine and cosine; they oscillate; for small t, e^it = 1+it; for small t, cos t is nearly 1 and sin t is nearly 0 [»feynRP_1963]

Quote: the most remarkable formula in mathematics: e^i \theta = cos \theta + i sin \theta

Quote: optimal instruction schedules by integer programming; up to 1000 instructions; 4x improvements at 14% cost [»wilkK6_2000]

Quote: linear systems are important because we can solve them and because the fundamental laws of physics are often linear, e.g., Maxwell's equations for electricity, the laws of quantum mechanics, and the approximations when displacements are small [»feynRP_1963]

Quote: solver for linear equations extended with integer division and modulus, sign extension, and bit slicing; uses balancing to eliminate some nonlinear operators before Gaussian elimination [»ramsN4_1996]

Quote: solve a geometric problem by reducing it to a series of n equations in n unknowns

Quote: algorithm for long division of natural numbers; includes the theory behind the algorithm [»hansPB6_1994]

Quote: an ordering relation has three properties: x not y<x; x<y and y x<z; and, either x<y or y<x [»russB_1919, OK]

Quote: order the inductive numbers by: m<n if n possesses every hereditary property possessed by the successor of m [»russB_1919, OK]

Quote: something is symmetrical if it is invariant under some transformation; e.g., Newtonian laws are symmetrical under translation [»feynRP_1963]

Quote: shouldn't there be types sufficiently different that they do not induce union or intersection types?