Group: sets
Topic: Kolmorgorov and algorithmic complexity
Topic: chaotic behavior
Topic: continuum in mathematics
Topic: data reduction
Topic: fractal geometry
Topic: geometry
Topic: history of mathematics
Topic: infinity and infinitesimal
Topic: lambda calculus
Topic: kinds of numbers
Topic: probability
Topic: randomness
Topic: random number generation
Topic: statistics
Topic: symbolic manipulation of formulas
Topic: topology
Group: algorithms
Group: computer science
Group: formalism
Group: philosophy of mathematics
Group: science
Topic: computational geometry
Topic: constraints
Topic: entropy
Topic: graph coloring
Topic: logic
Topic: mathematical proof
Topic: mathematical proof as a social process
Topic: numerical error
Topic: programming as mathematics
Topic: real numbers and floating point numbers
Topic: science as mathematics
 
Subtopic: notation
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
 Subtopic: algebra
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]
 Subtopic: analysis
Quote: there is a geometrical line through every finite set of points
 Subtopic: calculus
Quote: reduction in lambda calculus is like eliminating differentiation in the differential calculus [»wegnP10_1986]
 Subtopic: calculus of variation
Quote: the calculus of variations determines the path in space which minimizes the path's action
 Subtopic: constraint systems
Quote: efficient, incremental algorithm for solving user interface, constraint systems of linear equations and inequalities; based dual simplex method [»bardGJ12_2001]
 Subtopic: differential equations
Quote: use exponential functions to solve linear differential equations with constant coefficients [»feynRP_1965]
 Quote: the EDSAC subroutine library included the RungeKuttaGill process for solving differential equations [»wilkMV_1951]
 Subtopic: eigenvalue/eigenvector
Quote: if Tx = c x then x is an eigenvector and c is an eigenvalue [»simmGF_1963]
 Subtopic: imaginary powers
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
 Subtopic: integer programming
Quote: optimal instruction schedules by integer programming; up to 1000 instructions; 4x improvements at 14% cost [»wilkK6_2000]
 Subtopic: linear systems of equations
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
 Subtopic: long division
Quote: algorithm for long division of natural numbers; includes the theory behind the algorithm [»hansPB6_1994]
 Subtopic: ordering relation
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]
 Subtopic: symmetry
Quote: something is symmetrical if it is invariant under some transformation; e.g., Newtonian laws are symmetrical under translation [»feynRP_1963]
 Subtopic: unrelated types
Quote: shouldn't there be types sufficiently different that they do not induce union or intersection types?

Group: mathematics
Group: sets (7 topics, 148 quotes)
Topic: Kolmorgorov and algorithmic complexity (10 items)
Topic: chaotic behavior (27 items)
Topic: continuum in mathematics (7 items)
Topic: data reduction (9 items)
Topic: fractal geometry (8 items)
Topic: geometry (33 items)
Topic: history of mathematics (57 items)
Topic: infinity and infinitesimal (37 items)
Topic: lambda calculus (16 items)
Topic: kinds of numbers (24 items)
Topic: probability (21 items)
Topic: randomness (20 items)
Topic: random number generation (29 items)
Topic: statistics (12 items)
Topic: symbolic manipulation of formulas (12 items)
Topic: topology (29 items)
Related Topics
Group: algorithms (6 topics, 94 quotes)
Group: computer science (871 topics, 23489 quotes)
Group: formalism (9 topics, 478 quotes)
Group: philosophy of mathematics (11 topics, 330 quotes)
Group: science (45 topics, 1960 quotes)
Topic: computational geometry (20 items)
Topic: constraints (35 items)
Topic: entropy (14 items)
Topic: graph coloring (7 items)
Topic: logic (84 items)
Topic: mathematical proof (23 items)
Topic: mathematical proof as a social process (14 items)
Topic: numerical error (19 items)
Topic: programming as mathematics (27 items)
Topic: real numbers and floating point numbers (37 items)
Topic: science as mathematics (26 items)
