related
referenced
 
Group members
Group: sets
 
 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: Kolmorgorov and algorithmic complexity
 Topic: probability
 Topic: randomness
 Topic: random number generation
 Topic: statistics
 Topic: symbolic manipulation of formulas
 Topic: topology

Subtopic:
mathematical thought
Quote: Simon Stevin thought like a mathematician; defined terms, precise writing, no assumptions, facts logically derived from principles
[dijkEJ_1955]

Subtopic:
notation
Quote: development of math notation: variable names, functions, symbol lists, numeric rep, vectors/etc. as entities, quantity vs. representation
[falkAD8_1978]
 Quote: use 'x, y, z' for unknown lengths and 'a, b, c' for known lengths
[descR_1641a OK]
 Quote: consider algebras of one to six primitive letters, denoted i, j, k, l, m, n
[peirB_1881 OK]

Subtopic:
natural proof
Quote: a natural proof finds some simplicity of realworld instances and uses them to find a simple proof of correctness
[desaA10_2014]

Subtopic:
algebra
Quote: an algebra in math characterizes behavior like types in computer science
[wegnP10_1986]
 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: only the unit is always equal and simple; it can generate nothing by multiplication of itself except that by which it is multiplied
[alkhAJMM_825a]

Subtopic:
analysis
Quote: there is a geometrical line through every finite set of points
[leibGW_1686b]

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

Subtopic:
function
Quote: a function f associates a single value f(x) with each member x of its domain; the values are arbitrary
[laviS_1994]
 Quote: a function is a set of ordered pairs with one pair for each x; the values x are the domain of function f and the values y are its range
[stilJ_2013]

Subtopic:
primes
Quote: deterministic polynomialtime algorithm for primality testing; generalizes Fermat's Little Theorem to polynomial rings over finite fields
[agraM9_2004]
 Quote: linear algorithm to decompose program into primes; e.g., sequence, ifthen, whiledo
[formIR9_1982]
 Quote: guarantee RSA primes are different by dividing nbit random number space into 2^b subspaces; eliminates a class of signature authentication attacks
[peyrM3_2000]
 Quote: maybe pure mathematics is random; e.g., distribution of the primes; there's nothing there to prove
[chaiGJ_2001]

Subtopic:
engineering
Quote: engineers use mathematics to calculate properties and compare designs
[parnDL1_2010]

Subtopic:
game theory
Quote: convergence to a mixed Nash equilibrium can take prohibitively long; PPAD problems always have a solution; given an unbalanced node, find another
[daskC2_2009]
 Quote: a game is ultraweakly solved if it has a gametheoretic value for initial positions; weakly solved if there is a strategy for both players; strongly solved if there is a strategy for all legal positions
[bowlM11_17]
 Quote: headsup limit Texa holdem poker is essentially weakly solved and the dealer wins; first nontrivial imperfect game played competitively; variation of Counterfactual Regret Minimization of Nash equilibrium
[bowlM11_17]

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_1963x]
 Quote: the most remarkable formula in mathematics: e^i \theta = cos \theta + i sin \theta
[feynRP_1963x]

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

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 xrussB_1919 OK]
 Quote: order the inductive numbers by: mrussB_1919 OK]

Subtopic:
symmetry
Quote: something is symmetrical if it is invariant under some transformation; e.g., Newtonian laws are symmetrical under translation
[feynRP_1963x]

Subtopic:
unrelated types
Quote: shouldn't there be types sufficiently different that they do not induce union or intersection types?
[reynJC9_1983]

Related
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: numeric methods
 Topic: numerical error
 Topic: probabilistic and randomized algorithms
 Topic: programming as mathematics
 Topic: real numbers and floating point numbers
 Topic: science as mathematics

Subtopics
