Group: mathematics

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topic root
computer science
philosophy of mathematics
computational geometry
graph coloring
mathematical proof
mathematical proof as a social process
numeric methods
numerical error
probabilistic and randomized algorithms
programming as mathematics
real numbers and floating point numbers
science as mathematics

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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 up

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

Subtopic: notation up

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 up

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

Subtopic: algebra up

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 up

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

Subtopic: calculus up

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

Subtopic: function up

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 up

Quote: deterministic polynomial-time 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 n-bit random number space into 2^b sub-spaces; 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 up

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

Subtopic: game theory up

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 ultra-weakly solved if it has a game-theoretic 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: heads-up limit Texa hold-em 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 up

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 up

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

Subtopic: long division up

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

Subtopic: ordering relation up

Quote: an ordering relation has three properties: x not y xrussB_1919 OK]
Quote: order the inductive numbers by: mrussB_1919 OK]

Subtopic: symmetry up

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

Subtopic: unrelated types up

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

Related up

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 up

game theory
imaginary powers
integer programming
long division
mathematical thought
natural proof
ordering relation
unrelated types

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