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dz / TAOCP / vol2 / ch03 / 01Summary
3.1: Introduction
Node Tree
Nodes
| usefulness_of_random_numbers | |
| content | Usefulness of Random Numbers |
| children | numerical_analysis, recreation, simulation, aesthetics, computer_programming, cryptography, decision_making |
| simulation | |
| content | simulation |
| parents | usefulness_of_random_numbers |
| decision_making | |
| content | Decision Making |
| parents | usefulness_of_random_numbers |
| numerical_analysis | |
| content | Numerical Analysis |
| parents | usefulness_of_random_numbers |
| computer_programming | |
| content | Computer Programming |
| children | randomized_algorithms |
| parents | usefulness_of_random_numbers |
| cryptography | |
| content | Cryptography |
| parents | usefulness_of_random_numbers |
| aesthetics | |
| content | Aesthetics |
| parents | usefulness_of_random_numbers |
| recreation | |
| content | Recreation |
| parents | usefulness_of_random_numbers |
| randomized_algorithms | |
| content | Randomized Algorithms |
| parents | computer_programming |
| seq_rand_num | |
| content | Sequence of random independent numbers |
| children | distribution, sequence_of_sequences |
| distribution | |
| content | Distribution |
| children | uniform |
| parents | seq_rand_num |
| uniform | |
| content | Uniform |
| children | equally_probable (description) |
| parents | distribution |
| equally_probable | |
| content | Each number equally probable |
| parents | uniform |
| sequence_of_sequences | |
| content | Sequence of Sequences |
| parents | seq_rand_num |
| random_number_methods | |
| content | Methods to produce random numbers |
| children | mechanical, computer |
| mechanical | |
| content | mechanical |
| children | random_tables |
| parents | random_number_methods |
| computer | |
| content | computer |
| children | random_tables, arithmetic |
| parents | random_number_methods |
| random_tables | |
| content | Random Tables |
| parents | computer, mechanical |
| arithmetic | |
| content | Arithmetic |
| children | neumann_middle_square |
| parents | computer |
| neumann_middle_square | |
| content | Von Neumann's "Middle-square" method |
| children | dont_trust_rng_without_testing (moral of the story), poor_random_source, deterministic |
| parents | arithmetic |
| deterministic | |
| content | Deterministic |
| children | pseudorandom |
| parents | neumann_middle_square |
| pseudorandom | |
| content | Pseudorandom or Quasi-random |
| children | appear_random |
| parents | deterministic |
| appear_random | |
| content | only appear to be random |
| parents | pseudorandom |
| poor_random_source | |
| content | Comparatively poor source of random numbers |
| parents | neumann_middle_square |
| dont_trust_rng_without_testing | |
| content | middle-square method can give results, but it's dangerous to put much faith into until after elaborate computations have been performed |
| parents | neumann_middle_square |
| remarks | The context here is that many people tried different variations of the middle-square method, and managed to eventually find one that worked really well. But it took lots of testing and "elaborate computations" to get it there. |
| algo_k | |
| content | Alorithm K |
| children | dont_use_random_methods (lesson learned), knuth_1959, not_very_good, super_random, complicated, converges_6065038420 |
| super_random | |
| content | "super-random" number generator |
| parents | algo_k |
| not_very_good | |
| content | Not very good at all |
| parents | algo_k |
| knuth_1959 | |
| content | Constructed by Knuth in 1959 |
| parents | algo_k |
| complicated | |
| content | Complicated |
| parents | algo_k |
| converges_6065038420 | |
| content | Coincidentally converges on 6065038420 and transforms back into itself (AKA loops). |
| parents | algo_k |
| dont_use_random_methods | |
| content | Random Number Generators should not be generated with a random method chosen at random |
| parents | algo_k |