PRNG + LCG chapters

SUMMARY.md

@@ -23,6 +23,9 @@
     * [Box Muller Transform](contents/box_muller/box_muller.md)
         * [How costly is rejection sampling?](contents/box_muller/box_muller_rejection.md)
     * [Probability Distributions](contents/probability_distributions/distributions.md)
+* [Random Number Generation](contents/RNG/RNG.md)
+    * [Diehard Tests](contents/diehard/diehard.md.md)
+    * [Linear Congruential Generators](contents/LCG/LCG.md)
 * [Tree Traversal](contents/tree_traversal/tree_traversal.md)
 * [Euclidean Algorithm](contents/euclidean_algorithm/euclidean_algorithm.md)
 * [Monte Carlo](contents/monte_carlo_integration/monte_carlo_integration.md)

contents/RNG/RNG.md

@@ -0,0 +1,61 @@
+# Random Number Generation
+
+Quick, try to think of a number between 1 and 10.
+
+Ok, do you have your number?
+
+Was it 7?
+
+Probably not, right? I mean, there is no magic here.
+I put down 7 (seemingly at random), and you chose your number seemingly at random.
+In general, there should be about a 10% chance that we chose the same number; however, that is statistically not the case.
+
+For some reason, we naturally choose 7 more than any other integer. The exact probability of choosing 7 is currently up for debate, ranging from roughly 25% {{ "RNG_reddit" | cite }} to 45% {{ "RNG_Numberphile" | cite }}, and there are some interesting papers on related topics you might want to chek out as well {{ "Shepard197582" | cite }} {{ "navarro2008latent" | cite }}.
+
+My point is that we, as humans are really bad at coming up with random numbers.
+Computers, on the other hand, are some of the most sofisticated pieces of technology we have ever built.
+They have sometimes trillions of transistors, all working to provide answers to fundamental questions in science and technology.
+Surely they are good at creating random numbers, right?
+
+Yeah, not really. Like, they are fine, but they are machines built by people whowant precise answers.
+Randomness is not usually something people want when trying to add $$2+2$$.
+
+So then what do we do?
+Well, white noise (static) is truly random [CITE] and comes about all the time in nature, so we could just put a microphone somewhere and collect random numbers from the world around us.
+The problem is that nature is kinda slow at doing this and we want really fast simulations, so it's not in our best interest to just chill by a pond fishing for numbers.
+So instead let's come up with complex algorithms that *simulate* randomness as best as we can.
+From here on, rather than talking about generating truly random numbers, we will discuss creating "random enough" *pseudo* random numbers.
+
+In the literature, you might see Random Number Generation being shortened to RNG and Pseudo Random Number generation shortened to PRNG.
+The two are often used interchangeable, but there is a small destinction to be made.
+Namely that RNG is related to the entire process of generating random numbers, while PRNG is a subset of methods that use the computer to do so.
+In certain fields, other terms are used, but these will be covered on a case-by-case basis.
+
+In these chapters, we'll do our best to cover a bunch of different algorithms and their specific use-cases.
+Before doing that, we'll just talk about 2 things:
+1. Why we want randomness to begin with
+2. How to test for randomness
+
+## Why do we want random numbers?
+
+Monte Carlo, simulating nature, etc
+
+computer graphics / IFS
+
+Cryptographic hashing
+
+Note that we need different quality of RNG for this
+
+
+## Testing for Randomness
+
+Histogram test
+
+### Bibliography
+
+{% references %} {% endreferences %}
+
+<script>
+MathJax.Hub.Queue(["Typeset",MathJax.Hub]);
+</script>
+

contents/diehard/diehard.md

@@ -0,0 +1,14 @@
+# Diehard Tests
+
+## Birthday spacings
+## Overlapping permutations
+## Ranks of matrices
+## Monkey tests
+## Count the 1s
+## Parking lot test
+## Minimum distance test
+## Random spheres test
+## The squeeze test
+## Overlapping sums test
+## Runs test
+## The craps test

literature.bib

@@ -541,3 +541,43 @@ @misc{box_muller_wiki
   url={https://en.wikipedia.org/wiki/Box%E2%80%93Muller_transform},
   year={2022}
 }
+
+#------------------------------------------------------------------------------#
+# RNG
+#------------------------------------------------------------------------------#
+
+@misc{RNG_reddit,
+  title={Asking over 8500 students to pick a random number from 1 to 10 [OC]},
+  url={https://www.reddit.com/r/dataisbeautiful/comments/acow6y/asking_over_8500_students_to_pick_a_random_number/},
+  year={2023}
+}
+
+@misc{RNG_Numberphile,
+  title={Random Numbers - Numberphile},
+  url={https://www.youtube.com/watch?v=SxP30euw3-0},
+  year={2013}
+}
+
+@article{Shepard197582,
+title = {The internal representation of numbers},
+journal = {Cognitive Psychology},
+volume = {7},
+number = {1},
+pages = {82-138},
+year = {1975},
+issn = {0010-0285},
+doi = {https://doi.org/10.1016/0010-0285(75)90006-7},
+url = {https://www.sciencedirect.com/science/article/pii/0010028575900067},
+author = {Roger N Shepard and Dan W Kilpatric and James P Cunningham},
+}
+
+@article{navarro2008latent,
+  title={Latent features in similarity judgments: A nonparametric Bayesian approach},
+  author={Navarro, Daniel J and Griffiths, Thomas L},
+  journal={Neural computation},
+  volume={20},
+  number={11},
+  pages={2597--2628},
+  year={2008},
+  publisher={MIT Press}
+}