Ned Ruggeri ruggeri

Warmup: What Is A Programming Language?

A proof is a argument that a statement is true, where the argument is written in a formalized, very specific language. The concept of what a proof is can be confusing, so I want to make an extended analogy to computer programs and programming languages.

(I think that people who know computer programming are in a uniquely good position to understand mathematical logic.)

unit normal = normal(mean = 0, stddev = 1) What does stddev mean?

Mean is the expected value of the random variable: mean = \Int Pr(x) x It's not the most likely value necessarily. That would be the mode.

Let's say you sample from the normal distribution. What is the expected value of the squared error of the mean and the sample? How good is the mean value as a predictor of samples drawn from the normal distribution

The less good the mean value is at predicting, the more "random" the normal distribution is. The "wider" the dispersion.

Ubuntu instructions (https://certbot.eff.org/lets-encrypt/ubuntutrusty-other) summary:

$ sudo apt-get update
$ sudo apt-get install software-properties-common
$ sudo add-apt-repository ppa:certbot/certbot
$ sudo apt-get update
$ sudo apt-get install certbot

Graph Algorithms

Graph Types

Vertices and edges
- Vertex: city.
- Edge: road.
Undirected vs directed

Binary Search Trees

Operations

find
insert
delete
Each has time complexity proportional to depth of the tree.

Heaps

Priority Queue

Heaps are an implementation of the priority queue abstract data type:

insert(entry, priority).
- priority is an integer priority. Entries with "higher priority" will be extracted before entries with "lower priority."
Lower number often is "higher priority." This makes sense

	import random
	import re
	import string

	def load_dictionary():
	with open("dictionary.txt") as f:
	return f.read().splitlines()

	def filter_dictionary(dictionary):
	new_dictionary = []

	#include <iostream>
	#include <stdexcept>

	int max(int numbers[], unsigned int len)
	{
	std::cout << "len=" << len << ": starting function." << std::endl;

	if (len == 0)
	{
	throw std::invalid_argument("len must not be zero");

	import Control.Monad (forM, liftM)
	import Data.Array.IO (IOUArray, getElems, newListArray)
	import Data.Array.Base (unsafeRead, unsafeWrite)
	import Data.Function ((&))
	import Data.Time.Clock (NominalDiffTime, diffUTCTime)
	import Data.Time.Clock.POSIX (getPOSIXTime, posixSecondsToUTCTime)
	import System.Random.MWC (create, uniformR)

	-- TODO: I should be able to do this with the ST monad, but I'm not
	-- smart enough for that yet.

	import Control.Monad
	import Data.Array.IO
	import System.Random

	-- TODO: I should be able to do this with the ST monad, but I'm not
	-- smart enough for that yet.

	-- ArraySlice data type. I probably should be able to parameterize
	-- over the kind of MArray. Indeed, ArraySlice probably can implement
	-- MArray itself!