ruggeri

Graph Algorithms

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Graph Types

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

ruggeri

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

ruggeri

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.

ruggeri

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!

ruggeri

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.

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.)

ruggeri

#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");

ruggeri

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 = []