RobertTalbert

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RobertTalbert

import networkx as nx
import matplotlib as plt

# Generate the edge list using a list comprehension that invokes the actual relation you want. 
# For example, here is the relation of "divides", on the set {0,1,2,..., 20}. 
# We know a divides b if b mod a = 0. 

divides_edges = [(a,b) for a in range(21) for b in range(21) if b % a == 0] 
divides_graph = nx.DiGraph(divides_edges) 

RobertTalbert

# Code for generating random weighted graphs in networkX and printing off the edges

import networkx as nx
import matplotlib.pyplot as plt

from random import *

# Create a random graph with 10 nodes and a 50% chance of connection. 
# Change the 10 and 0.5 for graphs with more/fewer nodes and more/fewer connections.
G = nx.random_graphs.gnp_random_graph(10,.5)

RobertTalbert

List of graph isomorphism invariants

This is a running list of graph isomorphism invariants, that is, properties of graphs such that...

If $G$ and $H$ are isomorphic and $G$ has the property, then $H$ also has the property.

A logically equivalent way to say this is:

If $G$ has the property but $H$ does not, then $G$ and $H$ are not isomorphic.

RobertTalbert

Click here for the full documentation for networkX.

To do:	Enter:
Load networkx and matplotlib	import networkx as nx import matplotlib.pyplot as plt
Create an empty graph	G = nx.Graph()
Add an edge to G between nodes 2 and 3	G.add_edge(2,3)
Add several edges to G all at once	G.add_edges_from([(1,3), (2,4), (2,3)])
Print a list of the edges in G	for e in G.edges(): print(e)
Print a list of the nodes in G	for v in G.nodes(): print(v)

RobertTalbert

If you have difficulty affording groceries or accessing sufficient food to eat every day, or if you lack a safe and stable place to live, I encourage you to visit Replenish, a food resource for GVSU students. If you are comfortable doing so, please speak with me about your circumstances so that I can advocate for you and to connect you with other campus resources.

RobertTalbert

# To find the natural number solutions to x + y + z = 8

[(x,y,z) for x in range(9) for y in range(9) for z in range(9) if x+y+z == 8]

# To generate the ways to pick 6 donuts from an unlimited supply of glazed, chocolate, and jelly-filled

[(g,c,j) for g in range(7) for c in range(7) for j in range(7) if g+c+j == 6]

# Put `len( )` around these lists to find the number of items in the list. 

RobertTalbert

# The first recursive function we saw. 
# Turns out it has the closed formula f(n) = n(n+2) although we didn't prove it. 

def f(n): 
    if n == 0: return 0
    else: return f(n-1) + 2*n + 1
    
# AKA the factorial function: 

def g(n): 

RobertTalbert

\section{Appendix B: MTH 225 Learning Targets}
\label{sec:learning-targets}

\begin{subsubsection}{Module 1: Computer Arithmetic}
\begin{description}
\tightlist
    \item[CA.1] \textbf{(CORE)} \ I can represent an integer in base 2, 8, 10, and 16 and represent a negative integer in base 2 using two's complement notation.
    \item[CA.2] I can perform addition, subtraction, multiplication, and division in binary. 
\end{description}

RobertTalbert

Course module structure: The course content is split up into five modules:

• Module 1: Computer arithmetic. Representing integers in binary, octal, and hexadecimal; binary arithmetic; the Division Algorithm and modular arithmetic.

• Module 2: Logic. Logical propositions, conditional statements, truth tables, predicates, and quantification.