Isomorphism: A First Example

Isomorphism: A First Example MAT 320 Spring 2011 Dr. Bryant

Are Z5 and S = {0,2,4,6,8} Z10 the same?

Using colors to decide…

It seems like the answer is no… • Color-coding the elements of each ring shows that the multiplication tables don’t match up • However, notice something in the multiplication table for S: • This shows that 1S = 6 • Since 1 in Z5 was colored green, this means our coloring was wrong!

Start with empty tables and fill in based on color…

Since 6+6=2 in S, 2 is yellow…

It follows that 8 is blue and 4 is purple

With this new coloring… • …we see that the two rings have exactly the same structure • When two rings have exactly the same addition and multiplication tables (under some correspondence between their elements), we say the rings are isomorphic • iso = same, morphic = structure • Finding the correspondence is the hard part!

Isomorphism: A First Example

Isomorphism: A First Example

Presentation Transcript

Students First! A “Learning Reconsidered Example”

Gary’s Work on Graph Isomorphism

Graph Isomorphism

Subgraph Isomorphism in Graph Classes

Linear Programming – A First Example

A Good Example Of A Bad Example

Writing loops: a first example

Team A Example of a Worked Example

Stoke’s first problem (BSL example)

First Example in Respiratory Area

Example of A*

A First Example: The Bump in the Wire

A First Example: The Bump in the Wire

Example 2.1 A Conceptual Example

Graph Isomorphism

Isomorphism Checking in GROOVE

Running A First Example: The Web Bumper

Let’s first observe this example with a base of 10.

Analog IC Design First – A OPAMP Design Example.

Isomorphism in GRAPHS

A Physically-motivated Algorithm for the Graph Isomorphism Problem

Bootstrap First Web Page Example – Tutlane