Abstract Algebra IBL Wiki user:bmwoodruff

user:bmwoodruff:20130918

Anonymous (anonymous@undisclosed.example.com) — 2013-09-27T17:23:50+00:00

The Game Of Scoring The Game Of Scoring Misere Encryption Key Simple Shift Permutation Of The Alphabet First Encryption Key The Set Of Simple Shift Permutations Permutation Number Of Permutations Automorphism Of A Graph Automorphisms Of A Square

user:bmwoodruff:20130920

Anonymous (anonymous@undisclosed.example.com) — 2013-11-21T10:36:00+00:00

AutomorphismsOfASquare2 Automorphisms Of A Directed Square Simple Shift Repetition Cryptography Reading Assignment Once we have a set of permutations, we'd like to be able to combine them to get new permutations. The previous problem used repetition on simple shift permutations of the alphabet to obtain additional permutations. The next problem has you show that the composition of any finite collection of permutations on a set is always a permutation.

user:bmwoodruff:20130923

Anonymous (anonymous@undisclosed.example.com) — 2013-11-21T11:03:53+00:00

Automorphisms Of A Directed Square (:note:) Please work on the next problem again. I would like you to come to class with a written proof that uses induction. Here's a different problem, but the proof technique is related. !!!!!Example Provide a proof of the following claim. *'Claim

user:bmwoodruff:20130925

Anonymous (anonymous@undisclosed.example.com) — 2013-11-21T15:10:36+00:00

Much of our work up to this point has been based on the ability to compute a remainder. This is all based on the Division Algorithm. Division Algorithm Division Algorithm Proof If you are unable to complete this problem, then please move on to the next. You may find that reading chapter 0 in your abstract algebra text can help you with this one.

user:bmwoodruff:20130927

Anonymous (anonymous@undisclosed.example.com) — 2013-11-25T13:38:47+00:00

The Order Of A Permutation When Do Two Simple Shifts Span The SameSet (:include Definition.TheGameOfPermutationScoring:) (:include Problem.TheGameOfPermutationScoringOnASquare:) ---------- It would be nice if we could create a way to visually keeping track of which elements of $H$ have been taken. Let me describe how we can do this with an example. Suppose you are playing the game on a square (as above). Player one takes the permutation $(1,2,3,4)$. Then player $2$ chooses the element…

user:bmwoodruff:ben_s_outline

Anonymous (anonymous@undisclosed.example.com) — 2013-11-25T13:32:26+00:00

* 20130918 * 20130920 * 20130923 /* This page is not finished */ * 20130925 /* This page is not finished */ * 20130927 * 20130930 * 20131002 * 20131004 * 20131007 * 20131009 * 20131011 * 20131014 * My students will be using the following wiki for their course. * Ben's tagged pages I plan to have multiple threads running simultaneously through the semester. However, for development purposes, it will pro…

user:bmwoodruff:ben_s_tagged_pages

Anonymous (anonymous@undisclosed.example.com) — 2013-08-22T16:07:58+00:00

user:bmwoodruff:sandbox

Anonymous (anonymous@undisclosed.example.com) — 2013-09-24T17:11:09+00:00

!!!!Problem Here are two graphs on 4 vertices. List the elements in their automorphism groups using disjoint cycle notation. Then construct another graph on 4 vertices and list the elements of the automorphism group. ---------- We need a common notation to talk about permutations. Let's define one. !!!!!Definition (Permutation Disjoint Cycle Notation) Let $X$ be a finite set. A permutation of $X$ is called a cycle if there exists a single $a\in X$ such that for each $x\in X$ either $x=\sigm…