Abstract Algebra IBL Wiki

elements_of_style_for_proofs

bmwoodruff (bmwoodruff@undisclosed.example.com) — 2016-04-19T20:36:00+00:00

Elements of style for proofs Years of elementary school math taught us incorrectly that the answer to a math problem is just a single number, “the right answer.” It is time to unlearn those lessons; those days are over. From here on out, mathematics is about discovering proofs and writing them clearly and compellingly.

user:tarafife:tara_s_outline

tarafife (tarafife@undisclosed.example.com) — 2014-01-01T09:30:37+00:00

I'm going to be creating material for a course on the second half of Abstract Algebra. It will assume that students know the basic definitions and ideas about groups, especially automorphisms. Obviously I don't have a class, so no one will be using this any time soon. But if anyone wants to take problems from me that would be great.

problem:a_b_sqrt_2

tarafife (tarafife@undisclosed.example.com) — 2013-12-24T22:59:17+00:00

A B Sqrt 2 Problem Let be the set . Please show * that is a group under addition. We will denote this group . * and that is abelian * that is a group under multiplication. We will denote this group as . * ---------- Remarks * There are more properties, I will add them later. I'm going to add all the properties of a field.

problem:s_x_is_a_group - created

tarafife (tarafife@undisclosed.example.com) — 2013-12-24T22:50:21+00:00

S X Is A Group Problem Let be any set, and let be the set of permutations on . Please show that is a group under function composition. ---------- Remarks * Make remarks with a list. ---------- $\LaTeX$ version %%%%% % DEPENDENCIES % RequiredPackages: \usepackage{tikz} % RequiredMacros: \DeclareMathOperator{\aut}{Aut} %%%%% \begin{problem} Type the problem code here. \end{problem}

problem:when_do_two_simple_shifts_span_the_same_set - created

bmwoodruff (bmwoodruff@undisclosed.example.com) — 2013-11-25T13:46:37+00:00

====== When Do Two Simple Shifts Span The Sameset ====== ==== Problem ==== Consider the sets $H_{12}$ and $H_{15}$ of simple shift permutations on alphabets with 12 and 15 letters respectively. - For each $k\in\{0,1,2,\ldots,11\}$, make a list of the elements in $H_{12}$ that are in $\text{span}(\{\phi_k\})$ and state the order of $\phi_k$ as an element of $H_{12}$. - For each $k\in\{0,1,2,\ldots,14\}$, make a list of the elements in $H_{15}$ that are in $\text{span}(\{\phi_k\})$ and state …

problem:when_do_two_simple_shifts_span_the_sameset - removed

bmwoodruff (bmwoodruff@undisclosed.example.com) — 2013-11-25T13:46:21+00:00

isthegraphacayleygraphorder9-2.png - created

bmwoodruff (bmwoodruff@undisclosed.example.com) — 2013-11-07T14:15:40+00:00

isthegraphacayleygraphorder9-1.png - created

bmwoodruff (bmwoodruff@undisclosed.example.com) — 2013-11-07T14:15:39+00:00

cayleygraphtetrahedron.png - created

bmwoodruff (bmwoodruff@undisclosed.example.com) — 2013-11-07T14:15:39+00:00

cayleygraphorder6-2.png - created

bmwoodruff (bmwoodruff@undisclosed.example.com) — 2013-11-07T14:11:05+00:00

cayleygraphorder6-1.png - created

bmwoodruff (bmwoodruff@undisclosed.example.com) — 2013-11-07T14:11:05+00:00

firststepincayleygraph.png - created

bmwoodruff (bmwoodruff@undisclosed.example.com) — 2013-09-25T13:51:09+00:00

cayleygraphsofd4byhand.png - created

bmwoodruff (bmwoodruff@undisclosed.example.com) — 2013-09-23T16:53:33+00:00

differentgraphson_vertices.png - created

bmwoodruff (bmwoodruff@undisclosed.example.com) — 2013-09-23T14:41:40+00:00

problem:digraphsquare.png - created

bmwoodruff (bmwoodruff@undisclosed.example.com) — 2013-09-18T09:11:09+00:00

problem:symfourdiagramacdbbadc.png - created

joshuawiscons (joshuawiscons@undisclosed.example.com) — 2013-08-21T07:13:52+00:00

problem:symfourdiagramacdb.png - created

joshuawiscons (joshuawiscons@undisclosed.example.com) — 2013-08-21T07:13:52+00:00

problem:cayleygraphofd4.png - created

bmwoodruff (bmwoodruff@undisclosed.example.com) — 2013-08-14T23:21:48+00:00

wiki:graphpictures:labeledsquare.png - created

joshuawiscons (joshuawiscons@undisclosed.example.com) — 2013-08-09T06:11:40+00:00

wiki:graphpictures:labeledsquare.pdf - created

joshuawiscons (joshuawiscons@undisclosed.example.com) — 2013-08-09T06:02:11+00:00