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--- problem:why_we_need_associative [2013/08/09 00:13]
bmwoodruff created
+++ problem:why_we_need_associative [2013/08/09 18:16] (current)
bmwoodruff
@@ Line 1: / Line 1: @@
-\begin{problem}
+====== Why we need associative ======
+FIXME Add in the axioms of multiplication, as well as a few basic rules about solving equations (such as if $x=y$, then $ax=ay$.
+==== Problem ====
 Consider the equation $2x=3$.  Carefully solve this problem for $x$, where at each stage of your computation you should explain what rule you are using to performing.  Do not skip any steps in your computation.
@@ Line 7: / Line 11: @@
 Now go back through your work above and look for where you used the associative rule of multiplication. If you didn't use it, then check your work again, as you have definitely skipped explaining some step in your computation.
-\end{problem}
+----
+==== Remarks ====
-=== Comments ===
+  *This problem shows a student how crucial associativity is.
+  *It might be best to point them to a list of axioms, or something they can draw upon for their explanations.
+  *I was actually hoping to just have them tackle this one with small group presentations, then have a lively discussion about how detailed proofs should be, and then wrap it up as a class (pointing out how engrained associativity is in everything we do).
+  *As the semester unfolds, we can come back to the associative laws in various other settings.  One question will be, "What does associativity mean in a Cayley Graph?"
+----
+==== $\LaTeX$ version ====
+<code>
+%%%%%%%%%%
+% DEPENDENCIES
+% RequiredPackages: \usepackage{tikz}
+% RequiredMacros: \DeclareMathOperator{\aut}{Aut}
+%%%%%%%%%%
+\begin{problem}
+Type the problem code here.
+\end{problem}
+</code>
-This problem shows a student how crucial associativity is. It might be best to point them to a list of axioms, or something they can draw upon for their explanations. I was actually hoping to just have them tackle this one with small group presentations, then have a lively discussion about how detailed proofs should be, and then wrap it up as a class (pointing out how engrained associativity is in every thing we do).  Then as the semester unfolds, we can come back to the associative laws in various other settings.  One question will be, "What does associativity mean in a Cayley Graph?"
+----
+==== External links ====
+  *http://www.math.sjsu.edu/~hsu/courses/131a/axioms.pdf A list of axioms
-http://www.math.sjsu.edu/~hsu/courses/131a/axioms.pdf

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