Obviously

"Obvious is the most dangerous word in mathematics."
                -- E. T. Bell

In the last chapter we were introduced to the concept of betweenness of points, which is maybe the first time so far that we've smacked our collective foreheads and said, "No kidding. Do we really have to waste our time defining this idea that's so totally obvious?"  On some level, this is a legitimate complaint.  I mean, we can look at a line segment with P and R as its endpoints and immediately understand that every other point on the segment is between those two.  This picture completely jibes with our everyday understanding of what it means for a thing to be between two other things.  And in that world, betweenness doesn't seem confusing in the least.  You know that your C- in Geometry is somewhere between an F and an A (or between a D and an B, for that matter).  You know that my classroom is between Mrs. Brown's and Miss Forsberg's (and so is Mrs. Wavrunek's).  And you know that the Vikings are somewhere between awful and terrible.  These are facts.

Deviant Numbers

Last week we talked about why it was important to measure not only the center of a data set, but its spread as well, since data sets with very similar centers can look completely different in other important ways.  For example, my retirement fund netted me a whopping $300 in 2010.  I'm certain that, somewhere on Wall Street, there exists a fund manager who also cleared $300 last year--in other words, we had the same average returns on our investments--but our monthly statements probably look as though they were generated on separate planets.  While my fund may have gained or lost a few bucks month to month, his probably gained or lost a few million a day.  As a result, I live in a two-bedroom apartment in St. Louis Park, and he lives in a corporate penthouse in Manhattan.  So we need some way of measuring how our data varies from the average, from the mean, to make sense of it all.

The F Word

I know it's early in the year, but we need to have a discussion about some of the language that's been thrown around the room so far--in particular, the F word.  You know which one I'm talking about...FOIL.

Unknown Quantity

What is Algebra, exactly--especially this advanced variety we're currently studying?  Let's answer the first part of that question first, because it is, I think, the more interesting one.  Is it solving for x?  Graphing? Functions?  All of the above?  When I asked for a list of words/phrases/concepts that you talked about in your last Algebra class, you rather quickly--like, in under two minutes--came up with an impressively large list.  So thanks for that.

But what I really want to jump into your head when you think about Algebra, the word that should immediately lodge itself in your cerebral cortex, is structure.  Algebra defines the rules of the game for working with mathematical objects--in our case, (mostly) the real numbers.