by Eric Boyd

    On the flip side, high school teaching has some strong rewards as well.  You get summers off.  The school board will often pay for you to further your own education.  Oftentimes kids are not whiny but genuinely interested in what you have to say about math.  And honestly, you might just find yourself satisfied knowing you're giving back to your community by teaching.
    So yeah.  Pure math is harder than math education, but the reward may just be more satisfying.  Making a high school kid smile with understanding after plugging through a side-angle-side proof may brighten your day, but if you'd rather not spend all day around the one or two rude kids that seem to pop up in every high school classroom, pure math may be what you want to look into.  And if you change your mind halfway through your pure math work, you can always go back to high school education.  So eat that, Frank.

    "Why?" Frank the imaginary rabbit would ask me.  "Why did you change from a cushy math education major to a hard-as-nails pure math major?  Why give up the glorious life of luxury of teaching geometry to a bunch of math-hating tenth graders drowning in their own hormones?"  And I would say, "I don't answer questions from nonexistent creatures."  But then Cathie Trigueiro asked me the same question.  Guess you can't get out of everything.
    So, why would any sane, rational person switch from an education major to a pure math major?  The biggest reason, especially for someone indecisive like myself, is job options.  Being a math ed major prepares you specifically for one thing, and if somewhere along the way you decide you don't want to wake up every morning at five A.M. to stare down lunatic teenagers for eight hours a day you might just be stuck.  With the pure math major, though, you have the option of applying for either an education or math masters when the time comes, the more choices the merrier.  After all, a math masters opens up doors like…like…well, at least you can teach community college.  (Yes, there are other jobs out there for a math masters, but I'm too lazy to look them up.  And yes, they'll even let you teach high school with one.)  And honestly, teaching high school has its rewards, but none of them are monetary, so anyone with dreams of swimming in gold coins like Scrooge McDuck may want to opt out of math education.
    Secondly, math can, every once in awhile, be fun. Maybe if the mood is right and the lights are low, you'll find some enjoyment plowing through a proof.  It makes you think you're smart.  You can go to class the next day and maybe help one of your friends through the same proof, which always feels great.  And you probably learned something.

by Jeff Williams

      For the majority of undergraduates, the end of the school year begins a hiatus from math classes.  For those of us graduating, that hiatus could be longer.  So when I think back to each of the classes I've taken or helped teach, some interesting items come to mind.  For each class listed below, if you've taken it, ask yourself if you remember the claim.  And if so, can you justify it? 
231:  An integer's divisibility by 11 can be tested by adding every other digit and subtracting the remaining digits, and testing the result for divisibility by 11.  (Runner-up: the technique of proof by contradiction.)
261: Whether a function approaches a limit at any given point has nothing to do with the value that the function does/does not attain at that point.
262: Integration is the inverse of differentiation. (Runner-up: Radians actually make sense!)

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