This morning I was trying to come up with some good problems for students to use to find local maxima and minima. It's an awesome feeling to be able to combine everything I know about graphs and polynomials and end behavior to create polynomials within the window that I want that do what I want. It's cool to think that I don't have to just guess random things. So the graph is too long and skinny? I can do a vertical compression or a horizontal stretch. I want two local maxes and one local minimum, so I know I need to give it a negative leading coefficient and an even degree. It might be neat to come up with some sort of guidelines and have the students come up with their own polynomials. I wouldn't want them to just guess and check though. I might have them write something that says what they would have to do to a graph to get the desired results. It really forces you to use everything you know about polynomials and graph behavior and actually apply it.
God Loves Math: In which I select a random Bible verse from a random Bible verse generator ( this one ) and ask God to show me a new way of understanding Him, honoring Him, and loving Him while using a mathematical mindset to approach the section of scripture. Today's Random Bible Verse Romans 6:3 "Or don't you know that all of us who were baptized into Christ Jesus were baptized into his death?" Right before today's random verse, the author makes the point that, while we see God's grace when he forgives our sins, of course we should not keep on sinning... Then comes our random Bible verse. Then he makes this follow-up statement: "We were therefore buried with him through baptism into death in order that, just as Christ was raised from the dead through the glory of the Father, we too may live a new life." (Romans 6:4) This short section is talking about what the sin in our life should look like. The Bible is very clear that all have sinned and fall...
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