Good Math, Bad Math

Yesterday, I posted this article about the bozo who didn't like his college calculus course because it wasn't Christian enough. One of the commenters pointed out that there's actually a site online where a college professor from a Christian college actually has a collection of "devotionals" to be presented along with the lecture in a basic calculus course.

They're sufficiently insane that I have to quote a couple of them. No comment that I could possibly make could add anything to the sheer goofiness of these.

For the lesson on "Function Operations":

God's Surgical Improvements of our Actions

Genesis 50:15-21, Romans 3:9-10, 21-24

One of the more horrible images in the book of Genesis is that of Joseph being sold by his brothers into slavery. This type of hate turned into evil act is a common occurrence in our world, too. In the Genesis situation, though, we are given the gift of 20-20 hindsight because we know the end of the story. God used the brothers' evil action to prevent starvation of the descendants of Abraham. Joseph says, "You intended to harm me, but God intended it for good. .." [Gen. 50:20] In the same way, God makes our unrighteous actions righteous through Christ. He surgically improves our actions to his own purpose.

This idea of twisting something from one form into another is what happens when function operations work on elementary functions. You can start with two ordinary benign functions, the reciprocal function 1/x and sin(x), say, and put them together. Depending on how you put them together, you can create something interesting and easily understood, like sin(x)/x, or something with wild behavior, like sin(1/x). Either way, you have twisted one object into something very different.

For the lesson on the Limit definition of the derivative:

Secant Lines and Sanctification

Ps. 119:33-40 In differential calculus we study how a slope of a linear function can be generalized to the slope of a function whose graph is curved, creating the derivative of the original function. The definition of derivative uses a sequence of lines (secant lines) drawn through two points on a function that are approaching each other and a single point on the function curve. The derivative value or tangent line slope is defined to be the limiting slope value of this sequence of secant lines. (See the figures below.)

Figure 1 : Secant line between 1 and 1.8
Figure 2 : Secant line between 1 and 1.5 Figure 3: Tangent line to f at x=1

Once a person has been called to be a Christian, we are redeemed by Christ but not released from following the law of God. We are justified once but continue with the process of sanctification for the remainder of our lives. This sanctification process is like the limit process of the secant lines approaching the tangent line. There is one distinction between the concepts of sanctification and secant line limits, however. In the mathematical contexts, we accept results that are "sufficiently close," results that are in an epsilon-neighborhood of the desired quantity. While in our quest for perfection, the "better" we get the further we realize we are from satisfying all aspects of the law.

Ok, just one more. This one just about had me rolling on the floor! For the lesson on the chain rule:

Chain Reactions

1 Corin 5:16-21

Once students have seen the chain rule for differentiation of composed functions, it is natural to extend the chain rule to nested functions, where there is more than two functions that are composed. Fun problems to investigate are ones that are repeated applications of the same function. Try differentiating tan(tan(tan(tan(tan x)))) or ln(ln(ln(ln(ln(ln x))))), for example. Working your way from the outside to the inside yields a derivative which is product chain of related functions.

In a similar way, when we interact with other people there is a chain reaction to our behavior. Most people believe that abused children are more likely to become abusers themselves someday, for example. Less dramatic behavior also can have a reaction that extends beyond the initial engagement. A popular Warner Brothers film of 2000 "Pay it Forward" (based on a novel with the same name by Catherine Ryan Hyde) depicts how a chain of reactions to an initial act of kindness can change an entire community. Christians need to be specially mindful of this chain reaction, since we are ambassadors for Christ. Our verbal and nonverbal witness can yield unexpected results, especially under the influence of the Holy Spirit.

This, apparently, is how "real" Christians are supposed to teach math classes. I seriously wonder how they have time to actually cover the math in class if they spend time on this gibberish!