In today’s class, we were fortunate to have one of my colleagues from our division direct the class. This is the third time this class has been offered at Wayland. The first two times, this faculty member and I co-taught the class. I’ll be honest and tell you that being the sole teacher this semester has been an enormous challenge, much greater than the last two. It was extremely helpful to have someone in class bouncing ideas off of.
In the current scenario, I appear much more as the “expert” and less of the facilitator in the discussion. In an applied math course, that would be fine, but in this course, I am reluctant to accept that role. Today’s class was like the “good ole days”.
The two main topics we covered in class today were the scientific method and the way in which scientific knowledge develops. In discussing the scientific method, we went back over some of the original discussions of the class, centering on the issue of just “how” faith can affect or inform science.
The class proposed that faith can serve much like a feedback loop to weigh the conclusions of science against. Most of them were uncomfortable thinking of faith as a filter through which we choose to accept or deny the claims of science. Instead, it was determined that our faith and/or worldview helps us to evaluate the conclusions reached by science. In most cases, excepting bad experimental design, we don’t throw out the results (or data) but we can choose to re-evaluate the conclusions as long as they are rational and justifiable.
This is the true challenge in letting one’s faith affect scientific endeavor. The real difficulty is how you draw the line between allowing for, say, supernatural explanations (if at all) and allowing for paranormal explanations. In a classroom full of Christians with a strong conservative backgrounds, most, if not all, of us are comfortable in accepting the supernatural’s involvement in our world. However, far fewer of us would be willing to accept the paranormal.
Thus, in evaluating scientific conclusion we must answer the question of what provides the “best” explanation. Some answers to that question have been posed such as Occam’s Razor or the fact that the natural trumps the supernatural for all cases. We did not arrive at an answer that satisfied everyone.
We discussed the scientific method in greater detail. We followed that by a short discussion on the nature of scientific development/revolution as proposed by Thomas Kuhn in his book, The Structure of Scientific Revolutions
Next time, we will begin to cover some specific case studies of the interaction of faith and science throughout the history of science.
We will also discuss some of the claims made in Eric Snow’s paper: “Christianity: A Cause for Modern Science“. In this article, he gives a summary of a couple of papers in which the authors contend that either Christianity helped to create modern science through its worldview, or at the very least, aided in its development. They also contend that other cultures’ worldviews stifled the development of modern science, giving examples from China, India, Islam and others.
written by SplineGuy
In class on Tuesday, we stated and used the chain rule for partial derivative:
be a function of 
variables, such that 
is a function of 
variables for each 
then
for each 
-neighborhood and in trying to explain exactly what it was, I realized that we had some left some important results of the absolute value had not been established. Those results are well-known facts but we have emphasized the importance of fundamental principles in this class. We use (almost) nothing without first establishing the facts we need through proofs or use of axioms and definitions.
![A= \left[ \begin{array}{cc}A_{11} & O \\ A_{21} & A_{22} \end{array}\right]](/latexrender/pictures/1b62a68571c9e17e7fed4ad84aad5609.gif "A= \left[ \begin{array}{cc}A_{11} & O \\ A_{21} & A_{22} \end{array}\right]")
and 
are nonsingular. We derived that:![A^{-1} = \left[ \begin{array}{cc}A_{11}^{-1} & O \\[2ex] -A_{22}^{-1}A_{21}A_{11}^{-1} & A_{22}^{-1} \end{array}\right]](/latexrender/pictures/0124ace7f8a4bf56a611ee2e3963ec78.gif "A^{-1} = \left[ \begin{array}{cc}A_{11}^{-1} & O \\[2ex] -A_{22}^{-1}A_{21}A_{11}^{-1} & A_{22}^{-1} \end{array}\right]")
![A=\left[\begin{array}{cc|ccc} 1 & 2 & 0 & 0 & 0 \\ 2 & 3 & 0 & 0 & 0\\ \hline 4 & 3 & 1 & 0 & 0 \\ 1 & 2 & -2 & 1 & 0 \\ 9 & 2 & 0 & 0 & 1 \end{array}\right]](/latexrender/pictures/86f24539b1429418643907aff7157368.gif "A=\left[\begin{array}{cc|ccc} 1 & 2 & 0 & 0 & 0 \\ 2 & 3 & 0 & 0 & 0\\ \hline 4 & 3 & 1 & 0 & 0 \\ 1 & 2 & -2 & 1 & 0 \\ 9 & 2 & 0 & 0 & 1 \end{array}\right]")
and 
are easily calculable and thus, so is 
.
. Thus the argument takes the form:
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