I was going through mathematics tonight, and I realized that multiplying matrices tends to be similar to multiplying in numerical algebra, the famous FOIL. Using vectors, the multiplication of (x+y)(x+y) becomes x^2+2xy+y^2 in two dimensions. It’s as much a discovery as vectors themselves. Nowhere in the book of linear algebra does it show geometrically.

Meanwhile, I’ve been going through the advanced placement of calculus, and I’ve been finding nothing of what I had at Penn State. It only proves what I wrote about teaching mathematics – missing pieces of mathematics becomes critical in higher courses.

My overall view of mathematics reflects the struggles I’ve had with both subjects and the rules of life. Mainly it’s not spending the time and reviewing the subject.

I went on Zach Star on what linear algebra and its matrices mean. He used a circuit to illustrate the nullspace, which caused a flashback to the incident I had in eighth grade. It was a simpler circuit, but it appeared broken. I figured it could still work, which seems to match a nullspace.

  keep getting flashbacks of wisdom over a half century to late. It’s a special function of the human brain to return to any date in the past and determine long ago mistakes. For some reason, Newton keeps plaguing me with the understanding that many of the boys in my class were helping on the farms. It still doesn’t excuse why the coach never explained the rules of football to me so I could play with them!

I had chance last night to return to organic chemistry. As usual, I found the explanations of the means to identify compounds. This time it’s the nuclear magnetic resonance. I don’t think I had a thorough explanation.\ in Morrison and Boyd, but I could’ve muffed it.

I’ve begun a series of courses toward data science. The one on statistics goes over some material I’ve known, but the definitions of covariance and correlation are new to me as to their mathematical explanation.

 As today is the anniversary of my entry to State College, I reflect on the time I was a happy graduate student at Penn State. The peak comes in the middle years when I ran my own weekly show. I didn't get paid in college radio, but I had control over my income and my time.

Being a graduate teaching assistant combine an income with an enjoyable job and an open opportunity for advancement through learning. I ran my show how I wanted in conjunction with a partnet who complented my mangement.

KIhan Academy has a lecture on precession, and I also figured that the calendar would also move so that the solstices would not gradually be earlier. What I didn't consider were the perihelia and aphelia would moved along wth precession.

 This week I ran across Langrange multipliers. I found explanations in both MITOCW and khan. It reminds me of eigenstuff enough to understand them. I see a parallel with Lagrange multipliers. It even reminds me of engineering physics, at least the second time I took it in grad school.

I just finished a training on six sigma and started one on bookkeeping in LinkedIn. I also took one in differential equations. It starts much differently than when I took the subject at Penn State. It also starts with slope fields, sorely lacking in the previous course.

 In the times when my life did improve, a major obstacle lifted out in 1967, 1980, and 1990. I’d like a time when my life improved from better conditions.

card., which causes me to clean up the clutter.
I began an econometric class, which is really a simplified course in statistics. It goes further than the quantitative business from long ago., and my desperate meeting with Russell Smith in 1978.

I was going through fintech, which has a use for linear algebra. Covariances seem to have a place in a matrix.

I tried yet another video on eigens, and I uncovered another aspect finding them. Linear algebra came up under corporate finance. I’m still working on visualizing it, rather than understanding it abstractly

I had the though that K acts too much like me in extreme. His obsession about his name N and a lack of empathy gave me pause. I also know through the internet that he’s been struggling financially.

I finished the LinkedIn course on the foundation of SAPGUI, and the resemblance to accounting is quite obvious. There is even a connection to Microsoft Excel.