Tuesday, April 19, 2011 Lethbridge
6:15 am
The temperature is -8 C, with a high predicted of +3 C.
From the Environment Canada website:
Today A mix of sun and cloud. Fog patches dissipating this morning. High plus 3. UV index 6 or high. Tonight Cloudy periods. Low minus 8. Normals Max: 14°C Min: 0°C
12:05 PM tag: Mathematics
I made a few handwritten notes earlier this morning. Here are the points that I made at that time.
I am struggling with sections 1.3 and 2.1 plus the video Lecture 2. I recall reading a quote from Richard Feynman many years ago where he said that when that happens, begin again at page 1. I am doing that now.
There are some good sentences in Gilbert Strang's textbook.
"The beauty and variety of linear algebra, and its extreme usefulness" [p. v]
"The Four Fundamental Subspaces that are central to linear algebra" [p. v]
"The crucial operation in linear algebra is taking linear combinations of vectors [p. vi]
"When we take all linear combinations of the column vectors we get the column space. If this space includes the vector b, we can solve the equation Ax = b". [p. vi]
"A key goal is learning to 'read' a matrix. You need to see the meaning in the numbers. This is really the essence of mathematics - patterns and their meaning." [p. ix]
I am also struggling with notation and technology. I have at my fingertips 4 dramatically different technologies:
- handwriting
- web authoring (this website)
- APL (an excellent computer-based system for working with vectors and matrices)
- Mathematica (an excellent computer-based system for creating graphical displays).
But the real issue is my mind. Do I understand what I am doing?
Here is a quote from the biography of Feynman that I was reading last night:
"Feynman needed to fully understand every problem he encountered by starting from scratch, solving it in his own way, and often in several different ways. ... He urged each of us to create his or her own universe of ideas, so that our products, even if only answers to assigned classwork problems, would have their own original character - just as his own work carried the unique stamp of his personality." [p. 7]
I am going through a similar phase. I sense that this is important. It may be hard work but I am looking for understanding, not the answer to a particular problem. And handwriting seems to be the best approach, although all of the other approaches may make sense in a particular situation. Not only am I trying to learn some linear algebra, but I am trying to learn more about how to learn about linear algebra.
1:30 PM tag: Science
I am now sitting back and rereading the first few chapters of Lawrence Krauss's biography of Richard Feynman. My first impressions are very positive.
5:00 PM tag: Puzzles
I purchased the simplest version of a Go game for the iPad for $2.99. This will give me practice and help me decide if I should get back into this game.
I have played a few games and am definitely in need of practice. But the game itself with a simple tapping is actually fairly similar to playing with a real game and placing the stones on the board.