Sunday June 8, 2008 5:00 am Lethbridge, Alberta

It is +8 C with a high forecast of +13 C. Sunrise 5:24 Sunset 21:36 Hours of daylight: 16:12.
See current forecast here. See current news here.

This page last updated on: Monday, June 9, 2008 5:42 AM

A. Morning Musings

The forecast high for today is still 11 degrees below the long term average. The next few days do not look to be much better.

While looking at some of the material on linear algebra yesterday I cam across the phrase "row reduction". This did not ring any bells so I looked it up on the Web using Google. So far so good. But as I was lying in bed before getting up I began thinking about a similar approach to solving simultaneous equations using matrices and then I recalled using something called a determinant. Finally I recalled that the value of a determinant had something to do with computing the inverse of a matrix.

I just had a quick skim of the material I was planning to read this morning on linear algebra and did not see any mention of these topics. I think I will see what I can find on the Web on this before proceeding with my linear algebra. I am pretty sure that it is all fairly easy, but after 40+ years of non-use I am a little rusty.

Long Term Activities	Planned Activities for Today	Cumulative Total
Cull professional articles	Review Psychology articles	5 hr
Prepare pdf files of my papers	Digitize 3 professional papers	4 hr
Digitize slides	Digitize slide collection	10 hr
Put away stamps		0 hr

Learning Category	Planned Activities for Today	Time
Literature	Begin morning with a Rumi reading
Puzzles & Games	New York Times crossword puzzles	1 hr
Literature	Continue reading "The Age of Shiva" by Manil Suri	2 hr
Mathematics	Make a few notes on symmetry	1 hr

B. Actual Learning Activities

10:20 am

Notes on Symmetry - 19

Dale Burnett

Date	Mathematics	History
500 BCE	Pythagorus
399 BCE	Thaetetus classifies the 5 regular Platonic solids in 3 dimensions: tetrahedron, cube, octahedron, dodecahedron, icosahedron.
1048 - 1131	Omar Khayyam finds geometric method for solving cubic equations.
1200	Leonardo Fibonacci wtote the first original book on mathematics published in Europe. It introduced Hindu-Arabic numerals and place-value notation.
1439		Gutenberg invents the printing press
1452 - 1519		Leonardo da Vinci
1492		Columbus discovers America
early 1500s	del Ferro, Tartaglia, Cardano, Ferrari solve cubic & quartic equations
1564 - 1642	Galileo
1642 - 1727	Isaac Newton
1775 - 1783		American War of Independence
1777 - 1855	Carl Friedrich Gauss
1789 - 1799		French Revolution
1802 - 1829	Niels Henrik Abel proves that no formula exists for equations of degree 5.
1832	Evariste Galois dies at age 20.
1842 - 1899	Sophus Lie: Norwegian group theorist

	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21	22	23
Symmetry
Fearless Symmetry
Algebra
Abstract Algebra
Creating Escher-type Drawings
Handbook of Regular Patterns
Symmetry & the Monster
The Celtic Design Book
A Transition to Advanced Mathematics
Modern Abstract Algebra
Indra's Pearls

While looking at some of the material on linear algebra yesterday I came across the phrase "row reduction". This did not ring any bells so I looked it up on the Web using Google. So far so good. But as I was lying in bed this morning I began thinking about a similar approach to solving simultaneous equations using matrices and then I recalled using something called a determinant. Finally I recalled that the value of a determinant had something to do with computing the inverse of a matrix.

5:40 am

A quick search using "solving simultaneous equations using matrices" gave the following web site:

http://www.math.csusb.edu/math110/src/matrices/sol-sys.html

This was exactly what I wanted. Perfect.

Oops. I also need a web site that describes how to compute a determinant.

http://en.wikipedia.org/wiki/Determinant

http://people.richland.edu/james/lecture/m116/matrices/determinant.html

This all comes back to me now. And I was right - it is easy.

6:40 am

Goodman, F. M. (2006). Algebra: Abstract and Concrete

Chapter 1 Algebraic Themes

I have skimmed the content of Appendix E. Here is a list of the terms (i.e. concepts) that are discussed:

linear combination of a set of vectors
span of a set of vectors
linear independence
vector subspace (linear subspace)
basis of a vector subspace
standard basis
row reduction
linear transformation (linear map)
standard matrix
bijection
range of a linear transformation
kernel of a linear transformation
maximally linearly independent
spanning
minimally spanning
dimension of a vector subspace
inner product
Cauchy-Schwartz inequality
Euclidean distance function
orthogonal
orthonormal

None of the above looks familiar to me. I recognize the phrase Cauchy-Schwartz inequality, and know the Euclidean distance function, but the rest of this is new territory.

The important point to realize, right at the outset, is that these terms refer to ideas and very specific concepts.

I am going to create a series of 3x5 cards, one for each of the above concepts. The idea is to have a set of "flash cards" that I can review at any time, in any order, and test myself on my ability to remember the precise definition.

Tags: mathematics, symmetry

3:00 PM

Books on the Go Today

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