Thursday March 22, 2007 5:00 am Lethbridge Sunrise 7:31 Sunset 19:46 Hours of daylight: 12:15

A. Morning Musings

5:00 am It is +4 C at the moment with a forecast high of +12 C

CBC Headline: N. Korea Departs Nuclear Talks After Macau Row

Disarmament talks among 6 nations to resolve the question of N. Korea's nuclear energy program have broken down over the issue of when $25 million of N. Korean funds would be transferred from a bank in Macau. It is difficult to comment on the situation without knowing what is really happening, but certainly part of the difficulties are due to a genuine lack of trust and faith by all involved. This is always a difficult situation.

Canadian Headline: Canadian Boy, Parents Arrive in Toronto After Prison Stay

The boy and his parents had been held in a Texas detention center for the last 6 weeks. They had been caught with false Greek passports when their flight to Canada was diverted to Puerto Rico due to technical problems. They were then sent to Texas while their situation was reviewed. The parents are Iranian, but the boy was born in Canada when they were living here while seeking refugee status. This is one of those classic stories where a family gets caught up in the bureaucracy of international law.

Australian Headline: (from The Australian): Public Super 'Covered' In $4.7 bn Broadband Plan

This is a continuation of yesterday's story where the Labour party unveiled a plan for improved broadband service if it is elected. The Treasurer, Peter Costella had indicated that the nation's pension fund would be used to help fund the proposed broadband infrastructure. This entire issue is a political gambit by both parties leading up the federal election, likely in October - December of this year.

My weight is steady at 190. This is one of the plateaus that one hits while trying to maintain a downward trend. Hopefully I will nudge lower soon.

From rear window	South patio
Both images taken at 1:05 PM

B. Plan

Immediate
Mathematics	Read & make notes on Spivak, chap. 3 Functions	1 hr
Technology	Read manual for cell phone	1 hr
Literature	Begin reading "The Baron in the Trees " by Italo Calvino	1 hr
History	Begin reading "Maya"	1 hr
Later
Technology	Convert LPs to MP3 format
	Make notes for chap. 4 of "Switching to the Mac"
	Burn backup of images onto DVD
Mathematics	Make notes for "Mathematics: A Human Endeavor" ch 1
	Read "Fearless Symmetry" chap 9: Elliptic Curves
	Begin reading "Algebra: Abstract and Concrete" by Frederick Goodman
Model Trains	Add ground cover to oil refinery diorama
	Follow tutorial for version 8 of 3rd PlanIt
	Continue assembly of coaling tower
	Purchase DCC system
History	Read Watson "Ideas"
Philosophy	Read & make notes for "Breaking the Spell"
GO	Complete reading "Lessons in the Fundamentals of Go"
Puzzles	The Orange Puzzle Cube: puzzle #10
Major Goals
Learning	Review week's pages each Sunday
	Review all pages for the month at the end of each month
Technology	Review & edit iPhoto files for 2006
	Become proficient with cell phone
Model Trains	Become proficient with 3rd PlanIt software
	Install DCC on model train layout
GO	Learn to play GO at something better than a beginner level
Drawing	Learn to draw!! (I keep saying this, yet I have yet to put a pencil to paper).
Mathematics	Continue to play with mathematics.
Literature	Continue to read Literature
Bird Watching	Continue to engage in bird watching activities.

C. Actual/Note

5:30 am Another long standing item has been to learn how to use the various features on my cell phone. I will bring this item forward and see if I can make some progress. For example, I would like to learn how to send text messages. Now to brew a cup of coffee and settle back with the manual.

9:45 am I'm back from coffee at TUMs. Now to play a little with maths and the Spivak book on calculus.

	Mathematics 10 March 22
Mathematics Chronology
10:00 amThe first task is to open the Spivak book to chapter 3 on Functions. Calculus. Third Edition (1994) by Michael Spivak. Chapter 3: Functions There are a number of different classes of functions: polynomial functions rational functions The next group of functions that Spivak mentions involve trigonometric functions, which then may involve rational and/or polynomial expressions. But he fails to say what this group, or any other possible groups are called. Now to try google and see if I can obtain a list of the other types of functions. Ouch. The list is long and convoluted. Almost any defining attribute can be used to form a class of functions. Here are a few examples: continuous, differentiable, integrable convex, monotonic, unimodal trigonometric transcendental fractal odd or even vector-valued holomorphic, meromorphic, entire etc. Spivak does mention the idea of sum, product and quotient functions as well as composite functions. "If f and g are any two functions, we can define a new function f + g, called the sum of f and g, by the equation (f + g)(x) = f(x) + g(x). Note: The + symbol for f + g is a different idea than the + symbol for numbers. It is defined as the sum of two functions, whereas the + symbol for numbers is defined as the sum of two numbers. Similarly, one can define the product and quotient of two functions. A very important idea is the compostion of two functions. It is sometimes important to have a formal defintion for the ideas/concepts that we are discussing. There are three quite different ways to think about functions: intuitive (i.e. as a rule) formal (i.e. using a very precise analytic definition) visual (i.e. creating a graph for the function). This latter is often the best way of thinking about a function. Spivak then gives a large number of exercises, the majority of which require one to work carefully with the formal definitions of functions. I will give this a pass for the moment at least and focus on the idea of graphing a function. However, before doing that I will return to Kelley's book "The Humongous Book of Calculus Problems" and work through more of the problems involving polynomials. The Humongous Book of Calculus Problems (2006) by W. Michael Kelley. Chapter 2: Polynomials   Section (a) Exponential and Radical Expressions 2.7 Explain why the expession should be simplified as , rather than . There are two possible cases of interest: when x is positive and when x is negative. The more interesting case is when x is negative. Since the original expression first squares the value of x it obtains a positive number, to which one then applies the square root operation, obtaining a positive value. The absolute value of x ensures that this is positive, wheras when x is negative one would obtain a negative value if one used . 2.8 Simplify the expression . 11:00 am A very satisfying session.

12:20 PM Here are two more photos showing the beginning of the spring activity of the May tree in our backyard.

D. Reflection