August 10

Friday August 10, 2007 9:50 am Lethbridge

It is +12 C with a high forecast of +20 C. Sunrise 6:14 Sunset 20:59 Hours of daylight: 14:45

A. Morning Musings

9:50 am

We had a good morning walk to Tim Horton's for a coffee.

The main priority now will be to work on making the summary notes for my calculus learning.

Immediate	Description	Time
Literature	Continue reading "Number 9 Dream" by	1 hr
Mathematics	Continue ch. 1 of "A Transition to Advanced Mathematics"	1 hr
Mathematics	Complete notes for week 1b & 2a of "The Humongous Book of Calculus Problems"	2 hr
Mathematics	Continue reading "The Black Swan" by Nassim Taleb	1 hr

C. Actual Learning Activities

9:00 am

Mathematics 39

August 10, 2007

8:00 am

I will focus on working on the summary notes for the previous sections. I have already added some material to yesterday's notes for Session 2 (week 1b). Here is a list of what I have accomplished so far:

Session	Week	Description	Problems	Notes
		Preface		Yes
1	1a	1.1 Linear Geometry	Done	Yes
2	1b	1.2 Linear Inequalities and Interval Notation	Done	Yes
3	2a	1.3 Absolute Value Equations and Inequalities	Done	Yes
4	2b	1.4 Systems of Equations and Inequalities	Done
5	3a	2.1 Exponential and Radical Expressions	Done
6	3b	2.2 Operations on Polynomial Expressions	Done
7	4a	2.3 Factoring Polynomials	Done
8	4b	2.4 Solving Quadratic Equations	Done
9	5a	3.1 Adding and Subtracting Rational Expressions	Done
10	5b	3.2 Multiplying and Dividing Rational Expressions	Done
11	6a	3.3 Solving Rational Equations	Done
12	6b	3.4 Polynomial and Rational Equalities	Done
13	7a	4.1 Combining Functions	Done
14	7b	4.2 Graphing Function Transformations	Done
15	8a	4.3 Inverse Functions	Done
16	8b	4.4 Asymptotes of Rational Functions	Done
17	9a	5.1 Exploring Exponential and Logarithmic Functions	Done
18	9b	5.2 Natural Exponential and Logarithmic Functions
19	10a	5.3 Properties of Logarithms
20	10b	5.4 Solving Exponential and Logarithmic Functions

Using the timetable I have set up, this table shows that it should take me 8 weeks to complete the first 4 chapters. I began this on July 16. That is four weeks ago. Thus I am well ahead of schedule in terms of solving the problems but am well behind on the summary notes, which I only began a couple of days ago. If I maintain the same pace of a section a day, I should be up to date in another 4 weeks and will be on schedule for the overall timetable. Great.

I will try to continue working on the problems as well, but the emphasis will shift to bringing the notes up to date and getting myself in synchrony with problems and notes.

Session 3 (Week 2a)

Chapter 1 Linear Equations and Inequalities

Section 1.3 Absolute Value Equations and Inequalities

1. Activities

W. Michael Kelley (2006). The Humongous Book of Calculus Problems.

Complete problems 1.21 - 1.27 [p. 8 - 10]

Wayne W. Dyer (2007). Change Your Thoughts - Change Your Life.

Read Verse 3: Living Contentment [p. 13 - 18]

2. What's it all about?

This section describes solving equations and inequalities that involve the absolute value of an expression involving one unknown variable.

3. What am I able to do, now that I am finished this section?

I will be able to solve equations involving the absolute value of an expression involving one unknown.

I will be able to express the solution to an inequality involving an expression involving one unknown either algebraically, using interval notation and graphically.

4. What will I know?

I will understand the nature of the absolute value of an expression involving one unknown.

I will have a clear image of the geometric interpretation of an inequality involving an absolute value.

5. What are the key concepts?

absolute value

6. What are some relevant Web sites for this material?

Using your favorite search engine, and maybe one or two others, type in a few key words such as "absolute value equations " or "absolute value inequalities".

Here are six Web sites that I liked:

7. What concept map can I create for this section?

week2a

8. What types of Mathematica activities can I create?

This is useful if one is trying to learn more about some of the defined functions of Mathematica. It is also worthwhile if one is trying to see how one can use the absolute value function to obtain a graphical representation of a complex inequality.

Here is a Mathematica Notebook for this section.

9. What are some connections to other ideas?

The idea of interpreting the absolute value of an expression as a measure of the distance is useful.

10. What is my overall reaction to this section?

One must be very careful and meticulous when approaching this type of problem. It is very easy to forget the importance of both positive and negative values.

11. Comments on Dyer: 3. Living Contentment

Dyer suggests that the third verse of the Tao Te Ching implies that one should "bring happiness to every encounter in life". Try this advice when approaching any mathematics problem. Start off with the assumption that each problem is an opportunity to think, and that thinking is itself is an enjoyable activity. If the problem still leaves you confused, view this as an opportunity to learn something new. Once again, this is a positive event that allows you to grow. Fantastic. Every day is full of such opportunities.