Link to Calculus Learning Schedule

6:00 am

Continuing with the Weiner book. The topic is "Factoring a^n - b^n and a^n+b^n " on pages 6 - 7.

This session was relatively easy, but each example and exercise was a learning experience. The last exercise was particularly interesting as it reinforced the idea that one should look for patterns. I had deliberately avoided looking at the hint when I began the problem and missed the more valuable factoring. However once I saw the hint, I redid the exercise in red ink without difficulty.

I have a definite preference for my Pelikan M250 Tradition pen over the Lamy 2000. I also prefer the Waterman Florida Blue ink over the Pelikan blue-black ink.

Each of these sessions is having a noticeable effect on my learning. I would not have had any chance of completing any of these exercises a month ago. This may still only be basic algebra, but it is a necessary prerequisite to doing calculus later. I am feeling good about my progress. There is a sense of satisfaction in being able to handle complex expressions like these.

The self-imposed structure of a timetable for these activities is proving to be a valuable idea. The overall goal is that of 2 sections of the Kelley book each week. However at the moment I am still playing catch-up. I am currently doing a section of Weiner each day. I have had a closer look at the Weiner table of contents and now realize that there are 70 sections before I reach the chapter on evaluating limits.

If I maintain my original goal of 2 sections of Kelley each week, plus adding whatever is appropriate from Weiner and Dyer, plus whatever I create for Mathematica, then I should be ready to begin the section on Limits after 16 weeks. I am currently at the end of week 6. There are 47 sections in Weiner ( I have completed 5 so far) before I reach the chapter on Logarithms. At the moment I am ahead of schedule for Kelley (I am where I should be on September 10) but I am behind on Dyer, Weiner and Mathematica. Instead of the leisurely pace I had set of 1 section/day for Weiner, it looks like this should be closer to 4 sections/day until I get caught up. I definitely want to have my sections from Kelley & Weiner in synchrony as well as having my Mathematica activities at the same level. I think a slightly optimistic goal will be to move forward with Kelley by the end of September.

10:00 am

I have just completed the next section from Weiner.

This was an interesting session. Weiner introduced a couple of theorems that I had not seen before and showed how they could be used to find the rational roots (and hence the factors) of a polynomial with integral coefficients. This is a very powerful theorem but I have no idea of its history or how to prove it.

I also found a new use for Mathematica. When I compared my answer with that in Weiner, I could not see how to obtain the answer he provided. I then opened Mathematica and asked it to factor the polynomial. The answer agreed with what I had done. This is important when one is learning by self-study and does not have recourse to a professor or fellow students.

Here are the results of a google search:

• http://www.purplemath.com/modules/remaindr.htm
• http://www.mathwords.com/r/rational_root_theorem.htm
• http://mcraeclan.com/mathhelp/FactoringPolynomialRemainderTheorem.htm