Maybe I shouldn't have started this blog now, not with everything that's been going on.

Returning to my discussion of the field trip in my mechanics lecture subject last Saturday, it was the students’ good luck that the rain stopped in the evening and Anchors Away (closed since the morning) opened – just when the crowd was thinning and the lines were much shorter.

The also students rode the Rio Grande Rapids probably close to a dozen times in succession just before the closing of the park, just getting more and more drenched every time.

And that’s last week.

In my Mathematical Methods 1 class last Monday at the start of the eleventh week of classes, I started with the fourth to the last topic for the term, arithmetic sequences and series.

I discussed the two main formulas given two elements in order and the common difference, and the formula involving the first element and the common difference and the nth element.

After that we discussed arithmetic means, given several definitions: elements between two numbers in a sequence, and the mean of several numbers that may or may not be in a sequence. But there was another formula for getting the mean for a sequence. Same with getting the sum.

There were also some word problems related to the topic, such as getting the total number of detergent boxes needed to make a pyramid display in a store given the number at the base.

On Tuesday, the topic was geometric series. This was both relatively easier and more difficult.

It was easier because the subtopics we had were in the same order as what we talked about the day before.

It was also more difficult because they had forgotten all about how to simplify expressions with exponents.

I also told them how to get the nth root of a number using their scientific calculator. There was enough variations of calculators around that I had to pay special attention to people who couldn’t solve the examples we were discussing.

There are some for which the base had to be typed before the exponent. For others it was the other way around. One could only get the square and the cube root, so I had to teach those students to use the “x raised to the y” key and express y as the denominator of a fraction.

They also had to be reminded how to solve systems of equations that were of greater degree than one, especially since I didn’t have an example that gave two non first elements and asked for a third one.

Checking their exercises, in fact, I saw that a lot of people didn’t get it, so I had to review the solution with them at the start of the Thursday class before I went to the next topic that David and I had decided on, which is the binomial theorem.

We were also supposed to discuss infinite geometric series, but according to David he only took one as an example. We also skipped the topic of combinations and permutations, although that figured in one of the formulas needed for the binomial theorem. I just told David I’d mention the combination relation, but not in detail. Otherwise, for the students to be able to expand binomials raised to a certain power, they will still have to use Pascal’s triangle.

And I had to give them some more reminders about solving expressions with exponents.

And I’m out of time today. I’ll continue discussing this tomorrow. For now, the class is dismissed.