Author: Kate Poirier (Page 5 of 14)

Comment due Sunday, April 28

Test #2 will be given in class Wednesday, May 1 (right after spring break). The format will be similar to the format of Test #1 and Test #2.

Recall from Test #1 and Test #2 that one of the questions asked you a series of conceptual true/false questions where you had to justify your answer. Another question asked you for a series of examples of mathematical objects (mostly functions) satisfying certain conditions.

To prepare for Test #3, for this week’s OpenLab assignment, you will comment on this post with two questions that you come up with yourself, as well as their answers.

1. Your first question should be conceptual and phrased as a statement which is either always true or always false. Your answer should indicate whether the statement is true or false together with a sentence explaining the answer.
2. Your second question should be asking for an example of a mathematical object satisfying certain conditions. Your answer should provide this example together with together with a sentence explaining the example and why it satisfies the conditions.

You can use the Test #1 and Test #2 questions for inspiration (the different versions of the tests had similar questions, so check out your classmates’ solutions here and here).

Try to focus on the material covered in class since Test #2. You can see the list of topics on the schedule.

Comment due Sunday, April 14

Option 1

We missed pi day! Pi day is usually celebrated by eating pie on March 14, since $\pi$ is approximately 3.14.

While $\pi$ is a familiar constant to most math students, the constant $e$ is less well known. Some of you are seeing the constant $e$ for the first time in this class! We use the notation $e$ to represent an irrational number whose value is approximately 2.718.

There are different ways of defining $e$ but most of them are not geometric. (Compare this to $\pi$, which can be defined as the ratio of the circumference of a circle to its diameter.) The number $e$ appears naturally in contexts involving change, which is why you’ll see it again in your calculus class.

For this activity, you will watch one of the videos linked below (or another video of your choosing) which each describe where $e$ comes from together with some of its properties (there are lots of videos about $e$ because it has lots of properties!).

After you watch the video, comment on this post with a short summary of it. Be sure to include:

1. which video you watched,
2. one thing that you learned about $e$, and
3. a question you still have about $e$ (something you’re curious about).

Videos

1. e (Euler’s Number) – Numberphile
2. Transcendental Numbers – Numberphile
3. Euler’s Formula – Numberphile
4. A proof that e is irrational – Numberphile

BTW, Numberphile is a really fun YouTube account where they ask experts to talk about incredible math facts, so you might like to check out their other videos. The videos linked above are at varying degrees of difficulty, so don’t worry about trying to understand absolutely everything. Just try to find one thing that you learned. If you watch a video on $e$ other than the ones liked above, include the link to the video you watched in your comment

Option 2

You may have felt the earthquake that our area experienced on Friday morning, or maybe some of its smaller aftershocks. The epicenter of the first earthquake was in New Jersey and it registered at 4.8 on the Richter scale. You may have heard that the Richter scale is logarithmic, but what does that mean? Choose one of these videos to watch for an explanation of the Richter scale:

1. Richter scale | Logarithms | Algebra II | Khan Academy (this video is a bit old, so the east coast one it’s referencing isn’t the one we just experienced, but one from back in 2011)
2. The Connection Between Mathematics And Earthquakes Using Logarithms (this video was recorded after the recent 7.4 earthquake in Taiwan, but before our recent 4.8 earthquake)

In the comments below, include:

1. which video you watched,
2. one thing that you learned about the Richter scale, and
3. a question you still have about earthquakes (something you’re curious about).