**Making a successful CUSP 124 Podcast**

## Hints on recording and editing podcasts

The only things that you need to be able to do, in the way of
technical matters, to produce a podcast is to record digital audio,
edit out things you don't want, and then save the resultant audio as
a 32k bit/sec MP3 file and email it to me with a 1-paragraph
description (to be placed on our podcast feed page). I will post
your audio file as the next episode of our class podcast. If you
already have the software and hardware to do this, then please skip
to the next section of this web page. If not, then here are some
hints and links. Remember: keep your workflow simple. Your technical
goal is a clear, easily understood recording with no extraneous or
distracting noises, hesitations, silences, beginning and end cruft,
coughs, flubs, etc. Most of this involves cutting parts out; you may
need to play a bit with the volume in some sections, too. Spend most
of your time on *content* and *quality*.

The first thing you need when making a podcast is a device that records digital audio. This could be a desktop or laptop computer, or it could be a stand-alone digital audio recorder. Some things to keep in mind:

- Use a microphone that will work well with a group and choose a quiet location to do your recording. It is far better to start with a good, clean recording than to try to fix it with volume adjustments and filters in the editing software.
- Test your equipment ahead of time to verify that you can record reasonable quality audio and transfer it to your computer for editing.

Olympus DM-10 digital audio recorders and microphones are available from the Campus Media Center for checkout (you can access its documentation from the Olympus web site). I will be informing the CMC of our assignments so they will be ready for you.

The next thing you need to be able to do is edit the audio file and save it as MP3. If you use an Olympus DM-10, you can use Olympus software to convert their proprietary file format to something usable. If you have a Macintosh and iLife software, GarageBand works well and is easy to use. Otherwise, you can use the free Audacity software, which runs on Mac OS X, Linux, and Windows. To be able to save MP3 files, you will also need to download and install the LAME library, too.

Audacity is pretty easy to use, especially if all you need to do is edit things out (select with the I-beam, press "delete") and save as an MP3 (select "Edit/Preferences," set the MP3 prefs for 32k bits/second, and then select "File/Export"). Here is a good Audacity tutorial.

## Podcast Content

We will be producing eight podcast episodes during the quarter, each
done by one group of around five students. I will finalize the group
membership on the first day of class (hopefully, I will be able to
arrange for each group to have someone who has some familiarity and
experience with the recording and editing process). These podcasts
should be group discussions about the assigned topic. You may, for
example, assign roles to each group member, whether it be
researching a particular aspect of the topic or preparing
intelligent questions for others. If you want a target to shoot for,
you might listen to the In Our
Time podcast from BBC Radio 4. Note that I certainly
*don't* expect you to hit that target; I think that it is the
best podcast of the kind in existence. Listen to it before you do
your podcast for inspiration.

Podcast topics will be (check back during the quarter; I will be adding the later topics as the quarter progresses):

- "The Story of the Square Root of Two" This podcast is about irrational numbers and their relationship to the rational numbers. You should address the differences between these two sets of numbers and the concept of successive approximation and infinite sequences (and the difference between an approximation and an irrational number). Use the Heron Sequence as a method for approximating the square root of two as a specific example. Relate this sequence to approaches to finding the roots of functions. Summarize your understanding of the historical development of the notion of irrational numbers. Some additional sources to start you off:
- "Eudoxus of Cnidus" This podcast is about the life and times of
Eudoxus of Cnidus and his impact on mathematics. This is not just
a math podcast -- spend some time learning about and discussing
what is known about Eudoxus as a person. Your math research should
focus on his
*method of exhaustion*for computing the area of a circle. This is another type of successive approximation approach to solving a problem. Be sure to relate your findings to our in-class coverage of limits. Some additional sources to start you off: - "In Search of Infinity" This podcast is about infinity,
including its meaning and the historical evolution of our
understanding of it. Make sure you talk not only about the modern
concept of infinity, but also the origin of the concept, how it
has changed over time, and the people involved in our changing
understanding. Some places to start looking (besides the library, of
course) are:
- University of Toronto Mathematics Network.
- History of infinity (University of St. Andrews). There are a number of good references at this web page that you can use as jumping-off points.

- "Augustin Louis Cauchy" Cauchy was a French mathematician who developed the ε-δ definitions of limit and continuity. He was one of the most prolific mathematicians in history. Niels Henrik Abel once said of him, "Cauchy is mad and there is nothing that can be done about him, although right now, he is the only one who knows how mathematics should be done." Focus your podcast on Cauchy and his work in the context of his time and place. This could include strife between royalists and those seeking to overthrow feudal governance or between Catholics and Protestants. What kind of man was Cauchy, and how did he get that way? Of course, make sure you also spend some time on his mathematical works. Some starting points:
- "Newton v. Leibniz" Isaac Newton and Gottfried Wilhelm Leibniz both developed calculus independently, and there was a great deal of controversy over priority and plagiarism at the time. Nowadays, it is generally recognized that Newton developed it first, though because of his delay in publishing his work, Leibniz's work was truly original and not plagiarized. Interestingly, we use Leibniz's notation today. In this podcast, summarize the controversy at the time surrounding calculus. What was it about that period that led to two people developing calculus independently? Starting points:
- "From Bernoulli to l'Hôpital" At a time in the seventeenth century when there were only four men who knew calculus, Guillaume de l'Hôpital, one of the best French mathematicians, paid Johann Bernoulli to teach him. The result was the first calculus textbook and the rule that we now call "l'Hôpital's Rule". Therein lies a bit of controversy: was the book (and the rule) l'Hôpital's or Bernoulli's? Play the sleuth and find out for yourselves. Teach us about both men and their time. Starting points:
- "Michel Rolle: the story of a man and his theorem" It may be A bit of a tongue-in-cheek title, but please instruct us about the life and times of Michel Rolle. He can serve as an inspiration and role model for many of us, as he came from a poor family, was largely self-taught (there not being free compulsory education or financial aid at the time), and worked a variety of odd jobs during his lifetime. He became a member of the French Academy of Sciences, along with contemporaries such as Descartes. Make sure you discuss not only Rolle but also the meaning of the theorem that goes by his name. Starting points:
- "Pierre de Fermat" Even amateurs can have a significant impact
on mathematics. Pierre de Fermat was a lawyer who dabbled in
mathematics as a hobby. Among other things, he proved that the
points at which the derivative of a function are zero correspond to
local maxima or minima. He also left a great mystery for future
mathematicians: his so-called "Last Theorem". Besides discussing
Fermat himself, make sure you address the importance of finding
maxima and minima of functions. Also, summarize his last theorem,
how long it took to finally solve, and give your opinion(s) on
whether or not Fermat really had a proof of it (and, if not, why you
think he wrote his famous marginal note). Starting points:
- Fermat summary and biography at the University of St. Andrews.
- Fermat biography at Wikipedia.
- "The Proof" at PBS' Nova web site.

## Podcast Quality Ratings

- A
- The podcast presents its information in a manner that engages the listener throughout. The listener feels that he/she has learned something new by the end. The content goes beyond the assigned readings, bringing in additional material and integrating disparate information sources in a mature and sophisticated manner that demonstrates original thought. The podcast's structure shows advance planning, with an clear opening, smooth transitions among topics and speakers, and an ending that brings the topic to a close. The podcast avoids "filler" or unprofessional content; this doesn't mean that it can't be entertaining or demonstrate a good, relaxed mood. All of the members of the podcasting group participated substantively.
- B
- The podcast presents its information in a thoroughly competent manner. It is pleasant to listen to and easy to understand. Its information content is complete and it deals well with the complexities and scope of its subject. The podcast is a well-organized, unified whole. The podcast avoids "filler" or unprofessional content; this doesn't mean that it can't be entertaining or demonstrate a good, relaxed mood. All of the members of the podcasting group participated substantively.
- C
- The podcast is basically competent in its content and organization. The speakers use clear diction; it is easy to understand what they are saying. It may be incomplete in some minor ways or be disorganized to some extent. While sufficient, it does not "draw the listener in" or convey an impression of intellectual rigor. Most of the members of the podcasting group participated substantively.
- D
- The podcast's treatment of the subject is cursory or superficial. It lacks organization, resembling a "stream of consciousness" or a group of folks who got together to B.S. about the topic without advance preparation. If there is any preparation, the podcast amounts to a series of brief written paragraphs mechanically read aloud. There may be a clear lack of participation by one or more of the group.
- F
- A valid MP3 file was not submitted to me by the due date.