In responding to a comment on the last entry, I answered the questions of what equipment and software I am using to create our online course materials:
For our College Algebra course, we cover the last six chapters from an Intermediate Algebra textbook. There will be a lecture for each section of each of the chapters. It looks like every full section lecture will be about 20 - 30 minutes in length. I am shooting a screen (or slide) one at a time which comes to about 10 slides or so per section. This post was one of those slides. Each of those slides ranges from 2 - 5 minutes in length. I think that comes to a total of about 27 lectures about 30 minutes each. I will probably have the students order a DVD with hi-res versions of the video, but post compressed versions on the web, maybe even as podcasts available through an RSS feed.
In terms of software, I am doing everything the hard way since I am on a PC. I hear this would probably be easier with a Mac. Nevertheless, I am mostly using free software. For the screen capture, I use CamStudio. I piece all the slides together using Windows Movie Maker. The software I use for writing on the screen is the software that was included with my tablet. My first choice would have been to use a tablet PC but the cost was prohibitive. Instead, I went with the WACOM Intuos3 tablet. We purchased the 9x12 tablet which works well, but is probably larger than needed. The Corel Painter Essentials software was included with the tablet and it worked quite well for the screen casting.
I hope this answers your questions. I got most of my ideas from a podcast I watched in iTunes by the name of "Is All About Math".
I am currently developing an online course in College Algebra for Wayland. The hope is to have a series of video lectures, accompanied by a lecture notebook where the students will fill in the book as they watch the lectures. Below is a sample video from on the series.
A GUIDE TO GRADING EXAMS
by Daniel J. Solove
Associate Professor of Law, The George Washington
University Law School
December 14, 2006
It's that time of year again. Students have taken their
finals, and now it is time to grade them. It is something
professors have been looking forward to all semester.
Exactness in grading is a well-honed skill, taking
considerable expertise and years of practice to master. The
purpose of this post is to serve as a guide to young
professors about how to perfect their grading skills and as
a way for students to learn the mysterious science of how
their grades are determined.
Grading begins with the stack of exams, shown in Figure 1
The next step is to use the most precise grading method
possible. There never is 100% accuracy in grading essay
exams, as subjective elements can never be eradicated from
the process. Numerous methods have been proposed throughout
history, but there is one method that has clearly been
proven superior to the others. See Figure 2 below.
The key to this method is a good toss. Without a
good toss, it is difficult to get a good spread for
the grading curve. It is also important to get the
toss correct on the first try. Exams can get
crumpled if tossed too much. They begin to look as
though the professor actually read them, and this is
definitely to be avoided. Additional tosses are also
inefficient and expend needless time and energy.
Note the toss in Figure 3 below. This is an example
of a toss of considerable skill -- obviously the
result of years of practice.
Note in Figure 3 above that the exams are evenly
spread out, enabling application of the curve. Here,
however, is where the experts diverge. Some contend
that the curve ought to be applied as in Figure 4
below, with the exams at the bottom of the staircase
to receive a lower grade than the ones higher up on
According to this theory, quality is understood
as a function of being toward the top, and thus the
best exams clearly are to be found in this position.
Others, however, propose an alternative theory
(Figure 5 below).
They contend that that the exams at the bottom
deserve higher grades than the ones at the top.
While many professors still practice the
top-higher-grade approach, the leading authorities
subscribe to the bottom-higher-grade theory, despite
its counterintuitive appearance. The rationale for
this view is that the exams that fall lower on the
staircase have more heft and have traveled farther.
The greater distance traveled indicates greater
knowledge of the subject matter. The bottom
higher-grade approach is clearly the most logical
and best-justified approach.
Even with the grade curve lines established,
grading is far from completed. Several exams teeter
between levels. The key is to measure the extent of
what is referred to as "exam protrusion." Exams that
have small portions extending below the grade line
should receive a minus; exams with protrusions above
the grade lines receive a plus.
But what about exams that are right in the middle
of a line. In Figure 6 below, this exam teeters
between the A and B line. Should it receive and A-
or a B+?
This is a difficult question, but I believe it is
clearly an A-. The exam is already bending toward
the next stair, and in the bottom-higher-grade
approach, it is leaning toward the A-. Therefore,
this student deserves the A- since momentum is
clearly in that direction.
Finally, there are some finer points about
grading that only true masters have understood.
Consider the exam in Figure 7 below. Although it
appears on the C stair and seems to be protruding
onto the B stair, at first glance, one would think
it should receive a grade of C+. But not so. A
careful examination reveals that the exam is
crumpled. Clearly this is an indication of a sloppy
exam performance, and the grade must reflect this
fact. The appropriate grade is C-.
One final example, consider in Figure 8 below the
circled exam that is is very far away from the
others at the bottom of the staircase. Is this an
Novices would think so, as the exam has separated
itself a considerable distance from the rest of the
pack. However, the correct grade for this exam is a
B. The exam has traveled too far away from the pack,
and will lead to extra effort on the part of the
grader to retrieve the exam. Therefore, the exam
must be penalized for this obvious flaw.
As you can see, grading takes considerable time
and effort. But students can be assured that modern
grading techniques will produce the most precise and
accurate grading possible, assuming professors have
achieved mastery of the necessary grading skills.
DISCLAIMER FOR THE GULLIBLE:
This post is a joke. I do not grade like this.
Instead, I use an even more advanced method -- an
eBay grade auctioning system.
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In my Faith and Science course, when we covered the scientific models for origins of the universe, we studied the "mainstream" model of the Big Bang. I remember making the comment that for many Christians who are scientists, the idea of a Big Bang at the beginning of the universe is completely consistent with the idea of God as Creator. "God spoke and BANG, it was". I also commented that we are unable to determine what happened, if anything, prior to the Big Bang. In fact, the current version of the model only goes back to when the age of the Universe was about 10^-43 seconds old. Admittedly this is very close to the beginning, but it was not possible to know what happened before that or, at least, it was impossible to know what happened before the Big Bang.
Well,scientists at Penn State have begun to try to look beyond the birth of the universe. Using quantum tools with general relativity, Abhay Ashtekar and two of his post-doctoral researchers have developed a model that looks before the Big Bang to see a shrinking universe with much the same physics as ours. "Using quantum modifications of Einstein's cosmological equations, we have shown that in place of a classical Big Bang there is in fact a quantum Bounce," says Asktekar.
Since I can't claim to have the expertise to critique their science, I am curious to watch how this model is accepted in the scientific community.
For more, you can read the article in Scientific Daily:
Penn State Researchers Look Beyond The Birth Of The Universe
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I have tried to do a little research into the compatibility of Maple 11 with Microsoft Vista. A student of mine report that he attempted to run his new copy of Maple 11 on his new Vista machine and was unsuccessful. I could not find a statement on the Maplesoft website confirming or denying. I did see a MaplePrimes forum post that seemed to imply that it was not compatible but nothing official.
Does anyone know? I surely expect them to be working on this but finding no information was frustrating.
I am LaTEX disciple when it comes to writing up my own papers (No, not as in spandex, but the typesetting language). However, when I work with undergraduate students who have not had any exposure to such a language, I tend to encourage them to use Microsoft Word. I also encourage them to use the Equation Editor in the their math papers even though I must cringe as I read them. I don't cringe because they are using a Microsoft product, but that the mathematics typesetting is still just so unsightly.
I was pleased to discover a functionality in Word that I was unaware of. If you utilize the "styles" for different headings, such as Heading 1 for Chapter titles, Heading 2 for Section titles, etc., Word will automatically generate a table of contents for you. In Microsoft Word 2003, select Insert . . Reference . . Index and Tables. You have options for Tables of Contents, Table of Figures, etc.
For more details, see Microsoft Word Help FAQ. How to create a table of contents in Microsoft Word.
On a side note: Each time that Microsoft develops an upgrade to one of its products, it generally surveys its users in one way or another to see what functionality they would like to see included in their upgrades. In listening to one of my favorite podcasts, Windows Weekly with Paul Thurott, I learned that the VAST majority of requests with respect to Microsoft Office are features that are already present and people just haven't discovered them. That happens to be one of the motivations behind the User Interface redesign you see in Office 2007 (which I haven't yet played with). Ever since I discovered the Table of Contents, I am on the hunt for new features that I have missed.
Here is an absolutely amazing application related to some of the topics we are currently covering in my Linear Algebra course. Note the use of the terms "Vector Space", "linear combinations", "distance" between vectors.
It is definitely worth 5 minutes of your time to watch.
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In July, 1999, Paul and Jack Abad presented their list of "The Hundred Greatest Theorems." I was intrigued and though it might be interesting to re-post.
Their ranking is based on the following criteria: "the place the theorem holds in the literature, the quality of the proof, and the unexpectedness of the result."
The list is of course as arbitrary as the movie and book list, but the theorems here are all certainly worthy results.
1 The Irrationality of the Square Root of 2, Pythagoras and his school, 500 B.C.
2 Fundamental Theorem of Algebra, Karl Frederich Gauss, 1799
3 The Denumerability of the Rational Numbers, Georg Cantor, 1867
4 Pythagorean Theorem, Pythagoras and his school, 500 B.C.
5 Prime Number Theorem, Jacques Hadamard and Charles-Jean de la Vallee Poussin (separately), 1896
6 Godel’s Incompleteness Theorem, Kurt Godel, 1931
7 Law of Quadratic Reciprocity, Karl Frederich Gauss, 1801
8 The Impossibility of Trisecting the Angle and Doubling the Cube, Pierre Wantzel, 1837
9 The Area of a Circle, Archimedes, 225 B.C.
10 Euler’s Generalization of Fermat’s Little Theorem (Fermat’s Little Theorem), Leonhard Euler (Pierre de Fermat), 1760 (1640)
... (view the rest of the list)
For a long time I have been planning to work up my mathematical genealogy using "The Mathematical Genealogy Project" site. They have the aspirations of documenting the entirety of the genealogy of ALL the mathematicians of the world. I had not heard of the site until after I graduated with my doctorate but was surprised to find quite a few BIG names in my academic heritages. Names like Gauss, Euler, Leibniz, Weierstrass, Hilbert, Poisson, Fourier, Klein, as well as many others.
I have spent more time compiling my heritage than I probably have ought, but you can now download document with it all drawn out: