Code for Spanning Trees in a Sage Cell

It's been over a year since I've posted to this blog, mostly because I've been busy being department chair.  As I type this, I've got 313 days left on my term.  So the end is almost in sight.  I posted a page with code for computing the spanning trees of a graph a while ago on http://faculty.uml.edu/klevasseur/ads2/sage_cell/sage_cell.html but I'm not sure how much use it's had.

Here is a video that shows how to use this resource:


A comment from who finds this resource useful will make it more likely that I will find the time to add more!

Update from JMM2014: WeBWork, LaTeX, and Sage Cells

I was in Baltimore for a couple of days last week and concentrated on talks related to open source texts and software.   I spoke in one of the sessions on open source texts, outlining this project.

There were three main things I added to my "to do" list based on the talks I attended.

1. Start developing problem sets for WeBWork.   To that end, I've arranged for out WeBWork server at UMass Lowell to updated, and once that's done I hope to get started on developing problems.
2. Start the process of converting our book to LaTeX.   One of the talks, by David Farmer, convinced me that getting our "source content" into a mainstream  format is the way to go.
3. Embedded Sage Cells seem to be a good to introduce the use of Sage in mathematics.  I hope to gradually add content in that form to our web page.  I did a short test page showing how to create graphs at http://faculty.uml.edu/klevasseur/ads2/sage_cell/sage_cell_graphs.html

This should keep me busy for a while!

By the way, the Baltimore Convention Center is next door to Camden Yards and also near the birthplace of Babe Ruth.

Open Source Math Texts at the 2014 JMM

There are going to be sessions on open source math texts at the 2014 Joint Math Meetings in Baltimore January 15-18.   The sessions are on Friday January 17 , 8-10:55 and 3-4:55.  I'm speaking on our  text, Applied Discrete Structures.  Because of a family obligation, I requested a late time, and I got the last time slot in the afternoon session, at 4:40.   My Title is "What a Difference 30 Years Makes!  -Adventures in Mathematics Textbook Publishing."   The sessions will be in Room 349 of the Baltimore Convention Center.

I'd love to meet up with anyone who has been using our book!

A sphere in binary 11-space

In my discrete math class this week, did an example of a code that encodes three bits to eleven bits and can correct all two-bit errors.   This particular code was not meant to be particularly optimal, but for one particular example I ran with 3,000,000 bits, the number of errors was roughly 1/4 of what was predicted by the probabilities, given that two bit errors can be corrected.  There were 38 failures instead of a predicted 155.   This is no mystery since the packing of spheres in {0,1}^11 wasn't expected to be all that tight, and three bit errors can often be corrected.  

The encoding function is 

         (a, b, c) ----> (a, b, c, a + b, a + c, b + c, a + b + c, a + b, a + c, b + c, a + b + c)

To get an visualize the situation, I create the graph below.   The vertices are some of the points in the code space: the sphere of radius three centered around one of the code words.   The color coding is

• Yellow:   the code word - I used the zero word, but the space is symmetric everywhere.
• Blue:   points one unit from the code word
• Green:  points two units from the code word
• Brown:  points three units from the code word and further that three units from all other code words.
• Red:  points three units from the code word but also three units from another code word.

So all but the Red points, if received, will correct to the most likely transmitted word.   Only the Red ones are questionable and there is no most likely correction.

The Economic Impact of Applied Discrete Structures.

I've been starting to collect data to document the economic impact of Applied Discrete Structures.  In a class using our text, the cost to a student ranges from $0, if  he/she uses the pdf, to $30 a hard copy of purchased.   A rough estimate of the percentage students that buy a hard copy is 15%.   Prior to using our text at UMass Lowell, we used a text that cost $160 new, and around $120 used.   So a very conservative estimate of the impact on student costs would be $120 times the number of students enrolled in discrete math classes using our book.  Here are the estimated student savings, also with very conservative estimates for enrollments starting Fall 2011 through the Spring 2013 semester:

UMass Lowell:   300 students have saved a collective $36,000

Other Colleges:   75  students have saved a collective $9,000

That's $45,000 that students have saved in the first couple of years that the book has been available.   We're hoping that with increased exposure on open source textbook websites, we can dramatically increase the impact outside of UMass Lowell.

So far we are listed on the following sites:

• Merlot Open Textbook Services
• University of Minnesota Open Textbook Catalog
• The American Institute of Mathematics 
• U. of Puget Sound Open Content Math Curriculum
• collegeopentextbooks.org