MAA/DEPARTMENT LIAISONS NEWSLETTER
March 2000 Issue
Today's Editors: Jane Heckler and Dan Kalman
In this Issue.....
A Favorite Induction Proof
Elbert F. Cox, SUMMA
In spite of an early morning snow storm in Washington, DC, the third annual Liaisons Breakfast at the January Joint Mathematics Meetings was a great success by all accounts. Herb Kasube, an officer of the Illinois Section and member of the MAA Committee on Liaisons, served as Master of Ceremonies for a brief program of announcements and discussion. Participating liaisons from all over the country met to share ideas over breakfast. As a memento of the occasion, and in appreciation for their efforts as liaisons, participants received a special mouse-pad with featuring an MAA Liaisons logo. We hope that the breakfast will become a tradition, and that all liaisons will have a chance to attend one at a national meeting.
A Favorite Induction Proof
One session at the January meeting featured presentations by Arthur T. Benjamin, Donald S. Passman, and Gary W. Towsley, winners of this year's Deborah and Franklin Tepper Haimo Awards for Distinguished College or University Teaching of Mathematics. (Go to
on the internet for more information on the awards and recipients.)
Benjamin's presentation included his favorite induction proof, which is repeated here for your consideration.
A tromino is a plane figure composed of three squares:
The theorem states that if n is any power of 2, then an n x n square grid with one of the corner squares removed can be tiled using trominoes. The base case of this result, when n = 2 (the first
power of 2), is clear: a 2 x 2 square with one corner removed IS a tromino. For the induction step, suppose that the result holds for a 2 x 2 grid and consider the next case: a 2n x 2n grid with one corner square removed. Partition this 2n x 2n grid into 4 parts, each an n x n grid. One of the four contains the corner with the removed square, and by the induction hypothesis, that is tilable with trominoes. Now there remain three untiled n x n grids. Position one tromino at the point where these 3 meet, so that one square of the tromino lies in each of the three untiled grids. That leaves untiled three n x n grids with one corner removed, and these are tilable again by the induction hypothesis.
That completes the proof.
Elbert F. Cox, SUMMA
In the February Monthly, there is an absorbing article on the first African American to earn a math PhD in this country ("Elbert F. Cox: An Early Pioneer" by James A. Donaldson and Richard J. Fleming). A brief summary of the article (available at
http://www.maa.org/pubs/monthly_feb00.html) states that Cox "...earned the degree from Cornell University in 1925 and went on to a distinguished career that ended with his retirement after 37 years at Howard University." Cox grew up in a period when racism was openly expressed, including professions that blacks were incapable of a wide array of intellectual activities, higher mathematics among them. It is a sad chapter in the history of our entire nation, and of our own MAA, that such attitudes were so widely repeated and accepted.
More recently, the MAA has recognized the importance of attracting people from all backgrounds to study and contribute to mathematics. An MAA program called SUMMA (Strengthening Underrepresented Minority Mathematics Achievement) was established in 1990 to increase the representation of minorities in the fields of mathematics, science and engineering and improve the mathematics education of minorities. Toward those ends, SUMMA secured outside funding for a variety of activities and programs, including professional development for minority faculty and intervention programs for secondary students. More information about SUMMA is available on-line athttp://www.maa.org/summa/archive/summa_wl.htm.
MathServe 2000 Contest
The purpose of MathServe is to build bridges that connect the mathematics community to the service community. The intent of the contest is to inspire collaborative projects that utilize mathematical skills to address social, health, or environmental challenges.
All projects must be collaborative ventures between an educational institution--university or high school department of mathematical science--and a public, nonprofit or grassroots organization.
Work may be accomplished individually or in teams by faculty and/or students. Student participation is strongly encouraged.
Submissions are due at COMAP no later than May 1, 2000.
A copy of the Submission Form is available from the MathServe website at: http://www.comap.com/undergraduate/contests/mathserve/index.html
The MathServe Program is organized by the Consortium for Mathematics and Its Applications (COMAP), the sponsor of the Mathematical Contest in Modeling (MCM) and The Charles A. Dana Center of the University of Texas at Austin.
MAA Publications coming soon in 2000:
Here are some books in production:
Contest Book VI: American High School Mathematics Examinations 1989-1994
- by Leo Schneider, The Anneli Lax New Mathematical Library (early May)
Using History to Teach Mathematics
- Edited by Victor Katz, MAA Notes (early summer)
Teaching Resources for Undergraduate Statistics
- edited by Thomas Moore, MAA Notes, (early summer)
Topology Meets Chemistry (Jointly published with Cambridge University Press)
- by Erica Flapan (early summer)
April....Mathematics Awareness Month (www.maa.org/news/mam00.html)
April 14....Project NExT Applications due (www.maa.org/news/next2000.html)
June 30...Undergrad student paper deadline, Mathfest 2000 (www.maa.org/students/students_index.html)
August 3-5...Mathfest 2000, UCLA
The Liaisons Newsletter is produced at the headquarters office of the MAA. Comments, suggestions, and questions are welcome. Please direct them to any of the following:
Senior Assistant for Programs
Member, Subcommittee on MAA/Departmental Liaisons
Chair, Subcommittee on MAA/Departmental Liaisons
The Mathematical Association of America
1529 Eighteenth St., NW
Washington, DC 20036-1358
Voice: (800) 741-9415 Fax: (202) 483-5450