Bona's Bonus Problems

BBP

Bona's Bonus Problems are special mathematical challenges for Bona's students. A Bona's Bonus Problem is any mathematics problem in the problem section of a recent issue of Math Horizons, The American Mathematical Monthly, Mathematics Magazine, The College Mathematics Journal, Crux Mathematicorum, or the Pi Mu Epsilon Journal. Recent issues of each journal are kept in the waiting area in the Mathematics Suite (De La Roche 301). Each semester, Dr. Hill selects a few Bona's Bonus Problems and posts them on the bulletin board next to the door to the Mathematics Suite. Copies of the posted problems are available in a display atop the "Resources" bookcase in De La Roche 301. The posted problems are chosen for being particularly accessible, interesting, and complementary to our mathematics curriculum. If a student solves any Bona's Bonus Problem, posted or not, in accordance with the Rules below, the student may bring his or her solution to Dr. Hill (De La Roche 301 C) to receive the following benefits:

• the student's name will subsequently appear in the journal as a solver of the problem and the student's solution MAY be chosen to be PUBLISHED in the journal;
• the Mathematics Department will give the student a certificate of excellence and one (1) free tee-shirt with a groovy mathematical design;
• the student will be immortalized in the BBP Hall of Fame (the list of students who successfully solved one or more Bona's Bonus Problems).

   «  «  «  «     BBP Hall of Fame    «  «  «  «   

 Jack Fuller  solved Problem S122 of the November 2007 issue of Math Horizons.

 Kevin Miller  solved Problem 1139 of the Fall 2006 issue of The Pi Mu Epsilon Journal.

Tim McGue & Craig Vicini  jointly solved (under the name "St. Bonaventure University Problem-Solving Group") Problem 796 in the Sept. 2005 issue of the College Mathematics Journal. Tim and Craig presented their solutions of this problem and the Math Horizons problem (see below) at the 2006 SBU Student Showcase. Each solution was presented on a poster, along with descriptions of the problem-solving strategies that Tim and Craig used within the solution. At right: Craig and Tim at the Student Showcase.  Tim McGue & Craig Vicini  jointly solved (under the name "St. Bonaventure University Problem-Solving Group") Problem S98 in the Sept. 2005 issue of Math Horizons.

 Jerome Brabant  solved Problem S90 of the Nov. 2004 issue of Math Horizons. Jerome's solution was PUBLISHED in the April 2005 issue.

 Jerome Brabant  solved Problem 186 of the Sept. 2004 issue of Math Horizons.

 Jerome Brabant  solved Problem S88 of the Sept. 2004 issue of Math Horizons.

 Eric Cranmer  solved Problem S85 of the Feb. 2004 issue of Math Horizons

Rules

• An SBU student may work on a problem either alone or with another Bona's student. If two students work together, the pair must submit a solution jointly.
• A student may not receive help from anyone who is not submitting the solution with the student, although...
• ... a student may see Dr. Hill for boundless encouragement and general assistance. (An example of general assistance would be, ``Here is a book that has some relevant material.'')
• The problems in a particular issue of a journal have a deadline, beyond which the journal will not accept solutions. A student's solution must be received by Dr. Hill at least a few days before the Journal's deadline so that it can be submitted to the journal.

1. I'd like to try one of the problems, but I'm very busy. These problems would take a lot of time.

   Although there is no guarantee about the time required to solve a BBP (a math problem takes as much time as it takes), the posted BBPs are selected in part because they are similar to homework problems, albeit challenging ones, that could be given in an undergraduate math class. However, while in a math class you would have a few days or a week to solve a homework problem, the typical deadline for a BBP is several weeks after the problem is posted. Mathematics journals allows readers a long time to work on their problems precisely so that readers can work around their busy schedules. Consequently, the time pressure on a BBP is low.

2. One of the problems looked interesting, but I had no idea how to start it, so I gave up.
   

   When you are given a homework problem in a typical math class, you have a pretty good idea of what tools will be needed to solve it. For example, if you studied integration by parts today in Calc II and were assigned some problems at the end of the lecture, you can be fairly certain that at least some (perhaps most, perhaps all) of those problems will require integration by parts. In brief, you have a context for the homework problems. By contrast, a problem posed in a math journal does not have a context, so the reader does not immediately know what tools will help to solve it. Due to this lack of context, problems posed in math journals often seem quite challenging, even unapproachable. The first and most important step to solving one of these problems is not to give up.

   Confusion is the usual state of affairs for anyone, students and mathematicians (really) alike, working on a new and unfamiliar math problem. When a math teacher writes a problem on the board and then immediately solves it, the impression is given that any math problem is solved by writing down the problem, immediately knowing how to solve it, and then solving it. In fact, doing mathematics is rarely like that. Don't worry just because you don't know where to start. Know that when you are confused about a math problem, you are not alone.  

   If you are interested in one of the Bona's Bonus Problems but do not know where to start, see Dr. Hill for boundless encouragement and general assistance. And don't give up.