Bona's Bonus Problems

Math Horizons, The PME Journal, Crux MathematicorumThe College Mathematics Journal, Mathematics Magazine, The American Mathematical MonthlyBona'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 Pi Mu Epsilon Journal, Crux Mathematicorum, Mathematics Magazine, The College Mathematics Journal, or The American Mathematical Monthly. Recent issues of each journal are kept in the waiting area in the Mathematics Suite (De La Roche 301). The problems section of The PME Journal is conveniently posted online in the Problem Department of Pi Mu Epsilon's website.

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, chill@sbu.edu) 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 one (1) free tee-shirt with a groovy mathematical design and a copy of the journal's issue in which his or her name appears;
  • 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

 Mitch Kovacs '16  solved Problem 485 of the No. 1 2013 issue of the New York State Mathematics Teachers' Journal.
 Mitch Kovacs '16  solved Problem 1270 of the Fall 2012 issue of The Pi Mu Epsilon Journal.
 Mitch Kovacs '16  solved Problem 983 of the September 2012 issue of The College Mathematics Journal.
 Mitch Kovacs '16  solved Problem 3670 of the December 2011 issue of Crux Mathematicorum.
 Jennifer Dempsey '12 & Michael Murphy '13  jointly solved Problem 3629 of the April 2011 issue of Crux Mathematicorum.
 John Postl '11  solved Problem 931 of the September 2010 issue of The College Mathematics Journal.
 Daniel Winger '11  solved Problem 3539 of the May 2010 issue of Crux Mathematicorum.
 John Postl '11  solved Problem 3539 of the May 2010 issue of Crux Mathematicorum.
 Natalie Burns  solved Problem 1223 of the spring 2010 issue of The Pi Mu Epsilon Journal. At the time of her solution, Natalie was a high school senior.
 John Postl '11  solved Problem 1223 of the spring 2010 issue of The Pi Mu Epsilon Journal.
 John Postl '11  solved Problem 1218 of the spring 2010 issue of The Pi Mu Epsilon Journal.
 John Postl '11  solved Problem 1216 of the spring 2010 issue of The Pi Mu Epsilon Journal. John's solution was  PUBLISHED  in the fall 2010 issue.
 Natalie Burns  solved Problem 1210 of the fall 2009 issue of The Pi Mu Epsilon Journal. Natalie's solution was  PUBLISHED  in the fall 2010 issue. At the time of her solution, Natalie was a high school junior.
 John Postl '11  solved Problem 1207 of the fall 2009 issue of The Pi Mu Epsilon Journal.
 John Postl '11  solved Problem 3452 of the Sept. 2009 issue of Crux Mathematicorum.
 Troy Mulholland '11  solved Problem 3426 of the April 2009 issue of Crux Mathematicorum.
 Andrew Krull '10  solved Problem 1811 of the Feb. 2009 issue of Mathematics Magazine.
 John Grillo '09  solved Problem 1175 of the spring 2008 issue of The Pi Mu Epsilon Journal.
 John Grillo '09  solved Problem 1174 of the spring 2008 issue of The Pi Mu Epsilon Journal.
 Jack Fuller '10  solved Problem S122 of the November 2007 issue of Math Horizons.
 Kevin Miller '08  solved Problem 1139 of the Fall 2006 issue of The Pi Mu Epsilon Journal.
Craig Vicini and Tim McGue at the 2006 Student Showcase Tim McGue '07 & Craig Vicini '07  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.

 Tim McGue '07 & Craig Vicini '07  jointly solved (under the name "St. Bonaventure University Problem-Solving Group") Problem S98 in the Sept. 2005 issue of Math Horizons.
 Jerome Brabant '05  solved Problem S90 of the Nov. 2004 issue of Math Horizons. Jerome's solution was  PUBLISHED  in the April 2005 issue.
 Jerome Brabant '05  solved Problem 186 of the Sept. 2004 issue of Math Horizons.
 Jerome Brabant '05  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 submitted to the journal prior to the journal's deadline.

Top two reasons for not working on a Bona's Bonus Problem,
and Dr. Hill's responses to them

  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.

The Problem-Solving Seminar

When solving a math problem, persistance is trying various keys until you find one that unlocks the problem. The keys are problem-solving strategies. What is a problem-solving strategy? It’s what to try on a math problem when you don’t know what to try. Although there are a vast number of mathematical problems, only a small number of problem-solving strategies, in conjunction with basic mathematical knowledge, is required to tackle almost all of them. To learn more about problem-solving strategies, take MATH 281. The Problem-Solving Seminar.

In MATH 281, problem-solving strategies are studied and applied to a wide range of problems. As the same techniques are applied to widely-varying problems in calculus, discrete mathematics, geometry, and other areas, mathematics is revealed as a unified discipline rather than a collection of unrelated topics. The Seminar emphasizes the value of attempts and partial solutions—when a problem-solving technique does not seem to work on a particular problem, progress has been made on the problem and insight has been gained into the technique.

MATH 281 is a one-credit course offered during the fall semester. The prerequisites are MATH 152. Calculus II and MATH 207. Discrete Mathematics I. MATH 281 may be repeated for credit.

During previous Problem-Solving Seminars, students solved problems posed in the problems sections of the national undergraduate journals Math Horizons, The College Mathematics Journal, and the Pi Mu Epsilon Journal.

For more information...

...about Bona's Bonus Problems or The Problem-Solving Seminar, contact Dr. Hill (De La Roche 301-C, chill@sbu.edu). And don't give up.