Journal Problem Solving Group at RIT

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The Journal Problem Solving Group (JPSG) at RIT

Academic Year 2006-07

Organized by: Matthew E. Coppenbarger

Let me introduce this group by answering five of the most common questions that I am asked:

Question #1: Why would I want to spend my precious little time struggling to solve tough problems out of journals? (Answer)

Question #2: What are the journals that have available problems? (Answer)

Question #3: How can I get a copy of the problems? (Answer)

Question #4: These problems [in the journals] seem so tough. How can I get some practice or help with solving problems? (Answer)

Question #5: How is RIT’s track record for getting student’s names published in journals? (Answer)

You can participate with the JPSG in one of two ways:

(1) Voluntary.

(2) Undergraduate Research! Starting Fall 2005, you can attend the meetings as a part of the Undergraduate Research I (1016-370) or Undergraduate Research II (1016-470) class. Of course, you will be required to meet with me regularly and submit one or more problems to journals (depending on the number of credits that the class is worth).

Question #1: Why would I want to spend my precious little time struggling to solve tough problems out of journals?

Answer: Good question. I can think of three reasons.

(1) Learn some new mathematics. Many times you will try a problem because it seems like a very interesting question, but find that you must teach yourself a math topic that you haven’t had a class in yet. That will give you a head start for when you actually have to take that class.

(2) Get some experience with scientific writing. This is the part that students dread the most because you can’t send your solution to the problem editors as if you would turn in a homework assignment. You must write you solution in Word or LaTex (or something equivalent) and in a format that other mathematicians will understand how you solved the problem. Your solution must be concise, but as short as possible – otherwise the problem editors won’t put your solution in their journal.

(3) Pad your resume. After you graduate, most of you will either get a job or go on to graduate school. In either case, smart people will look at your resume along with a bunch of others and try to decide who would best fit in the position or within the department. Having your name published in a scientific journal will put you one step ahead of other applicants that did not.

An additional reason why journals have problem sections is because they are looking for inventive problems solvers that will find the most interesting solution. Sometimes, the inventive techniques that appear in the solutions can be used for a related problem (that may currently be unsolved). Mathematical research is not always about producing new stuff that no one else has ever seen before, but finding shorter solutions and/or more elegant solutions to questions that have already been answered.

Question #2: What are the journals that have available problems?

Answer: I have access to six journals with regular problems sections.

Journal	Abbreviation
Math Horizons	MH
Journal of Recreational Mathematics	JRM
The Pi Mu Epsilon Journal	PME
The College Mathematics Journal	CMJ
Mathematics Magazine	MM
American Mathematical Monthly	AMM

The journals above are ordered in terms of easiest problems (top) to toughest problems (bottom). More information about each journal can be found here.

Problems are not always available on a continuous basis for each journal. Most of these journals are published four times a year, except PME (two times a year) and AMM (ten times a year). Depending on the publisher, there may be gaps from when a due date occurs and with the next issue.

Question #3: How can I get a copy of the problems?

Answer: There are three ways.

(1) Subscribe to some or all of the journals (that is what the publishers would like you to do, but the subscriptions can be expensive).

(2) Try to find them in RIT’s library. Some, but not all, are available on the current publications section.

(3) Just to get a copy of the problems that I have in my office. Email me and I’ll see that you get a copy for free (for RIT faculty and current students only).

Question #4: These problems [in the journals] seem so tough. How can I get some practice or help with solving problems?

Answer: Some problems look tough, but are relatively easy. Some are the other way around. You never really know until you sit down and work with them.

(1) Try Jim Marengo’s problem solving class (1016-481). It runs in the Fall Quarter and specifically prepares students to take the Putnam Exam in December.

There is, however, a slight distinction between problems that appear in the Putnam exam and problems in journals. The Putnam problems are designed to have shorter and more concise solutions than many of the problems in journals.

(2) The Putnam problems are great practice for solving journal problems! Here is a very good site that gives more information about the Putnam exam along with all of the previous exams (since 1985) and all solutions (since 1995).

(3) For a nice introduction to problem solving and the difficulties in teaching the methods to students, read the following paper:

A. H. Schoenfeld, Teaching Problem Solving Skills, American Mathematical Monthly, 87 (1980) 794-805.

Email me or come to my office if you would like a copy of this article.

(4) Or are textbooks more your style? Try any one (or all) of these:

M.J. Erickson and J. Flowers, Principles of Mathematical Problem Solving, Prentice-Hall, NJ, 1999,

K.S. Williams and K. Hardy, The Red Book Of Mathematical Problems, Dover, NY, 1996, and

K.S. Williams and K. Hardy, The Green Book Of Mathematical Problems, Dover, NY, 1997, and

P. Zeitz, The Art and Craft of Problem Solving, Wiley, NY, 1999.

(5) If you are having trouble with a particular problem from a journal, try asking a faculty member for some help and/or advise. Five faculty members that regularly or occasionally work on journal problems are David Farnsworth, David Hart, Jim Marengo, Mike Radin, and myself. Because every mathematician loves trying to answer interesting questions, just about any other faculty member within the department is willing and qualified to help also, especially within their field of interest.

Question #5: How is RIT’s track record for getting student’s names published in journals?

Answer: We don’t have a lot yet, the problem solving group hasn’t been around very long. But we’re slowly building up a list of solved problems. Here is what we have so far. There are more in the pipelines, waiting to be published.

Summary of Problem Solvers at RIT
Journal	Problem	Proposed In Issue	Solution In Issue	Student Solver(s)	Type of Solution
MH	203	September 2006	February 2007	Aaron Kaufer (SMAC)	(1)
PME	1131	Fall 2005	Fall 2006	Andres E. Espinoza-Masias (VCSG)	(2)
PME	1128	Fall 2005	Fall 2006	Andres E. Espinoza-Masias (VCSG)	(2)
JRM	2629	October 2004 (32-1)	February 2006 (33-1)	Nathan Reff (SMAM)	(2)
MH	S99	September 2005	February 2006	Andrew Merrill (SPSP)	(2)
MH	S92	February 2005	September 2005	Abdullah Muhammad (EECB)	(2)
MH	189	November 2004	April 2005	Jason Moore (SMAM)	(2)
MH	185	September 2004	February 2005	Hans-Christian Rotmann (EEEB)	(2)
CMJ	769	January 2004	January 2005	Julia Bethel (SMAM) Julie Blackwood (SMAM) Ted Dziuba (SMAM) Hans-Christian Rotmann (EEEB) [Submitted jointly as The RIT Problem Solving Group]	(2)
AMM	10959	August 2002	January 2004	Prashant Bhoola (SCHB)	(2)

If you are interested, the exact wording of each problem is given here.

There are two ways that your name can appear in the journal once you have submitted a solution.

(1) You have written such a wonderful solution that the problem editors want to everyone else to read what you have written. The editors publish your solution (nearly) verbatim of what you sent to them.

(2) You sent in a correct solution, but someone else did too and in fact, sent in a better solution. In this case, you name is included in the list of “Also Solved By:”, which is given right after the main solution. It’s a consolation prize, but a worthwhile accomplishment nevertheless.

Another possibility is that you sent in an incorrect solution. This only happens very rarely. The problem editors won’t include your name, but will say how many incorrect solutions they received.