MATH PROBLEM SOLVING WEB PAGE

Web page for the Northwestern University Math Problem Solving Group.

Goals

  1. Acquire basic math problem solving skills.
  2. Help in training future candidates for the yearly Putnam Competition.

Activities

  1. Solve math problems proposed in magazines like Math Horizons, College Mathematics Journal and the Mathematics Magazine. Ideally we should solve at least one problem from each issue.
  2. Discuss solutions to problems and study mathematical subjects related to problem solving.

Unless otherwise stated, the level of the problems and results shown here should be undergraduate.

Last Modified: December 13, 2017

Index


Announcements

(There are no announcements at this moment.)


MathPSG Emailing List

Subscribe to the Math Problem Solving Group emailing list by sending an email to listserv@listserv.it.northwestern.edu with the following line in its body:
subscribe MathPSG Your Name
where Your Name means that you must write your name there.

Alternatively, please click in one of the following links, depending on whether you want to

Clicking on one of those links will fire up the mail program associated to your browser with the appropriate command for the listserver already typed in. Note however that if your choice is to subscribe MathPSG, you must add your name at the end of the line "subscribe MathPSG", otherwise the listserver will reply with an error message saying that the name is missing.

Note: Problems from magazines discussed and solved in the MathPSG emailing list may be submitted to the magazines in the name of the Northwestern University Math Problem Solving Group.

The MathPSG emailing list is moderated. Postings sent to the list will not be automatically forwarded to its members, they must await approval by the moderator.


How the group works

The Math PSG works on problems proposed by various math magazines (see below), and submits solutions to the magazines. The process works like this:
  1. Pick a problem not yet solved by the group, and for which the deadline for submission has not arrived yet.
  2. If you solve the problem, you can post your solution sending it by email to
    MathPSG@listserv.it.northwestern.edu
    or mailing it directly to the group coordinator. If you want to give a chance the other members of the group to think the problem too, instead of a complete solution you may post only some hints first.
  3. Some discussion of the solution may follow. After the solution is considered correct, and if nobody has anything to add, the coordinator will write a final version and submit it to the magazine in behalf of the group. If there is some discussion, or more that one solution posted, the coordinator will try to compose a "combined solution" with the different contributions.
Problems solved by the group and submitted to a magazine appear below in the column "submitted solutions".


Proposed Problems

These are problems proposed in magazines like Math Horizons, College Mathematics Journal, the Mathematics Magazine, Pi Mu Epsilon Journal, and Harvard College Mathematics Review. Ideally we should try to solve at least one problem from each issue and submit it to the magazine before the deadline.

Note: Downloading the lists of proposed problems requires authentication by password. I will distribute periodically the necessary username and password among the members of the Math Problem Solving Group. If you are a member of the group and have forgotten the password, let me know at MATHPSG-request@listserv.it.northwestern.edu.

source deadline submitted solutions (*)
- 2016 -
Math Horizons, Vol. 23, No. 2, Nov 2015 January 11, 2016 330, 332
College Mathematics Journal, Vol. 46, No. 3, May 2015 January 15, 2016 1051, 1053, 1054
College Mathematics Journal, Vol. 46, No. 4, Sep 2015 February 15, 2016 1057
Mathematics Magazine, Vol. 88, No. 4, Oct 2015 March 1, 2016 1976
Mathematics Magazine, Vol. 88, No. 5, Dec 2015 May 1, 2016 1983, 1984, 1985
College Mathematics Journal, Vol. 46, No. 5, Nov 2015 May 15, 2016 1061
Math Horizons, Vol. 23, No. 3, Feb 2016 May 31st, 2016 334, 337
Mathematics Magazine, Vol. 89, No. 1, Feb 2016 July 1, 2016 1986, 1987
Math Horizons, Vol. 23, No. 4, Apr 2016 August 10, 2016 338, 339
College Mathematics Journal, Vol. 47, No. 2, Mar 2016 August 15, 2016 1071
Mathematics Magazine, Vol. 89, No. 2, Apr 2016 September 1, 2016 1992
College Mathematics Journal, Vol. 47, No. 3, May 2016 October 15, 2016 1078, 1079
Mathematics Magazine, Vol. 89, No. 3, Jun 2016 November 1, 2016 1996, 1998, 1999
Math Horizons, Vol. 24, No. 1, Sep 2016 November 9, 2016 345
- 2017 -
Math Horizons, Vol. 24, No. 2, Nov 2016 January 11, 2017 346, 349
College Mathematics Journal, Vol. 47, No. 4, Sep 2016 February 15, 2017 1081, 1083
College Mathematics Journal, Vol. 47, No. 5, Nov 2016 February 15, 2017 1090
Mathematics Magazine, Vol. 89, No. 4, Oct 2016 March 1, 2017 2001, 2002, 2003, 2004, 2005
Mathematics Magazine, Vol. 89, No. 5, Dec 2016 May 1, 2017 2007, 2008, 2009, 2010
Math Horizons, Vol. 24, No. 3, Feb 2017 May 31, 2017 350
College Mathematics Journal, Vol. 48, No. 1, Jan 2017 June 15, 2017 1091, 1093, 1094, 1095
College Mathematics Journal, Vol. 48, No. 2, Mar 2017 June 15, 2017 1097, 1099
Mathematics Magazine, Vol. 90, No. 1, Feb 2017 July 1, 2017 2011, 2012, 2013
Math Horizons, Vol. 24, No. 4, Apr 2017 August 10, 2017 354,355
Mathematics Magazine, Vol. 90, No. 2, Apr 2017 September 1, 2017 2017, 2018, 2019
College Mathematics Journal, Vol. 48, No. 3, May 2017 October 15, 2017 1102
Mathematics Magazine, Vol. 90, No. 3, Jun 2017 November 1, 2017 2022, 2025
Math Horizons, Vol. 25, No. 1, Sep 2017 November 9, 2017 359
- 2018 -
Math Horizons, Vol. 25, No. 2, Nov 2017 January 11, 2018 362, 365
College Mathematics Journal, Vol. 48, No. 4, Sep 2017 February 15, 2018
College Mathematics Journal, Vol. 48, No. 5, Nov 2017 1111
Mathematics Magazine, Vol. 90, No. 4, Oct 2017 March 1, 2018

(*) Color red means that the solution submitted by us was selected for publication.


Problems for the Brave

Problems from magazines like the American Mathematical Monthly are traditionally (but not always) harder than the ones proposed in the magazines mentioned above. I am including them here just in case someone wants to try them.

(See note above about requiring username and password for downloading the lists of proposed problems.)
source deadline submitted solutions
- 2016 -
American Mathematical Monthly, Vol. 122, No. 8, Oct 2015 February 29, 2016
American Mathematical Monthly, Vol. 122, No. 9, Nov 2015 March 31, 2016 11865
American Mathematical Monthly, Vol. 122, No. 10, Dec 2015 April 30, 2016 11876
American Mathematical Monthly, Vol. 123, No. 1, Jan 2016 May 31, 2016
American Mathematical Monthly, Vol. 123, No. 2, Feb 2016 June 30, 2016 11892
American Mathematical Monthly, Vol. 123, No. 3, Mar 2016 July 31, 2016
American Mathematical Monthly, Vol. 123, No. 4, Apr 2016 August 31, 2016
American Mathematical Monthly, Vol. 123, No. 5, May 2016 September 30, 2016
American Mathematical Monthly, Vol. 123, No. 6, Jun-Jul 2016 November 30, 2016
- 2017 -
American Mathematical Monthly, Vol. 123, No. 7, Aug-Sep 2016 January 31, 2017
American Mathematical Monthly, Vol. 123, No. 8, Oct 2016 February 28, 2017
American Mathematical Monthly, Vol. 123, No. 9, Nov 2016 March 31, 2017
American Mathematical Monthly, Vol. 123, No. 10, Dec 2016 April 30, 2017
American Mathematical Monthly, Vol. 124, No. 1, Jan 2017 May 31, 2017
American Mathematical Monthly, Vol. 124, No. 2, Feb 2017 June 30, 2017
American Mathematical Monthly, Vol. 124, No. 3, Mar 2017 July 31, 2017
American Mathematical Monthly, Vol. 124, No. 4, Apr 2017 August 31, 2017
American Mathematical Monthly, Vol. 124, No. 5, May 2017 September 30, 2017
American Mathematical Monthly, Vol. 124, No. 6, Jun 2017 October 31, 2017
American Mathematical Monthly, Vol. 124, No. 7, Aug 2017 December 1, 2017 11992
- 2018 -
American Mathematical Monthly, Vol. 124, No. 8, Oct 2017 February 28, 2018
American Mathematical Monthly, Vol. 124, No. 10, Dec 2017 April 30, 2018

(*) Color red means that the solution submitted by us was selected for publication.


Lists of problems

Collections and archives with math problems (and some solutions).

Local links

External links


Mathematical Results

These are common mathematical results that can be used in the resolution of math problems.


Solved problems

This is a collection of solutions to some problems.


Problem Solving Groups


Other Links


Bibliography


Comments, suggestions...? email Miguel A. Lerma at: mlerma at math dot northwestern dot edu

WWW Address: "http://www.math.northwestern.edu/~mlerma/problem_solving/"