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: May 15, 2012

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 (*)
- 2010 -
Math Horizons, Vol. 17, No. 2, Nov 2009 January 10, 2009 236
College Mathematics Journal, Vol. 40, No. 5, Nov 2009 February 15, 2010 912, 914
Mathematics Magazine, Vol. 82, No. 4, Oct 2009 March 1, 2010 1827, 1830
Pi Mu Epsilon Journal, Fall 2009 (external link) March 1, 2010 1204, 1213
College Mathematics Journal, Vol. 41, No. 1, Jan 2010 April 15, 2010 920
Mathematics Magazine, Vol. 82, No. 5, Dec 2009 May 1, 2010 1832
Math Horizons, Vol. 17, No. 3, Feb 2010 June 1, 2010 243
College Mathematics Journal, Vol. 41, No. 2, Mar 2010 June 15, 2010 923, 925
Mathematics Magazine, Vol. 83, No. 1, Feb 2010 July 1, 2010 1837
Math Horizons, Vol. 17, No. 4, Apr 2010 August 10, 2010 245
Mathematics Magazine, Vol. 83, No. 2, Apr 2010 September 1, 2010 1841
College Mathematics Journal, Vol. 41, No. 3, May 2010 September 15, 2010 927, 930
Pi Mu Epsilon Journal, Spring 2010 (external link) October 1, 2010 1218
Mathematics Magazine, Vol. 83, No. 3, Jun 2010 November 1, 2010 1850
Math Horizons, Vol. 18, No. 1, Sep 2010 November 10, 2010 248
College Mathematics Journal, Vol. 41, No. 4, Sep 2010 December 15, 2010 931
- 2011 -
Math Horizons, Vol. 18, No. 2, Nov 2010 January 10, 2010 252, 254
College Mathematics Journal, Vol. 41, No. 5, Nov 2010 February 15, 2011 938
Mathematics Magazine, Vol. 83, No. 4, Oct 2010 March 1, 2011 1853, 1854
Pi Mu Epsilon Journal, Fall 2010 (external link) March 1, 2011 1231, 1232
College Mathematics Journal, Vol. 42, No. 1, Jan 2011 April 15, 2011 944
Mathematics Magazine, Vol. 83, No. 5, Dec 2010 May 1, 2011 1856, 1860
Math Horizons, Vol. 18, No. 3, Feb 2011 June 1, 2011 255
College Mathematics Journal, Vol. 42, No. 2, Mar 2011 June 15, 2011 946
Mathematics Magazine, Vol. 84, No. 1, Feb 2011 July 1, 2011 1861
Math Horizons, Vol. 18, No. 4, Apr 2011 August 10, 2011 258
College Mathematics Journal, Vol. 42, No. 3, May 2011 August 15, 2011 953
Mathematics Magazine, Vol. 84, No. 2, Apr 2011 September 1, 2011 1867
Pi Mu Epsilon Journal, Spring 2011 (external link) October 1, 2011 1237
Mathematics Magazine, Vol. 84, No. 3, Jun 2011 November 1, 2011 1874
Math Horizons, Vol. 19, No. 1, Sep 2011 November 10, 2011 263
College Mathematics Journal, Vol. 42, No. 4, Sep 2011 December 15, 2011 960
- 2012 -
Math Horizons, Vol. 19, No. 2, Nov 2011 January 10, 2012 266, 269
College Mathematics Journal, Vol. 42, No. 5, Nov 2011 February 15, 2012 961
Mathematics Magazine, Vol. 84, No. 4, Oct 2011 March 1, 2012 1876
Pi Mu Epsilon Journal, Fall 2011 (external link) March 1, 2012 1252
College Mathematics Journal, Vol. 43, No. 1, Jan 2012 April 15, 2012 968
Mathematics Magazine, Vol. 84, No. 5, Dec 2011 May 1, 2012 1882, 1885
Math Horizons, Vol. 19, No. 3, Feb 2012 June 1, 2012 273
College Mathematics Journal, Vol. 43, No. 2, Mar 2012 June 15, 2012 974
Mathematics Magazine, Vol. 85, No. 1, Feb 2012 July 1, 2012
Math Horizons, Vol. 19, No. 4, Apr 2012 August 10, 2012 274
College Mathematics Journal, Vol. 43, No. 3, May 2012 August 15, 2012
Mathematics Magazine, Vol. 85, No. 2, Apr 2012 September 1, 2012 1892
Pi Mu Epsilon Journal, Spring 2012 (external link) October 1, 2012

(*) 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
- 2010 -
American Mathematical Monthly, Vol. 116, No. 8, Oct 2009 February 28th, 2010
American Mathematical Monthly, Vol. 116, No. 9, Nov 2009 March 31st, 2010
American Mathematical Monthly, Vol. 116, No. 10, Dec 2009 April 30th, 2010
American Mathematical Monthly, Vol. 117, No. 1, Jan 2010 May 31st, 2010
American Mathematical Monthly, Vol. 117, No. 2, Feb 2010 June 30th, 2010 11481
American Mathematical Monthly, Vol. 117, No. 3, Mar 2010 July 31st, 2010 11492
American Mathematical Monthly, Vol. 117, No. 4, Apr 2010 August 31st, 2010
American Mathematical Monthly, Vol. 117, No. 5, May 2010 September 30th, 2010 11508
American Mathematical Monthly, Vol. 117, No. 6, Jun-Jul 2010 October 31st, 2010
American Mathematical Monthly, Vol. 117, No. 7, Aug-Sep 2010 December 31st, 2010
- 2011 -
American Mathematical Monthly, Vol. 117, No. 8, Oct 2010 February 28th, 2011
American Mathematical Monthly, Vol. 117, No. 9, Nov 2010 March 31st, 2011 11536
American Mathematical Monthly, Vol. 117, No. 10, Dec 2010 April 30th, 2011
American Mathematical Monthly, Vol. 118, No. 1, Jan 2011 May 31st, 2011
American Mathematical Monthly, Vol. 118, No. 2, Feb 2011 June 30th, 2011
American Mathematical Monthly, Vol. 118, No. 3, Mar 2011 July 31st, 2011
American Mathematical Monthly, Vol. 118, No. 4, Apr 2011 August 31st, 2011
American Mathematical Monthly, Vol. 118, No. 5, May 2011 September 30th, 2011
American Mathematical Monthly, Vol. 118, No. 6, Jun 2011 October 31st, 2011
American Mathematical Monthly, Vol. 118, No. 7, Aug-Sep 2011 December 31st, 2011
- 2012 -
American Mathematical Monthly, Vol. 118, No. 8, Oct 2011 February 29, 2012 11596
American Mathematical Monthly, Vol. 118, No. 9, Nov 2011 March 31, 2012
American Mathematical Monthly, Vol. 118, No. 10, Dec 2011 April 30, 2012
American Mathematical Monthly, Vol. 119, No. 1, Jan 2012 May 31, 2012
American Mathematical Monthly, Vol. 119, No. 2, Feb 2012 June 30, 2012
American Mathematical Monthly, Vol. 119, No. 3, Mar 2012 July 31, 2012
American Mathematical Monthly, Vol. 119, No. 4, Apr 2012 August 31, 2012
American Mathematical Monthly, Vol. 119, No. 5, May 2012 September 30, 2012

(*) 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/"