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Research Projects for Students

A research project can be a very important part of an education in mathematics. Besides the greatly increased learning intensity that comes from personal involvement with a project, and the chance to show colleges or graduate schools and potential employers the student's ability to initiate and carry out a complex scientific task, it gives the student an introduction to mathematics as it is: a living and developing intellectual organism where progress is achieved by the interplay of individual creativity and collective knowledge. 

High school and college students often have trouble finding appropriate topics for research projects in mathematics. This page presents some suggestions of where to look. These sources do not list project topics! But they present a wealth of mathematical subjects in an accessible way. Each of these subjects will have areas that invite further investigation.

  • Joseph Malkevitch of York College, CUNY, maintains the web page Mathematical Research for High School Students, which contains a rich selection of resources.

  • Ian Stewart in his Scientific American column "Mathematical Recreations" presents a new topic almost every month. He often includes references where students can find additional information. Recent topics include card shuffling (11/98), cake slicing and other fairness problems (12/98 and 1/99), origami tessellations (2/99).

  • The Math Forum website posts Problems of the Week in geometry, algebra, discrete math, trig & calculus. The site also links to Problems of the Week administered by others, including the challenging college-level problems of Macalester College, the interactive ESCOT Problem of the Week, and several team-based projects.

  • The Mathematical Association of America's "MAA Online" has four Online Columns (by Ivars Peterson, Keith Devlin, Frank Morgan and Alex Bogomolny). Each of these columns can be gleaned for project ideas. Don't miss the links to past columns!

  • This link is to a list of Research Project Ideas. This list is a copy of the list "Possible Science Fair Mathematics Projects" which was created by Afton H. Cayford, at The University of British Columbia.

  • John Lienhard's KUHF program "Engines of our Ingenuity" has almost 100 episodes relating to mathematics. Go to the Engines' Search Page and search on ``mathematics.'' The episodes are short but intense, and often come with a valuable reference list.

  • What's Happening in the Mathematical Sciences   is a publication (5 volumes are out) of the AMS and can be ordered from the AMS Bookstore.   Each issue has 10 or more articles by science writer Barry Cipra, each covering a new development in the mathematical sciences.  Subjects treated are on the frontiers of mathematical research, but reading about them can be useful in searching for an area to explore.

  • ABC News maintains an archive of John Allen Paulos' columns "Who's Counting". An excellent source of project ideas in probability and statistics.

  • +plus magazine is a monthly web publication, part of the Millenium Mathematics Project sponsored by the University of Cambridge and Cambridge University Press. Every month there are 5 or 6 very accessible articles on mathematical topics (along with puzzles and news).