Category Archives: Undergrad posts

Putnam exam


Past winners of this national competition include physicist and Nobel Prize Laureates Richard Feynman and Kenneth Wilson. Amongst mathematicians, the list of Putnam Fellows includes a huge number of famous mathematicians including Fields Medalist John Milnor and former UH Manoa Mathematics Professor William Hanf.

Each year, the examination will be constructed to test originality as well as technical competence. It is expected that the contestant will be familiar with the formal theories embodied in undergraduate mathematics.

It is assumed that such training, designed for mathematics and physical science majors, will include somewhat more sophisticated mathematical concepts than is the case in minimal courses. Thus the differential equations course is presumed to include some references to qualitative existence theorems and subtleties beyond the routine solution devices.

Questions will be included that cut across the bounds of various disciplines, and self-contained questions that do not fit into any of the usual categories may be included. It will be assumed that the contestant has acquired a familiarity with the body of mathematical lore commonly discussed in mathematics clubs or in courses with such titles as Survey of the Foundations of Mathematics.

It is also expected that the self-contained questions involving elementary concepts from group theory, set theory, graph theory, lattice theory, number theory, and cardinal arithmetic will not be entirely foreign to the contestant's experience.

For more information concerning the Putnam competition; which is given each year in December, contact Prof Pavel Guerzhoy.

December already past? Participate in the Hanf competition.


Past Putnam exams

1980 1990 2000
1981 1991 2001
1982 1992 2002
1983 1993 2003
1984 1994 2004
1985 1995 2005
1986 1996
1987 1997 2007
1988 1998 2008
1989 1999 2009

Program goals

Recipients of an undergraduate degree in mathematics study:

  • real analysis in one and several variables,
  • linear algebra and the theory of vector spaces,
  • several mathematical topics at the junior and senior level,
  • in
    depth at least one advanced topic of mathematics, an approved two-course

In addition, students acquire the ability and skills to:

  • develop and write direct proofs, proofs by
    contradiction, and proofs by induction,
  • formulate definitions and give examples and
  • read mathematics without supervision,
  • follow and explain algorithms,
  • apply mathematics to other fields.

Finally, recipients of an undergraduate degree in mathematics learn about research in mathematics.


LaTeX samples
Click here and scroll down to Presentation schedule
It's time to learn to use LaTeX!
  1. First you need to install it on your machine.
    • For Mac OS X users, I suggest MacTeX. Click on the "" link, download the file to your machine and run it. (You will need to unzip it first.)
    • For Windows users, I suggest proTeXt. This is a superset of MiKTeX but easier to install.
    • For Linux users, most Linux distributions come with TeX; otherwise I recommend TeX Live.
  2. The Not so short introduction to LaTeX is a very handy reference. It's worth reading Chapters 1.1-1.4 and then reading the first couple of pages of Chapter 2. All of the math symbols we'll need are in Chapter 3.Once you have LaTeX installed on your machine, open up TeXShop (Mac), TeXWorks (Windows), or your favorite Linux text editor. Download the following sample tex file and try to compile it: Sample File. (In TeXShop and TeXworks, look under the menu option "Typeset" and click on LaTeX.)