Wednesday, May 25, 2011

Monday, May 23, 2011

Undergraduate research: what is that ?

The Council on Undergraduate Research defines it as follows:
``An inquiry or investigation conducted by an undergraduate student that makes an original intellectual or creative contribution to the discipline.''
The word "original" is very important. An original contribution to knowledge rules out works of a severely expository or textbook nature, results that follow immediately from previous work (as in... use the previously obtained A=B to "discover" that 2A=2B, or something like that), or trivial derivations in existent or made-up ad hoc formal systems. The original contribution to the discipline must also go through a rigorous, external, peer-review process. Ideally, a rigorous, solid peer-review is a process which does not accept works simply because they are formally correct, indeed it demonstrates a pattern of rejecting a significant percentage of logically correct but otherwise not interesting enough (as judged by the reviewers) works. Also, note that being "peer-reviewed" is not the same with "being made public/disseminated" (a confusion that is still circulating). A valuable original contribution will be able to generate 'participative waves', engaging others in the area. Thus, when it comes to goals and assessment, 'undergraduate research' is not (and shouldn't be, in my opinion) different from good old 'research'. So it is a serious matter, and competitive universities recognize that. I found interesting the following straight-to-the-point statement (due to Jim Coleman, vice chancellor for research and professor of biology at the University of Missouri) on the central place of undergraduate research in the life of a good university:
``There is nothing more central to the mission of a university than activities associated with discovery, creation, innovation and scholarship. So, I think that what defines a great university is the integration of these activities into the entire fabric of the undergraduate experience.''
Integrating the research/scholarship into the undergraduate life is a challenging enterprise. There are no clear recipes, since there are students and students. Each individual case is unique and interesting in itself. The faculty's essential asset is their own involvement and demonstrated proficiency in research. Indeed the undergraduate research is driven, after all, by faculty research. Or, if you want, faculty research is a necessary condition for undergraduate research. One may ask, is it also a sufficient condition? This is not true, mainly because the student is a person, not a machine or a notebook on which the faculty mentor writes a paper. In the end, note that the complexities of (undergraduate) research that even an otherwise well prepared academic (mentor) faces, ultimately point to persons (as in real persons, and not ``the idea of a person''), and their participative experience.

Thursday, May 19, 2011

A Forgetful Number

A Forgetful Number - a poem by Vasko Popa (who "was the first [poet] in post-World War II Yugoslavia to break with the Socialist Realism") in the volume Secondary Heaven (Collected Poems), "Yawn of Yawns" (1968).

Image source (Riemann zeta function ζ(s) in the complex plane).

Solution to FQ-B1078

Solution to FQ-B1078 (Fibonacci Quarterly 48 (2010), no. 4, 367) submited on May 9, 2011 by the ONU-SOLVE problem group (faculty advisor - Mihai Caragiu).

Solution to AMM 11537

Solution to AMM 11537 (The American Mathematical Monthly 117 (2010), no. 10, p. 929), written by Mihai Caragiu and submitted on April 21, 2011.

Solution to AMM 11536

Solution to AMM 11536 (The American Mathematical Monthly 117 (9), November 2010, p. 835) written by Mihai Caragiu and submitted on March 30, 2011.

Solution to AMM 11527

Solution to AMM 11527 (The American Mathematical Monthly 117 (2010), no. 8, 742) written by Mihai Caragiu and submitted on February 28, 2011.

Solution to FQ-B1074

Solution to FQ-B1074 (Fibonacci Quarterly 48 (2010), no. 3, p. 278) submited on February 10, 2011 by the ONU-SOLVE problem group (faculty advisor Mihai Caragiu)

A classroom snippet

A linear algebra classroom snippet: symmetric matrices... with nice numbers. A grab bag of symmetric matrices

Thursday, May 5, 2011

An MGPF Path Towards a Fixed Point

MGPF - multidimensional greatest prime factor sequences
The MGPF conjecture: all MGPF sequences are ultimately periodic.