## Tuesday, December 6, 2011

### GPF sequences in Rutgers' Experimental Mathematics Seminar

Apparently the sequences introduced in the Fibonacci Quarterly paper by Greg Back and myself have been discussed in the RUTGERS EXPERIMENTAL MATHEMATICS SEMINAR (Neil J. A. Sloane's presentation was on February 17, 2011

## Thursday, June 30, 2011

### GPF sequences - a forum discussion

A discussion of the paper "The Greatest Prime Factor and Related Sequences" (JP Journal of Algebra, Number Theory and Applications 6(2), 403-409 (2006), by Mihai Caragiu and Lisa Scheckelhoff), with neat pictures, can be found

**here**(Mathematical Oddities Thread - The Something Awful Forums)## Monday, June 20, 2011

### An Euler-Fibonacci Sequence

*An Euler-Fibonacci Sequence*by Mihai Caragiu and Ashley Risch

*Far East Journal of Mathematical Sciences*, Volume 52, Issue 1, Pages 1 - 7 (May 2011)

abstract -

**here**

## Monday, May 23, 2011

### Undergraduate research: what is that ?

The

**Council on Undergraduate Research**defines it as follows: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``An inquiry or investigation conducted by an undergraduate student that makes an original intellectual or creative contribution to the discipline.''

*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:``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 isThere 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.''

*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***(as in***persons**real persons*, and not ``*the idea*of a person''), and their**.***participative experience*## Monday, March 7, 2011

### Ion Barbu: matematică, poezie şi arte (un citat concis...)

*Matematicile pun în joc puteri sufleteşti care nu sunt cu mult diferite de cele solicitate de poezie şi de arte.*(

**Ion Barbu**; sursa - citatepedia.ro)

## Tuesday, February 22, 2011

### music and computation

**Gottfried Wilhelm Leibniz**'s view on music (

**) has (at least) two straightforward interpretations. The first one is essentially**

*'the hidden arithmetical exercise of a mind unconscious that is calculating'**reductionist*(a

*'fallacy of the misplaced concreteness'*according to

**Alfred North Whitehead**) and tends to suggest that music is

*nothing but*computation (albeit in the background/unconscious, in a less obvious way). The second interpretation of the music-calculating connection runs somehow in the opposite direction, and tends to suggest that

**, an ethereal/ineffable/musical/higher-order quality. At this point, one might try to revisit the spirit of some traditional Gödelian themes**

*there is more to computation than meets the eye**...*

*Image source: http://en.wikipedia.org/wiki/File:FortranCardPROJ039.agr.jpg*

## Monday, January 24, 2011

### Fractals and partitions

A recent major breakthrough is announced

**here**(Emory University's site,

*eScienceCommons*). Looks like ultimately periodic sequences made the news. Also see

**here**a recent article by Ken Ono (

*The Last Words of a Genius*, Notices of the AMS Volume 57, Number 11, 1410-1419), and

**here**a relevant abstract by John Webb (

*An improved “zoom rate” for the Folsom-Kent-Ono l-adic fractal behavior of partition values*).

Image

**source**.

A relevant video - Ken Ono talk (Emory University YT Channel):

**http://youtu.be/aj4FozCSg8g**

**New Theories Reveal the Nature of Numbers**

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