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December 22, 2006

Musical combinatorial designs

The new edition of Handbook of Combinatorial Designs points to Tom Johnson's musical compositions based on

1. Kirkman's Schoolgirls Problem: "Fifteen young ladies of a school walk out three abreast for seven days in succession: it is required to arrange them daily so that no two shall walk abreast more than once." [T. P. Kirkman, Query VI. Lady's and Gentleman's Diary (1850), 48.] Johnson's 2005 score for three flutes or solo harp, "Kirkman's Ladies," is based on the solution to the follow-on problem (solved by Denniston in 1974): can all 455 triples from a 15-element set be arranged into 13 disjoint Kirkman Triple Systems of order 15, thereby allowing a walk for each of the 13 weeks of a school term, without any three girls walking together twice?

2. The specific t-(v, k, λ) design given in the Handbook's 4.6 Example. In describing his piece "Block Design for Piano," Johnson gives the definition of a 4-(12, 6, 10) design in musical terms: "There are 12 notes, distributed into 6-note arpeggios, in such a way that every combination of four particular notes comes together exactly 10 times in 10 different arpeggios."

See Recent works by Tom Johnson for more information on the compositions. For more information on the combinatorial designs, see pages 13 and 79 of

Handbook of Combinatorial Designs, 2nd ed., edited by Charles J. Colbourn, Jeffrey H. Dinitz. Boca Raton, FL: Chapman & Hall/CRC, 2007. Mathematics Library Quarto QA166.25 .H36 2007 Link to MNCAT record

December 14, 2006

Kurt Gödel: The Album

Photographs of Kurt Gödel, his family, friends, colleagues, houses and schools. Facsimiles of letters and telegrams to/from/about Gödel. Copies of his degree notices, lecture announcements, awards. Odd snippets like his lending library card, the bill from his wedding dinner, the sales receipt from his copy of Whitehead and Russell's Principia Mathematica. All helpfully captioned in both German and English. Unfortunately no index, but it's a pleasure to browse through the sections: Gödel's Life, Gödel's Work, Gödel's Vienna.

Kurt Gödel: Das Album = The Album, by Karl Sigmund et al. Wiesbaden: Vieweg, 2006. Mathematics Library QA29.G58 S54 2006 Link to MNCAT record

December 7, 2006

Quantitative Literacy

"Quantitative literacy (QL) can be described as the ability to adequately use elementary mathematical tools to interpret and manipulate quantitative data and ideas that arise in individuals' private, civic, and work lives. As with reading and writing literacy, quantitative literacy is a habit of mind that is best formed by exposure in many contexts."

--from the bylaws of the MAA's SIGMAA on Quantitative Literacy, as quoted by Current Practices in Quantitative Literacy, edited by Rick Gillman. MAA Notes no. 70. Washington, DC: Mathematical Association of America, 2006. Mathematics Library QA11 .M113x no.70 Link to MNCAT record

This collection includes many short case studies of QL courses at colleges and universities large and small, as well as essays on the nature and historical development of QL.

Terence Tao at half his age

"This book was written 15 years ago; literally half a lifetime ago, for me. . . . Clearly, my perspective on life and on mathematics is different now than it was when I was 15. I have not been involved in problem-solving competitions for a very long time now, and if I were to write a book now on the subject it would be very different from the one you are reading here. . . . As I wrote this book before my professional mathematics career, many of these insights and experiences were not available to me, and so in many places the exposition has a certain innocence, or even naivety. I have been reluctant to tamper too much with this, as my younger self was almost certainly more attuned to the world of the high-school problem solver than I am now."

--Preface to the second edition, Solving Mathematical Problems: A Personal Perspective, by Terence Tao. Oxford; New York: Oxford University Press, 2006. Mathematics Library QA300 .T326 2006 Link to MNCAT record
(first edition Deakin University Press, Geelong, Vic., Australia: 1992)

As an example of the kind of book Tao is writing now, see the Book Ring post, Fields Authors.