Research Interests

Rachel W. Hall
Department of Math and CS
St. Joseph's University
5600 City Ave.
Philadelphia, PA 19131

My research interests are currently Mathematical Music Theory and Ethnomathematics.  In particular, I am studying the mathematics of musical rhythm.  Previously, I studied Operator Algebras and completed my doctoral thesis on Hecke C*-Algebras.

Mathematics and Music

• Rachel W. Hall. Playing musical tiles. Bridges Proceedings, 2006. 
• Article (PDF)
• .Joseph E. Flannick, Rachel W. Hall, and Robert Kelly. Detecting meter in recorded music. Bridges Proceedings, 2005. 
• Article (PDF)
• Rachel W. Hall and Paul Klingsberg.  Asymmetric rhythms and tiling canons.  Preprint, 2006. To appear in the American Mathematical Monthly.
• Article (PDF)
• Audio files
• Rachel W. Hall and Paul Klingsberg.  Asymmetric rhythms, tiling canons, and Burnside's lemma.  Bridges Proceedings, pp. 189-194, 2004. 
• Article (PDF)
• Audio files
• Rachel W. Hall.  Math for poets and drummers.  Preprint, 2005.  Too appear in Horizons. Intended for teachers of mathematics or undergraduate math students.
• Article (PDF)
• Rachel W. Hall and Kresimir Josic.  The mathematics of musical instruments. Amer. Math. Monthly 108 (2001), no. 4, 347--357.
• Article (PDF)
• Presentations.
• ``Math for Poets and Drummers'' presentation, Dean's Colloquium, Saint Joseph's University, October 14, 2004. Slides (PDF, with linked MIDI and .WAV audio)
• ``Math for Poets and Drummers'' presentation, Arcadia University, February 15, 2005. Slides (PDF, with linked MIDI and .WAV audio)
• ``Math for Poets and Drummers'' presentation, Haverford College, April 7th, 2005. Slides (PDF, with linked MIDI and .WAV audio)

Ethnomathematics

• Rachel W. Hall.  A course in multicultural mathematics.  Preprint, 2006. To appear in PRIMUS.
• Article (PDF)
• Multicultural mathematics class.
• Class home page

C*-Algebras

I completed a thesis in the field of Operator Algebras under the direction of Nigel Higson . My thesis, entitled ``Hecke C*-Algebras'' concerns an analysis of Hecke algebras from the perspective of C*-algebra theory. A summary of the article ``Hecke C*-algebras, unitary representations, and the geometry of trees,'' which is based on my thesis research, is available here.

• Summary of ``Hecke C*-algebras, unitary representations, and the geometry of trees''
• Full text of my thesis ``Hecke C*-Algebras''

Other

This article uses complex analysis to explain a relation between pairs of power laws of centripetal attraction.  It is suitable for an undergraduate complex analysis class.

• Rachel W. Hall and Kresimir Josic.  Planetary motion and the duality of force laws.  SIAM Rev. 42 (2000), no. 1, 115--124
• Article (PDF)

Undergraduate Research

Two students, Bobby Kelly '02 and Joe Flannick '03, have written undergraduate theses under my direction.

• Bobby Kelly.  Mathematics of Musical Rhythm.  Undergraduate honors thesis.  Saint Joseph's University, 2002.
• Article (PDF)
• Slides from Bobby's final presentation (PDF)
• Joseph E. Flannick.  Rhythm Detection in Recorded Music.  Undergraduate honors thesis.  Saint Joseph's University, 2003.
• Article (PDF)
• Audio files

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Rachel W. Hall / rhall@sju.edu

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