Math 471: Mathematics of Aperiodic Order
The mathematics of aperiodic order is a very young mathematical discipline, which arose from the discovery of quasicrystals in the early 1980's. The physical motivation is the introduction and study of mathematical models of quasicrystals. Independently of the relevance to physics and more generally, one is interested in features of order in the absence of periodicity. The resulting mathematics is rich and fascinating, and it touches upon a number of established areas such as discrete geometry, harmonic analysis, combinatorics, spectral theory, and many more. In this course we will take an example-based approach and explore order features of structures such as Penrose and related tilings, which will guide us towards more general structures generated by inflation or a cut-and-project scheme. This course should be accessible to all interested students who have had some prior exposure to proof-based mathematics on the level of Math 3xx courses.
Meeting Time: TTh 10:50 AM -- 12:05 PM
Location: Herman Brown Hall 427
Email: [my last name] at rice dot edu
Office: Herman Brown Hall 434
Office Hour: Th 2:15 PM -- 3:15 PM and by appointment
Recommended Texts and Resources:
M. Baake and R. V. Moody (Editors), Directions in Mathematical Quasicrystals. CRM Monograph Series, 13. American Mathematical Society, Providence, RI, 2000.
N. P. Fogg, Substitutions in Dynamics, Arithmetics and Combinatorics. Lecture Notes in Mathematics, 1794. Springer-Verlag, Berlin, 2002.
D. Frettlöh and E. Harriss, Tilings Encyclopedia
U. Grimm, Quasicrystals
B. Grünbaum and G. C. Shephard,, Tilings and Patterns. W. H. Freeman and Company, New York, 1989.
Ch. Radin, Miles of Tiles. Student Mathematical Library, 1. American Mathematical Society, Providence, RI, 1999.
M. Senechal, Quasicrystals and Geometry. Cambridge University Press, Cambridge, 1995.
The final grade for the course will be based on your homework scores.
There will be weekly homework assignments with due date indicated on each problem set. These assignments will be accessible through OWL-Space. The homework is not pledged. You are encouraged to discuss the homework, and to work together on the problems. However, each student is responsible for the final preparation of his or her own homework papers.
If you have a documented disability that will impact your work in this class, please contact me to discuss your needs. Additionally, you will need to register with the Disability Support Services Office in the Allen Center.