| (Penrose tiling in front of the Mathematical Institute, Oxford) |
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LECTURE NOTES AND EXERCISES ♦ Part 1: Lecture notes on Geometry and Topology (version: September 4, 2014) ♦ Part 2: Lecture notes on Penrose tilings (version: September 8, 2014) It may be helpful to first read my Slideshow talk on Penrose tilings (from the Wadham College Mathematics Reunion, 21 March 2015) ♦ Exercises on Geometry, Topology, and Penrose tilings (version: September 8, 2014) HANDOUTS I gave the following handouts during the lecture course. For copyright reasons, I cannot put these online. If you have trouble finding them, ask me. ♦ The Extension Theorem (pages 150-155 from the book by Grünbaum and Shephard, "Tilings and patterns") ♦ Sir Roger Penrose, "Pentaplexity" (from Eureka 39, pages 16-22, reprint from The Mathematical Intelligencer 2) ♦ Martin Gardner, "Penrose tiling" (from the book by Martin Gardner, "Penrose tiles to trapdoor ciphers") ♦ E. C. Zeeman, "An Introduction To Topology" (Classification of Surfaces) WHAT ARE THE OXFORD MASTERCLASSES? The Oxford Masterclasses are organized by the CMI-PROMYS International Alliance. It is funded by the Clay Mathematics Institute and by a generous donation from a Wadham College alumnus. In August 2014, the program invited 19 European students, including 13 CMI-PROMYS Scholars, for a week-long summer program in Oxford designed to encourage ambitious high school students to explore the creative world of mathematics. The 2014 Masterclasses were held at Wadham College, Oxford, August 10 - August 16. I taught the lectures (about 20 hours), and I organized two guest lectures: Sir Roger Penrose (Wadham College) talked about Penrose tilings, and Dr Henry Cohn (Microsoft Research) talked about Sphere packing. Links about the Masterclasses and the CMI-PROMYS program: ♦ Article on the Wadham College website, with photos. ♦ Article on the PROMYS website. ♦ More about PROMYS on the Clay Mathematics Institute page. ♦ The PROMYS homepage |