Prof. Alexander F. Ritter, Associate Professor, University of Oxford.

Lectures on Geometry, Topology, and Penrose tilings

(Penrose tiling in front of the Mathematical Institute, Oxford)

Comments and corrections are very welcome, my contact details are here.


♦  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)


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)


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

Prof. Alexander F. Ritter. Contact me.
Associate Professor in Geometry, Mathematical Institute, Oxford.
The Roger Penrose Fellow and Tutor, Wadham College, Oxford.