References for the Advanced Calculus 2 lectures

In this note we list the bibliographic references for the Advanced Calculus 2 lectures given by Ricardo A. Sáenz at UNM, on Tuesday and Thursday, April 18 and 20.

Most of the material of the lectures can be found in the book Mathematics of Fractals, by Masaya Yamaguti, Masayoshi Hata and Jun Kigami, published by the AMS (1997). There you can find the proof of the existence and uniqueness of self-similar sets given a finite collection of contractions, and the proof of Hutchinson’s theorem.

Hutchinson’s theorem was proved by John E. Hutchinson and published in the paper “Fractals and self-similarity”, Indiana Univ. Math. Journal 30 (1981), pp. 713-747. You can find it in his webpage: Research Papers.

The fractal made of golden rectangles was published by Marc Frantz in the paper “A Fractal Made of Golden Sets”, Mathematics Magazine 82 (2009), pp. 243-254. You can find the paper in JSTOR: A Fractal Made of Golden Sets.

The Hausdorff dimension was published by Felix Hausdorff in the paper “Dimension und äußeres Maß” (Dimension and Outer Measure) in Mathematische Annalen 79 (1918), pp. 157-179. You can find the paper in the European Digital Mathematics Library: Dimension und äußeres Maß.

Ricardo Sáenz visits UNM

Ricardo A. Sáenz visited the University of New Mexico at Albuquerque from April 17 to April 21, and participated at several activities at the Department of Mathematics and Statistics. He taught the 3-hour minicourse Harmonic Analysis on Fractals to faculty and graduate students, gave talks at the Colloquium and the Analysis Seminar, and gave a pair of lectures at the course Advanced Calculus 2 to Junior and Senior undergraduates.

Together with Ma. Cristina Pereyra, they visited Taos Middle School, where they talk to approximately 160 8th-graders about Mathematics, the work of Mathematicians, and gave them activities on geometry.

He also talked to students about of Summer Research projects on fractals.

The Advanced Calculus 2 students and guests.

Schedule for Albuquerque activities

The schedule for the course Harmonic Analysis on Fractals by Ricardo A. Sáenz, as well as the rest of the lectures of his visit to UNM, is the following:

The description of these activities can be found in the program.

Ma. Cristina Pereyra visits the University of Colima

Ma. Cristina Pereyra visited the University of Colima from March 13 to March 17, and participated in several activities in the Facultad de Ciencias. She taught the 5-hour minicourse Dyadic Harmonic Analysis, gave lectures at both the Physics/Mathematics Colloquium and the CUICBAS Seminar, and attended the Fourier Seminar.

Moreover, she also attended an outreach visit at the Elementary School Liceo Llankay, where Ricardo A. Sáenz talk to 4-5 grade students about Mathematics and Mathematicians.

She also talked to Mathematics and Physics undergraduate mayors about UNM graduate programs.

Course attendees. From left to right: Ricardo A. Sáenz, Jaime Hernández, Magali Folch, Yair Castillo, Georgina Rojo, Manuel Torres, Blanca Radillo, Gari Peralta, Ma. Cristina Pereyra and Carlos Castaño.