Theory and Applications of Continued Fractions MATH X 451.50 | Fall 2022

Theory and Applications of Continued Fractions MATH X 451.50 | Fall 2022
For the Fall 2022 offering Dr. Michael Miller is offering a mathematics course on Theory and Applications of Continued Fractions at UCLA on Tuesday nights through December 6th. We started the first class last night, but there have been issues with the course listing on UCLA Extension, so I thought I’d post here for any who may have missed it. (If you have issues registering, which some have, call the Extension office to register via phone.)

For almost 300 years, continued fractions—that is, numbers representable as the sum of an integer and a fraction whose denominator is itself such a sum—have fascinated mathematicians with both their remarkable properties and their myriad applications in such fields as number theory, differential equations, and computer algorithms. They have been applied to piano tuning, baseball batting averages, rational tangles, paper folding, and plant growth … the list goes on. This course is a rigorous introduction to the theory and mathematical applications of continued fractions. Topics to be discussed include quadratic irrationals, approximation of real numbers, Liouville’s Theorem, linear recurrence relations and Pell’s equation, Hurwitz’ Theorem, measure theory, and Ramanujan identities.

Mike is recommending the Continued Fractions text by Aleksandr Yakovlevich Khinchin. I found a downloadable digital copy of the 1964 edition (which should be ostensibly the same as the current Dover edition and all the other English editions) at the Internet Archive at  Based on my notes, it looks like he’s following the Khinchin presentation fairly closely so far.

If you’re interested, do join us on Tuesday nights this fall. (We’ve already discovered that going 11 for 37 is the smallest number of at bats that will produce a 0.297 batting average.) 

If you’re considering it and are completely new, I’ve previously written up some pointers on how Dr. Miller’s classes proceed: Dr. Michael Miller Math Class Hints and Tips | UCLA Extension

This post was originally published on Chris Aldrich

I just couldn’t wait for a physical copy of The First Astronomers: How Indigenous Elders Read the Stars by Duane Hamacher, Ghillar Michael Anderson, Ron Day, Segar Passi, Alo Tapim, David Bosun and John Barsa (Allen & Unwin, 2022) to arrive in the US, so I immediately downloaded a copy of the e-book version.

@AllenAndUnwin @AboriginalAstro

This post was originally published on Chris Aldrich

Differential Topology—Two quarter sequence at UCLA Extension for Fall/Winter 2021

It hasn’t been announced officially in the UCLA Extension catalog, but Dr. Mike Miller’s anticipated course topic for Fall 2021 is differential topology. The anticipated recommended text is Differential Topology: An Introduction by David B. Gauld (M. Dekker, 1982 or Dover, 1996 (reprint)).

The offering is naturally dependent on potential public health measures in September, which may also create a class limit on the number of attendees, so be sure to register as soon as it’s announced. For those who are interested in mathematics, but have never attended any of Dr. Miller’s lectures, I’ve previously written some details about his stye of presentation, prerequisites (usually very minimal despite the advanced level of the topics), and other details.

A few of us have already planned weekly Thursday night topology study sessions through the end of Spring and into Summer for those interested in attending. Just leave a comment with your contact information and I’ll be in touch with details.

I hope to see everyone in the fall.

This post was originally published on Chris Aldrich

An Euclidean Declaration

An Euclidean Declaration
So far, my favorite part of Jordan Ellenberg‘s new book Shape: The Hidden Geometry of Information, Biology, Strategy, Democracy, and Everything Else is this footnoted observation:

“we hold these truths to be self-evident” wasn’t Jefferson’s line; his first draft of the Declaration has “we hold these truths to be sacred & undeniable.” It was Ben Franklin who scratched out those words and wrote “self-evident” instead, making the document a little less biblical, a little more Euclidean.

This post was originally published on Chris Aldrich