@UCLAExtension I know a follow up course to the first half of Differential Topology is being offered for Winter 2022, but it doesn’t seem to be on the site yet to register. Can someone fix this?

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

Gems And Astonishments of Mathematics: Past and Present—Lecture One

Gems And Astonishments of Mathematics: Past and Present—Lecture One

Last night was the first lecture of Dr. Miller’s Gems And Astonishments of Mathematics: Past and Present class at UCLA Extension. There are a good 15 or so people in the class, so there’s still room (and time) to register if you’re interested. While Dr. Miller typically lectures on one broad topic for a quarter (or sometimes two) in which the treatment continually builds heavy complexity over time, this class will cover 1-2 much smaller particular mathematical problems each week. Thus week 11 won’t rely on knowing all the material from the prior weeks, which may make things easier for some who are overly busy. If you have the time on Tuesday nights and are interested in math or love solving problems, this is an excellent class to consider. If you’re unsure, stop by one of the first lectures on Tuesday nights from 7-10 to check them out before registering.

Lecture notes

For those who may have missed last night’s first lecture, I’m linking to a Livescribe PDF document which includes the written notes as well as the accompanying audio from the lecture. If you view it in Acrobat Reader version X (or higher), you should be able to access the audio portion of the lecture and experience it in real time almost as if you had been present in person. (Instructions for using Livescribe PDF documents.)

We’ve covered the following topics:

  • Class Introduction
  • Erdős Discrepancy Problem
    • n-cubes
    • Hilbert’s Cube Lemma (1892)
    • Schur (1916)
    • Van der Waerden (1927)
  • Sylvester’s Line Problem (partial coverage to be finished in the next lecture)
    • Ramsey Theory
    • Erdős (1943)
    • Gallai (1944)
    • Steinberg’s alternate (1944)
    • DeBruijn and Erdős (1948)
    • Motzkin (1951)
    • Dirac (1951)
    • Kelly & Moser (1958)
    • Tao-Green Proof
  • Homework 1 (homeworks are generally not graded)

Over the coming days and months, I’ll likely bookmark some related papers and research on these and other topics in the class using the class identifier MATHX451.44 as a tag in addition to topic specific tags.

Course Description

Mathematics has evolved over the centuries not only by building on the work of past generations, but also through unforeseen discoveries or conjectures that continue to tantalize, bewilder, and engage academics and the public alike. This course, the first in a two-quarter sequence, is a survey of about two dozen problems—some dating back 400 years, but all readily stated and understood—that either remain unsolved or have been settled in fairly recent times. Each of them, aside from presenting its own intrigue, has led to the development of novel mathematical approaches to problem solving. Topics to be discussed include (Google away!): Conway’s Look and Say Sequences, Kepler’s Conjecture, Szilassi’s Polyhedron, the ABC Conjecture, Benford’s Law, Hadamard’s Conjecture, Parrondo’s Paradox, and the Collatz Conjecture. The course should appeal to devotees of mathematical reasoning and those wishing to keep abreast of recent and continuing mathematical developments.

Suggested Prerequisites

Some exposure to advanced mathematical methods, particularly those pertaining to number theory and matrix theory. Most in the class are taking the course for “fun” and the enjoyment of learning, so there is a huge breadth of mathematical abilities represented–don’t not take the course because you feel you’ll get lost.

Register now

I’ve written some general thoughts, hints, and tips on these courses in the past.

Renovated Classrooms

I’d complained to the UCLA administration before about how dirty the windows were in the Math Sciences Building, but they went even further than I expected in fixing the problem. Not only did they clean the windows they put in new flooring, brand new modern chairs, wood paneling on the walls, new projection, and new white boards! I particularly love the new swivel chairs, and it’s nice to have such a lovely new environment in which to study math.

The newly renovated classroom space in UCLA’s Math Sciences Building

Category Theory for Winter 2019

As I mentioned the other day, Dr. Miller has also announced (and reiterated last night) that he’ll be teaching a course on the topic of Category Theory for the Winter quarter coming up. Thus if you’re interested in abstract mathematics or areas of computer programming that use it, start getting ready!

Gems And Astonishments of Mathematics: Past and Present—Lecture One was originally published on Chris Aldrich

Algebraic Geometry Lecture 1

For those who are still on the fence about taking Algebraic Geometry this quarter (or the follow on course next quarter), here’s a downloadable copy of the written notes with linked audio that will allow you to sample the class:

Algebraic Geometry-Lecture 1 notes [.pdf file with embedded and linked audio]

I’ve previously written some notes about how to best access and use these types of notes in the past. Of particular note, one must download the .pdf file and open in a recent version of Adobe Acrobat to take advantage of the linked/embedded audio file. (Trust me, it’s worth doing as it will be like you were there with the 20 of us who showed up last night!)

For those who prefer just the audio files separately, they can be listened to here, or downloaded.

Lecture 1 – Part 1

If possible, click to play, otherwise your browser may be unable to play this audio file.

Lecture 1 – Part 2

If possible, click to play, otherwise your browser may be unable to play this audio file.

Again, the recommended text is Elementary Algebraic Geometry by Klaus Hulek (AMS, 2003) ISBN: 0-8218-2952-1.

For those new to Dr. Miller’s classes, I’ve written up some hints/tips about them in the past as well.

Algebraic Geometry Lecture 1 was originally published on Chris Aldrich

Introduction to Algebraic Geometry | UCLA Extension in Fall 2017

Introduction to Algebraic Geometry | UCLA Extension in Fall 2017
MATH X 451.42 Introduction to Algebraic Geometry by Dr. Michael Miller (UCLA Extension)

Algebraic geometry is the study, using algebraic tools, of geometric objects defined as the solution sets to systems of polynomial equations in several variables. This introductory course, the first in a two-quarter sequence, develops the basic theory of the subject, beginning with seminal theorems—the Hilbert Basis Theorem and Hilbert’s Nullstellensatz—that establish the dual relationship between so-called varieties—both affine and projective—and certain ideals of the polynomial ring in some number of variables. Topics covered in this first quarter include: algebraic sets, projective spaces, Zariski topology, coordinate rings, the Grassmannian, irreducibility and dimension, morphisms, sheaves, and prevarieties. The theoretical discussion will be supported by a large number of examples and exercises. The course should appeal to those with an interest in gaining a deeper understanding of the mathematical interplay among algebra, geometry, and topology.

Some exposure to advanced mathematical methods, particularly those pertaining to ring theory, fields extensions, and point-set topology.

Dr. Michael Miller has announced the topic for his Fall math class at UCLA Extension: Algebraic Geometry!!

Yes math fans, as previously hinted at in prior conversations, we’ll be taking a deep dive into the overlap of algebra and geometry. Be sure to line up expeditiously as registration for the class won’t happen until July 31, 2017.

While it’s not yet confirmed, some sources have indicated that this may be the first part of a two quarter sequence on the topic. As soon as we have more details, we’ll post them here first. As of this writing, there is no officially announced textbook for the course, but we’ve got some initial guesses and the best are as follows (roughly in decreasing order):

  1. Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra (Undergraduate Texts in Mathematics) 4th ed. by David A. Cox, John Little, and Donal O’Shea
  2. Algebraic Geometry: An Introduction (Universitext) by Daniel Perrin
  3. An Invitation to Algebraic Geometry (Universitext) by Karen E. Smith, Lauri Kahanpää, Pekka Kekäläinen, William Traves
  4. Algebraic Geometry (Dover Books on Mathematics) by Solomon Lefschetz (Less likely based on level and age, but Dr. Miller does love inexpensive Dover editions)

For those who are new to Dr. Miller’s awesome lectures, I’ve written some hints and tips on what to expect.

Most of his classes range from about 20-30 people, many of them lifelong regulars. (Yes, there are dozens of people like me who will take almost everything he teaches–he’s that good. This class, my 22nd, will be the start of my second decade of math with him.)

Mathematical Sciences Building, 520 Portola Plaza, Los Angeles, CA 90095

Introduction to Algebraic Geometry | UCLA Extension in Fall 2017 was originally published on Chris Aldrich