Brick exterior of the UCLA Mathematical Sciences building

Dr. Michael Miller Math Class Hints and Tips | UCLA Extension

Congratulations on your new math class, and welcome to the “family”!

Beginners Welcome!

Invariably the handful of new students every year eventually figure the logistics of campus out, but it’s easier and more fun to know some of the options available before you’re comfortable halfway through the class. To help get you over the initial hump, I’ll share a few of the common questions and tips to help get you oriented. Others are welcome to add comments and suggestions below. If you have any questions, feel free to ask anyone in the class, we’re all happy to help.

First things first, for those who’ve never visited UCLA before, here’s a map of campus to help you orient yourself. Using the Waze app on your smartphone can also be incredibly helpful in getting to campus more quickly through the tail end of rush hour traffic.

Whether you’re a professional mathematician, engineer, physicist, physician, or even a hobbyist interested in mathematics you’ll be sure to get something interesting out of Dr. Miller’s math courses, not to mention the camaraderie of 20-30 other “regulars” with widely varying backgrounds (from actors to surgeons and evolutionary theorists to engineers) who’ve been taking almost everything Mike has offered over the years (and yes, he’s THAT good—we’re sure you’ll be addicted too.) Whether you’ve been away from math for decades or use it every day or even if you’ve never gone past Calculus or Linear Algebra, this is bound to be the most entertaining thing you can do with your Tuesday nights in the Autumn and Winter. If you’re not sure what you’re getting into (or are scared a bit by the course description), I highly encourage you to come and join us for at least the first class before you pass up on the opportunity. I’ll mention that the greater majority of new students to Mike’s classes join the ever-growing group of regulars who take almost everything he teaches subsequently.

Don’t be intimidated if you feel like everyone in the class knows each other fairly well—most of us do. Dr. Miller and mathematics can be addictive so many of us have been taking classes from him for 5-20+ years, and over time we’ve come to know each other.

Tone of Class

If you’ve never been to one of Dr. Miller’s classes before, they’re fairly informal and he’s very open to questions from those who don’t understand any of the concepts or follow his reasoning. He’s a retired mathematician from RAND and long-time math professor at UCLA. Students run the gamut from the very serious who read multiple textbooks and do every homework problem to hobbyists who enjoy listening to the lectures and don’t take the class for a grade of any sort (and nearly every stripe in between). He’ll often recommend a textbook that he intends to follow, but it’s never been a “requirement”. More often that not, the bookstore doesn’t list or carry his textbook until the week before class. (Class insiders will usually find out about the book months before class and post it to the Google Group—see below).

His class notes are more than sufficient for making it through the class and doing the assigned (optional) homework. He typically hands out homework in handout form, so the textbook is rarely, if ever, required to make it through the class. Many students will often be seen reading various other texts relating to the topic at hand as they desire. Usually he’ll spend an 45-60 minutes at the opening of each class after the first to go over homework problems or questions that anyone has.

For those taking the class for a grade or pass/fail, his usual policy is to assign a take home problem set around week 9 or 10 to be handed in at the penultimate class. [As a caveat, make sure you check his current policy on grading as things may change, but the preceding has been the usual policy for a 20 years or more.]

Parking Options

Lot 9 – Located at the northern terminus of Westwood Boulevard, one can purchase a parking pass for about $12 a day at the kiosk in the middle of the street just before Westwood Blvd. ends. The kiosk is also conveniently located right next to the parking structure. If there’s a basketball game or some other major event, Lot 8 is just across the street as well, though it’s just a tad further away from the Math Sciences Building. Since more of the class uses this as their parking structure of choice, there is always a fairly large group walking back there after class for the more security conscious.

Lot 2 – Located off of Hilgard Avenue, this is another common option for easy parking as well. While fairly close to class, not as many use it as it’s on the quieter/darker side of campus and can be a bit more of a security issue for the reticent.

Tip: For those opting for on-campus parking, one can usually purchase a quarter-long parking pass for a small discount at the beginning of the term.

Westwood Village and Neighborhood – Those looking for less expensive options street parking is available in the surrounding community, but use care to check signs and parking meters as you assuredly will get a ticket. Most meters in the surrounding neighborhoods end at either 6pm or 8pm making parking virtually free (assuming you’re willing to circle the neighborhood to find one of the few open spots.)

There are a huge variety of lots available in the Village for a range of prices, but the two most common, inexpensive, and closer options seem to be:

  • Broxton Avenue Public Parking at 1036 Broxton Avenue just across from the Fox Village and Bruin Theaters – $5 for entering after 5:01 pm / $9 max for the day
  • Geffen Playhouse Parking at 10928 Le Conte Ave. between Broxton and Westwood – price varies based on the time of day and potential events (screenings/plays in Westwood Village) but is usually $5 in the afternoon and throughout the evening

Dining Options

More often than not a group of between 4 and 15 students will get together every evening before class for a quick bite to eat and to catch up and chat. This has always been an informal group and anyone from class is more than welcome to join. Typically we’ll all meet in the main dining hall of Ackerman Union (Terrace Foodcourt, Ackerman Level 1) between 6 and 6:30 (some with longer commutes will arrive as early as 3-4pm, but this can vary) and dine until about 6:55pm at which time we walk over to class.

The food options on Ackerman Level 1 include Panda Express, Rubio’s Tacos, Sbarro, Wolfgang Puck, and Greenhouse along with some snack options including Wetzel’s Pretzels and a candy store. One level down on Ackerman A-level is a Taco Bell, Carl’s Jr., Jamba Juice, Kikka (sushi), Buzz, and Curbside, though one could get takeout and meet the rest of the “gang” upstairs.

There are also a number of other on-campus options as well though many are a reasonable hike from the class location. The second-closest to class is the Court of Sciences Student Center with a Subway, Yoshinoya, Bombshelter Bistro, and Fusion.

Naturally, for those walking up from Westwood Village, there are additional fast food options like In-N-Out, Chick-fil-A, Subway, and many others.

Killing Time

For those who’ve already eaten or aren’t hungry, you’ll often find one or more of us browsing the math and science sections of the campus bookstore on the ground level of Ackerman Union to kill time before class. (During and after the pandemic, the bookstore began closing at 5:00 PM.) Otherwise there are usually a handful of us who arrive a half an hour early and camp out in the classroom itself (though this can often be dauntingly quiet as most use the chance to catch up on reading here.) If you arrive really early, there are a number of libraries and study places on campus. Boelter Hall has a nice math/science library on the 8th Floor.

Mid-class Break Options

Usually about halfway through class we’ll take a 10-12 minute coffee break. For those with a caffeine habit or snacking urges, there are a few options:

Kerckhoff Hall Coffee Shop is just a building or two over and is open late as snack stop and study location. They offer coffee and various beverages as well as snacks, bagels, pastries, and ice cream. Usually 5-10 people will wander over as a group to pick up something quick.

The Math Sciences Breezeway, just outside of class, has a variety of soda, coffee, and vending machines with a range of beverages and snacks. Just a short walk around the corner will reveal another bank of vending machines if your vice isn’t covered. The majority of class will congregate in the breezeway to chat informally during the break.

The Court of Sciences Student Center, a four minute walk South, with the restaurant options noted above if you need something quick and more substantial, though few students use this option at the break.

Bathrooms – The closest bathrooms to class are typically on the 5th floor of the Math Sciences Building. The women’s is just inside the breezeway doors and slightly to the left. The men’s rooms are a bit further and are either upstairs on the 6th floor (above the women’s), or a hike down the hall to the left and into Boelter hall. I’m sure the adventurous may find others, but take care not to get lost.

Informal Class Resources

Google Group

Over the years, as an informal resource, members of the class have created and joined a private Google Group (essentially an email list-serv) to share thoughts, ideas, events, and ask questions of each other. There are over 50 people in the group, most of whom are past Miller students, though there are a few other various mathematicians, physicists, engineers, and even professors. You can request to join the private group to see the resources available there. We only ask that you keep things professional and civil and remember that replying to all reaches a fairly large group of friends. Browsing through past messages will give you an idea of the types of posts you can expect. The interface allows you to set your receipt preferences to one email per message posted, daily digest, weekly digest, or no email (you’re responsible for checking the web yourself), so be sure you have the setting you require as some messages are more timely than others. There are usually only 1-2 posts per week, so don’t expect to be inundated.

Study Groups

Depending on students’ moods, time requirements, and interests, we’ve arranged informal study groups for class through the Google Group above. Additionally, since Dr. Miller only teaches during the Fall and Winter quarters, some of us also take the opportunity to set up informal courses during the Spring/Summer depending on interests. In the past, we’ve informally studied Lie Groups, Quantum Mechanics, Algebraic Geometry, and Category Theory in smaller groups on the side.

Dropbox

As a class resource, some of us share a document repository via Dropbox. If you’d like access, please make a post to the Google Group.

Class Notes

A few people within the class use Livescribe.com digital pens to capture not only the written notes but the audio discussion that occurred in class as well (the technology also links the two together to make it easier to jump around within a particular lecture). If it helps to have a copy of these notes, please let one of the users know you’d like them—we’re usually pretty happy to share. If you miss a class (sick, traveling, etc.) please let one of us know as the notes are so unique that it will be almost like you didn’t miss anything at all.

You can typically receive a link to the downloadable version of the notes in Livescribe’s Pencast .pdf format. This is a special .pdf file but it’s a bit larger in size because it has an embedded audio file in it that is playable with the more recent version of Adobe Reader X (or above) installed. (This means to get the most out of the file you have to download the file and open it in Reader X to get the audio portion. You can view the written portion in most clients, you’ll just be missing out on all the real fun and value of the full file.) With the notes, you should be able to toggle the settings in the file to read and listen to the notes almost as if you were attending the class live.

Viewing and Playing a Pencast PDF

Pencast PDF is a new format of notes and audio that can play in Adobe Reader X or above.

You can open a Pencast PDF as you would other PDF files in Adobe Reader X. The main difference is that a Pencast PDF can contain ink that has associated audio—called “active ink”. Click active ink to play its audio. This is just like playing a Pencast from Livescribe Online or in Livescribe Desktop. When you first view a notebook page, active ink appears in green type. When you click active ink, it turns gray and the audio starts playing. As audio playback continues, the gray ink turns green in synchronization with the audio. Non-active ink (ink without audio) is black and does not change appearance.

Audio Control Bar

Pencast PDFs have an audio control bar for playing, pausing, and stopping audio playback. The control bar also has jump controls, bookmarks (stars), and an audio timeline control.

Active Ink View Button

There is also an active ink view button. Click this button to toggle the “unwritten” color of active ink from gray to invisible. In the default (gray) setting, the gray words turn green as the audio plays. In the invisible setting, green words seem to write themselves on blank paper as the audio plays.

Future Classes

Often during the current class Dr. Miller will solicit ideas for future courses. Sometimes this is done informally and other times it’s done by way of a simple survey. If you have ideas of things you’d like to explore in the future, feel free to bring them up during the breaks. Generally Dr. Miller tends to stay on the abstract side of math and away from the “applied”, so you might not get much traction in suggesting things like applied statistics, but this shouldn’t keep you from trying.

Class History

For those interested in past years’ topics, here’s the list I’ve been able to put together since I started in the Fall of 2006:

Fall 2006: Complex Analysis
Winter 2007: Field Theory
Fall 2007: Algebraic Topology
Winter 2008: Integer Partitions
Fall 2008: Calculus on Manifolds
Winter 2009: Calculus on Manifolds: The Sequel
Fall 2009: Group Theory
Winter 2010: Galois Theory
Fall 2010: Differential Geometry
Winter 2011: Differential Geometry II
Fall 2011: p-Adic Analysis
Winter 2012: Group Representations
Fall 2012: Set Theory
Winter 2013: Functional Analysis
Fall 2013: Solved and Unsolved Problems in Number Theory (Skipped)
Winter 2014: Measure Theory
Fall 2014: Introduction to Lie Groups and Lie Algebras Part I
Winter 2015: Introduction to Lie Groups and Lie Algebras Part II
Fall 2015: Algebraic Number Theory
Winter 2016: Algebraic Number Theory: The Sequel
Fall 2016: Introduction to Complex Analysis, Part I
Winter 2017: Introduction to Complex Analysis, Part II
Fall 2017: Introduction to Algebraic Geometry
Winter 2018: Introduction to Algebraic Geometry: The Sequel
Fall 2018: Gems and Astonishments of Mathematics Past and Present 
Winter 2019: Introduction to Category Theory
Fall 2019: Combinatorics
Winter 2020: ??
Fall 2020: Cancelled due to coronavirus pandemic
Winter 2021: Cancelled due to coronavirus pandemic
Fall 2021: Differential Topology
Winter 2022: Differential Topology (not offered due to remote-only option for public health/COVID-19 reasons)
Fall 2022: Theory and Applications of Continued Fractions
Winter 2023: Nothing offered due to Extension scheduling issues
Fall 2023: Topics in Ring Theory and Modules
Winter 2023: Rational Points on Elliptic Curves
Fall 2024: Fundamentals of Point-Set Topology
Winter 2025: Fundamentals of Point-Set Topology II
Fall 2025: Introduction to Hilbert Spaces: An Adventure In Infinite Dimensions
Winter 2026: Fundamentals Of Hypercomplex Numbers

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Chris Aldrich

I'm a biomedical and electrical engineer with interests in information theory, complexity, evolution, genetics, signal processing, IndieWeb, theoretical mathematics, and big history. I'm also a talent manager-producer-publisher in the entertainment industry with expertise in representation, distribution, finance, production, content delivery, and new media.

26 thoughts on “Dr. Michael Miller Math Class Hints and Tips | UCLA Extension”

  1. 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.

    Prerequisites:
    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):

    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

    Algebraic Geometry: An Introduction (Universitext) by Daniel Perrin

    An Invitation to Algebraic Geometry (Universitext) by Karen E. Smith, Lauri Kahanpää, Pekka Kekäläinen, William Traves

    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
    Syndicated copies to:






    <em>Related</em>

    Author: Chris Aldrich

    I'm a biomedical and electrical engineer with interests in information theory, complexity, evolution, genetics, signal processing, theoretical mathematics, and big history.

    I’m also a talent manager-producer-publisher in the entertainment industry with expertise in representation, distribution, finance, production, content delivery, and new media.
    View all posts by Chris Aldrich

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  2. 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):* 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* Algebraic Geometry: An Introduction (Universitext) by Daniel Perrin* An Invitation to Algebraic Geometry (Universitext) by Karen E. Smith, Lauri Kahanpää, Pekka Kekäläinen, William Traves* 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. [http://boffosocko.com/2015/09/22/dr-michael-miller-math-class-hints-and-tips-ucla-extension/]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.)+Rama Kunapuli, +Dave Sneadhttp://boffosocko.com/2017/07/25/introduction-to-algebraic-geometry-ucla-extension/



  3. 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.
    Syndicated copies to:


    <em>Related</em>

    Author: Chris Aldrich

    I'm a biomedical and electrical engineer with interests in information theory, complexity, evolution, genetics, signal processing, theoretical mathematics, and big history.

    I’m also a talent manager-producer-publisher in the entertainment industry with expertise in representation, distribution, finance, production, content delivery, and new media.
    View all posts by Chris Aldrich

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  4. a tweet by Stephanie Hurlburt (Twitter)

    Okay so right now I go to coffee shops to solve math problems alone, it’s peaceful, I like it

    But someone mentioned they do cute tea parties with their girl squad & I said wow I want something like that but we all bring math textbooks & solve problems next to each other (1/2)

    It’s not specifically femme yet does involve tea, but I’ve noticed something informal like this at the Starbucks just two blocks West of CalTech in Pasadena.
    Separately but related, “adults” looking for a varied advanced math outlet in the Los Angeles area are welcome to join Dr. Mike Miller’s classes at UCLA Extension on Tuesday nights from 7-10pm. We’re working on Algebraic Geometry this quarter. For those who might need notes to play catch up, I’ve got copies, with full audio recordings, that I’m happy to share.
    Syndicated copies to:

    Syndicated copies:

    1. We did the “sequel” to Algebraic Geometry to delve further into the material. Join us for the fall? I’ll post something about what the course will be sometime in June/July later this year.

  5. 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!

    Syndicated copies to:







    Syndicated copies:

  6. Last night saw the wrap up of Dr. Michael Miller’s excellent Winter quarter class Introduction to Category Theory. As usual he passed out a short  survey to accept ideas for the Fall and Winter quarters this coming year at UCLA Extension.
    If you didn’t get a chance to weigh in, feel free to email him directly, or respond here with your suggestions (in order of preference) and I’ll pass them along.
    I keep a list of his past offerings (going back to 2006, but he’s been doing this since 1973) on my site for reference. He’s often willing to repeat courses that have been previously offered, particularly if there’s keen interest in those topics.
    Some of the suggestions on last night’s list included:
    combinatorics
    combinatorial group theory
    number theory
    game theory
    group theory
    ring theory
    field theory
    Galois theory
    real analysis
    point set topology
    differential equations
    differential geometry
    Feel free to vote for any of these or suggest your own topics. Keep in mind that many of the topics in the past decade have come about specifically because of lobbying on behalf of students.

    Syndicated copies to:
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  7. 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.

  8. 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

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  9. Quantum mechanics anyone? Dozens have been disappointed by UCLA’s administration ineptly standing in the way of Dr. Mike Miller being able to offer his perennial Winter UCLA math class (Ring Theory this quarter), so a few friends and I are putting our informal math and physics group back together.
    We’re mounting a study group on quantum mechanics based on Peter Woit‘s Introduction to Quantum Mechanics course from 2022. We’ll be using his textbook Quantum Theory, Groups and Representations:An Introduction (free, downloadable .pdf) and his lectures from YouTube.
    Shortly, we’ll arrange a schedule and some zoom video calls to discuss the material. If you’d like to join us, send me your email or leave a comment so we can arrange meetings (likely via Zoom or similar video conferencing).
    Our goal is to be informal, have some fun, but learn something along the way. The suggested mathematical background is some multi-variable calculus and linear algebra. Many of us already have some background in Lie groups, algebras, and representation theory and can hopefully provide some help for those who are interested in expanding their math and physics backgrounds.
    Everyone is welcome! 

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  10. Dr. Mike Miller announced in class last night that in the coming Winter quarter at UCLA Extension he’ll be offering a course on elliptic curves.
    The text for the class will be Rational Points on Elliptic Curves (Springer, Undergraduate Texts in Mathematics) by Joseph H. Silverman and John T. Tate. He expects to follow and rely more on it versus handing out his own specific lecture notes.

    He mentioned that while it would suggest a more geometric flavor, which it will certainly have, the class will carry an interesting algebraic component which those not familiar with the topic may not expect.

    To register, look for the listing sometime in the coming month or so when the Winter catalog is released.

  11. Pingback: Chris Aldrich
  12. I took one of his courses a couple years back. It was in differential topology if I recall correctly, we worked through topology up through Whitney’s embedding theorem. It was nice. It really is just for fun, the “homeworks” he gives are really up to you to do since he doesn’t collect them, and there was an “exam” but as long as you showed up to the classes and didn’t doodle the whole time it was fine (he really doesn’t want to give an exam, he just feels he has to in order to justify the grades he’s obligated to give out). All this to say it’s really up to you how much you want to get out of the class, if you put more effort in you’ll learn more and he’s always willing to discuss stuff.

  13. Can someone please record them? This is such a travesty that they’re not. Someone volunteers, records, and places it on YT. The world is then a much better place. Or, just at least release some notes.

    This is painful to know I can’t attend!

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