Algebraic Number Theory | UCLA Extension

Mike Miller is teaching Algebraic Number Theory in the Fall!

Only Me

Like a kid anxiously awaiting Christmas morning, I spent some time refreshing UCLA Extension’s web page over the weekend in hopes of seeing the announcement of Mike Miller’s Fall math course with no results.

I checked again a half hour ago and their site was down!

My salivating hit a fever pitch!

Refreshing, refreshing, refreshing… and now it’s live again with:

Mike Miller is teaching Algebraic Number Theory in the Fall!

Register quickly before it fills up.  And let the pool for the guesses about which textbook he’ll recommend begin!

Algebraic Number Theory

MATH X 450.8 | 3.00 units

In no field of mathematics is there such an irresistible fascination as in the theory of numbers. This course, the first in a two-quarter sequence, is an introductory, yet rigorous, survey of algebraic number theory, which evolved historically through attempts to prove Fermat’s Last Theorem. Beginning with a quick review of primality and unique factorization for ordinary integers, the course extends these notions to more exotic domains: quadratic, cubic, cyclotomic, and general number fields. This development is then applied to the representation of integers as sums of squares and, more generally, to classic Diophantine equations. Topics to be discussed include: Euclidean, principal ideal, and Noetherian domains; integral bases; binary quadratic forms; algebraic field extensions; and several remarkable theorems/conjectures of Ramanujan.

UCLA: 5137 Math Sciences
Tuesday, 7-10pm,
September 22 – December 8
11 meetings total
(no mtg 11/17)

See you all in just a few weeks!


A Note For the Reticent

Exercise Your Brain

As many may know or have already heard, Dr. Mike Miller, a retired mathematician from RAND and long-time math professor at UCLA, has been offering incredibly inexpensive upper level undergraduate and graduate level math courses for 30+ years through UCLA Extension.

Whether you’re a professional mathematician, engineer, physicist, physician, or simply a hobbyist interested in mathematics you’ll be sure to get something interesting out of this course, not to mention the camaraderie of 20-30 other “regulars” with widely varying backgrounds (actors to surgeons and evolutionary theorists to engineers) who’ve been taking almost everything Mike has offered over the years. Once most new students have taken one class, they’re incredibly prone to want to take them all (and yes, he’s THAT good — we’re sure you’ll be addicted too.)

“Beginners” Welcome!

Even if it’s been years since you last took calculus or linear algebra, Mike (and usually the rest of the class) will help you get quickly back up to speed to delve into what is often a very deep subject. Though there are a handful who will want to learn the subject for specific applications, naturally, it’s simply a beautiful and elegant subject for those who just want to meander their way through higher mathematics for the fun of it (this will probably comprise the largest majority of the class by the way.)

Whether you’ve been away from serious math for decades or use it every day or even if you’ve never gone past calculus, this is bound to be the most entertaining thing you can do with your Tuesday nights in the fall.  If you’re not sure what you’re getting into (or are scared a bit by the course description), I highly encourage to come and join us for at least the first class before you pass up on the opportunity – there’s no need to preregister or prepay if you’re unsure.  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.

For the reticent, I’ll mention that one of the first courses I took from Mike was Algebraic Topology which generally requires a few semesters of Abstract Algebra and a semester of Topology as prerequisites.  I’d taken neither of these prerequisites, but due to Mike’s excellent lecture style and desire to make everything comprehensible to the broadest number of students, I was able to do exceedingly well in the course. Also keep in mind that you can register to take the class for a grade, pass/fail, or even no grade at all to suit your needs/lifestyle.

My classes have the full spectrum of students from the most serious to the hobbyist to those who are in it for the entertainment and  ‘just enjoy watching it all go by.’

Mike Miller, Ph.D.


Textbook: Introductory Algebraic Number Theory

Update (8/19/15) Per my email conversation with Dr. Miller, despite that neither the Extension website nor the bookstore have a book listed for the class yet, he’s going to be recommending Introductory Algebraic Number Theory by Saban Alaca and Kenneth S. Williams (Cambridge University Press, 2003, ISBN: 978-0521183048).

Introductory Algebraic Number Theory


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César Hidalgo on Why Information Grows | The RSA

I’ve just recently finished the excellent book Why Information Grows by César Hidalgo. I hope to post a reasonable review soon, but the ideas in it are truly excellent and fit into a thesis I’ve been working on for a while. For those interested, he does a reasonable synopsis of some of his thought in the talk he gave the the RSA recently, the video can be found below.

The underlying mathematics of what he’s discussing are fantastic (though he doesn’t go into them in his book), but the overarching implications of his ideas with relation to the future of humankind as a function of our economic system and society could have some significant impact.

“César visits the RSA to present a new view of the relationship between individual and collective knowledge, linking information theory, economics and biology to explain the deep evolution of social and economic systems.

In a radical rethink of what an economy is, one of WIRED magazine’s 50 People Who Could Change the World, César Hidalgo argues that it is the measure of a nation’s cultural complexity – the nexus of people, ideas and invention – rather than its GDP or per-capita income, that explains the success or failure of its economic performance. To understand the growth of economies, Hidalgo argues, we first need to understand the growth of order itself.”

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No, It’s Not Your Opinion. You’re Just Wrong. | Houston Press

Before you crouch behind your Shield of Opinion you need to ask yourself two questions: 1. Is this actually an opinion? 2. If it is an opinion how informed is it and why do I hold it?

This has to be the best article of the entire year: “No, It’s Not Your Opinion. You’re Just Wrong.”

It also not coincidentally is the root of the vast majority of the problems the world is currently facing. There are so many great quotes here, I can’t pick a favorite, so I’ll highlight the same one Kimb Quark did that brought my attention to it:

“There’s nothing wrong with an opinion on those things. The problem comes from people whose opinions are actually misconceptions. If you think vaccines cause autism you are expressing something factually wrong, not an opinion. The fact that you may still believe that vaccines cause autism does not move your misconception into the realm of valid opinion. Nor does the fact that many other share this opinion give it any more validity.”

Jef Rouner
in No, It’s Not Your Opinion. You’re Just Wrong | Houston Press


Pictured: A bunch of people who were murdered regardless of someone's opinion on the subject
Pictured: A bunch of people who were murdered regardless of someone’s opinion on the subject
Syndicated copies to: Now Supports Fragmentions!

A fragmention is an extension to URL syntax that links and cites a phrase within a document by using a URL fragment consisting of the phrase itself, including whitespace.

I’ve been meaning to do it for ages, but now supports fragmentions.

“A fragmention is an extension to URL syntax that links and cites a phrase within a document by using a URL fragment consisting of the phrase itself, including whitespace.”


Proposed Fragmention Icon
Proposed Fragmention Icon

To take advantage of the functionality, append a # and the text you’d like to highlight on the particular page after the address of the particular web page. Add a + to indicate whitespaces if necessary, though typically including a single, unique keyword is typically sufficient to highlight the appropriate section.


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I’m a sucker for references to math and pastry

Math is about understanding processes and not just eating end results.


hat can I say? I’m a sucker for references to math and pastry.


“One of the wonderful features of math is that, like with pastry, it can use quite simple ingredients to make very complicated situations. This can also make it rather offputting, like making puff pastry. Actually, I don’t think puff pastry is that difficult if you follow the instructions carefully. But even if you don’t want to try doing it yourself, perhaps you can still enjoy the fact that such simple ingredients can turn into delicious puff pastry. Math is about understanding processes and not just eating end results.”

Eugenia Cheng, mathematician, amateur chef
in How to Bake Pi: An Edible Exploration of the Mathematics of Mathematics (Basic Books, 2015)
How to Bake Pi
How to Bake Pi
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Chris Aldrich on VH1’s “Dating Naked”!

Let's get one thing straight: the Chris Aldrich on VH1's upcoming new season of "Dating Naked: Playing for Keeps" is NOT me -- first of all, I'm way better looking.


ver the past couple of months leading up to to the launch of VH1’s new season of “Dating Naked: Playing for Keeps” , I’ve been entertained by friends who have seen little snippets and notices about the show and wondering why and how I got involved in front of the camera. Honestly, it’s mostly been the why question. Ego-bruisingly, only one so far has wanted to know if they could get the “unblurred” cut of the show.

Let’s get one thing straight: the Chris Aldrich on VH1’s Dating Naked is NOT me — first of all, I’m way better looking.

Fortunately as we’re getting closer, there’s now “artwork” to support the fact that it’s not me.

The "other" Chris Aldrich
The “other” Chris Aldrich

It would be nice to have some PR on Hollywood’s busiest corner, but the price was too high.

Once the show launches on the 22nd, I almost can’t wait to see what happens to the Google ranking for my searches on my name.  I’m sure I’ll have some further entertainment in relation to my twitter account @chrisaldrich and other parts of my social media presence. I’m almost tempted to make a few changes in the bio sections to increase the ambiguity and cause some trouble.

I’m reminded of Wes Moore’s book “The Other Wes Moore: One Name, Two Fates“, unfortunately I’m not quite sure that my writing a book about my experience with “The Other Chris Aldrich” would be so uplifting or inspiring to others. I’d also be more worried that I’d have to change the subtitle to “One name, One Fate.”



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The Math That Connects Pluto to DNA — NOVA Next | PBS

The Math That Connects Pluto to DNA by Alex RileyAlex Riley (NOVA Next | PBS)
How a mathematical breakthrough from the 1960s now powers everything from spacecraft to cell phones.

Concurrent with the recent Pluto fly by, Alex Riley has a great popular science article on PBS that helps put the application of information theory and biology into perspective for the common person. Like a science version of “The Princess Bride”, this story has a little bit of everything that could be good and entertaining: information theory, biology, DNA, Reed-Solomon codes, fossils, interplanetary exploration, mathematics, music, genetics, computers, and even paleontology. Fans of Big History are sure to love the interconnections presented here.

Reed-Solomon codes correct for common transmission errors, including missing pixels (white), false signals (black), and paused transmissions (the white stripe).
Reed-Solomon codes correct for common transmission errors, including missing pixels (white), false signals (black), and paused transmissions (the white stripe).
Microscopic view of glass DNA storage beads
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Little Free Library #8424 Progress

My Little Free Library is getting closer to launch...

Almost the same moment I saw my first Little Free Library, I decided that I wanted to host one of my very own, so I registered with the intent of building one in my free time. The registration arrived and I’d drafted some very serious custom plans, but just never gotten around to purchasing the supplies and building it.

Recently I saw something a bit more quirky and interesting than my original plans that I could up-cycle, so I made the purchase (happy belated birthday to me)!  It’s got two spacious shelves with two doors including a glass fronted one, and it’s got the capacity for at least 6 linear feet of books. We’re nearly ready to go.

Little Free Library #8424 (prelaunch)
Little Free Library #8424 (prelaunch)

I’m hoping to get some mounting materials and have the library up and running soon.  My plan is to specialize in literary fiction, though I’m sure we’ll also stock a fair amount of popular science and non-fiction as well as thriller, mystery, and suspense as well.

Invitations to the “launch” party should be coming shortly! If you’ve got some books you’d like to donate toward the cause, let me know in the comments below. Be sure to include a Book Crossing ID number on them if you’d like to track where your favorite objects head off to in the future.


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Game Theory’s Tit-for-Tat is Just a Mathematically Complete Version of Religion’s Golden Rule

Francis Fukuyama (1952- ), American political scientist, political economist, author
in The Origins of Political Order: From Prehuman Times to the French Revolution (Farrar, Straus and Giroux, 2011)


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