Quotes | Chris Aldrich

Introduction to Lie Groups and Lie Algebras | UCLA Extension

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, is offering a course on Introduction to Lie Groups and Lie Algebras this fall through UCLA Extension. 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 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 (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 the rest of the class) will help you get quickly back up to speed to delve into what is often otherwise a very deep subject. If you’re interested in advanced physics, quantum mechanics, quantum information or string theory, this is one of the topics that is de rigueur for delving in deeply and being able to understand them better. The topic is also one near and dear to the hearts of those in robotics, graphics, 3-D modelling, gaming, and areas utilizing multi-dimensional rotations. And naturally, it’s simply a beautiful and elegant subject for those who have no need to apply it to anything, but who just want to meander their way through higher mathematics for the fun of it (this will 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 or Linear Algebra, 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. 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, I was able to do exceedingly well in the course.) I’m happy to chat with those who may be reticent. 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.

As a group, some of us have a collection of a few dozen texts in the area which we’re happy to loan out as well. In addition to the one recommended text (Mike always gives such comprehensive notes that any text for his classes is purely supplemental at best), several of us have also found some good similar texts:

Given the breadth and diversity of the backgrounds of students in the class, I’m sure Mike will spend some reasonable time at the beginning [or later in the class, as necessary] doing a quick overview of some linear algebra and calculus related topics that will be needed later in the quarter(s).

Further information on the class and a link to register can be found below. If you know of others who might be interested in this, please feel free to forward it along – the more the merrier.

I hope to see you all soon.

Introduction to Lie Groups and Lie Algebras

MATH X 450.6 / 3.00 units / Reg. # 249254W
Professor: Michael Miller, Ph.D.
Start Date: 9/30/2014
Location UCLA: 5137 Math Sciences Building
Tuesday, 7-10pm
September 30 – December 16, 2014
11 meetings total (no mtg 11/11)
Register here: https://www.uclaextension.edu/Pages/Course.aspx?reg=249254

Course Description

A Lie group is a differentiable manifold that is also a group for which the product and inverse maps are differentiable. A Lie algebra is a vector space endowed with a binary operation that is bilinear, alternating, and satisfies the so-called Jacobi identity. This course, the first in a 2-quarter sequence, is an introductory survey of Lie groups, their associated Lie algebras, and their representations. This first quarter will focus on the special case of matrix Lie groups–including general linear, special linear, orthogonal, unitary, and symplectic. The second quarter will generalize the theory developed to the case of arbitrary Lie groups. Topics to be discussed include compactness and connectedness, homomorphisms and isomorphisms, exponential mappings, the Baker-Campbell-Hausdorff formula, covering groups, and the Weyl group. This is an advanced course, requiring a solid understanding of linear algebra and basic analysis.

The Single Biggest Problem in Communication

The single biggest problem in communication is the illusion that it has taken place.

apocryphally attributed to George Bernard Shaw,
but more likely William H. Whyte in Fortune, “Is Anybody Listening?” Start Page 77, Quote Page 174, Published by Time, Inc., New York (September 1950)

“We didn’t cover much, but we sure did learn.”

We had to prove the theorems ourselves—with hints, of course—and as a result didn’t get very far, covering perhaps a fourth of what might be done in a conventional lecture. But so what? The most persistent myth of mathematics education is that what is covered is the same as what is learned. We didn’t cover much, but we sure did learn.

Steve Mitchell, algebraic topologist
on learning mathematics in Steve Mitchell short biography

To Understand God’s Thought…

To understand God’s thought, we must study statistics, for these are the measure of His purpose.

Florence Nightingale, OM, RRC (1820-1910), English social reformer and statistician, founder of modern nursing, renaissance woman
in Florence Nightingale’s Wisdom, New York Times, 3/4/14

Florence Nightingale developed the polar pie chart to depict mortality causes in the Crimean War.

Information Theory is Something Like the Logarithm of Probability Theory

To put it saucily: information theory is something like the logarithm of probability theory. In early modern times the logarithm simplified multiplication into addition which was more accessible to calculation. Today, information theory transforms many quantities of probability theory into quantities which allow simpler bookkeeping.

More seriously, information theory is one of the most universal concepts with applications in computer science, mathematics, physics, biology, chemistry and other fields. It allows a lucid and transparent analysis of many systems and provides a framework to study and compare seemingly different systems using the same language and notions.

Dr. Daniel Polani, reader in Artificial Life, University of Hertfordshire
in “Research Questions”

Not only a great quote, but an interesting way to view the subjects.

Why a Ph.D. in Physics is Worse Than Drugs

I have known more people whose lives have been ruined by getting a Ph.D. in physics than by drugs.

Jonathan I. Katz, Professor of Physics, Washington University, St. Louis, Mo.
in “Don’t Become a Scientist!”

In the essay, Dr. Katz provides a bevy of solid reasons why one shouldn’t become a researcher. I highly recommend everyone read it and then carefully consider how we can turn these problems around.

Editor’s Note: The original article has since been moved to another server.

How might we end the war against science in America?

The Two Cultures

A good many times I have been present at gatherings of people who, by the standards of the traditional culture, are thought highly educated and who have with considerable gusto been expressing their incredulity of scientists. Once or twice I have been provoked and have asked the company how many of them could describe the Second Law of Thermodynamics. The response was cold: it was also negative. Yet I was asking something which is the scientific equivalent of: Have you read a work of Shakespeare’s?

I now believe that if I had asked an even simpler question — such as, What do you mean by mass, or acceleration, which is the scientific equivalent of saying, Can you read? — not more than one in ten of the highly educated would have felt that I was speaking the same language. So the great edifice of modern physics goes up, and the majority of the cleverest people in the western world have about as much insight into it as their neolithic ancestors would have had.

C.P. Snow, Kt., CBE (1905 – 1980), an English physical chemist and novelist
in 1959 Rede Lecture entitled “The Two Cultures”

C. P. Snow, English physicist, author, and diplomat.

Fundamental Difference Between Science and Politics

What I do know is that there is a fundamental difference between science and politics. In fact, I’ve come to view them more and more as opposites.

In science, progress is possible.

Nate Silver, statistician
in The Signal and the Noise: Why So Many Predictions Fail-but Some Don’t (Penguin Books, 2012)

God Could Have Caused Birds to Fly With Their Bones Made of Solid Gold

Surely, God could have caused birds to fly with their bones made of solid gold, with their veins full of quicksilver, with their flesh heavier than lead, and with their wings exceedingly small. He did not, and that ought to show something. It is only in order to shield your ignorance that you put the Lord at every turn.

Salviati’s (Galileo’s voice) response to Simplicio (Pope Urban VIII)
Galileo Galilei in Dialogue Concerning the Two Chief World Systems

Galileo's Dialogo Title Page — Title Page from Galileo’s Dialogo

Beauty, Melody, and Entropy are an Equivalence Class

Suppose that we were asked to arrange the following in two categories–

distance, mass, electric force, entropy, beauty, melody.

I think there are the strongest grounds for placing entropy alongside beauty and melody and not with the first three.

Sir Arthur Stanley Eddington, OM, FRS (1882-1944), a British astronomer, physicist, and mathematician
in The Nature of the Physical World, 1927

One Cool Judgment is Worth a Dozen Hasty Councils

One cool judgment is worth a dozen hasty councils. The thing to do is to supply light and not heat.

Woodrow Wilson (1856–1924), 28th U.S. president

Axiom of Choice? “Would you rather be deaf or blind?”

‘Should you just be an algebraist or a geometer?’ is like saying ‘Would you rather be deaf or blind?’

Sir Michael Francis Atiyah, OM, FRS, FRSE, FAA, a British mathematician
in Mathematics in the 20th Century

All cell biologists have two cells of interest

Although not everyone is mindful of it, all cell biologists have two cells of interest: the one they are studying, and Escherichia coli.

Frederick Neidhardt (1931 — ), professor of Microbiology and Immunology
as quoted in The Machinery of Life by David S. Goodsell

Regard the World as Made of Information

Regard the physical world as made of information, with energy and matter as incidentals.

John Archibald Wheeler (1911-2008), American theoretical physicist
[attributed by Jacob Bekenstein in “Information in the Holographic Universe” (Scientific American, 2007)]

It has taken great minds to discover simple things

It behooves us always to remember that in physics it has taken great minds to discover simple things. They are very great names indeed which we couple with the explanation of the path of a stone, the droop of a chain, the tints of a bubble, the shadows in a cup.

Sir D’Arcy Wentworth Thompson CB FRS FRSE (May 2, 1860 – June 21, 1948), a Scottish biologist, mathematician and classics scholar
in On Growth and Form, 1917

Category: Quotes