On Playing Checkers

Evie: I have a strategy to win.
Papa: What is your strategy?
Evie: I have two strategies. One is not telling you what my strategy is. The other is my strategy to win.

eight minutes later…

Evie: Do you want to know my strategy??!

This post was originally published on Chris Aldrich

David Quammen on Books
David Quammen (1948 ― ), science, nature, and travel writer
in The Boilerplate Rhino: Nature in the Eye of the Beholder

 

This post was originally published on Chris Aldrich

Introduction to Lie Groups and Lie Algebras (Part 2) | UCLA Extension

Introduction to Lie Groups and Lie Algebras (Part 2) | UCLA Extension

Dr. Mike Miller, who had previously announced a two quarter sequence of classes on Lie Groups at UCLA, has just opened up registration for the second course in the series. His courses are always clear, entertaining, and invigorating, and I highly recommend them to anyone who is interested in math, science, or engineering.

Philosophy is written in this grand book, the universe which stands continually open to our gaze. But the book cannot be understood unless one first learns to comprehend the language and read the letters in which it is composed. It is written in the language of mathematics, and its characters are triangles, circles and other geometric figures without which it is humanly impossible to understand a single word of it; without these, one wanders about in a dark labyrinth.

Galileo Galilee (1564–1642) in Il saggiatore (The assayer)

Prior to the first part of the course, I’d written some thoughts about the timbre and tempo of his lecture style and philosophy and commend those interested to take a peek. I also mentioned some additional resources for the course there as well.  For those who missed the first portion, I’m happy to help fill you in and share some of my notes if necessary. The recommended minimum prerequisites for this class are linear algebra and some calculus.


Introduction to Lie Groups and Lie Algebras (Part 2)

Math X 450.7 / 3.00 units / Reg. # 251580W
Professor: Michael Miller, Ph.D.
Start Date: January 13, 2015
Location: UCLA, 5137 Math Sciences Building
Tuesday, 7-10pm
January 13 – March 24
11 meetings total
Class will not meet on one Tuesday to be annouced.

Register here: https://www.uclaextension.edu/Pages/Course.aspx?reg=251580

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 is the second in a 2-quarter sequence that offers an introductory survey of Lie groups, their associated Lie algebras, and their representations. Its focus is split between continuing last quarter’s study of matrix Lie groups and their representations and reconciling this theory with that for the more general manifold setting. Topics to be discussed include the Weyl group, complete reducibility, semisimple Lie algebras, root systems, and Cartan subalgebras. This is an advanced course, requiring a solid understanding of linear algebra, basic analysis, and, ideally, the material from the previous quarter.Internet access required to retrieve course materials.

Recommended Textbook

Hall, Brian. Lie Groups, Lie Algebras, & Representations (Springer, 2004) ISBN: 9781441923134

 

A photograph of Sophus Lie's very full and bushy beard.
“I wouldn’t lie to you. This is Sophus’s beard.”

 

Introduction to Lie Groups and Lie Algebras (Part 2) | UCLA Extension was originally published on Chris Aldrich

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

God Could Have Caused Birds to Fly With Their Bones Made of Solid Gold was originally published on Chris Aldrich

Meaning according to Humpty Dumpty

Meaning according to Humpty Dumpty
Humpty Dumpty (in a rather scornful tone): When I use a word, it means just what I choose it to mean – neither more or less.
Alice: The question is, whether you can make a word mean so many different things?
Humpty Dumpty: The question is, which is to be master – that’s all.
Alice: (Too much puzzled to say anything, so after a minute Humpty Dumpty began again)
Humpty Dumpty: They’ve a temper, some of them – particularly verbs, they’re the proudest – adjectives you can do anything with, but not verbs – however, I can manage the whole of them! Impenetrability! That’s what I say!
Alice: Would you tell me, please what that means?
Humpty Dumpty (looking very much pleased): Now you talk like a reasonable child. I meant by impenetrability that we have had enough of that subject, and it would be just as well if you’d mention what you mean to do next, as I suppose you don’t mean to stop here all the rest of your life.
Alice (in a thoughtful tone): That’s a great deal to make one word mean.
Humpty Dumpty: When I make a word do a lot of work like that, I always pay it extra.
Alice (too much puzzled to make any other remark): Oh!

This post was originally published on Chris Aldrich