Algebraic Number Theory: The Sequel | UCLA Extension

I know you’ve all been waiting for the announcement with bated breath! We’ve known for a while that Mike Miller’s Winter course would be a follow-on course to his Algebraic Number Theory course this Fall, but it’s been officially posted, so now you can register for it: Algebraic Number Theory: The Sequel.

I’m sure, as always, that there are a few who are interested, but who couldn’t make the Fall lectures. Never fear, there’s a group of us that can help you get up to speed to keep pace with us during the second quarter. Just drop us a note and we’ll see what we can do.

Algebraic Number Theory: The Sequel

In no field of mathematics is there such an irresistible fascination as in the theory of numbers. This course, the second 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 the previous quarter’s work, the course continues discussions on the structure of algebraic number fields, focusing particular attention on primes, units, and roots of unity in quadratic, cubic, and cyclotomic fields. Topics to be discussed include: norms and traces; the ideal class group; Minkowski’s Translate, Convex Body, and Linear Forms theorems; and Dirichlet’s Unit Theorem.

UCLA: 5137 Math Sciences
Tuesday, 7-10pm,
January 5 – March 15
11 meetings total

MATH X450.9
3.00 units

Recommended Textbook

We’ll be using Introductory Algebraic Number Theory by Saban Alaca and Kenneth S. Williams (Cambridge University Press, 2003, ISBN: 978-0521183048).

Introductory Algebraic Number Theory

Eugenia Cheng, author of How to Bake Pi, on Colbert Tonight

Earlier this year, I read Eugenia Cheng’s brilliant book How to Bake Pi: An Edible Exploration of the Mathematics of Mathematics. Tonight she’s appearing (along with Daniel Craig apparently) on the The Late Show with Stephen Colbert. I encourage everyone to watch it and read her book when they get the chance.

How-to-bake-pi

You can also read more about her appearance from Category Theorist John Carlos Baez here: Cakes, Custard, Categories and Colbert | The n-Category Café

My brief review of her book on GoodReads.com:

How to Bake Pi: An Edible Exploration of the Mathematics of MathematicsHow to Bake Pi: An Edible Exploration of the Mathematics of Mathematics by Eugenia Cheng
My rating: 4 of 5 stars

While most of the book is material I’ve known for a long time, it’s very well structured and presented in a clean and clear manner. Though a small portion is about category theory and gives some of the “flavor” of the subject, the majority is about how abstract mathematics works in general.

I’d recommend this to anyone who wants to have a clear picture of what mathematics really is or how it should be properly thought about and practiced (hint: it’s not the pablum you memorized in high school or even in calculus or linear algebra). Many books talk about the beauty of math, while this one actually makes steps towards actually showing the reader how to appreciate that beauty.

Like many popular books about math, this one actually has very little that goes beyond the 5th grade level, but in examples that are very helpfully illuminating given their elementary nature. The extended food metaphors and recipes throughout the book fit in wonderfully with the abstract nature of math – perhaps this is why I love cooking so much myself.

I wish I’d read this book in high school to have a better picture of the forest of mathematics.

More thoughts to come…

What An Actual Handwaving Argument in Mathematics Looks Like

I’m sure we’ve all heard them many times, but this is what an actual handwaving argument looks like in a mathematical setting.

Handwaving during Algebraic Number Theory

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Photo taken at: UCLA Math Sciences Building

Handwaving during Algebraic Number Theory

A photo posted by Chris Aldrich (@chrisaldrich) on

On Being a Secretary

For five years he [Thomas Hobbes (1588-1679)] served as personal secretary to, yes, Francis Bacon. In fact, I’ve noted over a course of years that the job of a secretary can be utterly fulfilling just in case one’s boss happens to be Francis Bacon.

Daniel N. Robinson, (March 9, 1937-  ), philosopher
in Great Ideas of Philosophy, 2nd Edition, Lecture 28 “Hobbes and the Social Machine”

 

Great Ideas of Philosophy

Brief Review: The Rule of Four by Ian Caldwell and Dustin Thomason

The Rule of FourThe Rule of Four by Ian Caldwell and Dustin Thomason
My rating: 4 of 5 stars

A nice little thriller about an obscure text from the Renaissance (quattrocento) set in modern times. This falls into the genre of historical fiction that’s similar to Dan Brown‘s Robert Langdon series or films like the Nicolas Cage National Treasure series, though not quite as “rompish.” I have to imagine that those who liked Mr. Penumbra’s 24-Hour Bookstore, Gentlemen and Players, and The Thirteenth Tale will enjoy this quite a lot.

Those who are fans of historical fiction, cryptography, puzzles, books about books, and history in general, are sure to enjoy it.

Spoilers follow:

The Vincent Taft character could have been a better “heavy” but was pretty functional in the story given his limited appearances in the actual plot. I saw the Savonarola portion of the plot a mile away, but to most unaware of this part of history this will be an interesting historical diversion/lesson. I thought the ending was a bit too literary given the more plot-motivated feel of the rest of the narrative, but in all, it was relatively satisfying given Tom’s full back-story. I can see this being adapted into film, but it will take some creative ideas to better linearize the plot and to make the ending a bit bigger for the screen.

View all my reviews

Sir Francis Bacon smacks down Republican party front-runners

A

s I watch the unfolding of the 2016 presidential election, I find myself wondering more and more where I can register to vote for the “scientific party?”

The electorate seems to want to focus primarily (only?) on the Judeo-Christian principles upon which our country was founded. Though I have no qualm with these principles, they seem to miss the firmer and primary base upon which the country was built at the dawn of the Age of Reason.

THOSE WHO HAVE TAKEN UPON THEM TO LAY DOWN THE LAW of nature as a thing already searched out and understood, whether they have spoken in simple assurance or professional affectation, have therein done philosophy and the sciences great injury. For as they have been successful in inducing belief, so they have been effective in quenching and stopping inquiry; and have done more harm by spoiling and putting an end to other men’s efforts than good by their own.

Sir Francis Bacon, (22 January 1561 – 9 April 1626), English philosopher, statesman, scientist, jurist, orator, essayist and author
in the preface to Novum Organum (1620)

 

Pourbus' Francis Bacon

Read the original 1620 edition in Latin

Johns Hopkins on film: A guide to university cameos big and small

“Homewood campus, Peabody Conservatory, East Baltimore campus have made cameos big and small over the years”

Source: Johns Hopkins on film: A guide to university cameos big and small

It’s almost like they write some of this stuff just for me. Though I was already aware of most of the movies they mentioned, they did miss a few:

Washington Square (1997) directed by Agnieszka Holland in Hollywood Pictures/Caravan Pictures production has a stunning cameo of the interior of the Peabody Library – this cameo is the only reason I vaguely remember the film at all.

The Johns Hopkins Science Review (1948-1955) This production is also particularly notable as being the television debut (October 8, 1951) of actor and alum John Astin who now heads the JHU Drama program and for whom the eponymous theater in the Merrick Barn is named.

Fratricide (1966) – A very independent short black and white film (with no credits) starring professor Richard Macksey that was produced by a group of students which included later Hollywood luminaries Walter Murch (who just a few years later co-wrote THX 1138 with George Lucas), Caleb Deschanel, and Matthew Robbins, who coincidentally co-wrote Crimson Peak with Guillermo del Torro which comes out in theaters today.

I have a nagging feeling there are a few more, but they’re just not coming to me at the moment…

By the way, for those suffering through Head of State, you should know in advance that the Shriver Hall scene doesn’t appear until the very end of the movie and then plays through the credits.

Johns Hopkins was a prettier more "college-y" campus, so it got cast over Harvard in "The Social Network."
More like Johns Hopkins, Fall 2009.  Johns Hopkins was a prettier more “college-y” campus, so it got cast over Harvard as Harvard in “The Social Network.”

Winter Q-BIO Quantitative Biology Meeting February 15-18, 2016

Bookmarked Winter Q-BIO Quantitative Biology Meeting February 15-18, 2016 (w-qbio.org)
The Winter Q-BIO Quantitative Biology Meeting is coming up at the Sheraton Waikiki in Oahu, HI, USA

A predictive understanding of living systems is a prerequisite for designed manipulation in bioengineering and informed intervention in medicine. Such an understanding requires quantitative measurements, mathematical analysis, and theoretical abstraction. The advent of powerful measurement technologies and computing capacity has positioned biology to drive the next scientific revolution. A defining goal of Quantitative Biology (qBIO) is the development of general principles that arise from networks of interacting elements that initially defy conceptual reasoning. The use of model organisms for the discovery of general principles has a rich tradition in biology, and at a fundamental level the philosophy of qBIO resonates with most molecular and cell biologists. New challenges arise from the complexity inherent in networks, which require mathematical modeling and computational simulation to develop conceptual “guideposts” that can be used to generate testable hypotheses, guide analyses, and organize “big data.”

The Winter q-bio meeting welcomes scientists and engineers who are interested in all areas of q-bio. For 2016, the meeting will be hosted at the Sheraton Waikiki, which is located in Honolulu, on the island of Oahu. The resort is known for its breathtaking oceanfront views, a first-of-its-kind recently opened “Superpool” and many award-winning dining venues. Registration and accommodation information can be found via the links at the top of the page.

Source: Winter Q-BIO Quantitative Biology Meeting

Shinichi Mochizuki and the impenetrable proof of the abc conjecture

Read The biggest mystery in mathematics: Shinichi Mochizuki and the impenetrable proof of the ABC Conjecture (Nature News & Comment)
A Japanese mathematician claims to have solved one of the most important problems in his field. The trouble is, hardly anyone can work out whether he's right.

The biggest mystery in mathematics

This article in Nature is just wonderful. Everyone will find it interesting, but those in the Algebraic Number Theory class this fall will be particularly interested in the topic – by the way, it’s not too late to join the class. After spending some time over the summer looking at Category Theory, I’m tempted to tackle Mochizuki’s proof as I’m intrigued at new methods in mathematical thinking (and explaining.)

The abc conjecture refers to numerical expressions of the type a + b = c. The statement, which comes in several slightly different versions, concerns the prime numbers that divide each of the quantities a, b and c. Every whole number, or integer, can be expressed in an essentially unique way as a product of prime numbers — those that cannot be further factored out into smaller whole numbers: for example, 15 = 3 × 5 or 84 = 2 × 2 × 3 × 7. In principle, the prime factors of a and b have no connection to those of their sum, c. But the abc conjecture links them together. It presumes, roughly, that if a lot of small primes divide a and b then only a few, large ones divide c.

Thanks to Rama for bringing this to my attention!