ZZ Top and the Heroes of Mathematics

My summer reading, , follows the mathematical discoveries and subsequent works of Joseph Lagrange, Leonhard Euler, Adrien Legendre, and Carl Gauss.  My goal in mathematics is to make the kinds of significant discoveries that these mathematicians made.

Euler lived in the 18th century; he proved some theorems about primes of the form which had been conjectured in the 17th century by another famous mathematician, Pierre de Fermat.  Lagrange, who succeeded Euler as the director of the Prussian Academy of Sciences, and Legendre both studied quadratic forms and their applications to Euler’s work.  One of the applications of the theory of quadratic forms is to generalize Euler’s proofs.  However, Legendre developed the theory in a much more modern and natural way.  In addition, he made significant developments in the theory of quadratic reciprocity.  Finally, Gauss synthesized all of the above ideas.  He is widely considered to be the finest mathematician ever. 

I am fascinated by who these famous mathematicians were, whereas during my engineering studies I was more interested in the how and why questions.  For example, there is a famous result in algebraic number theory credited to Ernst Kummer: the number field generated by the 23rd root of unity does not have unique factorization while the number fields generated by the nth root of unity for , had all been found to have unique factorization.  My question was, “how the heck was Kummer able to figure this out?” to which my professor responded, “…he was some kind of genius.”

I may not be a genius in the same class as Kummer and Gauss, but I wouldn’t be studying mathematics if I didn’t enjoy it or if I didn’t think I could be successful in it.  I hope one day, I will be in a position to make a significant mathematical discovery on par with the heroes of mathematics.

 

A Voting Philosophy

A friend of mine recently wrote a blog post entitled,  “Know Your Politicians or Stay Home.”  I agree with my friend’s premise that if one knows nothing about either or any of the candidates in a political race, one should not vote, for how can one make an informed choice?  In the opposite extreme, only a few people close to politics will have perfect information about even one candidate. 

I recall an article a few years back which seemed to decry the fact that people were too busy in their daily lives – preparing their kids to school, etc… – to really get into the upcoming election.  Elections are not important enough that people should alter their lives in order that they can study the candidates in depth.  However, there is so much information, albeit limited information, readily available on a daily basis about political candidates.  I believe it is reasonable to make a choice based on this limited information.

In a perfect world, a voter would examine the world view of each candidate, and choose those whose world views are a close match to his own.  The final choice would be based on how well each candidate would perform his job.  To evaluate a candidate’s world view, one needs to pay attention to what he says and does, although it is hard to determine precisely a candidate’s intent and character from his actions and words.  To evaluate how well a candidate would perform his job, one should look at past performance.  However, accurately evaluating a person’s job performance is difficult.

Often what a candidate says, or what is said about a candidate, can convey information about the candidate’s world view or his suitability for the job.  I’ve argued that Barney Frank’s own words show that he is not suited for Congress.  This New York democrat has been endorsed by noted white supremacist David Duke, revealing information about his world view.

Legislators have public voting records that can be used to evaluate candidates for a legislative position.  Judges have public records of their decisions on legal cases.  In California, we have propositions on our ballots.  Here, the law of unintended consequences rules – the California bullet train, which is bogged down with lawsuits and money trouble, came out of the proposition process. 

Presidents and governors are often judged by the economic or social health of the country or state.  This is not completely fair, but it is reasonable.  Bill Clinton was re-elected to a second term because the United States had been experiencing a period of prosperity.  However, the Monica Lewinsky scandal showed poor judgment.  If the scandal had occurred during his first term, Clinton would not have had such an overwhelming victory.

In summary, there is a wealth of information – though most likely incomplete information – available about candidates’ characters, past performances, abilities, etc…  It is reasonable to use this incomplete information coupled with logical thought and reflection about the information to make a choice on election day.

Watts Up With That?

There’s more ugliness like what went on recently with Oregon State University. This professor exposed corruption within the California University system that had ties to the California Air Resources Board’s botched PM2.5 rules. As we’ve seen recently, this PM2.5 regulatory action is so vile that the EPA does unannounced human experimentation.

From WND:

What’s academia’s response to a whistleblower who exposes fraudulent research and faked credentials on a panel of experts?

Fire the whistleblower, of course.

That’s the allegation in a new complaint filed against the regents of the University of California by the American Center for Law and Justice on behalf of former professor James E. Enstrom.

The lawsuit explains that Enstrom was a UCLA research professor for decades – until he blew the whistle on “junk environmental science and scientific misconduct at the University of California” and was dismissed.

“The facts of this case are…

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Extracurricular Mathematics

This summer, I am working on two math projects outside of school.  I am doing this because there is so much to learn in mathematics, and because it is fun!

The first project is a book: .  One of my professors at CSU Channel Islands recommended it as a “lovely” book.  I am reading through it and solving the problems at the end of each chapter.  An exciting thing I learned: the group of reduced positive definite quadratic forms with a given discriminant, D, is isomorphic to a subgroup of the ideal class group of the quadratic number field with the same discriminant, D.  This was a surprising result because it was not immediately clear to me how quadratic forms, the subject of chapter two of Primes…, were connected to quadratic number fields, a topic we learned in Algebraic Number Theory spring semester.

I am also developing ideas for a paper to be published in The College Mathematics Journal.  The theme is the mathematics of planet Earth.  I need to choose a topic soon; I am leaning towards an environmental topic like ecology or wind energy because I deal with those in my day job.  Actually, I’ve developed some methods at work for modeling wind energy production.  I hope to incorporate these in my paper.

The above two projects will keep me busy and out of trouble during the summer.  Hopefully, I’ll learn some more new things.  Feel free to share below what projects you have taken on this summer.

Barney Frank and His “Hoodie” Comment

At the University of Massachusetts Dartmouth graduation ceremony last month, Barney Frank said the following about a man, Hubie Jones, who had received an honorary degree: “Hubie, I think you have a hoodie you can wear and nobody will shoot at you.”  Mr. Frank has issued an apology for his remark, which in today’s culture is akin to a free pass.  But not on this blog.

Barney’s Apology

Obviously, Mr. Frank was referring to the Trayvon Martin shooting.  The facts of that case will be shown at trial, but the evidence made public thus far does not suggest that Trayvon Martin was shot because he was wearing a hoodie.  At least one prominent lawyer agrees:

Alan Dershowitz Weighs in on Trayvon Martin Shooting Case

Not only wrong on the facts, Mr. Frank’s comment was also patronizing.  By implying that a chief benefit of a college degree for a black man is to protect him from being victimized because of his race would seem to be insulting to black people as well as to those who would better themselves by pursuing higher education.  What is it about people like Mr. Frank who make these types of asinine comments with the intent of portraying themselves as racially sensitive?

Too often, people in public service like Mr. Frank who have made comments like the above – comments that reveal their lack of both awareness  and depth of thought – are given a free pass by their employers.  In this case, Mr. Frank’s employers have been the voters in his Massachusetts district.  However, since he is retiring this year, Massachusetts voters will not have the chance to fire him.

The Political Culture and Abortion

There is a woman named Julia Brownley who is running for United States congress in my district which includes parts of Ventura County.  Her commercial lists her pro-choice stance first among her attributes and the reasons we should vote for her.  The zeal with which she and other recent candidates have proclaimed their pro-choice stances begs the following question: have politicians and their constituencies crossed the line from being pro-choice to being pro-abortion?

Abortion is a horrible thing.  The fact that abortion is a legal practice in the United States does not make abortion less horrible.  At the very least, abortion takes away from the pool of America’s future thinkers, writers, and innovators.  At its worst, abortion can be a vehicle for the practice of eugenics,as exemplified by this well-publicized Live Action report on sex-selective abortions:

There is an episode of “Family Guy” in which the baby consoles the dog on his failed love life by saying, “…someday you’ll find a woman who loves abortion as much as you do.”  This is funny because no one likes abortion.  But considering the above, perhaps the baby is right.