In the Wall Street Journal’s (7/17, Ip) Careers column, Greg Ip writes, “A four-year college degree, seen for generations as a ticket to a better life, is no longer enough to guarantee a steadily rising paycheck.” Since “the economic expansion that began in 2001 and now appears to be ending, the inflation-adjusted wages of the majority of U.S. workers didn’t grow, even among those who went to college.” According to the “government’s statistical snapshots,…the typical weekly salary of a worker with a bachelor’s degree, adjusted for inflation, didn’t rise last year from 2006 and was 1.7 percent below the 2001 level.” Ip explains that “[c]ollege-educated workers are more plentiful, more commoditized, and more subject to…downsizings.” Employers seek workers with skills that are “more narrow, more abstract, and less easily learned in college.” Also, “today’s college graduates are far more likely to be competing against educated immigrants and educated workers employed overseas.” Ip concludes, “In short, a college degree is often necessary, but not sufficient, to get a paycheck that beats inflation.”

There is no question that earning a doctorate degree creates more career opportunities both in terms of salary eligibility and type of employment. Unfortunately, these opportunities come at the price of many years of foregone labor market earnings. Many doctorate degree candidates are unable to find work in their field while they are actively pursuing their degree, which can lower earnings even further over the course of their academic career. In addition, doctorate degree programs are expensive, and often require candidates to borrow substantially in order to complete them. On the positive side, however, lost earnings, even if invested at the time they are earned, are more than likely to be compensated and eventually surpassed in the years immediately following graduation. As for the price of earning a doctorate degree, student loan providers generally offer very reasonable interest rates compared to other lenders and allow students to repay over the course of many years, usually without requiring any payment until graduation.

According to the U.S. Census Bureau, doctorate degree holders will earn, on average, just under one million dollars more than their masters degree holding counterparts over the course of their working lives. If financial incentive were the only consideration, doctorate degree holders would have sufficient justification to pursue advanced degrees. Often, however, the career aspirations of highly skilled individuals in general, and in particular doctorate degree holders, can’t be measured by salary alone. They often attach great significance to the opportunities that a doctorate can provide, such as the ability to do a type of work they care about and for which they have been trained. For that reason, no single measure can satisfactorily describe the doctoral labor market.

Unemployment figures for those holding doctorate degrees favor higher education. Doctorate degree graduates are almost always several points below the national unemployment average. This is hardly surprising considering the lack of qualified individuals for upper echelon positions. As education requirements for employment rise, competition often declines.

Considering the more prevalent positive effects that earning a doctorate degree can have on one’s career, via future earnings, employability and job satisfaction, the negatives associated with obtaining a PhD become somewhat inconsequential. This is especially true if one looks at the overall period for which a doctorate is a valuable resource, as opposed to the years spent earning it. Those who achieve this educational milestone will be able to reap the benefits for a lifetime.

By Search for Classes
Published: 7/28/2006

This is a great little applet to graph equations.  It has saved me quite a few times.

http://www.walterzorn.com/grapher/grapher_e.htm

Here is one of the questions from my Programming Languages homework which took me a bit of thinking to figure out.  The answer, is of course, surprisingly simple and straightforward (as most correct answers are).  I hope this helps someone.  Don’t cheat, make sure it makes sense to you before just copying it.

Q:  Write a grammar for the language consisting of strings that have n copies of the letter a followed by the same number of copies of the letter b, where n > 0.  For example, the strings ab, aaaabbbb, and aaaaaaaabbbbbbbb are in language but a, abb, ba, and aaabb are not.

A:
        <S> -> <A>
        <A> -> a<A><B> | a<B>
        <B> -> b 

Proof:
aaaabbbb
<S>                -> <A>
                      -> a<A><B>
                      -> aa<A><B><B>
                      -> aaa<A><B><B><B>
                      -> aaaa<B><B><B><B>
                      -> aaaab<B><B><B>
                      -> aaaabb<B><B>
                      -> aaaabbb<B>
                      -> aaaabbbb

aaabb
<S>          -> <A>
                      -> a<A><B>
                      -> aa<A><B><B>
                      X -> aaa<A><B><B><B> OR aaa<B><B><B>

Edit: 7.27.2007

So the simpliest correct answer is:

<S> -> a<S>b | ab

NiCE!  It seems I over complicate even the easiest things