Archive for January, 2012

With the news today about a proposed overhaul of college financial aid that would create a dependence between aid programs and the affordability of an institution, there is a sense that the trend of migrating more collegiate-level education to the online classroom will continue at an accelerated pace.

In order for an educational institution to improve affordability and value for students, they drastically need to either cut costs, improve enrollment using the same resources, or both. Online education has the potential to reach whole new markets around the world, as shown by the recent example of Sebastian Thrun‘s class Introduction to Artificial Intelligence. The Stanford professor allowed anyone to enroll for the class for free and taught the exact same course material and handed out the same homework assignments as the paying students. The response was overwhelming, to the tune of more than 160,000 students world-wide. Some students created an online study group on the aggregation website Reddit. Here is NPR’s story about Thrun’s class on All Things Considered.

That this is more affordable to an institution is unquestionable. Once the lectures are recorded, universities need only provide the server capacity to handle student clients from all over the world. Online tests and homework assignments make the job of grading that much easier. Humans need not be involved once everything is in place.

The benefits of online education are numerous, but two points stand out above the rest: the lowering of educational costs, and the ease with which quality education will reach parts of the world (and the country) where this was not possible before. One of the greatest causes for concern with a young family is the kids’ college fund. Wages have to keep up not only with inflation, but with already-astronomical and still rising educational costs.

Thrun’s experiment in reaching students around the world made him realize the importance of reaching such a wide and socio-economically disadvantaged audience. He has now started an online university called Udacity, offering free online coursework to anyone around the world. Other initiatives have been in place for longer, such as the Khan Academy, MIT’s OpenCourseWare initiative and the OpenCourseWare Consortium.

Initiatives like these indicate that the established providers of quality education are about to see a rapid rise in competition for students and their tuition fees. As the competition heats up, there is a push for more conventional universities to shift to a more technology-driven curriculum in order to lower their cost-per-student. It may be easy to dismiss faculty concerns as threats to entrenched interests, but there are some genuine concerns.

Once the material has been recorded and uploaded, universities have little incentive to update the material as often, given the relatively higher cost to re-record lectures and keep the material fresh. There would be a disturbance in the environment that fosters bidirectional exchanges of ideas and the organic atmosphere between students and instructors that tends to improve lecture styles year-over-year. The material and focus of the lectures may not be as dynamic and responsive to student needs as the semester progresses. Finally, there would be a threat to the teaching profession as fewer professors are hired, reducing the amount of fundamental research done at the university.

Indeed at Stanford University itself, there is a renewed sense of urgency to provide a more diverse portfolio of online coursework such as their Center for Professional Development and the Stanford Engineering Everywhere programs. It remains to be seen whether the online classroom will ultimately prove to be a great boon to education, but it is clear that the upside in the short-term far outweighs the downside.

Read Full Post »

An even faster Fourier transform

A group of MIT researchers have found a way to speed-up the fast Fourier transform for certain types of input data. The technique is described in an unpublished paper, which can be downloaded at this link.

From their abstract:

We consider the problem of computing the k-sparse approximation to the discrete Fourier transform of an n-dimensional signal. We show:
• An O(k log n)-time algorithm for the case where the input signal has at most k non-zero Fourier coefficients, and
• An O(k log n log(n/k))-time algorithm for general input signals.
Both algorithms achieve o(n log n) time, and thus improve over the Fast Fourier Transform, for any k = o(n). Further, they are the first known algorithms that satisfy this property. Also, if one assumes that the Fast Fourier Transform is optimal, the algorithm for the exactly k-sparse case is optimal for any k = nΩ(1).
We complement our algorithmic results by showing that any algorithm for computing the sparse Fourier transform of a general signal must use at least Ω(k log(n/k)/ log log n) signal samples, even if it is allowed to perform adaptive sampling.

Read Full Post »

Logic and madness

What do Bertrand Russell (philosopher, logician and mathematician), Gottlob Frege (the great logician), Georg Cantor (inventor of set theory), David Hilbert (inventor of Hilbert spaces), Kurt Gödel (guru of incompleteness theory), Ludwig Wittgenstein (god of 20th century philosophy), the Greek city of Athens, the Oresteian trilogy and a dog named Manga all have in common?

They all star in the 2009 graphic novel Logicomix: An Epic Search for Truth, written by Apostolos Doxiadis and Christos Papadimitriou, drawn by Alecos Papadatos and colored by Annie Di Donna. It’s a rip-roaring tale of passion and madness, mixing fiction and reality, with frequent breaches of the fourth wall, and all presented through bright and colorful art and word balloons. For anyone interested in Logic, Mathematics or Philosophy, it presents Russell’s maddening journey during his quest for establishing the foundations of mathematics through logical certainty. It was during this journey that Russell, along with Alfred North Whitehead, wrote their seminal three-volume work, Principia Mathematica.

I first read about the book in the New York Times’ Sunday Books Review way back in the fall of 2009, but was only able to read it during a recent vacation. The story is engaging and entertaining, with just enough provocation for those who are more theoretically inclined to continue learning about these pioneer logicians beyond the pages of the book itself. The art is very reminiscent of Hergé’s ligne claire drawing style. Highly recommended.

Read Full Post »