What Is Research?

October 31, 2009

Math websites falling into disuse?

Filed under: Uncategorized — vipulnaik @ 3:06 pm
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Since I recently blogged about Math Overflow website, I’ve been wondering what happened to various other math websites that once looked promising, and how they’re faring. Some of them seem to be going strong, but none of them seem to have been exploding in popularity.

Tricki

I blogged twice about Tricki, the Tricks Wiki, which went live in April 2009 (see the annoucement by Tim Gowers). Tricki held a lot of promise. Of late, the enthusiasm seems to have slowed down, though this might be a temporary phenomenon. The most recently created article and the most recent comments appear to be two weeks old as of today (October 27, 2009). According to Alexa data, the site has a rank of 1,200,000+ worldwide and about 550,000-600,000 in the United States. For comparison, subwiki.org, which I run, has Alexa data showing a site rank of 500,000-550,000 in the world and 150,000-200,000 in the United States, while Math Overflow has Alexa data showing a rank of 350,000 worldwide and about 60,000 in the United States (the numbers you see clicking on the links may be different if you don’t view this post within a few hours of my writing it).

Tricki also hasn’t been mentioned on Gowers’ blog since June 25, 2009 and on Terence Tao’s blog since August 2009.

Is the Tricki falling into disuse? Clearly, the initial spate of interst seems to have subsided, but it might well regain a slower and steadier momentum in some time.

Planetmath

I remember a time when Wikipedia had much less mathematical content than planetmath, which was one of the first places to check mathematics on the Internet. Planetmath appears to be going strong, though not as strong as before. While their message forum seems reasonably active, their latest addition was about a week ago, and they seem to be getting somewhere between 0 and 2 new articles in a day, and around the same number of revisions a day. Not exactly dead, but not bubbling with life. Their Alexa data indicates fairly steady performance with a traffic rank of around 130,000 over the last six months, but a decline over a longer timeframe — setting the drop-down parameter to “max” below the chart shows that their traffic rank and daily pageviews have been following over the longer run. Why? Decline in quality? Probably not — it’s more likely that people are increasingly using Wikipedia.

October 27, 2009

Are textbooks getting too expensive?

Filed under: Uncategorized — vipulnaik @ 11:26 pm

I recently came across a post by John Baez on the n-category cafe titled Cheaper Online Textbooks?. Baez’s post has a number of interesting links: a piece on “Affordable Higher Education” by CALPIRG, a piece on the legislation based on this report by Capital Campus News, an article in the Christan Science Monitor on the rising cost of textbooks, and a blog post in the Chronicle of Higher Education on an e-textbook program. So, reading about all these posts, I began to wonder: are textbooks getting too expensive? And should anything be “done” about it?

Are textbook prices soaring?

So I decided to look at the range of calculus books. The general impression from the things I read seemed to be that it would be hard to get a decent textbook for under $100. So, I went and typed calculus on Amazon, and looked at the first page of search results. Among these search results was Calculus for Dummies ($12.99), Forgotten Calculus ($11.53), Calculus Made Easy ($26.95), Schaum’s Outline of Calculus ($12.89), and The Complete Idiot’s Guide to Calculus ($12.89). Most of these books would seem reasonable for a low-level introductory semester or two quarters in calculus — admittedly, they may not be suitable for all calculus courses, but if price really is a primary consideration, it isn’t as if there are no options. There is also a wikibook on Calculus and an old public domain book on calculus. If you want somewhat more advanced stuff for free, you can try MIT’s OpenCourseWare course on single variable course, which includes video lectures, their course on calculus with applications, and their course on multivariable calculus.

Okay, so perhaps calculus is a bad example? Well, I decided to pick point set topology. The standard book for this is the second edition of Munkres’ book, which I think is one of the best, and it costs $107.73 on Amazon. But searching for topology on Amazon gives a number of other considerably cheaper books, such as Mendelson ($7.88), Gamelin and Greene ($10.17), Springer Undergraduate Math Series book by Crossley ($23.40), Schaum’s Outline of General Topology ($12.89), among many others. None of them seem as good as Munkres, but they all cover the basic material — and reasonably well, it seems.

Of course, I have picked on calculus and topology, both topics that are more than fifty years old, and where most of the material that should be included in an elementary textbook is widely known. In other words, the field for writing books is wide open. No publisher or author has significant scarcity power. When we are looking at exotic topics such as the theory of locally finite groups, then yes, you probably wouldn’t find cheap textbooks. But most undergraduate-level textbooks would likely be of the level of calculus or topology texts, and not exotic texts on locally finite groups.

Why do instructors choose expensive textbooks when cheaper alternatives exist?

Why do instructors choose $100+ calculus textbooks or Munkres’ topology textbook when there are so many cheaper books available on the market? One explanation, pointed out in a comment to Baez’s post, is the “moral hazard” explanation. This states that instructors do not need to bear the costs of buying the textbooks, so they just prescribe the “best” textbook based on their personal criteria rather than taking the price into consideration.
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October 26, 2009

Polymath again

Filed under: Culture and society of research — vipulnaik @ 10:42 pm
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Timothy Gowers and Michael Nielsen have written an article for Nature magazine about the polymath project (I blogged about this here and here).

In the meantime, Terence Tao started a polymath blog here, where he initiated four discussion threads (1, 2, 3 and 4) on deterministic ways to find primes (I’m not quite sure how that’s proceeding — the last post was on August 28, 2009). (UPDATE: A new post (thread 5) was put up shortly after I published my blog post).

Around the same time, Gil Kalai started a polymath on the polynomial Hirsch conjecture (1, 2, 3, 4 and 5).

Also, some general discussion posts on polymath projects: by Tim Gowers and by Terence Tao.

It remains to be seen whether any of these projects are able to reach successful conclusions or make substantial inroads into the problem. If there is another success for a polymath project, then that would be a major booster to the idea of polymath projects. Otherwise, it might raise the question of whether the unexpected degree of success of the first polymath project led by Gowers (which aimed for, and got, an elementary proof of the density Hales-Jewett theorem) was an anomaly.

Math overflow

Filed under: Uncategorized — vipulnaik @ 10:26 pm
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In recent times, the Math Overflow website has been getting a lot of “press”, which is to say, it has been mentioned in some highly prominent math blogs. It was reviewed in Secret Blogging Seminar by Scott Morrison, who is also involved with Math Overflow, and it was mentioned by quomodocumque, Timothy Gowers, Terence Tao, the n-category cafe and others.

Math Overflow is a website where people can ask math-related questions (the questions should be of interest to people at the level of Ph.D. student or higher), answer the questions, and rate the answers. It uses the Stack Exchange software, which is used for many other websites, such as Stack Overflow. Funding for the website is being provided by Ravi Vakil of Stanford University, and it has a bunch of moderators — but anybody who earns enough points through participation can rise to the status of moderator. For more information, see the Math Overflow FAQ.

Participation on the website has been increasing rapidly since the first post (September 28). Here’s the Alexa data, which seem to indicate that usage has been growing (Alexa is not very reliable for low-volume sites, since it uses a small sample of users and most Math Overflow users may not be using Alexa’s toolbar).

The software and site layout seem well-designed to encourage participation. The long-term performance seems unclear, since a lot depends on how effectively the site is able to allow users to fruitfully explore past questions and answers and discover things similar to what interests them. But, as of now, it has a bunch of interesting questions, and seems to have reached the ears of a lot of people who’re interested in asking good questions and giving good answers.

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