Month: May 2011

Categories
Uncategorized

5/21/2011 Quote of the Day – Why Study Math?

I just came across the following video from WeUseMath.org. The site aims to answer the question “When will I use math?”

Today’s quote of the day is from David Bailey (at 4:52 in the video).

It’s worth doing. It’s something that, I’ve never heard anyone say, “I wish I didn’t take so much math.”

I cannot recall anyone I know expressing regret for taking too many math courses, but I have heard people express regret for taking too few.

I’m reminded of the following quote from Paul Graham.

But while you don’t literally need math for most kinds of hacking, in the sense of knowing 1001 tricks for differentiating formulas, math is very much worth studying for its own sake. It’s a valuable source of metaphors for almost any kind of work. I wish I’d studied more math in college for that reason.

Undergraduation [March 2005]

The video also reminded me of the following quote from Steven Landsburg.

If you enjoy mathematics, and have a knack for it, you cannot go wrong by taking math courses no matter where you think you’re eventually headed. Top-ranked economics Ph.D. programs almost always prefer to admit students with strong math backgrounds over students with strong economics backgrounds; I’m told the same is true in biology and I suspect it’s the same way in many other disciplines. In the economics department where I teach, we frequently admit math majors with few (or even zero!) economics courses on their transcripts; we would never admit an economics major with inadequate math training.

The Big Questions, p. 240 [2009]

Fortunately, with all the free courses available on the internet, it’s now possible to take more math (for free!). Check out the OCW Consortium site for information on available courses. For another example of mathematicians faring well, check out the Wall Street Journal’s 2009 article, Doing the Math to Find the Good Jobs.

Categories
Uncategorized

5/20/2011 Quote of the Day

Today’s quote is from Gilbert Strang.

This is like a grown-up course. I’m figuring you’re here to learn, so it’s not my job to force it. My job is to help it, and I hope this is some help.

MIT 18.085 Computational Science and Engineering I, Recitation 1 (49:18) [Fall 2008]

The quote conveys Strang’s priority to help students learn.

Schooling can sometimes present obstacles that interfere with learning. Credits, requirements, grades, rote assignments and other aspects of school can all distract from learning. While I understand their intended purpose, I suspect that there are ways to minimize such distractions. Treating a course as a “grown-up course” sounds like it might be Strang’s way to mitigate distractions, benefiting the students that are “[there] to learn.”

The distinction between schooling and education is addressed in the following quote, attributed to Mark Twain.

I never let schooling interfere with my education.

I haven’t been able to trace the quote’s origin. The quote conveys Twain’s belief that the objectives and/or outcomes of schooling and education are misaligned.

Categories
Uncategorized

Intuitive Interpretation of Unexpected Binomial Coefficients

This post will give an intuitive interpretation of the presence of the combination formula (which equals the binomial coefficient) in math problem solutions and probability distributions that are seemingly unrelated to combinations. For example, the binomial coefficient shows up in the probability mass function of the binomial distribution and the negative binomial distribution.

Wikipedia has the following definition for combination:

In mathematics a combination is a way of selecting several things out of a larger group, where (unlike permutations) order does not matter. In smaller cases it is possible to count the number of combinations. For example given three fruit, an apple, orange and pear say, there are three combinations of two that can be drawn from this set: an apple and a pear; an apple and an orange; or a pear and an orange. More formally a k–combination of a set S is a subset of k distinct elements of S. If the set has n elements the number of k-combinations is equal to the binomial coefficient

The binomial coefficient indexed by n and k is denoted \tbinom nk. The formula below, for evaluating binomial coefficients, uses factorials.

\binom nk = \frac{n!}{k!\,(n-k)!} \quad \mbox{for }\ 0\leq k\leq n

Continue reading “Intuitive Interpretation of Unexpected Binomial Coefficients”

Categories
Uncategorized

5/19/2011 Quote of the Day

I am going to start posting quotes that I like to my blog. I have been recording quotes that I like for a few years. I will continue to update my list, and use it as a source for quotes to post. A great source for quotes is Bartlett’s Familiar Quotations.

Today’s quote is from Doron Zeilberger.

Whenever I want to learn a new subject, I announce a graduate course in it, since the best way to learn is by teaching. But even better than teaching humans is teaching computers, i.e. program! Since computers will not let you wave your hands and wing it.

Opinion 37 [April 15, 1999]

Also from the same source is the following quote.

In order to understand something really deeply, you should program it.

Opinion 37 [April 15, 1999]

I have never taught a course, so I cannot fully relate to his experience of learning by teaching. However, my unfamiliarity with teaching is one of the reasons that I think that programming is a great way to learn something. While teaching a course requires students, a classroom, a lesson plan, and other constraints, “teaching computers” only requires a computer and a programming language.

Categories
Uncategorized

Installing Your Own Personal WeBWork Server, Part IV

Part I | Part II | Part III | Part IV

This series of posts covers the installation of WeBWork. This post, Part IV of the series, will cover how to configure your WeBWork server so that you can access the 20,000 freely available problems.

… Continued from Part III

The last post of this series, Part III, concluded with an image showing the virtual machine and the WeBWork site loaded on my computer. Let’s pick up where we left off, by loading the virtual machine and pointing our browser to http://localhost:14627/webwork2. It is not necessary to log in to the wwadmin account on the Ubuntu machine, as Apache will serve the web pages without logging in. However, it is necessary that the virtual machine is turned on. The window can be minimized to free desktop space. I should mention at this point that I logged into the wwadmin account a few days ago and updated the machine’s software using Ubuntu’s update manager. I am not exactly sure why, but this caused problems with the WeBWork installation (i.e., I received errors when trying to use the site), so I reverted to an earlier snapshot of the virtual machine. I wanted to mention this in case you were considering upgrading the software. An upgrade of the WeBWork software would possibly solve the issues that I was having, but I have not tried this yet.

Continue reading “Installing Your Own Personal WeBWork Server, Part IV”