Paul Raff

This is the first lesson in your calculus course. Get comfortable with the basics, or they will come back and bite you every single time.

First off, remember your rules for manipulating equalities and inequalities:

1. You can add/subtract whatever you want to each side of an equality or inequality. So if you have something like
   
   then you can, for example, add 3 to both sides to end up with
   
2. You can’t multiply/divide by zero on each side of an inequality! Dividing by zero is always shunned, but multiplying by zero is useless since it turns both sides of the equation to zero. It’s a black hole, and there’s no going back.
3. You can multiply both sides of an equation by any number, but you must flip the inequality if multiplying by a negative number! So if you have something like
   
   then you can divide both sides by -3, but you need to remember to flip the sign to end up with
   

Second, know your functions and know what they look like. Use the first widget to look at some very common functions, and use the second to play around by plotting whatever functions you want.

The math is coming back.

Wolfram:Alpha will be my lovely assistant. It has a lot of widgets, like this one:

Zach Samuels and I wrote a paper for the 2010 MIT Sloan Sports Analytics Conference, and we’re going this weekend to present it. This is the first year that they had an academic paper portion of the conference, so we’ll see how it goes.

Our paper deals with head-to-head sports fantasy leagues, where managers compete against each other, usually during a week. In a head-to-head matchup, the competing managers try to best the other in a majority of the statistical categories that are being fought for by the players on their teams. A naive strategy, probably implemented by the vast majority of fantasy managers (myself included), attempts to simply pick the best players available in the draft, which roughly corresponds to just aiming to be good at all statistical categories. What we showed, however, is that there are many strategies involving “punting” (i.e. not caring about) categories that defeats this naive strategy.

What I have now is a large (and ever-growing) data set from these simulations that I want to analyze further.

For our simulations, we sampled all statistics with a Gaussian Distribution. Truthfully enough, the lack of time before the paper deadline was a large reason I stuck to this, but it’s time to consider what is more appropriate. For example, here are the career points statistics for Kobe Bryant (thanks to Google Charts and my nifty Java back-end for it):

So you see, a normal distribution looks feasible, especially when you take out the zero-point games, most likely games he didn’t play in at all. However, for other statistics, especially low-valued statistics (like turnovers), the situation is a little different:

This histogram SCREAMS binomial distribution (with p = .35 or thereabouts). I may just have to punt myself and just sample directly from the discrete distribution obtained from all historical data!

With anything in life, the simpler the better. This type of motto is forgotten with the chain rule in most calculus texts, which should really be left as simply the following:

Teaching how to apply the chain rule is, in theory, simple: teach your students to identify when we’re dealing with a composition of two functions, find your outer function f and your inner function g, and go to town. Nevertheless, calculus texts, always fond of killing as many trees as possible, like to pad the section with “generalized” versions of other derivative rules, which are simply specialized versions of the chain rule. For example, the following take up most of Rogawski’s section on the chain rule (it has been modified to use prime notation instead of Leibniz notation):

So now, when approached with a problem, the typical student now wonders whether to use one of five different things, even though it’s always the chain rule.

Thoughts?

Disclaimer: I applied for a job at Google and didn’t get it, after going through what seemed like the largest number of interviews possible. I don’t agree with their decision.

I’ve been dallying around with the Google Chart API for a while now, and think it’s a great tool to incorporate analytical data into websites, as the current state of mainstream data visualization is lacking. I just noticed that you can do LaTeX code quickly and easily, like the following:

It says you need to know TeX, but it looks like they are actually using LaTeX. What we really need now, however, is an online LaTeX editor, something akin to Google Docs for the scientific world (although there are still too many of you biology and chemistry folks that still use Microsoft Word). This is the project I wanted to work on under Google’s support, and I know it would have made them billions of dollars. I guess I’ll have to go it alone, along with the other reader of this blog!

Now I can start doing what I have wanted to for a while – talk about teaching mathematics on this blog.

I am a big fan of getting things on the cheap. That’s why I’ve been a fan of Woot! for quite a while now. They’re great for many reasons, and I just love the efficiency of the idea: manufacturers (ahem, iRobot) have too much of some loot, and there are a bunch of suckers out there. So lower the price to some sweet amount, and get rid of your goods.

This method doesn’t seem to work well with flowers, though. I ordered some for my boo, mainly because I was lazy and we’re more focused on the impending arrival of Pete and Tiffany. However, they didn’t come. So I wrote to Woot:

I ordered the Valentine’s woot on Monday with the order number in the title, and it hasn’t come yet. Being that I was guaranteed delivery *before* Valentine’s Day and that the tracking confirms this didn’t happen, I’m hoping to get a refund/credit+ for woot . . .

My response? Lacking, at best:

I’m very sorry, it looks like the order was held up because of weather issues. I have refunded your shipping.

Refunded the $5 shipping? Great! I gave them one more chance to make the correct decision before my credit card company does it for me. Lessons learned:

• Don’t buy flowers online.
• (Applicable in other areas) A lot of goodwill built up over years can still easily vanish.

I had the following interesting email thread with a person today (name omitted for privacy):

(12/7/2009 8:55PM) Person A:

If they are still available, Id love to buy both.

Thanks,

Person A

(12/8/2009 9:18AM) Me:

Hi Person A,

Thanks for your email. I have one marked to be sold on Friday, but if you can come tonight (after 9pm, though) then I’ll sell both. Otherwise, as I’ll be gone Wednesday and Thursday, I’ll have to wait to see if the other person will come buy one (I am fairly confident he will come) – if you can’t make it tonight but still want one of them, I’ll sell it for $15 instead of $20.

I live very close to the corner of Front and Catherine. Hopefully that made sense. Let me know about tonight. Thanks again!

[paul]

(12/8/2009 1:31PM) Person A:

Paul,

I could definately do tonight. I’ll take both. This is a gift for someone. What else do I need? The game? Any game in particular for these?

Thanks,

Person A

(12/8/2009 1:34PM) Me:

Hi Person A,

Thanks for your email. These guitars work specifically with the Guitar Hero set of games, and I am pretty sure (but not certain) that they don’t work with the Rock Band set of games.

So – pretty much you want to get any of the Guitar Hero games. I don’t have anything else – I used to have it, but I turned in my games in a double-reward turn-in offer and sold the Wii system on ebay.

So – give me a time when you’ll come tonight and I’ll verify. Then call me at my mobile below when you’re there, and I’ll come out with the goods.

[paul]

(12/8/2009 3:05PM) Person A:

Paul,

F rock band! I like guitar hero. I am a stand up comic and your last email prompted me to write 5 minutes on how buying ANYTHING on craigslist feels like a drug deal. Maybe it was your use of the word “goods” or maybe it was because the last player piano I bought was filled with hash.

Expect me around 9 on the money.

(12/8/2009 4:01PM) Me:

Hi Person A,

Ha – very good then! See you at 9.

[paul]

Interesting, huh? Well, maybe it’s boring. Regardless, it’s different, and it has made me think about the differences in discourse via Craigslist, as opposed to “normal” e-mail discourse (whatever that is).

So, I am asking everyone to submit to me (via email to paul@myraff.com) their own Craigslist threads for the sale of a certain item. It can be in whatever format you want – I will do the parsing – but you can be assured of the following, if you don’t do it yourself:

1. Names will be masked.
2. Contact information will be masked.
3. Specific home addresses will be masked.

What I hope to do is create a corpus of roughly 5000 email threads for the items and do a linguistic analysis of the text. Sadly I can’t go straight to Craigslist since all they do is arrange for the sending of the first email, and they are gone after that.

I find myself constantly finding the same code over and over again, so they will start getting posted. To start off, here’s how to take a Document Object Model (XML Document) and convert it to a String:

TransformerFactory transfac = TransformerFactory.newInstance();
Transformer trans = transfac.newTransformer();
trans.setOutputProperty(OutputKeys.OMIT_XML_DECLARATION, "no");
trans.setOutputProperty(OutputKeys.INDENT, "yes");
StringWriter sw = new StringWriter();
StreamResult result = new StreamResult(sw);
DOMSource source = new DOMSource(doc);
trans.transform(source, result);
return sw.toString();

One of my credit cards was compromised yesterday. With my wife, that now comes to three in the past year, and I view it as a way of life at this point, as I check my transactions online daily and can spot discrepancies quickly. Being on a graduate student salary, I don’t have much to lose!

The compromise was easy to spot, as I got confirmation emails from Microsoft thanking me for the purchase of an XBOX Live Gold Account, 10000 Microsoft Points (valued at $125), and two games. It seems that the thief not only had my credit card information, but my email address also, which isn’t surprising.

What is surprising is the clearly outsourced capability of Microsoft to deal with the matter. When I called Microsoft to inform them of this issue, the lady on the other end seemed incredulous that an account could be opened in my name that I didn’t open myself, and it took about 20 minutes to get the Gold Account canceled. She said I would have to dispute the charges with my bank, which I had already done in 3 minutes.

Not only that, but the culprit potentially may not be too bright, based on the email confirmation I received of the cancellation:

Billy Ver? Billy Ver? Facebook brings up a few options, but nothing worth pursuing.

I emailed Microsoft with all of this information (ticket number 1109336330), asking them to investigate. We’ll see what happens. Stay tuned.