UPDATE: For more from me about T-SQL Window Functions, check out my Pluralsight course!

I have been speaking and writing a bunch lately on T-SQL window functions. There is always more to learn, it seems.

Framing for many of the window functions was introduced with 2012. It is very important to understand how framing works from both a performance and logical perspective. The default frame is RANGE BETWEEN UNBOUNDED PRECEDING AND CURRENT ROW. If you don’t specify a frame where it is supported this is what you will get. Using this default will give you worse performance than if you specify ROWS BETWEEN UNBOUNDED PRECEDING AND CURRENT ROW. It might also give you results that you do not expect as well.

Window aggregate functions were introduced with 2005 and supported only the PARTITION BY option in the OVER clause. This allows you to add summary calculations without losing detail. In…

Importance on the Web

As a society living in the “Information Age,” it comes as no surprise that we are faced with the task of sorting through vast oceans of content. With the admission that most content is actually junk, we must wisely choose the objects of our analysis. The appropriately named site UselessJunk.com certainly doesn’t deserve the same attention as the BBC World News page, and yet within the monstrous heart of the internet, it requires the maturity of the human psyche to discriminate their relative worth.

However, as with many real-world systems, there is a method to the madness. We have the following two important observations to inspire our quest:

• The internet is a human construction, and hence
• The internet intrinsically reflects some level of human interest in its content.

If the second statement is true, that the internet somehow reflects what information people want to absorb (or…

In the last post, I talked about imaginary numbers, complex numbers, and how to use them to rotate vectors in 2d.

In this post, I want to share another interesting type of number called a “Dual Number” that uses the symbol ε (epsilon) and has a neat trick of automatically calculating the derivative of a function while you calculate the value of the function at the same time.

Dual numbers are pretty similar to imaginary numbers but there is one important difference. With imaginary numbers, i^2 = -1, but with dual numbers, ε^2 = 0 (and ε is not 0!). That may seem like a small difference, but oddly, that opens up a whole interesting world of mathematical usefulness.

Before we dig into automatic differentiation, I want to go over the mathematical basics for how dual numbers behave.

Basic Dual Number Math

Adding dual numbers is the same as adding…

My new book, Probability and Statistics for Data Science: Math + R + Data, pub. by the CRC Press, was released on June 24!

This book arose from an open-source text I wrote and have been teaching from. The open source version will still be available, though rather different from the published one.

This is a math stat book, but different from all others, as the subtitle states: Math + R + Data. Even the topic ordering is rather different, with a goal of bringing in data science-relevant material as early as possible.

I’ve placed an excerpt from the book at http://tinyurl.com/y6hf7x66. I believe it epitomizes the intent and style of the book. Also, I’ve placed the front matter at http://tinyurl.com/yy9hx6db