How can a manager improve their interpersonal skills?

What math skills will be very useful for a tech/software/search product manager?

• Math skills are useful in, but limited to, understanding the market, metrics, and algorithms. But math is a very big field! For a product manager who wants to improve his/her math so as to become better at his work, where should he start?

• Answer:

  The single most useful math for a product manager is a good intuitive understanding of applied arithmetic, certainly nothing more complex then high school algebra. Of course everyone understands this math to some degree, but most people are not comfortable actually putting it to work for them. A product manager should know the product's numbers by heart and do quick back of the envelope estimations for any prospective change. They should be able to design metrics that properly characterize progress. Here is a simple example of this not working: if you have a "share feature" and you are measuring its success as the number of shares, this is almost certainly misleading if your user base is growing. If your number of shares doubles that sounds good, but if your number of users quadrupled in the same period that means a much lower percentage of users are sharing, which is really bad. Showing a graph of the number of shares is mostly useless without also showing something like "Rate of sharing". This is the kind of utter failure of successful numerical thinking which is, in my opinion, the most likely thing to doom a product or feature. If you have really mastered that and you want to go further, I recommend learning basic statistics and R (http://www.r-project.org). Statistics will advance your data analysis abilities, and R is the intellectual's verison of Excel--it will let you draw gorgeous graphs, put the most sophisticated data analysis techniques at your fingertips, and unlike Excel makes it easy to automate all your analysis. The best way to learn R is to read this book (it is barely 100 pages, covers 95% of what you need to know, and teaches you statistics along the way): http://www.amazon.com/Introductory-Statistics-R-Peter-Dalgaard/dp/0387954759