If an individual buys insurance for less than the full year, e.g. only 3 months out of the 12 months, will the individual be subject to the individual mandate penalty?

The individual will be subject to a penalty for each month the individual does not maintain minimum essential coverage.  However, individuals are exempt from the penalty for short coverage gaps, which is a continuous period of less than 3 months.

If an individual does not have coverage for a continuous period that begins in one taxable/calendar year and ends in the next, for purposes of applying the short coverage gap rules to the first taxable/calendar year, the months in the second taxable/calendar year are not counted.  For purposes of applying the short coverage gap rules to the second year, the months in the first taxable/calendar year are counted.  For example, if the individual lacked coverage from November 1, 2015 until the end of February 2016, November and December of 2015 are treated as a short coverage gap on the 2015 tax return and thus exempt from penalty.  On the 2016 return, however, November and December of 2015 are included in the continuous period that includes January and February 2016. That continuous period is not less than 3 months so, on the 2016 return, January and February of 2016 are not exempt months under the short coverage gap exemption and therefore the individual would be subject to penalty for January and February of 2016.