PHP overall. PHP can be used for everything you mentioned.
The login, register, member section are very easy to do - there are many, many resources on the web to help you out.
Creating PDFs using PHP is not a fun task - http://www.fpdf.org/
- that site is your best bet. From experience using it, it is very easy, but very tedious.
Any language can do math.
PS: Should learn Python 2.7