In light of being a "math and science guy", I think I have good spelling and grammar skills. There are way too many people on the internet these days who can't put together a damn sentence. Hell, I've even seen manufactured products with glaring spelling mistakes. Talk about no QA! I'm not claiming that my punctuation and grammar are flawless, but let's review a few things.

You're = contraction for "you are"
your = possessive, as in "That is your fucking problem"
ur = I don't care how cute this looks on an internet post. It's not "you are" and it's not "your". It's "urrrr", and it's not a fucking word.

it's = "it is"
its = possessive, as in "The dog licked its balls." You don't put an apostrophe here for the same reason you don't put one in "his" and "hers".

there = a location
their = possessive
they're = "they are"
An example that uses all three: "They're overe there, showing each other their vaginal rashes."

Some general rules: