Don't forget that every year divisible by 4 is a leap year, except that century years are only leap years if divisible by 400 (e.g., 2000 was a leap year, but 1900 was not).
Another question in my homework.. not really sure how to go about solving it... It there some sort of method to solve this using modular arithmetic?
First you need to calculate the number of days of the last $1014$ years.
That is $365\times 1000 +$ the number of leap years over the last $1014$ years (not necessarily 1014/4!)
Once you found that, divide by $7$ and you will obtain a remainder between $0$ and $6$.
Today is Friday/Saturday (depending on your time zone), add the remainder to today's day and you're done.