Can you give me some examples of Mathematical Investigatory Project? Badly needed...?

Answer 1

1. Why not investigate the Fibonacci numbers and
how they occur in nature? Also investigate their
mathematical properties.

2. Investigate the 3x + 1 problem. It has a huge
body of literature associated with it.
There is even a paper by Schorer at occampress.com
which claims to have a proof of this problem.