"My wonderment and question to you is: Has “science” attempted to prove that UFO’s exist?
If scientists have not even studied the subject matter then how can they determine one way or another?"

What do you think SETI is?
But a means of providing proof.

And there would been advantage in terms of national security if one could actually contact the UFOs if they were visiting this planet- so wouldn't be surprising if quite few scientists were given this task.
One rather famous one was Project Blue Book:

"Project Blue Book was one of a series of systematic studies of Unidentified flying objects (UFOs) conducted by the United States Air Force (U.S.A.F.). Started in 1952, it was the second revival of such a study. A termination order was given for the study in December 1969, and all activity under its auspices ceased in January 1970.

Project Blue Book had two goals: to determine if UFOs were a threat to national security, and to scientifically analyze UFO-related data. Thousands of UFO reports were collected, analyzed and filed. As the result of the Condon Report, which concluded there was nothing anomalous about any UFOs, Project Blue Book was ordered shut down in December 1969. This project was the last publicly known UFO research project led by the USAF.[1]"
http://en.wikipedia.org/wiki/Project_Blue_Book

And other govt did similar projects.

"I can not debate the existence of ghosts since I have not studied that subject matter, but I have studied the subject of UFO’s and I feel that more study of such aircraft can lead to very interesting developments.

At this point I expect that you ask for my qualifications in this area of research."

No, you could be goat herder.

"I could give you a long list that would indicate my proficiency in various sciences, but on the internet I could say anything at all, and if you could not verify the info it would make no difference in the outcome of our debate.

So, instead of giving you a long list that you would not believe anyway, I will simply point to some information that is relevant to the subject matter and you can judge for your self if my contention that UFO’s are worth studying is right or wrong."

I'm not debating it.
I simply have not seen anything I consider conclusive.
All that is needed one.

Mountains of fuzzy pictures doesn't prove anything. Granted someone might need to wade mountains of crap in order to find something of value. But I have little interest in doing this nor is there any value to me in a piles of maybes.
The result of Science is not here are 10 possible answers.
When the UN gives six possible answers- that ain't better than one. But instead it's a statement that all 6 are probably wrong- after all, 5 out 6 of their "scientists" say it's wrong.

If you have spent enormous amount time wading through this junk and you imagine you confidence that UFO are real. This should **mean** you can pick the evidence which proves your point the best. And if this doesn't convince people and it can shown to problematic, then by own selection, all the rest is crap.