I have heard I can deduct my expenses for prospecting and mineral collection. I was told it was expenses for equipment and possibly travel.

Yes, you may be able to deduct expenses for prospecting and mineral collection if the activity is a business and not a hobby. 

How do you distinguish between a business and a hobby?

In making the distinction between a hobby or business activity, take into account all facts and circumstances with respect to the activity. A hobby activity is an activity not done for profit. This includes activities done mainly for sport, recreation, or pleasure. No one factor alone is decisive. You must generally consider these factors in determining whether an activity is a business engaged in making a profit:

• Whether you carry on the activity in a businesslike manner and maintain complete and accurate books and records.
• Whether you have personal motives in carrying on the activity.
• Whether the time and effort you put into the activity indicate you intend to make it profitable.
• Whether you depend on income from the activity for your livelihood.
• Whether your losses are due to circumstances beyond your control (or are normal in the startup phase of your type of business).
• Whether you or your advisors have the knowledge needed to carry on the activity as a successful business.
• Whether you were successful in making a profit in similar activities in the past.
• Whether the activity makes a profit in some years and how much profit it makes.
• Whether you can expect to make a future profit from the appreciation of the assets used in the activity

Generally, if the IRS classifies your business as a hobby, it won't allow you to deduct any expenses or take any loss for it on your tax return.  If you prospecting and mineral collection activities are considered a business then you can deduct expenses to offset income.

This link When the IRS Classifies Your Business as a Hobby has information you may find useful.