what is the maximum dollars one is allowed to travel to the usa with.?

I think it's 10,000 without having to declare it. You can bring more, however you have to report that.

Money and Other Monetary Instruments

You may bring into or take out of the country, including by mail, as much money as you wish. However, if it is more than $10,000, you will need to report it to CBP. Ask the CBP officer for the Currency Reporting Form (FinCen 105). The penalties for non-compliance can be severe.

“Money” means monetary instruments and includes U.S. or foreign coins currently in circulation, currency, traveler’s checks in any form, money orders, and negotiable instruments or investment securities in bearer form.

I don't believe there is a maximum but you must declare any amount over $10,000