During a wheel landing touchdown approximately 1000 feet from the approach end of the runway, the aircraft swerved slightly to the left. The student pilot applied right rudder and the airplane "over-corrected to the right." During an attempt to apply rudder to correct back to the left, the student pilot inadvertently applied the left brake. The airplane nosed forward "before any further correction could be made" and the propeller contacted the runway. Subsequently, the airplane nosed over and came to rest inverted.