(a) In addition to land and minerals granted to the permanent school fund under the constitution and other laws of this state, the permanent school fund shall include:
(1) the mineral estate in river beds and channels;
(2) the mineral estate in areas within tidewater limits, including islands, lakes, bays, and the bed of the sea which belong to the state; and
(3) the arms and the beds and shores of the Gulf of Mexico within the boundary of Texas.
(b) The land and minerals dedicated to the permanent school fund shall be managed as provided by law.