The New Mexico college of agriculture and mechanic arts [New Mexico state university] shall be an institution of learning open to the children of all the residents of this state, and such other persons as the board of regents may determine, under such terms, rules and regulations as may be prescribed by said board of regents; shall be nonsectarian in character and devoted to practical instruction in agriculture, mechanic arts, natural sciences connected therewith, as well as a thorough course of instruction in all branches of learning bearing upon agriculture, and other industrial pursuits.