Columbia will face Davidson in the Eastern semi-finals at Raleigh, N.C., on Friday. The winner of that game will face the winner of the North Carolina-St. Bonaventure contest for the right to go to the NCAA quarter finals at Los Angeles, March 23rd.

In the Mid-East tournament, Kentucky is a slight favorite. Houston and U.C.L.A., the top two teams in the country, are heavily favored to win the Mid-West and Western regional and repeat their January clash in the National semi-finals.

Although in recent years no Ivy team has ever reached the NCAA finals, Columbia rates an outside chance on the merit of seven-footer Dave New mark and its great outside shooting. Princeton with Bill Bradley was the last Ivy team to reach even the NCAA quarter finals.

In New York, plans are almost finished for the 31st National Invitational Tournament. This year, the selection committee expanded the field from 14 to 16 teams because of the number of outstanding independents available.

Dayton, Big-Eight runner-up Kansas, and Bradley, second finisher in the Missouri Valley Conference, are co-favorites to take the title.

Duke expects to join the fold despite its loss to North Carolina State in the semi-finals of the Atlantic Coast Tournament. North Carolina held the ball for almost 15 minutes in the second half in gaining a record 12-10 victory.

Two small college teams are also among the entries. St. Peter's of New Jersey, ranked third nationally in scoring behind Houston and U.C.L.A., and Long Island University, the number one ranked small college team in the country.