Coming off its first NCAA tournament appearance since 1946, the Harvard men’s basketball team is lining up a tough non-conference schedule before it begins next year’s Ivy League season.

CBSSports’ Jon Rothstein reported yesterday that Harvard will face Saint Mary’s, California, and Memphis in 2012-2013, all on the road.

The official schedule from Harvard Athletics for the upcoming season lists only five games so far—the Crimson’s home-and-away series with Brown and Yale, and a game at home against Holy Cross—meaning that Harvard may have other games against major conference opponents that have not yet been announced. WEEI also reported that Harvard will play Boston College again next year, a team that the Crimson has now defeated in four straight meetings.

Over the past several seasons, Harvard has had increasing success against major programs in the early part of the year. The team won the Battle 4 Atlantis over Thanksgiving break in the Bahamas after with wins Utah, Florida St., and Central Florida. The team also lost three of its non-league games—at UConn, at Fordham, and against Vanderbilt in the NCAA Tournament—finishing the year with a 14-3 non-Ivy record.

Harvard is 0-2 all-time against Cal, though the two haven’t met in a little over a decade. The Crimson has never played Saint Mary’s or Memphis in its program history.

Despite Harvard’s title in the Ancient Eight last season, the Crimson isn’t the only team to have games slated against major-conference opponents. Of the matchups scheduled and announced for next season, perhaps the most surprising is Yale’s Jan. 6 game against Florida in New Haven, as it is rarity for a team from a power conference like the SEC to agree to play in the cramped facilities of the Ivy League.

Harvard will announce the rest of its schedule later in the summer.