New York University does have its own cheerleaders, as a matter of fact. But that didn't stop Alicia Keys from becoming a one-woman cheer squad when she visited the school last month. She was at NYU's Skirball Center to film a live performance and do a Q&A with an all-student audience. "I see your shining spirits, and I see all your dreams, and I see all your endless possibilities," Keys gushed, an encouraging elder stateswoman at the wisened age of 28.

And what did the crowd of glowing young acolytes get to see in return? The same thing you will, in this exclusive Pepsi Music performance: a great six-and-a-half song set of greatest hits and spanking new material, plus a candid interview in which Keys discussed some of the personal angst that she overcame before recording her fourth album, The Element of Freedom, which comes out Dec. 15.

Above, you can check out her live version of the album's first teaser, "Doesn't Mean Anything," followed by what's scheduled to be the second single, "Try Sleeping With a Broken Heart":

Keys described "Try Sleeping With a Broken Heart" as a "super duper duper new song." It's subsequently leaked into the public stratosphere, but her NYU performance marked the world premiere in any medium of the soon-to-be-anthem for the romantic sad sacks of the world.

If you're curious what the "half" in that six-and-a-half song count was about, above, the answer follows: Keys preceded a rousing version of "You Don't Know My Name"—and an explanation of how a conversation with Kanye West inspired the track—with a healthy excerpt from "Empire State of Mind," her collaboration with Jay-Z. Even without Hova on hand, she can lead the charge for NYC as well as NYU.

The hits keep on coming, going all the way back to the first key to her rise, "Fallin'": 

Next up, revived from her sophomore album, is "If I Ain't Got You," a thematic cousin to the current single:

And who could resist "No One"? The answer, we believe, is imbedded in the title. 

In her audience Q&A, excerpted below, Keys candidly discusses the tough times surrounding the making of her last album. "That record was very, very difficult for me... I felt overworked, very sad. My grandmother was very sick at the time... It gave me a different perspective on what was important." Though she says she was surrounded by businesspeople who she realized didn't have her best interests at heart, "I also realized there was a certain part of me that had to change." 

"Finally, [with] this record Ireally learned to have a balance to it. I actuallylearned there's more creativity to be found when you balance the actualproductivity of doing it with going places, seeing people that you love, takinga drive, taking a walk... these things inspire you." And in turn, as the NYU students quickly discovered, she's determined to inspire: