Taking that too far, of course, could be repulsively obsequious. The correct calibration is everything. And it’s worth acing, because a professor or administrator who takes a genuine interest in you can be a bridge to other influential people inside and outside the school, to limited-space seminars, to special collaborations, to exclusive summer programs, to competitive internships, to graduate work and more.

Damian Walker saw that at U.N.C.-Chapel Hill, from which he graduated last spring. “The most influential thing I did here was find mentors,” he told me. And he found them largely by opening up to them.

Walker attended U.N.C.-Chapel Hill as a Carolina Covenant scholar, which means that his family was poor enough for him to qualify for full financial aid. He told me that early on he went to an open campus discussion about police violence against minorities. Several faculty members were also there, and he approached Judith Cone, the vice chancellor for innovation, entrepreneurship and economic development.

“I didn’t know who she was,” he recalled. “Short lady. I shared my story about how police shootings affected my life, my family. She gave me her business card and said, ‘Follow up.’ I still have that business card to this day.” He went to see her in her office and kept going to see her in her office, and with the encouragement and help of her and other faculty members, he cobbled together the money to go to an educational conference in Massachusetts, to meet with entrepreneurs in New York City and to spend the summer between his junior and senior years interning for a company in China. He’s about to head back to China to teach English for a while. He’s well on his way to fluency in Mandarin, which he thinks will give him a definite edge in any future business career.

Walker is an example of what a mammoth study by Gallup, Purdue University and the Strada Education Network has found. Previously known as the Gallup-Purdue Index and now called the Strada-Gallup Alumni Survey, it has questioned about 100,000 American college graduates of all ages about their college experiences, looking for connections between how they spent their time in college and how fulfilled they say they are now.