WATCH: Obama Speaks At Rutgers University, Takes Shots At Donald Trump

President Obama called on graduates of Rutgers University Sunday to take on their "shared challenges" and fight back against some of rhetoric of the 2016 presidential campaign.

He didn't mention his name, but he did criticize the language of the presumptive Republican nominee, Donald Trump, saying: "It's not cool to not know what you're talking about."

"That's not challenging political correctness," he said, saying some have become too "confident in our ignorance."

"There are a whole lot of folks who are book smart but have no common sense," he said.

Obama's appearance at Rutgers University's 250th commencement was the first time a sitting president has spoken at the college.

The 250th Anniversary Commencement was held Sunday in High Point Solutions Stadium at Rutgers University–New Brunswick on the Busch Campus in Piscataway.

To loud cheers and screams, Obama opened his speech by reciting a part of the Rutgers cheer, saying: "R-U Rah Rah!"

Obama noted some of the traditions of Rutgers that have made it unique, such as "chicken fingers and mozzarella sticks on your cheese steaks" and "fat sandwiches" at grease trucks and nights out at Old Queens tavern.

"I'm sure Michelle would approve," he said, noting the First Lady's attempts to build a healthier America.

"I came here for a simple reason: to finally settle this pork roll versus Taylor Ham question," he said.

But Obama said he came simply because he was asked - for three years, saying that extensive effort may have been a first. He also noted that Rutgers has reportedly the most diverse student body in the nation.

"America converges here," he said.

On that note, Obama took aim at Trump's call to block Muslims from entering the United States, saying the idea "doesn't just run counter to our history as the world's melting pot; it contradicts the evidence that our growth, our innovation" boosted America because of immigration.

"That's how we became America," he said.

Obama also ripped Trump's idea to build a wall along the U.S. border with Mexico, saying the "biggest challenges cannot be solved in isolation."

Obama also mocked politicians who expressed skepticism of climate change, noting that a United States senator once brought a snowball to Congress "as proof" that the scientific phenomenon doesn't exist.

He said "imagine if your fifth-grade science teacher" had seen that. "He'd get a D."

"You may wonder where this strain of anti-intellectualism came from," he said. "In politics and in life, ignorance is not a virtue."

Obama said those moments of "ignorance" are only "sporadic moments" in history, and that future generations will ultimately prove what''s right.

"You're not only better educated; you've been more exposed to the world. You're more diverse," he said. "You have a healthy skepticism for conventional wisdom."

He said this about people who pine for the good old days: "Take it with a grain of salt."

"The good old days weren't all that good," he said. "By almost every measure, the nation is better, the world is better than it was 50 years ago or 30 years ago or even 8 years ago."

Obama noted that in his tenure, marriage equality is the law of the land, the infant mortality rate has been cut by a "significant amount" and the deficit has been cut by two thirds.

He called on lawmakers to ensure that women are paid the same as men, saying "it's long past the time that we passed laws to make sure women are getting paid the same."

"Class of 2016, it is your turn now to shape our nation's destiny as well as your own and to get to work," he said.