BOWLING GREEN, Ky. — Crosby J. Gardner has never had a girlfriend. Now 20 and living for the first time in a dorm here at Western Kentucky University, he has designed a fast-track experiment to find her.

He ticks off the math. Two meals a day at the student dining hall, three courses per meal. Girls make up 57 percent of the 20,068 students. And so, he sums up, gray-blue eyes triumphant, if he sits at a table with at least four new girls for every course, he should be able to meet all 11,439 by graduation.

“I’m Crosby Gardner!” he announces each time he descends upon a fresh group, trying out the social-skills script he had practiced in the university’s autism support program. “What is your name and what is your major?”

The first generation of college students with an autism diagnosis is fanning out to campuses across the country. These growing numbers reflect the sharp rise in diagnosis rates since the 1990s, as well as the success of early-learning interventions and efforts to include these students in mainstream activities.

But while these young adults have opportunities that could not have been imagined had they been born even a decade earlier, their success in college is still a long shot. Increasingly, schools are realizing that most of these students will not graduate without comprehensive support like the Kelly Autism Program at Western Kentucky. Similar programs have been taking root at nearly 40 colleges around the country, including large public institutions like Eastern Michigan University, California State University, Long Beach, the University of Connecticut and Rutgers.

For decades, universities have provided academic safety nets to students with physical disabilities and learning challenges like dyslexia. But students on the autism spectrum need a web of support that is far more nuanced and complex.

Their presence on campus can be jarring. Mr. Gardner will unloose monologues — unfiltered, gale-force and repetitive — that can set professors’ teeth on edge and lead classmates to snicker. When agitated, another student in Western Kentucky’s program calms himself by pacing, flapping his hands, then facing a corner, bumping his head four times and muttering. One young woman, lost on her way to class and not knowing how to ask for directions, had a full-blown panic attack, shaking and sobbing violently.

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Autism affects the brain’s early development of social and communication skills. A diagnosis of autism spectrum disorder can encompass an array of people, from the moderately impaired and intellectually nimble like Mr. Gardner, a junior majoring in biochemistry, to adults with the cognitive ability of 4-year-olds. Until 2013, students who could meet college admission criteria would most likely have received a diagnosis of Asperger’s syndrome, which has since been absorbed into autism spectrum disorder.

The social challenges of people on the spectrum can impede their likelihood of thriving not only in college, but also after graduation. Counselors in programs like Western Kentucky’s not only coach students who struggle to read social cues, but also serve as advocates when misreadings go terribly awry, such as not recognizing the rebuff of a sexual advance.

When a professor complains about a student who interrupts lectures with a harangue, Michelle Elkins, who directs the Western Kentucky program, will retort: “I am not excusing his behavior. I am explaining his brain function.”

Breaking the Ice

At suppertime, the dining hall at Western Kentucky’s student union is crowded, clamorous and brightly lit. Students in the Kelly program, who often have sensory hypersensitivities as well as social discomfort, usually prefer eating alone in their rooms.

But one night this fall, some gathered for a weekly dinner with peer mentors — students hired by the program to be tutors and social guides. The Kelly students tentatively approached a meeting place in the lobby. As they recognized their mentors among the milling crowd, relief flooded their faces.

The meal began awkwardly. One Kelly student buried himself in a textbook. Another gazed around the dining hall, humming.

Gradually, the mentors drew them out. How was your day? Have you tried any clubs? Jacob, a freshman from Tennessee who is in a Chinese immersion curriculum and asked that his last name not be used to protect his family’s privacy, said he had joined the French, Spanish and German clubs.

“When do you sleep?” I inquired with a smile.

A few mentors laughed appreciatively. Jacob looked puzzled. “I don’t get the humor in that question,” he said.

When the topic shifted to a social event coming up at the center — a video game party — conversational buy-in was guaranteed. Even so, as various games were suggested, the dinner table exchanges were more proclamation than conversation:

“In my opinion, Pokémon Go is a stupid idea,” Mr. Gardner shouted.

Ms. Elkins fixed him with a look. “Good you added, ‘in my opinion,’ Crosby,” she said.

The autism program’s home, a matter-of-fact clinical education building at the edge of the university, is a peaceful, dimly lit haven from the churning campus. The 45 undergraduates in the program spend three hours a day here, four days a week.

They study, meeting with tutors, and confer with counselors and a psychologist to review myriad mystifying daily encounters. The counselors maintain ties with dorm supervisors, professors and the career center, mediating misunderstandings.

By 2019, the program, which started with three students a little over a decade ago, anticipates being able to admit 77 students. Like most such programs on other campuses, it charges a fee; W.K.U.’s is $5,000 a semester, much of which may be covered by federal vocational rehabilitation funds.

In addition to shoring up academic and organizational skills, the program aims to ease students into the social flow of campus. This year, group discussions will tackle topics that include sex and dating.

Some of these students have enough self-awareness to feel the excruciating loneliness of exclusion. “One student told me, ‘I was so excited about college because I hear you don’t get bullied there, and I don’t know what that’s like,’” said Sarah McMaine-Render, the program’s manager.

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Others remain relatively oblivious to the social world surging around them.

Impulse control is an issue for many of these students: They will stand up and abruptly leave class. Some need reminders about basic hygiene. Because having a roommate can be unnerving, most have single rooms in the dorms.

But they all have the requisite academic ability: Before applying to the support program, they must be admitted by the university. Some are exceptionally bright. “I have a 4.0 G.P.A. but David leaves me behind in the dust,” Liz Ramey, 19, a student mentor, said of David Merdian, a Kelly sophomore who studies mathematical economics with a concentration in actuarial science.

With the program’s help, some of the students, most of whom are male, can enter the four-year university directly from high school. Others first try community college. After Kaley Miller graduated from high school, relatives, who did not believe she could live independently, put her in a group home and then a residential home with elderly adults, where she spent her days doing factory piecework. Finally, at a psychiatrist’s suggestion, Ms. Miller’s parents decided to let her try a college that provided support for students on the spectrum.

When she moved into a W.K.U. dorm, Ms. Miller, 24, a junior and a meticulous art student, reacted in wonderment. “There were so many people my age and everyone was so normal,” she said.

Out of the Shadows

In 2012, Andy Arnold, who was given an autism spectrum diagnosis as a child, enrolled as a freshman at Western Kentucky.

“It was terrifying,” he recalled. “I was anxious and went off my meds. I’d forget to shower and brush my teeth. I would do rituals, like walking around outside the dorm. I kept grabbing at the back of my neck.

“I started skipping classes. I didn’t really know how to study, so I fell behind quickly. I ate too much. I behaved irrationally to people.”

He dropped out.

He lived at home, taking online courses for a few years, then reapplied to W.K.U. Now 23, he is back at school — and this time, he is in the autism support program.

“I feel less panicky,” Mr. Arnold said. “I like getting to know people here at the center. We have something in common.”

It is hard to know how many students with autism attend four-year schools. A 2012 study in the journal Pediatrics found that about 50,000 teenagers with the diagnosis turn 18 each year and 34.7 percent attend college. Without support, though, few graduate.

That is in part because many students with an autism diagnosis do not step forward, fearing stigma. Some experts speculate that for every college student on the spectrum who identifies himself or herself with a diagnosis, there may be two more who are undisclosed.

But as the growth of the so-called neurodiversity movement prompts people on the spectrum to define themselves as different but not deficient, more students are emerging from the shadows. The Bridges to Adelphi program at Adelphi University in Garden City, N.Y., serves about 100 students with autism. At the University of Texas in Dallas, 450 students with the diagnosis have registered for services with the Student AccessAbility office.

Their presence on campuses is also a testament to the tenacity of familiesand disability advocates who, since the 1990s, when awareness of autism began to mushroom, have pressed for earlier diagnoses and interventions. Much of that battle unfolded in public secondary schools, leading to more services.

Over the last decade, officials at mainstream universities began realizing that growing numbers of spectrum students were being admitted — and, like Mr. Arnold, were foundering.

It was one thing for administrators to authorize accommodations like extra time on tests for students with dyslexia or attention deficit disorder. But how should they bolster students whose behavior was the primary expression of the disability — who could not stop shouting out answers in class and feared dorm showers?

And so the new autism support programs vary in emphasis. Some are based in disability resource centers, while others are in mental health offices, focusing on social skills and anxiety reduction.

“Our mission is to help them transition into the university, be successful here, and then transition out of the university to be successful in adult life,” said Pamela Lubbers, who directs one of the country’s most structured, coordinated programs, with 17 students, at Rutgers-New Brunswick.

Ms. Lubbers meets weekly with students, working them through a standardized “to do” checklist to help them identify small-step tasks to feel less overwhelmed, review their goals (“Describe the best social interactions you had this week”), and problem-solve. (“You think you left your I.D. on the campus bus. What steps will you take to find or replace it?”)

But even with support, these students often need extra time to graduate. Indeed, many do not make it that far. Some crumble under academic and organizational stress. Others succumb to campus allures like alcohol and drugs.

And others are expelled on sexual harassment grounds. They are so eager to fit in that they may, for example, comply with the demands of a bully who says, “ ‘I’ll be your friend and go to dinner with you every night next week if you kiss that girl,’” said Jane Thierfeld Brown, who consults with families and colleges about supporting students on the spectrum.

But with support, there are also those, like Ryan Hodges, who surpass expectations.

Mr. Hodges received his diagnosis at age 4. “In high school did we know he’d go to college? No,” said his father, Jeff, a Nashville businessman. “Did we hope? Yes.”

They set their sights on W.K.U. because of the program. Now 23, Ryan has grown immeasurably in social confidence, his father said, and is on track to graduate at the end of this semester.

Whether they are prepared for the next transition remains an open question. Most programs do not keep tabs on their students after graduation.

Despite the career coaching offered for Kelly students, some still cannot present themselves well in job interviews. Living at home again, unemployed, they may regress.

“The goal is not necessarily a college degree but becoming an independent, successful adult,” Dr. Brown said. “And a bachelor’s degree doesn’t guarantee that.”

Still, many graduates from Western Kentucky’s program are employed. Mrs. McMaine-Render, who stays in touch with some through social media, mentions one who works in film, others in technology, some in retail, and another who is applying for graduate school in physics.

What about their social lives?

Mrs. McMaine-Render paused and looked at her lap. “Sometimes I’m too scared to ask,” she said.

The Supercenter Challenge

Always with an eye toward life after college, the program encourages students to learn practical skills.

Hence Western Kentucky’s weekly trip to Walmart.

One recent Friday afternoon, Mrs. McMaine-Render drove seven students in the program’s van, which resounded with cheerful non sequiturs.

“I don’t mean to be rude but could you not talk now?” one student told another. “Your voice is very loud in my head!”

Mrs. McMaine-Render pulled into the parking lot and nudged the students out of the van. They ambled toward the store, blithely indifferent to incessantly roaming cars. Then she waved and drove off, leaving them to tackle the Walmart Supercenter on their own.

In a frenzy, the group scattered. Some boys barreled up and down aisles, flinging items at random into their clattering shopping carts. Essentials: Twix. Strawberry Twizzlers. Doughnuts. Frosted cookies. Six-packs of Coke. Slippers. Napkins. Pokémon cards. More Pokémon cards.

One boy decided he wanted to reheat chicken wings in his dorm. He needed a baking tin. But that meant locating the cookware aisle. Which meant finding an employee, then asking for directions. Scary!

Checking out was another challenge. For the students’ entire lives, their purchases had been paid for by adults. Now they were peering at register totals, fumbling for credit cards, swiping and swiping, then attempting the chip system, one way and then the other, forgetting PINs. Over all, they did just fine.

They reassembled outside, sweating and smiling, surrounded by the fruits of their considerable shopping labors.

Ms. Ramey, the student mentor, picked them up. On the drive back to school, the students toggled between yakking about their shopping victories and falling silent, drained. Ms. Ramey pulled up to their dorms, one by one.

One by one, they unloaded their bags and, without so much as a “thank you” or even “goodbye,” set off.

“Have a good weekend!” she kept prompting.

Startled, each boy looked back at the car, bewildered. Another missed social cue?

Oh, right! Jolted, some remembered to smile, and even to wave farewell.