GT. FIRST CLASS REINALDO VAILLANT, who grew up "a block from Yankee Stadium" and now lives in Watertown, N.Y., has decided to earn a degree in computer technology.

So he is taking a course in Arizona history. "I'm learning about the Navajo Indians," said Sergeant Vaillant, who has been using his laptop to read lectures, answer his instructor's questions and communicate with other students.

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His route to a campus 2,100 miles from home is provided by eArmyU, an ambitious new program that enables soldiers to take classes — and earn associate's, bachelor's and master's degrees — from 20 colleges around the country. It also makes the phrase "Army boots" a complete sentence.

In the case of Sergeant Vaillant, a medical specialist at Fort Drum, about 70 miles north of Syracuse, who hopes someday to go on to a bachelor's degree in management information systems, the best choice for now seemed to be Rio Salado College in Tempe, Ariz., which is how he ended up studying Arizona history. "I've only been in the class two days, and I'm ready to take the midterm," Sergeant Vaillant said.

Meanwhile, he pronounced the "tech package" he received from the Army — including a Hewlett-Packard XE3 notebook computer, an HP DeskJet 940c inkjet printer and numerous accessories — "awesome."

No one has ever accused the Pentagon of thinking small. Even as some institutions are rethinking their e-learning ventures, the Army has surged ahead. In December 2000, it selected PwC Consulting, an arm of PricewaterhouseCoopers that is now being acquired by I.B.M., to run the program, agreeing to pay the company $453 million over five years. The first students were online two months later.

Jill Kidwell, a PwC partner overseeing eArmyU, said that soldiers on some bases stood in line all night to be among the first to register and to receive the free equipment. It is theirs to keep so long as they complete 12 semester hours of instruction over the next two years.

Only soldiers with at least three years of Army service ahead of them are eligible. The Army is making the investment in education partly to improve retention, and it seems to be working.

Already, said Betty Nass, the Army's project manager for eArmyU, 15 percent of eArmyU students have extended their enlistments so that they can continue to take classes. She pointed out that each re-enlistment saves the Army, which currently has 482,000 men and women in uniform, the cost of training someone new.

Right now, eArmyU has 20,000 students, amounting to about 4 percent of Army ranks; the goal is to increase that to 80,000 by 2005. About 2,000 courses are offered through the program, which enlists institutions — like Empire State College in Saratoga Springs, N.Y., Thomas Edison State College in Trenton and Penn State's World Campus — that are already experienced in e-learning.

Although some of those colleges offer "synchronous" courses in which students and instructors gather in virtual classrooms, all eArmyU classes are asynchronous, making it possible for combat personnel, whose schedules and locations can change without notice, to participate.

The Army has long offered courses through its on-base education centers. "But soldiers were enrolling in classes, then dropping out as they moved around the world," Ms. Kidwell said. "The goal was to take the classes to them." Among the overseas bases where eArmyU is available are Camp Casey in South Korea and Patton Barracks in Heidelberg, Germany.

Linda Frank, an administrator at Empire State College, said, "Students are supposed to begin and end classes on the same dates, though if a student is deployed, the instructor can make an exception.

"Not long after we started the program, Sept. 11 happened, and we had to give the soldiers quite a bit of flexibility."

As Ms. Nass explained, "The mission always comes first."

Yet the medium may turn out to be the mission. "These soldiers are learning to use these computers that are important to us in battle," Capt. Edlyn E. Smith, a company commander at Fort Benning, Ga., was quoted as saying in the base's newspaper, The Bayonet. So when students enroll in eArmyU, he said, "not only are they helping themselves out, but they are also helping out the mission."

They are also helping colleges stay afloat. The Army's venture represents a big cash infusion into e-learning. In particular, eArmyU could be a boon to the nation's more than 100 historically black colleges, according to an article in the Journal of Higher Education. Lacking the resources to take part alone, six such schools — Bethune-Cookman, Alabama A&M, Florida A&M, Grambling State, Morgan State and North Carolina Central — have formed a consortium to offer courses through eArmyU.

The program is also a boon to dozens of private contractors, including Smarthinking.com, a company based in Washington that offers soldiers tutoring online. There is also a virtual college library, provided by the University of Georgia.

First Sgt. Denver Smith, who runs thearmylink.com, a popular Web site for soldiers, described the program as "by far the best education program to hit the military" since he joined the Army two decades ago.

"The vast majority of soldiers tout the flexible hours as one of the strongest points of the program," he said by e-mail from Fort Lewis, Wash.

At Fort Drum, Sergeant Vaillant couldn't stop talking about the free laptop. "It's got a 1.06-gigahertz processor, 128 megs of RAM and a 10-gigabyte hard drive, and it's loaded with all the 2002 software," he said.

As for the education, he said, "So far, so good."