Paul Allen’s gift to the University of Washington’s computer science school won’t increase the number of students who can enroll there; the UW is looking to the state Legislature to pick up that tab.

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When it received a $50 million gift from Paul Allen and Microsoft on Thursday, the University of Washington was given money for an endowment that will go far toward raising the prestige and reach of its computer science school.

But that endowment won’t increase the number of students who can major in computer science, which is the most popular choice of majors for incoming freshmen — and one of the hardest to get into.

Rather, the endowment is aimed at providing seed money to the new Allen School for Computer Science & Engineering for new initiatives — anything from early-stage research to equipment that can’t be purchased through other means. It won’t pay for a new building, or faculty salaries.

The UW looks to the state Legislature for funding to bump up the number of students who can go to the school.

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State money is used to hire more faculty, teaching assistants, advisers and technical support staff, said Ed Lazowska, a computer science professor and past chair of the department.

And in recent years, it’s been successful at getting that money.

In each of the past two state budgets, the department has received money to increase the number of spots for computer science majors. It’s now enrolling about 370 new undergraduate students each year, double the number it was able to accommodate in 2012.

This year, it is asking for $6 million from the Legislature to increase the number of students it graduates by 120 degrees per year. Most of that increase would be in bachelors degrees, Lazowska said.

The UW is getting help from some of its biggest supporters. On Thursday, Microsoft President Brad Smith went to Olympia to lobby on behalf of the school, Lazowska said.

The other thing the Allen School needs is space — for classrooms, offices, large gatherings and labs.

That’s why it is building a second computer science center, a 135,000-square-foot-building that’s being funded by private companies (including Microsoft, Amazon and Zillow, to name a few) and by the state.

Although computer science and engineering is a tough program to get into, the picture is getting better. In 2016, 43 percent of bachelor’s applicants were admitted to the program. In previous years, the admission rate was lower.

Still, “it’s heartbreaking that we are unable to accommodate a substantial number of students who would thrive in the program,” said Lazowska, who serves on the CSE undergraduate admissions committee.

Students are usually admitted at the end of their freshman year or the start of their sophomore year. But the school also admits some students directly, at the same time they are admitted to the university as freshmen. This year, direct admission will be offered to 150 students. All but five of them are Washington residents.

Lazowska said the school’s percentages of in-state students versus out-of-state and international students is similar to the UW’s overall breakdown. (About 70 percent of UW Seattle’s students are in-state, 16 percent are out-of-state and 14 percent are international students.)

For students who don’t get in, there are a number of other majors that are popular second choices. They include electrical engineering; the Information School; human-centered design and engineering; and applied and computational mathematical sciences.

Most students find another major if they can’t get into computer science, Lazowska said. “There are very few transfers to other schools or to UW’s branch campuses.”