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America’s jobs machine finally may be churning out jobs for new college grads.

That is particularly true for students who majored in math or science, though the number of jobs available in those fields varies greatly from state to state.

Some 64 percent of hiring professionals surveyed by the Chicago-based consulting company Challenger, Gray & Christmas last month said that their companies plan to recruit from the pool of 1.8 million college graduates who will enter the job market this spring. Employers in February had about 4.2 million unfilled jobs, according to the U.S. Bureau of Labor Statistics.

Last year, graduates with degrees in math and science had two times as many entry-level jobs to apply for than students with other majors, primarily because not as many students are pursuing these degrees. On a per capita basis, Colorado topped the list in math- and science-related job openings in 2013, while Mississippi was last, according to data released this year from a labor market consultant group Burning Glass Technologies, based in Boston.

After Colorado, states that had the most entry-level STEM jobs per capita last year were Alaska, Massachusetts, Washington state and Maine .

Jobs in science, technology, engineering and mathematics, commonly called STEM jobs, tend to offer higher pay. The average advertised salary for entry-level STEM jobs requiring at least a bachelor’s degree is more than $66,000, compared to $52,000 for non-STEM jobs, Burning Glass Technologies said.

Overall, starting salaries for 2014 graduates have increased 1.2 percent from a year ago, the National Association of Colleges and Employers reported last month. The biggest jump occurred in health sciences, where salaries increased 3.7 percent, the group said.

The latest jobs report released last week showed the U.S. unemployment rate fell to 6.3 percent in April. Private-sector employment in March surpassed the prerecession peak. Though the unemployment rate for 20- to 29-year-olds who graduated from college in 2013 was still 10.9 percent, that figure was down from 15.5 percent in 2009 when the recession was ending, the most recent data from the U.S. Bureau of Labor Statistics show.

“All of these trends bode well for those entering the job market this spring,” said John A. Challenger, chief executive officer of Challenger, Gray & Christmas.

Not everyone is so optimistic. Heidi Shierholz, an economist with the Economic Policy Institute, a think tank in Washington, doubts that the economy has really turned around for young college grads. “Since the unemployment rate of young college graduates remains significantly elevated, the class of 2014 will join a sizable backlog of unemployed college graduates from the last five graduating classes in an extremely difficult job market,” Shierholz said in a new report.

The number of STEM jobs available in each state were gleaned from the 2014 analysis of entry-level jobs posted on more than 32,000 online websites last year by Burning Glass Technologies. Since up to 90 percent of job openings for college-educated workers are posted online, looking at online job postings provides information on the types of jobs that employers are seeking to fill and where .

This gender gap in unemployment is likely because of the kinds of jobs young men and women are seeking. More young females are entering nursing and teaching, which are less sensitive to downturns, Shierholz of EPI explained.