In early June, first-year doctoral student James Holmes stood before professors of neuroscience here for an oral exam that marked the beginning of at least four more years of intense study of how the brain works.

Days later, though, school administrators received an email from Mr. Holmes saying that he dropped out of the program. He didn’t give a reason.

What happened over the next month is now the focus of law-enforcement officials who say Mr. Holmes entered a packed movie theater in Aurora, Colo., and shot 70 people early Friday. So far, they have learned that between the time he left school and the massacre, Mr. Holmes applied for membership at a shooting range, whose owner on Sunday described Mr. Holmes’s answering-machine message as “incoherent, bizarre, freakish at best.” The suspect also bought an AR-15 semiautomatic rifle, a military-style gun popular with sportsmen since a federal ban on its sale expired eight years ago.

Meanwhile, police said, Mr. Holmes had bought thousands of rounds of ammunition via the Internet and received “high-volume” deliveries by mail to his home and school, for what authorities described as an arsenal of weapons and explosives.

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