What was going on when I was born?

The slaying of Kathleen J. Williams at the Waldorf-Astoria Hotel last Sept. 22 touched off one of New York City's most extensive police investigations. On some days as many as 30 detectives were involved. During tens of thousands of hours of work, they questioned hundreds of people and checked thousands of fingerprints until they matched the single blood-smudged print that led to the arrest last Thursday of Juan E. Robles. But the investigation has raised anew questions about how the police decide to use their resources.

That Cosmopolitan Girl has appeared on cable television, discussing affairs of the heart. On the same channel, the Newsweek Woman examines affairs of state. Next month, the Essence Woman makes her debut - exploring black affairs as well as offering health and beauty tips. Lured by the promise of cable television, excited by the electronic revolution, increasing numbers of magazine publishers are being drawn to video. Some have leaped in with both feet - the Hearst Corporation, with its joint venture in the Hearst/ABC cable channel, and Playboy Enterprises, with the Playboy Channel. The majority of publishers, however, are developing programming that they sell to cable or syndication or even to the networks.

The Reagan Administration informed Israel today that it could buy American-designed components for a new fighter aircraft to be built in Israel, State Department officials said. The Administration's decision was seen by Israeli officials as being aimed at gaining increased Israeli flexibility in the negotiations on the withdrawal of troops from Lebanon. Moshe Arens, the Israeli Defense Minister, who until recently was his country's Ambassador to Washington, said the decision was ''good news.'' Arens Expresses Hope on F-16's ''I'm grateful to the President of the United States,'' Mr. Arens said, ''and particularly grateful to the Secretary of State, George Shultz, who I know has worked hard to bring about this release.''

The Chicago Mercantile Exchange and the Chicago Board Options Exchange are close to an agreement to give their members access to each other's markets. The move has important implications for the present structures of both the commodities and securities industries. More immediately, it has brought to the surface a long-simmering dispute between the Chicago Board of Trade, the nation's biggest commodity futures exchange, and its offspring, the Options Exchange, which operates the largest stock and index trading markets. On Friday, members of the Board of Trade circulated a petition asking members to exercise their right to join the Options Exchange and used their vote to block a move by the exchange to link up with the Board of Trade's major rival, the Chicago Merc. That exchange, the second-biggest commodity futures market, is rapidly gaining on its chief competitor among the nation's 11 major commodity exchanges.

The Rangers could not have cut it much closer and still come away with a victory last night. And Mike Bossy couldn't have come much closer to cutting that victory out of their hands and forcing overtime. The Rangers had built a 7-2 lead at Madison Square Garden in the first two periods. But in the third, they let it slide away until, with 43 seconds left in the game, Denis Potvin scored the Islanders' fourth goal of that period, on a power play, to slice the lead to 7-6.

New York State is considering a major revamping of the social studies curriculum for secondary schools to put greater emphasis on sociological, political and economic issues rather than following the traditional chronological approach to history. The proposals, being developed for the State Education Department, have sharply divided the academic community both in the state and nation. Proponents of the revisions say that they stress the study of ideas and concepts and de-emphasize the memorization of dates and other facts. A coursemight, for instance, concentrate on the political or economic system of a country and use that focus as a way of also studying a nation's history. Moreover, the changes would give less emphasis to the study of Western civilization - now the vehicle for teaching the history of the world - so that more attention can be given to Asia, Africa and Latin America, consistent with a Board of Regents policy promoting global perspectives.

Western Pennsylvania is speckled with the yellow of daffodils and forsythia, hopeful signs among hills that are still brown from winter and often covered with coal and steel industry waste. But in this small town on the north bank of the Ohio River, a rebirth is occurring that may signal more than the coming of spring. In early April, the Jones & Laughlin Steel Corporation reopened part of Crucible Steel's old works here, which it purchased for an undisclosed price from Crucible's parent, Colt Industries, in February. The plant, which has made steel since 1905, had been closed since October, when 4,500 workers lost their jobs.

A chart in Business Day last Tuesday with an article about industrial flight from the North was incorrectly captioned. The data showed the net migration to or from states and regions during 1980-82.

A sharply higher proportion of the nation's unemployed, traditionally discounted as nonvoters, went to the polls in 1982, according to a Census Bureau study released today. The census report, based on interviews with 50,000 Americans in mid-November, found that blacks, government workers, older women and residents of Middle Western and North Central states were also more likely to say they had voted in the Congressional elections of 1982 than in the previous off-year races in 1978. But the greatest increase of all was among the jobless, of whom 34.1 percent said they voted in 1982, as against 27.4 percent in 1978. The study found that 48.4 percent of women and 48.7 percent of men reported voting in 1982, a statistically insignificant difference. In previous studies of Congressional elections, back to 1964, the Census Bureau found the percentage of men who reported voting was higher than that of women.

''From the mid-1970s and continuing into the present day, viewers have become increasingly evaluative, judgmental and critical of the programming offered to them by the three commercial television networks.'' -John Bowen, communications consultant. (A1:5.)

International Intense talks are under way in preparation for the Western economic summit meeting in May. The differences most troublesome to Washington and its allies are their conflicting views on East-West trade, what to do about stabilizing the dollar and the larger issue of how to get the world economy growing again. (Page D1.)

An article in some copies of Metropolitan Report on Friday about the slaying of a Queens tavern owner incorrectly described the parole status of the murder suspect, Charles Dingle. Mr. Dingle had twice been denied parole but was released from prison last August after serving two-thirds of a five-year sentence for robbery.