What was going on when I was born?

The Chrysler Corporation and its Chrysler Canada Ltd. subsidiary are caught between conflicting demands from American and Canadian authorities in the fight to stave off corporate bankruptcy. At issue is an agreement between the Canadian Government and Chrysler Canada, reached last May, requiring the subsidiary to invest $1 billion (Canadian funds) in Canadian facilities between 1980 and 1985. The Canadian dollar is worth about 84 cents in United States currency.

Because of a typographical error, the short-interest table in Business Day yesterday incorrectly stated the position of the International Business Machines Corporation. The correct figure is 557,558 shares.

Rupert Murdoch, the publisher of The New York Post and other newspapers around the world, has completed a conditional agreement to buy The Times of London and its affiliated publications. The purchase by Mr. Murdoch, a 49-year-old Australian, depends upon his reaching new trade union agreements within the next three weeks, and is subject to Government approval. The Canadian-based Thomson Organization, which is selling The Times because it has chronically lost money, said that its agreement with Mr. Murdoch included detailed guarantees that he would do nothing to lower the tone or character of the 195-year-old newspaper, which is widely regarded as one of the finest in the world. Included in the sale are The Times's sister publication, The Sunday Times, and three respected weeklies - The Times Literary Supplement, The Times Education Supplement and The Times Higher Education Supplement. At a news conference in London today, Mr. Murdoch said: ''I am not seeking to acquire these papers in order to change them into something entirely different. Whatever proposals for progress may be developed, there will be no fundamental change in the characteristics.''

''MOUNTAINS are the beginning and end of all natural scenery,'' John Ruskin observed in the 1800's. In their slopes and valleys are found ''the noblest and best ground given to man,'' Ruskin continued. ''In these districts only, art of the highest kind seems possible.'' These words of the English art and social critic inspired another Briton, Ralph Whitehead, who set out in 1902 seeking such surroundings of unbridled scenic beauty in which to start an artsand-crafts colony. Whitehead found his dream in the eastern Catskill Mountains in Woodstock, N.Y., which today is two hours from Manhattan by car or bus and not far from half a dozen of the state's best skiing and cold-weather recreation areas. Woodstock is perhaps best known for its summer festivals, plays and easy life style. And English socialists, independent artisans, abstract and landscape artists, folk and rock musicians, beatniks and hippies have all helped give Woodstock a certain rebel reputation. But, on a cold, crisp winter weekend, the town seems at peace with itself, and offers opportunities to relax dreamily before a crackling fire in a country inn, to browse, without the summer's crowds, in art galleries, antiques stores and boutiques, to Metropolitan Baedeker amble through snowy woods, to ski downhill or cross-country, and to go sledding, snowmobiling, ice skating and hiking, with or without snowshoes.

A record $3 billion in new cash flowed into the nation's money market mutual funds in the week ended Wednesday, lifting their total assets to $81.7 billion, the Investment Company Institute reported yesterday. The aggregate assets of the 98 funds were the highest ever, and represented an increase of nearly $7 billion since the beginning of the year, according to the institute, a trade group for mutual funds.

Mayor Koch asked a statewide lawyers' group yesterday to help convince the State Legislature to pass 33 bills he has proposed dealing with criminal justice. But he received a generally unenthusiastic response from lawyers and judges, who questioned his proposals and his recent public statements about the courts. Mr. Koch sought support for his legislative proposals - outlined in a report made public Wednesday - during a 45-minute appearance before about 175 persons at an annual lunch meeting in Manhattan of the criminal justice section of the New York State Bar Association. ''The time has come for the bar to join in a movement for the desperately needed reform of our criminal-justice system,'' the Mayor urged.

Railroads will no longer be able to set rates collectively under a new policy of the Interstate Commerce Commission. Seeking to stimulate competition, the I.C.C. directed the railroads to end their pricing agreements in 90 days and to propose alternative pricing arrangements. The industry opposes the measure. (Page D1.) International trade has become an issue of conflict within the Reagan Administration. A greater diffusion of authority in the trade field may result if the State Department is given broader powers at the expense of the Office of the United States Trade Representative and the Commerce Department. (D1.)

The Hostages The pledges to Iran will be carried out as long as they are ''consistent with domestic and international law,'' the Reagan Administration announced. The White House said that former President Carter, after meeting with the freed hostages, had advised President Reagan to abide by the accords but never to do ''any favors for the hoodlums who persecuted innocent American heroes.'' (Page A1, Col. 6.) Anger increased in Washington amid the many reports of harsh conditions forced on the Americans during their 444 days of captivity. Members of Congress introduced resolutions to renounce the accords with Iran, but Congressional leaders warned against precipitate action. (A7:5-6.)

In a region where a 7 or 8 percent growth in gross national product is not exceptional, Singapore is in a position to make good on its plans to become the banker for Southeast Asia. In the last seven years, Singapore has attracted scores of financial institutions interested in assisting the oil-fed economies of Indonesia and Malaysia and servicing the foreign companies moving into the region. Under a Government mandate, Singapore gives many of the same advantages as Nassau or Grand Cayman Island. But, unlike other tax havens, Singapore has a healthy domestic financial market, short-term and long-term offshore markets and is a vigorous foreign exchange center rivaling Tokyo and Hong Kong.

In the oil industry, he is called Mr. Wildcatter. And despite the recent sale of a hefty part of his smaller leases to a Canadian conglomerate, Marvin Davis, from all indications, intends to hold onto that title. ''We haven't sold the whole compa@ny, not by a long shot,'' Mr. Davis says. ''We still have 54 rigs running today on the leases we have left.''

President Reagan, in another set of actions underscoring his Inauguration Day declaration that ''government is the problem,'' today ordered a 15 percent reduction in travel by Federal employees, a 5 percent reduction in consulting services, and limits on furniture procurement and ''unnecessary'' office refurbishments. On his third day in office, the President also chose Vice President Bush to head a new interagency study group aimed at easing Government regulations. Mr. Bush said the Reagan Administration would lift some regulations even before the study group got started. ''We're seeking real reform and tangible results,'' Mr. Reagan told reporters at a surprise appearance in the White House press briefing room as Mr. Bush stood at his side. He said the study group would ''cut away the thicket of irrational and senseless regulations.''

''We thought the Americans couldn't care. We'd say to ourselves: 'They don't care.