IF YOUR POLAROID SWINGER gets ripped off before you even have a chance to take a picture of John Harvard's statue in the Yard then you'll probably realize that the city you now live in is not as cloistered and idyllic as the college you are now attending.

In fact, Cambridge is a distinctive, diverse unique city struggling with more than its share of urban problems, problems that a student at Harvard may only catch hints of even if he is here for four years.

From the panhandlers and hare krishna drummers outside the Coop to bell-bottomed young professionals lunching upstairs at Barney's, from the little old ladies shopping for bedspreads at Woolworth's to the tight little knots of blue coliar workers who gather at Whitney's every night for a beer after work. Cambridge probably has as varied a population as any other six square miles in the country.

Not only that, but even excluding temporary residents such as students. Cambridge is still the tenth most densely populated city in the country. The city's 20,000 persons per square mile--64.6 persons per acre--have made such problems as housing and crime especially difficult in an area that is not one community but a conglomerate of distinct neighborhoods and interests.

In the eastern third of the city, the concrete towers of sprawling MIT and the barren public housing blocs in the Model Cities area form an uneasy triangle with the crowded frame duplexes in the multi-ethnic working-class neighborhood of East Cambridge. Tensions are strong in this area: the percentage of blacks in East Cambridge is the lowest in the city, while the percentage in the neighboring public housing is the highest.

Students and other young transients form the bulk of the population in the high-rent area between MIT and Harvard, where apartment buildings, duplexes, department stores, bars and public buildings form an impersonal jumble which has few stable families and little neighborhood identity.

Riverside, a predominantly black slum area on the fringes of Harvard, huddles directly across the Square from the fashionable Brattle Street area where Cambridge's middle class white liberals pay an average of nearly $50,000 for their homes. To complete the potpourri, the neighborhoods of North Cambridge contain a blend of blacks elderly people, working class families, students grouped in apartments, and Cambridge's wealthy who inhabit the shady lanes west of Kirkland St.

THE ALLURE of living near Harvard and MIT has drawn large numbers of students and young professionals into Cambridge. The influx of young people who are either affluent or communally-oriented has sent rents sky-rocketing and sent working class families looking for homes elsewhere. Although Cambridge has lost population since 1960, there has been a 45 per cent increase in the number of 20-to-24-year olds in the past decade. Meanwhile, the median rent has gone from $63 to $119 a month.

For permanent residents, living in Cambridge with Harvard and MIT is somewhat like sleeping between two elephants--whenever they sprawl their Cambridge bedfellows suffer. It is said there was once a competition between Harvard and MIT to be the first to swallow Central Square. MIT won. Cambridge citizens are losing. They pay higher property taxes as more land goes to tax-free universities, and higher rents as less land is available for housing. Harvard's new Administration has promised to be more careful where it tramples, to avoid displacing more low-income tenants. After buying the Hotel Continental earlier this year to use as a student dormitory, the University pledged to make payments toward what the city was losing in tax revenues from the Hotel's sale.

Unable to substantially check university growth, Cambridge's answer to their housing crisis is rent control. The city first instituted a rent control program in 1970, after a decade of spiraling rents. Four-fifths of Cambridge's residents pay rent to absentee landlords.

The large increase in the student and transient population in Cambridge has aggravated another problem--crime. Cambridge's densely populated, high turnover areas of young people attract burglars from all over the Boston area. Robbers find the-high quality stereos or TVs most young people own easy to make off with in this area where few people know their neighbors. George Powers, planning and research officer for the Cambridge City Police, said that burglaries are much less frequent in both the working class communities of East and North Cambridge and in the wealthy Brattle St. area. "These are stable, family communities," Powers said. "People know each other so that strangers look suspicious."

Cambridge's crime rate has climbed steadily for the past ten years. Last year, the city had the nation's highest crime index for an urban area its size, according to the FBI. Most of these were crimes against property, rather than crimes of violence, with break-ins and auto thefts predominating.

The crime problem students will most likely face is bicycle theft. Robert Tonis, chief of the Harvard Police, estimates that 150 bikes are stolen from Harvard students each year. A chain and lock are not footproof deterrents. A bike chained to a parking meter or sign can be lifted over the top. Most chains can be with a bolt-cutter and even if a ten-pound motorcycle chain securely attaches the front wheel to a root thieves will often settle for the rear wheel as frame. One of the authors of this article had hi Raleigh stolen while writing the place, in fact.

One theory holds that most bicycle thefts on be traced to junkies who sell them on the street to support their drug habits. A Cambridge detective has estimated that 60 per cent of Cambridge crimes are drug related.

TWO YEARS AGO, The New York Time characterized Cambridge as a traditional Old World city. Since then, however, much of the local flavor has made way for Boskin Robbin's 3 Flavors and other nation-wide chains. The impending John F. Kennedy Library Center or Boylston St. in the present MBTA yard will further transform the Harvard Square area in the next five years. Over a million tourists a year unexpected to visit the Kennedy Library. Undoubtedly, streets will have to be rerouted to handle new floods of traffic. Coffeehouses and bookstores will flee before an onslaught of hotels tourist shops and hamburger joints.

The city has already made plans to extend the MBTA subway line out to Fresh Pond and he explored the possibility of building a giant underground garage. Many developers--inspired by the boom the library is expected to bring to the Square--have announced plans to build high-rise apartments, hotels and luxury stores. For example, Kanovas Corporation has received permits to build a 19-story structure next to the library site which city planning officials say will be a Holiday Inn.

While the Cambridge community has been undergoing a social tempest. Cambridge politic have been modernized more slowly. The city's often compared to Berkeley, Calif., as a center of "youth culture." But while young people have had a tremendous social impact on Cambridge, so far the city has effectively barred them from local voter rolls and prevented them from having much of an impact on city politics. While radicals tool over the city government of Berkeley two year ago, council elections in tradition-tied Cambridge last year produced only a shaky liberal majority in a City Council shared with ethnic and commercial interests.

Barbara Ackermann, Cambridge's first woman mayor, heads the Council's liberal coalition which includes such diverse figures as black woman radical Saundra Graham and Harvard Ed School dean Frances H. Duehay '55. On the other side Alfred Vellucci, former mayor and longtime opponent both of Harvard reformers and commercial development interests, represents the more settled working-class interests of East Cambridge. Reflecting his neighborhood's fear of university expansion. Vellucci has repeated suggested that Cambridge pave over Harvard Yard to solve the Square's parking problem an that the city transform the Lampoon Castle into public urinal.

So as you focus your camera on the vista of Cambridge from the tenth-floor terrace of Holyoke Center during your tour of Harvard remember that there is more to Cambridge that meets the lens of your Polaroid Swinger.