FAMED AS A hotbed of debate over academic freedom, New York's most elite school is also a playpen for sexual hijinks, sophomoric antics and the wacky indulgences of the children of the rich. While their parents shell out $33,246 a year in tuition, Columbia University students doff their clothes at naked parties, flock to sex toys workshops, broadcast porn on campus TV, bake anatomically correct pies for the "Erotic Cake-Baking Contest" and heat up the steps of the Low Library in a mass makeout session called the "Big Kiss." And of course, there's always the stimulating game, "Guess the Number of Condoms in the Jelly-Bean Jar." Others volunteer for the bullwhip at Conversio Virium, the university-sanctioned S&M club that means "exchange of power" in Latin. It calls itself a "discussion group" that provides "education and peer support" and promotes "safe, sane and consensual play." But the club doesn't just talk. Late on the night of Nov. 13, a Daily News reporter sat in room 303 of Hamilton Hall, a venerable classroom building where Columbia students have studied Poe, Plato and Plutarch for nearly 100 years. As a female student volunteer stood facing the blackboard, and two dozen Columbians watched, a lecturer who identified himself only as Dov flogged her repeatedly with leather whips, rubber hoses - and a cat-o'-nine-tails. "I'm Dov, and these are my toys," he said, and for the next 14 minutes he demonstrated lashing techniques. The activity was consensual, but the squeals of delight mingled with the occasional yelps of pain. Columbia would make no specific comment on the club or the flogging incident. Ivy Leaguers were unaware the reporter was in attendance. Dov is not employed by the school, which doesn't police or censor club activities. Referring only to student organizations generally, spokesman Robert Hornsby said the "university has a limited role in regulating student speech or private conduct." The result: Columbia Gone Wild. New York's Smartest still dream of winning a Nobel Prize. And bookworms still pull all-nighters in the Butler Library. But the 2 million-volume monument to the mind, which stays open 24 hours a day, doubles as a temple of earthier desires. "Having sex in the stacks of Butler Library is one of the ultimate Columbia experiences," said Miriam Datskovsky, the sex columnist for The Spectator, the student newspaper. "There's very little dating. It's predominately a hookup scene," said the 21-year-old, a senior from an Orthodox Jewish background who writes the "Sexplorations" column. "Everything is so much easier and so much quicker - you go to dinner and then have sex," she added. Consider the party scene. But it's no reason to get dressed up. In fact, there's no reason to get dressed at all: The merrymakers of Morningside Heights host naked parties, lingerie-only parties - and the more bourgeois "clothing-optional parties with naked rooms." And taxpayers indirectly foot a chunk of the tab because bond offerings and loans from the state Dormitory Authority and federal Department of Education partially fund the renovation of dorms where naked frolickers muster. Columbia wouldn't comment on this use of university space. Lee Bollinger, the school's $779,673-a-year president and a world-class expert on free speech, wasn't available. The soirees aren't exactly orgies: "It's more like naked students sitting around drinking martinis, defying societal conventions and trying to act nonchalant at the same time," said Birk Oxholm, a religion major who graduated last year. "They're trying to act like it's not about sex. But they're not really succeeding," he added. One hostess, who staged a Halloween-themed "Naked Witches & Warlocks Party" last month, called it a "great unshackling from the clothing that so defines and imprisons us." But it was a "sex-neutral event," she said. The same cannot be said of several X-rated campus happenings: . "Sex Toys 101." The university's Health Services division teamed up with Toys in Babeland, a SoHo sex shop, to host a sex toys workshop in John Jay Hall on Feb. 15. Though it was part of "Safer Sex Week," the playthings on display on W. 114th St. included bondage and S&M tools like whips, paddles, "floggers" and "slappers." . "Sexhibition." The annual campus sex fair, held in April, featured phallic ring toss games, orgasm-for-beginners workshops and discreet liaisons in the "Tent of Consent." . "Thug Play with Princess Wendy." Another session of the S&M club, taking place Oct. 30 in Hamilton Hall, was advertised as "beating, punching and slamming boys into lockers, and why bullies are so so so much fun!" The speaker discussed "boot service," the "fine art of humiliation" and how a $5 meat mallet can be used as a toy. But "Princess Wendy" also provided safety tips, counseling students to avoid kicking one another in the kidneys and spine. "I like to hurt people," she said. "I don't like to send them to the hospital." She also advised some 30 devotees, "If you're new to kicking and trampling, start out slow." Conversio Virium's officers declined to address questions. Columbia's student activities coordinator, a university employee who advises the club, didn't respond to an e-mail. But the Baltimore-based National Coalition for Sexual Freedom, which advocates for S&M groups, contacted The News at the request of the students. "Educating people about the safest flogging techniques so they don't accidentally strike the kidneys is responsible behavior," said spokeswoman Susan Wright. "Basically, what they're doing is S&M 101." . "Smut TV." CTV, Columbia's in-house, student-run TV station, has a faculty adviser, uses school equipment and space, gets $5,021 a year in student activity fees - and is hungry for new viewers. So at 10 p.m. on Oct. 17, it entered the hard-core porn business: Broadcasting into scores of dorms and lounges, it aired a five-minute clip, downloaded from the Internet, of a naked couple engaged in sex. The footage ran during a sex advice show called "Sexiled" - which is student slang for getting kicked out of one's room so a roommate can have sex - and even some jaded Columbians who'd tuned in said they were offended. CTV, which isn't edited, censored or monitored by the administration, said in a statement that airing porn was a "lapse of judgment." It was "inconsistent with broadcast standards" and won't happen again, said Alisa Gross and Nihar Shah, CTV's student co-presidents. . "The Naked Run." In the chill of November, at the stroke of midnight, a group of exhibitionists, led by the track team, dons running sneakers - and nothing else - for a sprint down College Walk and up Broadway. So does anything go at Columbia? Actually, no. Flogging and bondage are accepted, but the school apparently draws the line at another form of communication between the sexes: love letters. They were good enough for Cleopatra, who sent them to Mark Antony, and F. Scott Fitzgerald, who exchanged them with his wife, Zelda. But Columbia University Health Services lists love letters as a form of nonphysical sexual harassment, according to its Web site. "What's next for Columbia? Objecting to a little ankle?" said Greg Lukianoff, president of the Foundation for Individual Rights in Education, a nonpartisan free speech watchdog group that examines academia. dfeiden@nydailynews.com