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In Class: Extensive writing is required, all on topics from the past. First-week assignment: one- to two-page description of a physical object or building. Third-week assignment: five pages on a day in the life of a particular individual, or a specific moment or hour. Other assignments might be to describe someone's appearance and effect on others, or a landscape or townscape. Students also study narrative voices (say, ironic voices like Tacitus, Gibbon and Gore Vidal), the evolution from poetic myth to historical narration (Homer and Hesiod to Herodotus) and ''romantic immersion'' (sometimes Carlyle and his relationship to Dickens). Final assignment: a 15- to 20-page historical narrative, which Professor Schama collects in a thick anthology. ''It's a wonderful class!'' he says, ''at least for me.''
Your Chances: Last semester 25 applicants submitted writing samples for 15 seats.
ANNA DEAVERE SMITH, New York University
C.V.: Performance artist and playwright, MacArthur Foundation ''genius'' award winner and actor featured on the NBC series ''The West Wing.''
Teaches: One semester a year. Last semester, she taught a graduate seminar and a freshmen seminar, ''A Real Play of Identities.''
In Class: Ms. Smith says she tried to get the entering freshmen to think about identity at a time when they were in new surroundings and thinking about remaking themselves. One question she posed in class: Who could you never be? When one student said she could never be a leader, Ms. Smith arranged for her to interview N.Y.U.'s president, John Sexton, and then ''perform'' him, in the same way Ms. Smith interviews people and uses their own words and mannerisms to interpret them on stage. Students also had to interview and portray each other. ''It was difficult,'' Serena Chen, a student, says.
Your Chances: The 16 students last semester were chosen from more than twice that many applicants, based on essays they wrote on why they wanted to take the course. It was the only freshmen seminar requiring an essay.
BILLY COLLINS, Lehman College, City University of New York
C.V.: Former United States poet laureate, current poet laureate of New York State and winner of the National Poetry Series competition.
Teaches: One graduate seminar in creative writing this year. Until two years ago, Mr. Collins taught three courses a semester, including freshmen composition. He says he liked teaching composition to freshmen because it was so needed, but he found himself grading papers in motel rooms and on airplanes en route to poetry readings and lectures. ''It was constant,'' he says. ''It was almost like having a little dog trailing me.'' He estimates he has spent ''at least nine years of my life correcting freshmen essays.''
In Class: Mr. Collins mixes theory and practice. He talks about Harold Bloom's theory on the ''anxiety of influence'' and how writers seek to transcend those who precede them. Then he has students ''springboard'' off the work of others. Catherine Perry, who is taking her second class with Mr. Collins, says he requires a lot of reading and writing. ''Some of his assignments are really stringent,'' she says. ''But in class, he is so relaxed about everything. Everything he says is just a suggestion. He never says, 'Do this' or 'Do that.'''
Your Chances: For decades he was one of an army of professors teaching freshmen composition. You didn't ask for Billy Collins, you just got him. No longer. Ms. Perry says she ''desperately clawed to get in'' this semester. ''He likes to cap his graduate classes at 12, and there were 17 enrolled. I just kept begging.'' She is auditing it.
MICHAEL S. DUKAKIS, Northeastern
C.V.: Democratic candidate for president, 1988; three-term Massachusetts governor; teacher since 1979 (when not running for office or in office).
Teaches: Two courses a semester, including the summer term. (The only extra he gets, says Richard M. Freeland, Northeastern's president, is a little more secretarial help.) Topics include the presidency, public management, health policy, state and local government and urban development.
In Class: A lot of case studies, followed by short policy memorandums. The midterm for ''Public Policy Analysis'' is a longer memorandum in which students are encouraged to talk to people in the field. ''Often he was able to use his stature as a public figure to help students get answers and calls back,'' says Shannon Blakely, a third-year student. She says he also uses his pull to help students find internships, and he writes recommendations. His comment: ''Teaching is hard. It is not just telling war stories. Guys like me ought to connect with these young kids.''