Today, we introduce a few of the nominees who have already made New York a better place through their selfless actions and unflagging dedication.

Here's the equation that helps explain why Yvette Beck is an award-winning math teacher: She's a devoted "calculus mom" to her Bronx students at Lehman HS.

"When I get into class the first day, I tell them, 'I don't want competition. I want everyone to look out for each other,' " said Beck, 50, who teaches advanced-placement calculus to seniors, ranging from those who failed their Regents exams to valedictorian-level students.

"We're what we consider a calculus family. We become a solid unit," said Beck, who hands out her home phone number to students and invites them to add their own number to a sign-up sheet.

She encourages them to call her at all hours - and on weekends - for homework help and "for whatever help they need," and motivates them to mentor each other in study groups.

Beck hopes the student-helping-student process reinforces a life lesson.

"They take care of each other. In life, you have to take care of your neighbor. Life would be better if we took care of each other, and it's the same thing in math," said the Queens mother of three.

"They're really so great," said Beck, who began teaching in 1973.

Her approach works. Last year, 97.4 percent of her 38 students passed the Advanced Placement calculus AB exam, she said.

She was a winner of the 2002 Siemens Award for Advanced Placement, for "exemplary teaching and enthusiastic dedication to both students and subject," given by the New Jersey-based Siemens Foundation.

"She does so much good for the kids and they really appreciate her," said her son Judah Beck, a chemistry teacher at Lehman, who nominated his mom for the Liberty Educator Medal. "Some of them became teachers because of her."

"I can't imagine waking up in the morning and doing anything else," said Yvette Beck, who arrives at school every day at 7 a.m. to give one-on-one tutorials.