Professor Alex losevich, far left, uses humor and other techniques to inspire MUs state competition teams and Putnam Exam participants: John Fischer, Stan Eshelman, Greg Jones, William McClain and Derrick Hart.
"Why aren't you done yet?" thunders Assistant Professor Alex losevich to the students in his class. Rather than cowering, the five students in Math 395, Mathematical Problem Solving, take their professor's bellowing in stride. They smile and redouble their efforts to solve the problem in question: Let P(x) be a polynomial of degree n such that P(x)= Q(x)P"(x) where Q(x) is a quadratic polynomial and P"(X) is the second derivative of P(x). Show that if P(x) has at least two distinct roots then it has n distinct roots. The students finally solve the problem after some additional back-and-forth.
This is not a typical MU mathematics class. There is no syllabus, problem sets or exams, and there are no easy problems. The purpose of Math 395 is to train students for the premier college mathematics competition, the William Lowell Putnam Examination.
Each year several thousand students throughout North America compete in the rigorous exam, which is legendarily difficult. The median score is 0/120, and a score of 60/120 ranks in the top 10 nationally. Last year, MU senior GregJones scored 38/120, easily ranking in the top 10 percent nationwide. Iosevich hopes that he can significantly improve in this year's exam.
To prepare MU students for the exam, every Monday evening Iosevich assigns problems that emphasize a certain area of mathematics, such as combinatorics or analysis. The students work on the problems independently and meet on Thursday without Iosevich to compare solutions. Or the lack thereof.
The following Monday, Iosevich gives hints on any unsolved problems, and the students have an opportunity to work on them in class. Finally, Iosevich explains the philosophy behind the problems and the connections with research mathematics.
The five—Stan Eshelman, John Fischer, Derrick Hart, Greg Jones and William McClain—are all mathematics majors looking for a little extra in a math class. Eshelman, a senior from Clinton, Mo., enjoys the challenge. Hart, a junior from Lake of the Ozarks, likes competition and persuaded his high school friend Fischer to sign up for the class as well. Fischer, a first-year student, appreciates the individual attention; he's "psyched" about the upcoming exam. And McClain, a senior frorn St. Louis who is planning to attend graduate school in mathematics next year, speaks for all of them when he says that he is taking the class simply because he enjoys doing mathematics problems. "They're fun," he says.
Iosevich, who joined the MU faculty this academic year, was motivated to teach this class by his own experiences as an undergraduate at the University of Chicago. There, he participated in the Putnam competition once and scored well. However, he felt he could have scored much higher if he were more motivated.
At MU, Iosevich's job as professor is to make sure that his students perform at the highest possible level, and "yell at them when they're bums," he says with tongue in cheek.
Of course, the real purpose of the class is more than just coaching. By preparing for the Putnam competition, Iosevich says he hopes that what they get out of the class is not just an interest in the content but an appreciation for serious mathematics.
