It's a six-hour math test so difficult that most of the 4,200 college students who take it receive a score of 0 out of a possible 120.
The William Lowell Putnam Mathematical Competition for university undergraduates is an annual exam that pits the best math students in North America against one another. And a team of Bruins recently achieved UCLA's best result in more than 40 years — finishing third out of more than 400 colleges and universities, behind only Harvard and MIT. A UCLA team finished third at the 1968 Putnam.
The performance was an impressive step up from last year's 12th place finish, but it wasn't wholly surprising to UCLA’s coach, mathematics professor Ciprian Manolescu. "Talking to the students after the exam in December, I knew they did well and I was expecting a great result," he said. "I didn't quite imagine we would be third, though."
Two UCLA students ranked in the top 20 of the more than 4,200 entrants: sophomore Tudor Padurariu (11th place, with 66 points) and junior Xiangyi Huang (18th, 59 points). They, along with freshman Dillon Zhi (among the top 150, with 39 points), were selected by Manolescu in advance to represent UCLA in the team competition.
Among UCLA's other top scorers in the individual competition were Francisc Bozgan, who ranked 83rd, Peihao Sun, who finished in the top 250, Zhongnan Li and Man Cheung Tsui (top 325), Ufuk Kanat and Cheng Mao (top 500), and Derek Jung and Tianyi Zhang (just outside the top 500). All earned between 22 and 44 points.
"To be in the top three universities in Putnam — better than Princeton, Stanford, Yale and many others — we are of course very happy," Bozgan said.
Manolescu is a Putnam legend himself: As a Harvard undergraduate, he scored among the top five in three competitions. As UCLA's coach, he led students in intense three-hour practice sessions each week, during which the team took sample exams and worked on problem-solving skills at a blackboard.
The students credited their success to those practices — Bozgan said they were "crucial" and Huang called them "wonderful" — and to Manolescu’s coaching.
"No one can coach these problems better than Professor Manolescu," said Kanat, a freshman who came 7,000 miles from Turkey to attend UCLA.
The Putman exam covers many subjects, including advanced calculus, number theory and advanced algebra. Given the range of knowledge required and the prospect of tackling 12 difficult problems in six hours over two sessions, the team's practice sessions emphasized strategy and time management. "To solve a Putnam problem, you have to know the answer or very quickly see a trick to break down the problem," Padurariu said.
Zhi said the test was difficult, but not more so than he had expected. "You have to balance your time between finding the solutions — working them out in your head — and writing them down. Sometimes in the process of writing your solution, you find out that what you thought worked in your head didn’t actually work out and then you have to think about it again."
Professor Dimitri Shlyakhtenko, chair of UCLA’s mathematics department, praised Manolescu for inspiring the members of the team. "Ciprian is not only a fantastic researcher, but also a wonderful mentor," he said. "He inspires them to succeed, to grow, and to mature mathematically."
Now, Shlyakhtenko hopes the team's success will become one of several factors that attract more students to UCLA to pursue mathematics. "Their performance is a reflection of the fact that UCLA’s mathematics department undergraduate program is following the same steep upward trajectory as our faculty and our graduate program," he said. "It also reflects the attention and investment we are making in undergraduate education."
Among other things, under the leadership of Sorin Popa, its previous chair, the department created Mathematical Merit Undergraduate Scholarships, which are aimed at bringing exceptional mathematics students to UCLA. Harvard, MIT and Princeton each offer several undergraduate math scholarships; UCLA’s mathematics department awards only one per year. Shlyakhtenko said he hopes that donor support will enable the department to increase the resources available for outstanding undergraduates.
For the students, success at the Putnam reinforced the wisdom of their decisions to study math at UCLA. "I wanted to go to a university where I could take any course I want. Here, I don’t have to take basic, easy courses," said Kanat, who is already planning to take graduate-level courses next year. "UCLA offers us a great opportunity."
Padurariu agrees. "The professors are outstanding scholars and, fortunately, also very good teachers," he said. "I have definitely learned a lot here."
Preparing for the Putnam was not only an opportunity for the students to share mathematical ideas and plan for their future as scholars, but also, according to Huang, a chance to get to know one another better. "I got to be very good friends with Tudor, Francisc and Cheng," he said. "I greatly benefited from our discussions. I feel very thankful to be able to represent UCLA, and am extremely appreciative of Professor Manolescu’s careful instruction. UCLA has many pioneering mathematicians and it is a great place to study math."
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