Monthly Archives: May 2010

Concluding 2010 Spring

Thanks all for participating POW actively. Here’s the list of winners:

1st prize:  Jeong, Seong-Gu (정성구) – 수리과학과 2007학번

2nd prize: Kim, Chiheon (김치헌) – 수리과학과 2006학번

3rd prize: Suh, Gee Won (서기원) – 2009학번

Congratulations!

In addition to those three people, I have selected two students. They received 1 movie ticket each.

Lim, Jae Won (임재원) – 2009학번

Kim, Ho Jin (김호진) – 2009학번

정성구 (2007학번) 30 pts
김치헌 (2006학번) 20 pts
서기원 (2009학번) 19 pts
임재원 (2009학번) 12 pts
김호진 (2009학번) 7 pts
최홍석 (2006학번) 6 pts
라준현 (2008학번) 6 pts
Prach Siriviriyakul (2009학번) 6 pts
강동엽 (2009학번) 5 pts
권성민 (2009학번) 4 pts
권용찬 (2009학번) 2 pts
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Solution: 2010-11 Integral Equation

Let z be a real number. Find all solutions of the following integral equation: \(f(x)=e^x+z \int_0^1 e^{x-y} f(y)\,dy\) for 0≤x≤1.

The best solution was submitted by Gee Won Suh (서기원), 2009학번. Congratulations!

Here is his Solution of Problem 2010-11.

Alternative solutions were submitted by 최홍석 (화학과 2006학번, +3), 정성구 (수리과학과 2007학번, +3).

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Solution: 2010-10 Metric space of matrices

Let  Mn×n be the space of real n×n matrices, regarded as a metric space with the distance function

\(\displaystyle d(A,B)=\sum_{i,j} |a_{ij}-b_{ij}|\)

for A=(aij) and B=(bij).
Prove that \(\{A\in M_{n\times n}: A^m=0 \text{ for some positive integer }m\}\) is a closed set.

The best solution was submitted by Gee Won Suh (서기원), 2009학번. Congratulations!

Here is his Solution of Problem 2010-10.

Alternative solutions were submitted by 정성구 (수리과학과 2007학번, +3), 김치헌 (수리과학과 2006학번, +3), 강동엽 (2009학번, +2).

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Solution: 2010-9 No zeros far away

Let M>0 be a real number. Prove that there exists N so that if n>N, then all the roots of \(f_n(z)=1+\frac{1}{z}+\frac1{{2!}z^2}+\cdots+\frac{1}{n!z^n}\) are in the disk |z|<M on the complex plane.

The best solution was submitted by Jeong, Seong Gu (정성구), 수리과학과 2007학번. Congratulations!

Here is his Solution of Problem 2010-9.

Alternative solutions were submitted by 최홍석(화학과 2006학번, +3), 김호진(2009학번, +3), 김치헌 (수리과학과 2006학번, +3).

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