Tag Archives: 박민재

Concluding 2014 Fall

pow2014fall-624Thanks all for participating POW actively. Here’s the list of winners:

  • 1st prize (Gold): Park, Minjae (박민재) – 수리과학과 2011학번
  • 2nd prize (Silver): Chae, Seok Joo (채석주) – 수리과학과 2013학번
  • 3rd prize (Bronze): Lee, Byeonghak (이병학) – 수리과학과 2013학번
  • 4th prize: Park, Jimin (박지민) – 전산학과 2012학번
  • 5th prize: Park, Hun Min (박훈민) – 수리과학과 2013학번

박민재 (2011학번) 30
채석주 (2013학번) 22
이병학 (2013학번) 20
박지민 (2012학번) 19
박훈민 (2013학번) 15
장기정 (2014학번) 14
허원영 (2014학번) 4
정성진 (2013학번) 3
김태겸 (2013학번) 3
윤준기 (2014학번) 3

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Solution: 2014-19 Two complex numbers

Prove that for two non-zero complex numbers \(x\) and \(y\), if \(|x| ,| y|\le 1\), then \[ |x-y|\le |\log x-\log y|.\]

The best solution was submitted by Minjae Park (박민재), 수리과학과 2011학번. Congratulations!

Here is his solution of the problem 2014-19.

Alternative solutions were submitted by 박훈민 (수리과학과 2013학번, +3), 이병학 (2013학번, +3), 채석주 (2013학번, +2), 박지민 (2012학번, +3), 김범수 (2010학번, +3), 장기정 (2014학번, +3), 정경훈 (서울대 컴퓨터공학과 2006학번, +3, his solution), 윤성철 (홍익대학교 수학교육과, +3), 진형준 (인천대 2014학번, +2), 장유진 (홍익대학교 2013학번, +3), 정요한 (서울시립대학교 수학과, +3), 조현우 (경남과학고 3학년, +3).

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Solution: 2014-17 Zeros of a polynomial

Let \[p(x)=x^n+x^{n-1}+a_{n-2}x^{n-2}+\cdots+a_1 x_1 + a_0\] be a polynomial. Prove that if \(p(z)=0\) for a complex number \(z\), then \[ |z| \le 1+ \sqrt{\max (|a_0|,|a_1|,|a_2|,\ldots,|a_{n-2}|)}.\]

The best solution was submitted by Minjae Park (박민재, 수리과학과 2011학번). Congratulations!

Here is his solution of the problem 2014-17.

An alternative solution was submitted by 조현우 (경남과학고등학교 3학년, +3).

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Solution: 2014-16 Odd and even independent sets

For a (simple) graph \(G\), let \(o(G)\) be the number of odd-sized sets of pairwise non-adjacent vertices and let \(e(G)\) be the number of even-sized sets of pairwise non-adjacent vertices. Prove that if we can delete \(k\) vertices from \(G\) to destroy every cycle, then \[ | o(G)-e(G)|\le 2^{k}.\]

The best solution was submitted by Minjae Park (박민재, 수리과학과 2011학번). Congratulations!

Here is his solution.

An alternative solution was submitted by 김경석 (+3, 경기과학고 3학년). One incorrect solution was received (BHJ).

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Solution: 2013-21 Unique inverse

Let \( f(z) = z + e^{-z} \). Prove that, for any real number \( \lambda > 1 \), there exists a unique \( w \in H = \{ z \in \mathbb{C} : \text{Re } z > 0 \} \) such that \( f(w) = \lambda \).

The best solution was submitted by 박민재. Congratulations!

Similar solutions are submitted by 김동률(+3), 김범수(+3), 김호진(+3), 박지민(+3), 박훈민(+3), 양지훈(+3), 이시우(+3), 전한솔(+3), 정성진(+3), 조정휘(+3), 진우영(+3), Koswara(+3), Harmanto(+3). Thank you for your participation.

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Solution: 2013-16 Limit of a sequence

For real numbers \( a, b \), find the following limit.
\[
\lim_{n \to \infty} n \left( 1 – \frac{a}{n} – \frac{b \log (n+1)}{n} \right)^n.
\]

The best solution was submitted by 박민재. Congratulations!

Similar solutions are submitted by 김범수(+3), 박훈민(+3), 장경석(+3), 정성진(+3), 진우영(+3), 김홍규(+2), 박경호(+2). Thank you for your participation.

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Concluding 2012 Fall

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

  • 1st prize: Lee, Myeongjae  (이명재) – 2012학번
  • 2nd prize: Kim, Taeho (김태호) – 수리과학과 2011학번
  • 3rd prize: Park, Minjae (박민재) – 2011학번
  • 4th prize: Suh, Gee Won (서기원) – 수리과학과 2009학번
  • 5th prize: Lim, Hyunjin (임현진) – 물리학과 2010학번

Congratulations! We again have very good prizes this semester – iPad 16GB for the 1st prize, iPad Mini 16GB for the 2nd prize, etc.

2012 Fall POW


이명재 (2012학번) 32
김태호 (2011학번) 30
박민재 (2011학번) 25
서기원 (2009학번) 21
임현진 (2010학번) 17
김주완 (2010학번) 10
조상흠 (2010학번) 8
임정환 (2009학번) 7
김홍규 (2011학번) 5
곽걸담 (2011학번) 5
김지원 (2010학번) 5
이신영 (2012학번) 5
윤영수 (2011학번) 5
엄태현 (2012학번) 4
조준영 (2012학번) 3
박종호 (2009학번) 3
정종헌 (2012학번) 2
장영재 (2011학번) 2
양지훈 (2010학번) 2
최원준 (2009학번) 2
김지홍 (2007학번) 2
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Solution: 2012-20 the Inverse of an Upper Triangular Matrix

Let \(A=(a_{ij})\) be an \(n\times n\) upper triangular matrix such that \[a_{ij}=\binom{n-i+1}{j-i}\] for all \(i\le j\). Find the inverse matrix of \(A\).

The best solution was submitted by Minjae Park (박민재), 2011학번. Congratulations!

Here is his Solution of Problem 2012-20.

Alternative solutions were submitted by 서기원 (수리과학과 2009학번, +3), 이명재 (2012학번, +3), 김태호 (수리과학과 2011학번, +3), 임현진 (물리학과 2010학번, +3), 박훈민 (대전과학고 2학년, +3), 윤성철 (홍익대학교 수학교육학과 2009학번, +3), 어수강 (서울대학교 수리과학부 석사과정, +3).

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KAIST Math Problem of the Week 2012 봄 시상식 박민재 이명재 서기원 조준영 김태호

Concluding 2012 Spring

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

  • 1st prize: Park, Minjae (박민재) – 2011학번
  • 2nd prize: Lee, Myeongjae  (이명재) – 2012학번
  • 3rd prize: Suh, Gee Won (서기원) – 수리과학과 2009학번
  • 4th prize: Cho, Junyoung (조준영) – 2012학번
  • 5th prize: Kim, Taeho (김태호) – 수리과학과 2011학번

Congratulations! As announced earlier, we have nicer prize this semester – iPad 16GB for the 1st prize, iPod Touch 32GB for the 2nd prize, etc.

KAIST Math Problem of the Week 2012 봄 시상식 박민재 이명재 서기원 조준영 김태호

박민재 (2011학번) 41
이명재 (2012학번) 34
서기원 (2009학번) 29
조준영 (2012학번) 17
김태호 (2011학번) 16
서동휘 (2009학번) 5
임정환 (2009학번) 5
이영훈 (2011학번) 4
임창준 (2012학번) 3
Phan Kieu My (2009학번) 3
장성우 (2010학번) 2
홍승한 (2012학번) 2
윤영수 (2011학번) 2
변성철 (2011학번) 2
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Solution: 2012-12 Big partial sum

Let A be a finite set of complex numbers. Prove that there exists a subset B of A such that \[ \bigl\lvert\sum_{z\in B} z\bigr\lvert \ge \frac{ 1}{\pi}\sum_{z\in A} \lvert z\rvert.\]

The best solution was submitted by Minjae Park (박민재), 2011학번. Congratulations!

Here is Solution of Problem 2012-12.

Two incorrect solutions were submitted (M.J.L., W.S.J.).

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