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문제 관련해서 설명했다간 괜히 부정행위같은거 걸릴까 쫄리니 나중에 씀

쉽게 나왔고 30분 일찍 나옴

긴장해서 어그려 끌어서 대단히 미안함


1시반 됐으니 업데이트함

원서 접수한 인원 46명


계속 검토할까 했는데 화장실 너무 많이 가는거 미안해서 그냥 나옴


디시에 백슬래시 쓰면 죄다 깨지고 짤려서 텍 형식으로는 안씀



1. group of order 2020 is not simple

2. A, B: ideals. Then A+B, AB are ideals

3. zeta: primitive p^2-root of unity
(1) zeta mapsto zeta^k are all Q-automorphisms of Q(zeta) iff p does not divide k
(2) Q(zeta) contains a subfield of Galois group Z/Zp

4. f.d.v.s. V. The number of elements of basis are same

5. M_sigma is a permutation matrix of sigma in Sn.
(1) If sigma is a cycle, when M is diagonalizable over R?
(2) If sigma is a permutation, when M is diagonalizable over R?
(3) Show that M is diagonalizable over C

6. y0 > 0, y' = y-y^2
(1) Solve y.
(2) Show that y goes to 1 as t goes to infty

7. f(z) = a0 + a1z + ... + ad z^d
lim(R to infty) int _{|z|=R} zf'/f dz?

8. v_(k+1) leq vk - sk + uk
sum uk converges, (uk), (sk), (vk) nonnegative
Show that sk goes to zero and vk has limit

9. There is no entire positive harmonic function

10. 무슨문제였나 기억 안남. 댓글로 알려줘
Define d(x,A) = inf{d(x,y): y in A}. Prove or disprove:
cl(A) = cap_{n=1 to infty} {x: d(x,A) < 1/n}

11. Is finite prod of Hausdorff is Hausdorff? Is infinite prod of Hausdorff is Hausdorff?

12. (1) What is compact space? What is nornal space?
(2) Show that compact Hausdorff is normal

13. (1) Show that the sphere is a regular surface
(2) a: regular value of f. Show that f^(-1)(a) is a regular surface

14. X = U cup V, U and V are coordinate nbd. If U cap V is connected, show that X is orientable

15. Gaussian curvature of x^2/a^2+y^2/b^2+z^2/c^2 = 1 at each point