# Analysis, PDE and Mathematical Physics at MSU

 Humor Problems

### Humor

 In a dark, narrow alley, a function and a differential operator meet: "Get out of my way - or I'll differentiate you till you're zero!" "Try it - I'm e^x..." Same alley, same function, but a different operator: "Get out of my way - or I'll differentiate you till you're zero!" "Try it - I'm e^x..." "Too bad... I'm d/dy." Q: What is the value of the contour integral around Western Europe? A: Zero. Q: Why? A: Because all poles are in Eastern Europe! Q: What is the difference between a Ph.D. in mathematics and a large pizza? A: A large pizza can feed a family of four... A newlywed husband is discouraged by his wife's obsession with mathematics. Afraid of being second fiddle to her profession, he finally confronts her: "Do you love math more than me?" "Of course not, dear - I love you much more!" Happy, although sceptical, he challenges her: "Well, then prove it!" Pondering a bit, she responds: "Ok... Let epsilon be greater than zero..."

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### Problems

Analysis is full of elementary formulated problems which have a large significance for quite non-elementary subjects. We suggest to your attention some of them.

 Let D1,…, DN are discs on the plane. Their centers are c1,…, cN. For each center count two numbers: m(ci)= the number of our discs conataining ci, i=1,…,N; and M(ci) =the number of discs in the sequence 2D1,…, 2DN conatining ci, i=1,…,N. Here 2D stands for the disc with the same center but the doubled radius. Obviously 1 ≤ mi≤ Mi ≤ N. Give an elementary prove that there exists an absolute constant A such that independently of the number N and independently of collection D1,…, DN there exists 1≤j≤ N such that Mj ≤ A≤ mj. One is given the collection of N different positive integers: a1, a2,…, aN. Prove that whatever the collection of N-1 positive integers 0

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