Ziv’s Math World

My name is Ziv. I am a high school Chinese student who love exploring mathematics! Currently, my favorite fields include complex analysis and abstract algebra!

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An inequality problem

Let be a continuous integrable real function on , then     Solution 1 By Cauchy-Schwarz inequality,     Solution 2 By Jensen’s inequality, since is a convex function, we have     So     Solution 3 By Hölder’s Inequality, we get     Choose , we get the case of solution 1. We…

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  • An inequality problem

    Let be a continuous integrable real function on , then     Solution 1 By Cauchy-Schwarz inequality,     Solution 2 By Jensen’s inequality, since is a convex function, we have     So     Solution 3 By Hölder’s Inequality, we get     Choose , we get the case of solution 1. We […]

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  • Abstract Algebra – Sylow Theorems and Its applications

    In abstract algebra, finite group theory is in its core. Now from Lagrange theorem, we have Lemma 1 Let be a subgroup of a finite group . Then the order of is a divisor of the order of . This theorem states the necessary condition for a finite group to be a subgroup of a […]

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  • An approximation problem

    Problem: Let us call an irrational number well approximated by rational numbers if for any natural numbers there exists a rational number such that     Solution: 1. Pick     Why does it work ? Let’s say we let . Then we have     and     We now proceed in proving that […]

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  • On IMO2017 P2

    I did IMO 2017 P2 with my friends yesterday. Now I would like to share my thoughts on this problem. Problem: Let be the set of real numbers. Determine all functions such that, for any real numbers and ,     The initial step must be taking certain values, testing its properties and then start […]

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  • Alcohol Withdrawal Seizure Treatment & Prevention

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