### Lecture 2. Metric and Normed spaces

This is my lecture notes on An Introduction to Functional Analysis.

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### Lecture 1. Topology

This is my lecture notes on An Introduction to Functional Analysis.

Lecture 2→

I hope one can understand that singular value decomposition is a beautiful song even without such nice melody.

"Relativity without mathematics may be compared with “Painless Dentistry,” or “Ski-ing without falling,” or “Reading without Tears.”"

Clement V. Durrell Readable Relativity G. Bell & Sons Ltd. 1926

### What is the optimal amount of troops?

This is one of questions from the course Principles of Economics with Calculus.

Suppose that the United States military is fighting two wars at the same time. The wars are taking place in two fronts, A and B. Consider the problem of a general who has to decide how to allocate $M$ units of troops among the two fronts. Based on a recent analysis, the general knows that the benefit of placing a units of troops in front A is $10ln(a)$ and the benefit of placing b units of troops in front B is $20ln(b)$.

QUESTION. What is the expression for the optimal amount of troops that should be placed in front A? (Ignore indivisibility/integer problems by assuming that soldiers can be allocated fractionally to both fronts).