سوال ۲۸ کنکور ارشد علوم کامپیوتر ۱۳۹۷

PASSAGE 3

The study of optimization as an independent topic must, of course, be regarded as a branch of applied mathematics. As such it must look to various areas of pure mathematics for its unification, clarification, and general foundation. One such area of particular relevance is functional analysis.

Functional analysis is the study of vector spaces resulting from a merging of geometry, linear algebra, and analysis. It serves as a basis for aspects of several important branches of applied mathematics including Fourier series, integral and differential equations, numerical analysis, and any field where linearity plays a key role. Most of the principal results in functional analysis are expressed as abstractions of intuitive geometric properties of ordinary three-dimensional space.

Some readers may look with great expectation toward functional analysis, hoping to discover new powerful techniques that will enable them to solve important problems beyond the reach of simpler mathematical analysis. Such hopes are rarely realized in practice. The primary utility of functional analysis for the purposes of this book is its role as a unifying discipline, gathering a number of apparently diverse, specialized mathematical tricks into one or a few general geometric principles.

28- Functional analysis serves as a basis in areas dealing with ----------.