سوال ۱۱ کنکور ارشد ریاضی ۱۴۰۲

PASSAGE 1:

Much of the classical theory of optimization, motivated primarily by problems of physics, is associated with great mathematicians: Gauss, Lagrange, Euler, the Bernoulis, etc. During the recent development of optimization in decision problems, the classical techniques have been reexamined, extended, sometimes rediscovered, and applied to problems having quite different origins than those responsible for their earlier development. New insights have been obtained and new techniques have been discovered. The computer has rendered many techniques obsolete while making other previously impractical methods feasible and efficient. These recent developments in optimization have been made by mathematicians, system engineers, economists, operations researchers, statisticians, numerical analysts, and others in a host of different fields.

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. Its appeal as a unifying discipline stems primarily from its geometric character. 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.

According to the passage, which sentence is correct?