Yuri K. Shestopaloff
Elementary Functions and Equations. Fermat Last Theorem and Associated
Transformations of Geometrical Forms. Third Revised Edition, 2019, 306 p.
ISBN 9781927731093 (9781927731093)
The third revised
edition of the book introduces properties of elementary functions and equations
with regard to their geometrical, physical and, in some instances, philosophical
interpretation. The material shows when and how these functions can be used for
developing adequate models of natural phenomena, systems and processes. The
importance of relationships of mathematical concepts and constructs with
geometry and physical reality is often underestimated, while we live in an
inherently geometrical world. All our knowledge came from a 3D space. Both
fundamental concepts and examples of particular applications are presented,
which can be used for modeling of different phenomena in diverse areas 
physics, biology and others. The study of relationships of Fermat Last Theorem
(FLT) with certain geometrical transformations, and an elementary proof of FLT,
considered in the previous edition, received further development. The introduced
geometrical concepts and methods can be used for other problems in number
theory. The prerequisite for the material is a familiarity with the first year
algebra and calculus.
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