Change And Invariance A Textbook On Algebraic Insight Into Numbers And Shapes 1st Edition Ilya Sinitsky by Ilya Sinitsky, Bat-sheva Ilany instant download after payment.

The world – according to philosophers, scientists, and artists – is an amalgamation of that which is static and that which varies: an ongoing interplay of change and invariance. Already in ancient times, this interplay was noted: King Solomon stated “… there is nothing new under the sun” (Ecclesiastes 1:9), while Greek philosopher Heraclitus claimed that “you cannot step twice into the same river.”
In the early twentieth century, renowned Dutch artist M. C. Escher expressed the concept of the connection between invariance and change through his series of “Metamorphosis” drawings – the shapes in the drawings gradually changed into other shapes that were entirely different (fish into birds, birds into buildings, and so forth). Authors worldwide, including such names as the Russian Ivan Bunin, or Rosa Montero from Spain, explore the themes of body and soul based on the scientific fact that each and every cell in the human body is completely replaced at least every few years.
Alongside exploring that which is constantly changing, there is a parallel search for those quintessential components that remain permanent in a constantly fluctuating world. This has intrigued thinkers since time immemorial when, for instance, they contemplated the periodicity of the heavens and the constancy of the constellations. Indeed, most of the basic scientific laws were formulated by observing what remained invariant despite certain changes. Today, conservation laws in physics describe our fundamental understandings of the world, and every conservation law (conservation of energy, conservation of charge, to name but two) expresses the fact that a particular property remains constant despite changes in the system. Einstein, in fact, defined his theory of relativity as “a theory of space-time invariance.” In mathematics, the idea of invariants is explored intensively...