[2/2] What's the Use?: The Unreasonable Effectiveness of Mathematics (This is the base. Why do we need mathematics in everyday life?) (Category Math)

Continue. storyAbout this popular science book, I will tell you the content of the remaining chapters.

4. Königsberg kidneys It all starts with the problem of Königsberg bridges, the emergence of graph theory, and then their application for organ transplantation in the UK. 5. Be careful in cyberspace. - here in the classics we are talking about encryption, then about asymmetric encryption, the use of this decomposition into prime numbers, and then the transition to elliptic curves 6. Numerical plane Here the author talks about natural numbers, rational, irrational and complex. He tells how complex numbers came to be, and that their representation is no longer a numerical line, but a numerical plane where interpretation is related to sines and cosines. Interestingly, for many physical problems, the use of complex numbers makes it easier to describe and solve problems. 7. Dad, you learned to multiply triplets. - a story about Hamilton quaternions, which make it easier to describe and solve the problem of transforming the position of objects in three-dimensional space. This is very useful in a three-dimensional schedule. 8. That's the bounce. An interesting chapter where the author moves from the calculation of spring parameters to Lorentz attractors and chaos theory 9. Trust me, I'm Fourier's. - here the author tells about the decomposition into a Fourier series, then about the transformation of Rodon and how all this is used in conditional CT devices to restore a three-dimensional image over a large number of two-dimensional projections from different directions 10. Smile, please! - A short chapter on image preservation, where there is a story about jpeg, and also about the use of wavelets to store fingerprint images in the FBI archives 11. Are we almost there? The author talks about how GPS works and what areas of physics and mathematics are needed for geopositioning. 12. Thawing the Arctic The story as a model for magnets was reused to analyze the melting of ponds on the surface of the ice. Very interesting and non-trivial example 13. Get a topologist. A basic story that begins with Moebius, Klein bottle and quickly move on to invariants and the story of homology ncohomology, as well as applied topology, where the author tells about constant homologies, which can be used to analyze the coverage of a certain area by sensors. This chapter is not so easy to read. 14. Fox and hedgehog This chapter concludes the book and in it the author reflects on the nature of mathematical thinking and its role in human civilization, using the metaphor of foxes and hedgehogs, as well as the fantastic image of mathematician-eating aliens. As Stewart famously said, “The fox knows many different things, and the hedgehog knows one thing, but more.” To illustrate, he introduces the image of “mathematical aliens.” Imagine a civilization that preys on mathematics to survive and is forced to seek new mathematical ideas wherever it can. Then she flies to visit us and begins to eat our mathematics, starting with the delights of higher mathematics. Then we begin to disappear generally accepted things - phones, computers, the Internet, geolocation, ... These aliens stop, but we only have arithmetic, which they disdained, and the Stone Age around us.

Through this story, Ian shows the fundamental importance of mathematics to the world around us, although most people are unaware of it. Ian proposes to popularize this and increase the number of people involved in mathematics, where it is perceived as a rich creative discipline, not a primitive caricature, as it is often presented. And the book ends with a phrase. Yes, the fox knows many secrets, and mathematics - only one, but very big. It's called mathematics, and it's transforming our world. #PopularScience #Math #Physics