Stories About Maxima and Minima (Mathematical World/Volume 1) by V. M. Tikhomirov (PDF)

Description

Throughout the history of mathematics, maximum and minimum problems have played an important role in the evolution of the field. Many beautiful and important problems have appeared in a variety of branches of mathematics and physics, as well as in other fields of sciences. The greatest scientists of the past—Euclid, Archimedes, Heron, the Bernoullis, Newton, and many others—took part in seeking solutions to these concrete problems. The solutions stimulated the development of the theory, and, as a result, techniques were elaborated that made possible the solution of a tremendous variety of problems by a single method. This book presents fifteen “stories” designed to acquaint readers with the central concepts of the theory of maxima and minima, as well as with its illustrious history. This book is accessible to high school students and would likely be of interest to a wide variety of readers. In Part One, the author familiarizes readers with many concrete problems that lead to discussion of the work of some of the greatest mathematicians of all time. Part Two introduces a method for solving maximum and minimum problems that originated with Lagrange. While the content of this method has varied constantly, its basic conception has endured for over two centuries. The final story is addressed primarily to those who teach mathematics, for it impinges on the question of how and why to teach. Throughout the book, the author strives to show how the analysis of diverse facts gives rise to a general idea, how this idea is transformed, how it is enriched by new content, and how it remains the same in spite of these changes.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐Great book!

⭐This is a very nice introduction to maxima and minima. The first part talks about the history of extremal problems (finding max or min) in different fields. For instance, Heron’s problem in geometry, Snel’s problem in refraction of light, Newton in aerodynamics(control). In these areas, it describes how various people attempted to solve these problems using geometry, trigonometry, algebra, etc. Working with him through these problems is a great highschool overview.The second part then unifies all these problems, and solves them again using the same general principle (Differentiation method), This replication really knocks the ideas into your head. Tikhomirov concludes with a description of Lagrange multipliers and how to use them, a good peek into where you can go from the book.All in all, I think math should be thought like this: motivate with the reason behind the problem, illustrate with solution attempted or found by the inventor and finish with the guiding principles for the group of problems.Very good text. It makes math beautiful and useful.

⭐

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