JOURNEY THROUGH THE WONDERS OF PLANE GEOMETRY, A

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Geometry is one of the most beautiful aspects of mathematics. This beauty is because you can "see" geometry at work. Most people are exposed to the very basic elements of geometry throughout their schooling with the most concentrated study in the secondary school curriculum. High schools in the United States offer one year of concentrated study of geometry that shows students how a mathematician functions, since everything that is accepted beyond the basic axioms must be proved. Unfortunately, as the course is only one year long, there is still very much in geometry left unexplored for the general audience. That is the challenge of this book, in which we will present a plethora of amazing geometric relationships. We begin with the special relationships of the Golden Ratio, before considering unexpected concurrencies and collinearities. Next, we present some surprising results that arise when squares and similar triangles are placed on triangle sides, followed by a discussion of concyclic points and the relationships between circles and various linear figures. Moving on to more advanced aspects of linear geometry, we consider the geometric wonders of polygons. Finally, we address geometric surprises and fallacies, before concluding with a chapter on the useful concept of homothety, which is not included in the American year-long course in geometry. Request Inspection Copy Sample Chapter(s) Introduction Chapter 9: Geometric Surprises Contents: About the Authors Introduction The Golden Ratio in Geometry Unexpected Concurrencies Unexpected Collinearities Squares on Triangle Sides Similar Triangles on Triangle Sides Discovering Concyclic Points Circle Wonders Polygons and Polygrams Geometric Surprises Geometric Fallacies Homothety, Similarity, and Applications Index Readership: This book is suitable for secondary/high school level students and teachers, as well as a general readership, particularly those interested in bridging the gaps in their knowledge of geometry.

MATH JOURNEY THROUGH DIFFERENTIAL EQUATIONS OF PHYSICS

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Mathematics is the language of physics, and over time physicists have developed their own dialect. The main purpose of this book is to bridge this language barrier, and introduce the readers to the beauty of mathematical physics. It shows how to combine the strengths of both approaches: physicists often arrive at interesting conjectures based on good intuition, which can serve as the starting point of interesting mathematics. Conversely, mathematicians can more easily see commonalities between very different fields (such as quantum mechanics and electromagnetism), and employ more advanced tools. Rather than focusing on a particular topic, the book showcases conceptual and mathematical commonalities across different physical theories. It translates physical problems to concrete mathematical questions, shows how to answer them and explains how to interpret the answers physically. For example, if two Hamiltonians are close, why are their dynamics similar? The book alternates between mathematics- and physics-centric chapters, and includes plenty of concrete examples from physics as well as 76 exercises with solutions. It exploits that readers from either end are familiar with some of the material already. The mathematics-centric chapters provide the necessary background to make physical concepts mathematically precise and establish basic facts. And each physics-centric chapter introduces physical theories in a way that is more friendly to mathematicians. As the book progresses, advanced material is sprinkled in to showcase how mathematics and physics augment one another. Some of these examples are based on recent publications and include material which has not been covered in other textbooks. This is to keep it interesting for the readers. Request Inspection Copy Sample Chapter(s) Preface Chapter 1: Introduction Contents: Preface About the Author Acknowledgments Introduction Ordinary Differential Equations The Hamiltonian Formalism of Classical Mechanics Banach & Hilbert Spaces Linear Operators The Fourier Transform Schwartz Functions & Tempered Distributions Green's Functions Quantum Mechanics Variational Calculus Appendix A: Primer on Measure Theory Appendix B: Functional Calculus Solutions to the Odd-Numbered Exercises Bibliography Index Readership: Advanced undergraduate and graduate students of mathematics and physics with an interest in mathematical physics. Instructors can use it to design a comprehensive course on differential equations after paring down some of the material. Or alternatively, it also serves as a good basis for more specialized classes on, e.g., quantum mechanics or electromagnetism that place more emphasis on the necessary mathematics.