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The author presents a complex history of the Pythagorean Theorem, examining the earliest evidence of knowledge of the theorem to Einstein's theory of relativity.
STEMathematics is an instructional resource designed primarily for secondary level mathematics teachers and students interested in discovering how mathematics describes (and is applied to) our natural world. This resource provides both the historical elements and the technical aspects of various topics in mathematics that provide instructional context in the sciences, technology, and engineering, (STEM) disciplines. The purpose of STEMathematics is to help teachers become more personally interested in the topics they teach and to gain a broader perspective of how mathematics can be integrated with other subject disciplines.
If you've ever thought that mathematics and art don't mix, this stunning visual history of geometry will change your mind. As much a work of art as a book about mathematics, Beautiful Geometry presents more than sixty exquisite color plates illustrating a wide range of geometric patterns and theorems, accompanied by brief accounts of the fascinating history and people behind each. With artwork by Swiss artist Eugen Jost and text by math historian Eli Maor, this unique celebration of geometry covers numerous subjects, from straightedge-and-compass constructions to intriguing configurations involving infinity. The result is a delightful and informative illustrated tour through the 2,500-year-old history of one of the most important branches of mathematics.
This unique textbook provides an accessible introduction to Einstein's general theory of relativity, a subject of breathtaking beauty and supreme importance in physics. With his trademark blend of wit and incisiveness, A. Zee guides readers from the fundamentals of Newtonian mechanics to the most exciting frontiers of research today, including de Sitter and anti-de Sitter spacetimes, Kaluza-Klein theory, and brane worlds. Unlike other books on Einstein gravity, this book emphasizes the action principle and group theory as guides in constructing physical theories. Zee treats various topics in a spiral style that is easy on beginners, and includes anecdotes from the history of physics that will appeal to students and experts alike. He takes a friendly approach to the required mathematics, yet does not shy away from more advanced mathematical topics such as differential forms. The extensive discussion of black holes includes rotating and extremal black holes and Hawking radiation. The ideal textbook for undergraduate and graduate students, Einstein Gravity in a Nutshell also provides an essential resource for professional physicists and is accessible to anyone familiar with classical mechanics and electromagnetism. It features numerous exercises as well as detailed appendices covering a multitude of topics not readily found elsewhere. Provides an accessible introduction to Einstein's general theory of relativity Guides readers from Newtonian mechanics to the frontiers of modern research Emphasizes symmetry and the Einstein-Hilbert action Covers topics not found in standard textbooks on Einstein gravity Includes interesting historical asides Features numerous exercises and detailed appendices Ideal for students, physicists, and scientifically minded lay readers Solutions manual (available only to teachers)
Calculus in 3D is an accessible, well-written textbook for an honors course in multivariable calculus for mathematically strong first- or second-year university students. The treatment given here carefully balances theoretical rigor, the development of student facility in the procedures and algorithms, and inculcating intuition into underlying geometric principles. The focus throughout is on two or three dimensions. All of the standard multivariable material is thoroughly covered, including vector calculus treated through both vector fields and differential forms. There are rich collections of problems ranging from the routine through the theoretical to deep, challenging problems suitable for in-depth projects. Linear algebra is developed as needed. Unusual features include a rigorous formulation of cross products and determinants as oriented area, an in-depth treatment of conics harking back to the classical Greek ideas, and a more extensive than usual exploration and use of parametrized curves and surfaces. Zbigniew Nitecki is Professor of Mathematics at Tufts University and a leading authority on smooth dynamical systems. He is the author of Differentiable Dynamics, MIT Press; Differential Equations, A First Course (with M. Guterman), Saunders; Differential Equations with Linear Algebra (with M. Guterman), Saunders; and Calculus Deconstructed, AMS.
The interest earned on a bank account, the arrangement of seeds in a sunflower, and the shape of the Gateway Arch in St. Louis are all intimately connected with the mysterious number e. In this informal and engaging history, Eli Maor portrays the curious characters and the elegant mathematics that lie behind the number. Designed for a reader with only a modest mathematical background, this biography brings out the central importance of e to mathematics and illuminates a golden era in the age of science.
Jeder kennt p = 3,14159..., viele kennen e = 2,71828..., einige i. Und dann? Die "viertwichtigste" Konstante ist die Eulersche Zahl g = 0,5772156... - benannt nach dem genialen Leonhard Euler (1707-1783). Bis heute ist unbekannt, ob g eine rationale Zahl ist. Das Buch lotet die "obskure" Konstante aus. Die Reise beginnt mit Logarithmen und der harmonischen Reihe. Es folgen Zeta-Funktionen und Eulers wunderbare Identität, Bernoulli-Zahlen, Madelungsche Konstanten, Fettfinger in Wörterbüchern, elende mathematische Würmer und Jeeps in der Wüste. Besser kann man nicht über Mathematik schreiben. Was Julian Havil dazu zu sagen hat, ist spektakulär.

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