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This book gathers the best presentations from the Topic Study Group 30: Mathematics Competitions at ICME-13 in Hamburg, and some from related groups, focusing on the field of working with gifted students. Each of the chapters includes not only original ideas, but also original mathematical problems and their solutions. The book is a valuable resource for researchers in mathematics education, secondary and college mathematics teachers around the globe as well as their gifted students.

The theoretical aspects underpinning diffractive optics are initially explored, including the main equations in diffraction theory and diffractive optical transformations. Application of electromagnetic field theory for...

Bartel Leendert van der Waerden made major contributions to algebraic geometry, abstract algebra, quantum mechanics, and other fields. He liberally published on the history of mathematics. His 2-volume work Modern Algebra is one of the most influential and popular mathematical books ever written. It is therefore surprising that no monograph has been dedicated to his life and work. Van der Waerden's record is complex. In attempting to understand his life, the author assembled thousands of documents from numerous archives in Germany, the Netherlands, Switzerland and the United States...

How Does One Cut a Triangle? is a work of art, and rarely, perhaps never, does one find the talents of an artist better suited to his intention than we find in Alexander Soifer and this book.

Peter D. Johnson, Jr.

This delightful book considers and solves many problems in dividing triangles into n congruent pieces and also into similar pieces, as well as many extremal problems about placing points in convex figures. The book is primarily meant for clever high school students and college students interested in geometry, but even mature mathematicians will find a lot...

Nanophotonics deals with the diffraction of light from objects with nanoscale features. This book is devoted to achievements in diffractive optics, focusing on the creation of new nanophotonic components and devices, as well as instrumentation and available information technology. It describes methods of calculation of diffractive optical elements to solve actual problems of nanophotonics. Coverage includes mathematical methods for calculation of diffraction gratings, calculation of modes of inhomogeneous waveguides, integral methods of calculation of electromagnetic field near the focus,...

Diffractive Nanophotonics demonstrates the utility of the well-established methods of diffractive computer optics in solving nanophotonics tasks. It is concerned with peculiar properties of laser light diffraction by microoptics elements with nanoscale features and light confinement in subwavelength space regions. Written by recognized experts in this field, the book covers in detail a wide variety of advanced methods for the rigorous simulation of light diffraction. The authors apply their expertise to addressing cutting-edge problems in nanophotonics.
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Now in its third decade, the Colorado Mathematical Olympiad (CMO), founded by the author, has become an annual state-wide competition, hosting many hundreds of middle and high school contestants each year. This book presents a year-by-year history of the CMO from 2004-2013 with all the problems from the competitions and their solutions. Additionally, the book includes 10 further explorations, bridges from solved Olympiad problems to 'real' mathematics, bringing young readers to the forefront of various fields of mathematics. This book contains more than just problems,...