Designed for advanced high school students, undergraduates, graduate students, mathematics teachers, and any lover of mathematical challenges, this two-volume set offers a broad spectrum of challenging problems -- ranging from relatively simple to extremely difficult. Indeed, some rank among the finest achievements of outstanding mathematicians. Translated from a well-known Russian work entitled Non-Elementary Problems in an Elementary Exposition, the chief aim of the book is to acquaint the readers with a variety of new mathematical facts, ideas, and methods. And while the majority of the problems represent questions in higher ("non-elementary") mathematics, most can be solved with elementary mathematics. In fact, for the most part, no knowledge of mathematics beyond a good high school course is required. Volume One contains 100 problems, with detailed solutions, all dealing with probability theory and combinatorial analysis. Topics include the representation of integers as sums and products, combinatorial problems on the chessboard, geometric problems on combinatorial analysis, problems on the binomial coefficients, problems on computing probabilities, experiments with infinitely many possible outcomes, and experiments with a continuum of possible outcomes. Volume Two contains 74 problems from various branches of mathematics, dealing with such topics as points and lines, lattices of points in the plane, topology, convex polygons, distribution of objects, nondecimal counting, theory of primes, and more. In both volumes the statements of the problems are given first, followed by a section giving complete solutions. Answers and hints are given at the end of the book. Ideal as a text, for self-study, or as a working resource for a mathematics club, this wide-ranging compilation offers 174 carefully chosen problems that will test the mathematical acuity and problem-solving skills of almost any student, teacher, or mathematician.
Описание: Whimsically and delightfully presented mathematical recreations by the author of Alice in Wonderland are solved by arithmetic, algebra, geometry, trigonometry, differential calculus and transcendental properties. 6 illustrations. Two books bound as one.
Описание: Nearly 300 mathematical brain-teasers from the fields of arithmetic, algebra, plane and solid geometry, trigonometry, number theory, and general recreational mathematics. From simple to complex; all challenge the reader to devise solutions more elegant than the ones provided. Offers hours of brain-bending amusement. 270 problems. 121 illustrations. Solutions. List of Sources.
Описание: "A very useful addition to the chemical literature." -- Journal of the American Chemical Society. Designed to aid students and teachers in advanced physical chemistry, spectroscopy, or quantum chemistry courses, this carefully written book is unique in the variety of problems covered and the detail of the solutions provided. The book consists of 12 chapters, each of which includes a short introduction, followed by approximately 20 problems with detailed solutions. Also provided in each chapter are approximately 10 "supplementary" problems, with answers but no solutions. Chapter headings include: Atomic Physics and the Old Quantum Theory Waves and Superposition Postulates and Formalism of Quantum Mechanics Simple Exactly Soluble Problems in Wave Mechanics Angular Momentum Perturbation and Variation Theory Hydrogen-Like Atoms Electronic Structure of Atoms Electronic Structure of Molecules Radiation and Matter Molecular Spectroscopy Scattering Theory Assuming some facility with calculus, mechanics, and electricity and magnetism, the authors offer thorough and up-to-date coverage of both modern subject matter and standard topics. Interspersed among classic examples are lucid applications involving such topics as Fourier transforms, Poisson brackets, uncertainty, the virial theorem, van der Waals forces, lasers, tunneling, group theory, and the Born approximation. Students will also find 10 helpful appendixes covering a range of mathematical topics, a list of references cited in solutions to the problems, and a Subject Index. With its unique variety of problems, unusually detailed solutions, and wide range of applications, this book not only expounds the principles of quantum theory but also helps students develop the proper intuition for solving problems in a complex and subtle field of endeavor.
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