Описание: This convenient volume offers a popular selection of 100 practice problems -- with hints and solutions -- for students preparing for undergraduate-level math competitions. The challenging brainteasers will also appeal to anyone interested in problems concerning real numbers, differential equations, integrals, polynomials, sets, and other mathematical topics. The hints are very helpful and the solutions are easy to follow. Questions drawn from geometry, group theory and linear algebra involve subjects ranging from multivariate integration to finite series to infinite sums and classical analysis. The only prerequisite is a high school-level background in mathematics. Problem-solvers at varying degrees of proficiency will find this treasury of top-notch numerical puzzles an invitation to hone their mathematical skills as well as a source of stimulating entertainment.
Описание: An introduction to both classical scattering theory and to the time-dependent theory of linear equations in mathematical physics, this text is suitable for advanced undergraduates and graduate students of physics and applied mathematics. Topics include proof of the existence of wave operators, some special equations of mathematical physics -- including Maxwell equations, the linear equations of elasticity and thermoelasticity, and the plate equation -- exterior boundary value problems, radiation conditions, and limiting absorption principles. The self-contained treatment provides background for a complete understanding of all concepts, and an extensive reference list offers suggestions for further reading. Based on the author's lectures at the University of Bonn in 1983-84, this volume will prove useful to researchers as well as students.
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: Approximately 1,000 problems -- with answers and solutions included at the back of the book -- illustrate such topics as random events, random variables, limit theorems, Markov processes, and much more.
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: One of the most useful and practical expositions of Fourier's series, and spherical, cylindrical, and ellipsoidal harmonics, this classic offers a basic but thorough treatment of material that is assumed in many other studies but rarely available in concise form. Includes 190 problems, approximately half with answers. 1893 edition.
Описание: Combining three books into a single volume, this text comprises Multicolor Problems, dealing with several of the classical map-coloring problems; Problems in the Theory of Numbers, an elementary introduction to algebraic number theory; and Random Walks, addressing basic problems in probability theory. The book's primary aim is not so much to impart new information as to teach an active, creative attitude toward mathematics. The sole prerequisites are high-school algebra and (for Multicolor Problems) a familiarity with the methods of mathematical induction. The book is designed for the reader's active participation. The problems are carefully integrated into the text and should be solved in order. Although they are basic, they are by no means elementary. Some sequences of problems are geared toward the mastery of a new method, rather than a definitive result, and others are practice exercises, designed to introduce new concepts. Complete solutions appear at the end.
Описание: This original collection features 100 of the best puzzles from the mid-20th-century column The Graham Dial, submitted by an international readership of workers in applied mathematics. Most include details of several problem-solving methods plus critiques of their efficacy, challenging readers to improve on the solutions. Themes include engineering situations, logic, number theory, and geometry.
This well-known text uses a limited number of basic concepts and techniques -- Hamilton's principle, the theory of the first variation and Bernoulli's separation method -- to develop complete solutions to linear boundary value problems associated with second order partial differential equations such as the problems of the vibrating string, the vibrating membrane, and heat conduction. It is directed to advanced undergraduate and beginning graduate students in mathematics, applied mathematics, physics, and engineering who have completed a course in advanced calculus. In the first three chapters, Professor Sagan introduces Hamilton's principle and the theory of the first variation; he then discusses the representation of the vibrating string, the vibrating membrane and heat conduction (without convection) by partial differential equations. Bernoulli's separation method and infinite series solutions of homogeneous boundary value problems are introduced as a means for solving these problems. The next three chapters take up Fourier series, self-adjoint boundary value problems, Legendre polynomials, and Bessel functions. The concluding three chapters address the characterization of eigenvalues by a variational principle; spherical harmonics, and the solution of the Schroedinger equation for the hydrogen atom; and the nonhomogeneous boundary value problem. Professor Sagan concludes most sections of this excellent text with selected problems (solutions provided for even-numbered problems) to reinforce the reader's grasp of the theories and techniques presented.
Virtually unobtainable for many years, these two books by Lewis Carroll (C. L. Dodgson) have now been reprinted in their entirety for the pleasure of modern enthusiasts of mathematical puzzles. Written by the 19th-century mathematician who gave us Alice in Wonderland and Through the Looking Glass, they contain an unusual combination of wit and mathematical intricacy that will test your mathematical ingenuity and provide hours of stimulating entertainment. Pillow-Problems is one of the rarest of all Lewis Carroll's works. It contains 72 mathematical posers ranging from those that can be solved by arithmetic, simple algebra, or plane geometry, to those that require more advanced algebra, trigonometry, algebraical geometry, differential calculus, and transcendental probabilities. Both numerical answers and fully worked out solutions are given, each in a separate section so that you can test your methods of problem-solving even after you have looked up the answer to a problem. In A Tangled Tale, Carroll embodies some of his most perplexing mathematical puzzles in the ten knots or chapters of a delightful story that has all the charm and wit of his better-known works. The Tale was originally printed as a monthly magazine serial, and many readers sent in solutions to the problems that were posed in it. In the long Appendix to The Tale, which contains the answers and solutions to the problems, Carroll uses the answers sent in by readers as the basis for illuminating and entertaining discussions of the many wrong ways in which the problems can be attacked, as well as the right ways.
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. "