This book is sold as a companion volume to the book, Techniques of Problem Solving. The Solutions Manual addresses most end-of-chapter exercises in the book proper.

This volume and Kvant Selecta: Algebra and Analysis, II (MAWRLD/15) are the first volumes of articles published from 1970 to 1990 in the Russian journal, Kvant. The influence of this magazine on mathematics and physics education in Russia is unmatched. This collection represents the Russian tradition of expository mathematical writing at its best.

This book provides a systematic introduction to various geometries, including Euclidean, affine, projective, spherical, and hyperbolic geometries. Also included is a chapter on infinite-dimensional generalizations of Euclidean and affine geometries. A uniform approach to different geometries, based on Klein's Erlangen Program is suggested, and similarities of various phenomena in all geometries are traced. An important notion of duality of geometric objects is highlighted throughout the book. The authors also include a detailed presentation of the theory of conics and quadrics, including the theory of conics for non-Euclidean geometries. The book contains many beautiful geometric facts and has plenty of problems, most of them with solutions, which nicely supplement the main text.

Flatland: A Romance of Many Dimensions is an 1884 novella by Edwin A. Abbott, still popular among mathematics and computer science students, and considered useful reading for people studying topics such as the concept of other dimensions.

This volume and Kvant Selecta: Algebra and Analysis, I (MAWRLD/14) are the first volumes of articles published from 1970 to 1990 in the Russian journal, Kvant. The influence of this magazine on mathematics and physics education in Russia is unmatched. This collection represents the Russian tradition of expository mathematical writing at its best.

There is a tradition in Russia that holds that mathematics can be both challenging and fun. One fine outgrowth of that tradition is the magazine, Kvant, which has been enjoyed by many of the best students since its founding in 1970. The articles in Kvant assume only a minimal background, that of a good high school student, yet are capable of entertaining mathematicians of almost any level. Sometimes the articles require careful thought or a moment's work with a pencil and paper. However, the industrious reader will be generously rewarded by the elegance and beauty of the subjects.

This book tells the story of Diophantine analysis, a subject that, owing to its thematic proximity to algebraic geometry, became fashionable in the last half century and has remained so ever since. This new treatment of the methods of Diophantus - a person whose very existence has long been doubted by most historians of mathematics - will be accessible to readers who have taken some university mathematics. It includes the elementary facts of algebraic geometry indispensable for its understanding. The heart of the book is a fascinating account of the development of Diophantine methods during the Renaissance and in the work of Fermat. This account is continued to our own day and ends with an afterword by Joseph Silverman who notes the most recent developments including the proof of Fermat's Last Theorem.

The second edition of this book includes revised, updated, and additional material on the structure, theory, and application of classes of dynamic models in Bayesian time series analysis and forecasting. In addition to wide ranging updates to central material, the second edition includes many more exercises and covers new topics at the research and application frontiers of Bayesian forecastings.

The purpose of this book is to explore the rich and elegant interplay that exists between the two main currents of mathematics, the continuous and the discrete. Such fundamental notions in discrete mathematics as induction, recursion, combinatorics, number theory, discrete probability, and the algorithmic point of view as a unifying principle are continually explored as they interact with traditional calculus. The book is addressed primarily to well-trained calculus students and those who teach them, but it can also serve as a supplement in a traditional calculus course for anyone who wants to see more. The problems, taken for the most part from probability, analysis, and number theory, are an integral part of the text. There are over 400 problems presented in this book.

This unique book explores both theoretical and experimental aspects of nonlinear vibrations and stability of shells and plates. It is ideal for researchers, professionals, students, and instructors. Expert researchers will find the most recent progresses in nonlinear vibrations and stability of shells and plates, including advanced problems of shells with fluid-structure interaction. Professionals will find many practical concepts, diagrams, and numerical results, useful for the design of shells and plates made of traditional and advanced materials. They will be able to understand complex phenomena such as dynamic instability, bifurcations, and chaos, without needing an extensive mathematical background. Graduate students will find (i) a complete text on nonlinear mechanics of shells and plates, collecting almost all the available theories in a simple form, (ii) an introduction to nonlinear dynamics, and (iii) the state of art on the nonlinear vibrations and stability of shells and plates, including fluid-structure interaction problems.

Algebraic geometry is often employed to encode and decode signals transmitted in communication systems. This book describes the fundamental principles of algebraic coding theory from the perspective of an engineer, discussing a number of applications in communications and signal processing. The principal concept is that of using algebraic curves over finite fields to construct error-correcting codes. The most recent developments are presented including the theory of codes on curves, without the use of detailed mathematics, substituting the intense theory of algebraic geometry with Fourier transform where possible. The author describes the codes and corresponding decoding algorithms in a manner that allows the reader to evaluate these codes against practical applications, or to help with the design of encoders and decoders. This book is relevant to practicing communication engineers and those involved in the design of new communication systems, as well as graduate students and researchers in electrical engineering.

Originating with Andreas Floer in the 1980s, Floer homology has proved to be an effective tool in tackling many important problems in three- and four-dimensional geometry, and topology. This book provides a comprehensive treatment of Floer homology, based on the Seiberg-Witten monopole equations. After first providing an overview of the results, the authors develop the analytic properties of the Seiberg-Witten equations, assuming only a basic grounding in differential geometry and analysis. The Floer groups of a general three-manifold are then defined, and their properties studied in detail. Two final chapters are devoted to the calculation of Floer groups, and to applications of the theory in topology. Suitable for beginning graduate students and researchers, this book provides the first full discussion of a central part of the study of the topology of manifolds since the mid 1990s.

This is a concise and elementary introduction to contemporary measure and integration theory as it is needed in many parts of analysis and probability theory. Undergraduate calculus and an introductory course on rigorous analysis in R are the only essential prerequisites, making the text suitable for both lecture courses and for self-study. Numerous illustrations and exercises are included to consolidate what has already been learned and to discover variants and extensions to the main material. Hints and solutions can be found on the authors website, which can be reached at