<div>This book presents the mathematical methods that students need when preparing&nbsp;for competitions, whether for the International Mathematical Olympiad (IMO) for high school students or the Putnam competition for undergraduate students.&nbsp; The book features six parts, each subdivided into several chapters.&nbsp; The six major sections address counting methods, number theory, inequalities and the theory of equations, metrical geometry, analysis, and number representations and logic. Each chapter provides detailed solutions to a series of problems as well as approximately 30 more problems; the text thus provides about 1,000 problems to be solved. In addition to its value to students preparing for competitions, this volume is a useful resource for those seeking a thorough and practical review of mathematical methods. For high school, undergraduate,&nbsp;and graduate students in mathematics</div>

Concepts and Problems for Mathematical Competitors (Dover Books on Mathematics)

Humor & Entertainment

Sarana, Alexander

Pogorui, Anatoliy

Rodríguez-Dagnino, Ramón M.

Puzzles & Games

Dover Publications

This book is the first of two volumes on random motions in Markov and semi-Markov random environments. This first volume focuses on homogenous random motions. This volume consists of two parts, the first describing the basic concepts and methods that have been developed for random evolutions. These methods are the foundational tools used in both volumes, and this description includes many results in potential operators. Some techniques to find closed-form expressions in relevant applications are also presented. The second part deals with asymptotic results and presents a variety of applications, including random motion with different types of boundaries, the reliability of storage systems and solutions of partial differential equations with constant coefficients, using commutative algebra techniques. It also presents an alternative formulation to the Black-Scholes formula in finance, fading evolutions and telegraph processes, including jump telegraph processes and the estimation of the number of level crossings for telegraph processes.

Random Motions in Markov and Semi-Markov Random Environments 1: Homogeneous Random Motions and their Applications (Mathematics and Statistics)

Science & Math

Swishchuk, Anatoliy

Mathematics

Wiley-ISTE

This book is the second of two volumes on random motions in Markov and semi-Markov random environments. This second volume focuses on high-dimensional random motions. This volume consists of two parts. The first expands many of the results found in Volume 1 to higher dimensions. It presents new results on the random motion of the realistic three-dimensional case, which has so far been barely mentioned in the literature, and deals with the interaction of particles in Markov and semi-Markov media, which has, in contrast, been a topic of intense study. The second part contains applications of Markov and semi-Markov motions in mathematical finance. It includes applications of telegraph processes in modeling stock price dynamics and investigates the pricing of variance, volatility, covariance and correlation swaps with Markov volatility and the same pricing swaps with semi-Markov volatilities.

Random Motions in Markov and Semi-Markov Random Environments 2: High-dimensional Random Motions and Financial Applications (Mathematics and Statistics)

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