Problems and Solutions in Stochastic Calculus with Applications

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【簡介】 Problems and Solutions in Stochastic Calculus with Applications exposes readers to simple ideas and proofs in stochastic calculus and its applications. It is intended as a companion to the successful original title Introduction to Stochastic Calculus with Applications (Third Edition) by Fima Klebaner. The current book is authored by three active researchers in the fields of probability, stochastic processes, and their applications in financial mathematics, mathematical biology, and more. The book features problems rooted in their ongoing research. Mathematical finance and biology feature pre-eminently, but the ideas and techniques can equally apply to fields such as engineering and economics. The problems set forth are accessible to students new to the subject, with most of the problems and their solutions centring on a single idea or technique at a time to enhance the ease of learning. While the majority of problems are relatively straightforward, more complex questions are also set in order to challenge the reader as their understanding grows. The book is suitable for either self-study or for instructors, and there are numerous opportunities to generate fresh problems by modifying those presented, facilitating a deeper grasp of the material. 【目錄】

Problems and Solutions in Mathematical Olympiad

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【簡介】 The series is edited by the head coaches of China's IMO National Team. Each volume, catering to different grades, is contributed by the senior coaches of the IMO National Team. The Chinese edition has won the award of Top 50 Most Influential Educational Brands in China. The series is created in line with the mathematics cognition and intellectual development levels of the students in the corresponding grades. All hot mathematics topics of the competition are included in the volumes and are organized into chapters where concepts and methods are gradually introduced to equip the students with necessary knowledge until they can finally reach the competition level. In each chapter, well-designed problems including those collected from real competitions are provided so that the students can apply the skills and strategies they have learned to solve these problems. Detailed solutions are provided selectively. As a feature of the series, we also include some solutions generously offered by the members of Chinese national team and national training team. 【目錄】 Ingenious Computation of Rational Numbers Absolute Value First-Degree Equation with One Variable System of First-Degree Equations Application of a System of First-Degree Equations Setting Up (Systems of) Equations to Solve Word Problems (System of) First-Degree Inequalities Multiplication and Division of Polynomials with Integer Coefficients Line Segments Angles Sum of the Interior Angles of a Triangle Parallel Lines Assigning Variables Unnecessary for Solution Undetermined Coefficients Synthetic Division and Polynomial Remainder Theorem Simplifying and Evaluating an Algebraic Formula Logical Inference I Logical Inference II Divisibility Odd Numbers and Even Numbers Prime Numbers and Composite Numbers The Rule of Sum and the Rule of Product Number of Divisors Positional Notation Modular Arithmetic First-Degree Diophantine Equation with Two Unknowns The Drawer Principle