Versatile and comprehensive in content, this book of problems will appeal to students in nearly all areas of mathematics. The text offers original and advanced problems proposed from 1995 to 2016 at the Mathematics Olympiads. Essential for undergraduate students, PhD students, and instructors, the problems in this book vary in difficulty and cover most of the obligatory courses given at the undergraduate level, including calculus, algebra, geometry, discrete mathematics, measure theory, complex analysis, differential equations, and probability theory. Detailed solutions to all of the problems from Part I are supplied in Part II, giving students the ability to check their solutions and observe new and unexpected ideas. Most of the problems in this book are not technical and allow for a short and elegant solution. The problems given are unique and non-standard; solving the problems requires a creative approach as well as a deep understanding of the material. Nearly all of the problems are originally authored by lecturers, PhD students, senior undergraduates, and graduate students of the mechanics and mathematics faculty of Taras Shevchenko National University of Kyiv as well as by many others from Belgium, Canada, Great Britain, Hungary, and the United States.

Contains many original and advanced problems for undergraduate students Includes problems for all obligatory mathematical courses, including calculus, algebra, geometry, complex analysis, measure theory, and probability theory Includes detailed solutions in Part II to all problems presented in Part I Useful to university instructors for composing assignments and preparing course material Includes supplementary material: sn.pub/extras

Autorentext

Dr. Volodymyr Brayman received his PhD in probability and statistics from the Institute of Mathematics of National Academy of Sciences of Ukraine in 2007. He is currently an Assistant Professor at the Department of Mathematical Analysis at Taras Shevchenko National University of Kyiv. He is an expert in stochastic processes, a jury member in various mathematical competitions, and an author of numerous problems proposed at the competitions. He co-authored with Prof. Alexander Kukush a problem book titled 'Undergraduate Mathematics Competitions (1995-2016)', Taras Shevchenko National University of Kyiv (ISBN 978-3-319-58672-4), published with Springer. Prof. Andrii Chaikovskyi received his PhD in differential equations from Taras Shevchenko National University of Kyiv in 2001 and completed his postdoctoral degree in differential equations (Habilitation) in 2012. He is currently the Head of the Department of Mathematical Analysis at Taras Shevchenko National University of Kyiv. He is the author/coauthor of more than 60 research papers. His research interests include abstract differential and difference equations and approximation theory. Dr. Oleksii Konstantinov is an Associate Professor of the Department of Mathematical Analysis at Taras Shevchenko National University of Kyiv. His research interests include Operator Theory, Mathematical Scattering Theory and Differential Operators. Prof. Alexander Kukush received his PhD in probability and statistics from Kyiv University in 1982 and completed his postdoctoral degree in probability and statistics (Habilitation) in 1995. He is a Professor of the Department of Mathematical Analysis at Taras Shevchenko National University of Kyiv. He is the author/coauthor of more than 150 research papers and 4 books. His research interests include mathematical and applied statistics, actuarial and financial mathematics. Prof. Yuliya Mishura received her PhD in probability and statistics from Kyiv University in 1978 and completed her postdoctoral degree in probability and statistics (Habilitation) in 1990. She is currently a Professor of the Department of Probability, Statistics and Actuarial Mathematics at Taras Shevchenko National University of Kyiv. She is the author/coauthor of more than 300 research papers and 12 books. Her research interests include theory and statistics of stochastic processes, stochastic differential equations, fractional calculus and fractional processes, stochastic analysis. Dr. Oleksii Nesterenko received his PhD in mathematical analysis from Taras Shevchenko National University of Kyiv in 2007. He is currently an Associate Professor of the Department of Mathematical Analysis of Taras Shevchenko National University of Kyiv. He is the author/coauthor of more than 10 research papers. His research interests include approximation theory.

Inhalt
Foreword.- Preface.- Part I.- Problems (1995-2016) .- Part II. Solutions (1995-2016).- References.- Thematic Index.