E-Book Overview
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.
E-Book Content
Problem Books in Mathematics
Volodymyr Brayman Alexander Kukush
Undergraduate Mathematics Competitions (1995–2016) Taras Shevchenko National University of Kyiv Second Edition
Problem Books in Mathematics Series editor: Peter Winkler Department of Mathematics Dartmouth College Hanover, NH 03755 USA
More information about this series at http://www.springer.com/series/714
Volodymyr Brayman Alexander Kukush •
Undergraduate Mathematics Competitions (1995–2016) Taras Shevchenko National University of Kyiv Second Edition
123
Volodymyr Brayman Department of Mathematical Analysis Taras Shevchenko National University of Kyiv Kyiv Ukraine
ISSN 0941-3502 Problem Books in Mathematics ISBN 978-3-319-58672-4 DOI 10.1007/978-3-319-58673-1
Alexander Kukush Department of Mathematical Analysis Taras Shevchenko National University of Kyiv Kyiv Ukraine
ISSN 2197-8506
(electronic)
ISBN 978-3-319-58673-1
(eBook)
Library of Congress Control Number: 2017939622 1st edition: © Publishing House “Kyiv University” 2015 2nd edition: © Springer International Publishing AG 2017 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. Printed on acid-free paper This Springer imprint is published by Springer Nature The registered company is Springer International Publishing AG The registered company address