Undergraduate Mathematics Competitions (1995–2016): Taras Shevchenko National University of Kyiv (Problem Books in Mathematics)

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. Front Matter....Pages i-xiv Front Matter....Pages 1-2 1995....Pages 3-5 1996....Pages 7-8 1997....Pages 9-10 1998....Pages 11-12 1999....Pages 13-13 2000....Pages 15-17 2001....Pages 19-20 2002....Pages 21-23 2003....Pages 25-26 2004....Pages 27-29 2005....Pages 31-33 2006....Pages 35-37 2007....Pages 39-41 2008....Pages 43-45 2009....Pages 47-49 2010....Pages 51-53 2011....Pages 55-57 2012....Pages 59-61 2013....Pages 63-64 2014....Pages 65-66 Front Matter....Pages 1-2 2015....Pages 67-68 2016....Pages 69-71 Front Matter....Pages 73-74 1995....Pages 75-81 1996....Pages 83-87 1997....Pages 89-93 1998....Pages 95-101 1999....Pages 103-105 2000....Pages 107-112 2001....Pages 113-117 2002....Pages 119-124 2003....Pages 125-131 2004....Pages 133-138 2005....Pages 139-144 2006....Pages 145-151 2007....Pages 153-159 2008....Pages 161-168 2009....Pages 169-174 2010....Pages 175-182 2011....Pages 183-188 2012....Pages 189-198 Front Matter....Pages 73-74 2013....Pages 199-204 2014....Pages 205-209 2015....Pages 211-216 2016....Pages 217-223 Back Matter....Pages 225-228 Foreword 6 Preface 8 Contents 11 Part I Problems 13 1995 15 1996 18 1997 20 1998 22 1999 24 2000 25 2001 28 2002 30 2003 33 2004 35 2005 38 2006 41 2007 44 2008 47 2009 50 2010 53 2011 56 2012 59 2013 62 2014 64 2015 66 2016 68 Part II Solutions 71 1995 73 1996 80 1997 85 1998 90 1999 97 2000 100 2001 106 2002 111 2003 117 2004 124 2005 130 2006 136 2007 143 2008 150 2009 158 2010 164 2011 172 2012 178 2013 188 2014 194 2015 199 2016 205 References 212 Thematic Index 213