Integration has a long history: its roots can be traced as far back as the ancient Greeks. The first genuinely rigorous definition of an integral was that given by Riemann, and further (more general, and so more useful) definitions have since been given by Lebesgue, Denjoy, Perron, Kurzweil and Henstock, and this culminated in the work of McShane. This textbook provides an introduction to this theory, and it presents a unified yet elementary approach that is suitable for beginning graduate and final year undergraduate students.

This comprehensive book is a state-of-the-art review of research and practices of mathematics education in Singapore. It traces the fascinating journey from the original development of the Singapore mathematics curriculum in the 1950s to the present day, and reports on diverse findings about the Singapore experience that are not readily available in print. All of the authors are active mathematics educators or senior mathematics teachers in Singapore, thus adding authenticity and distinctiveness to the stories covered in this book. The issues they so earnestly explore in this book will undoubtedly be of interest to graduate students, mathematics educators, and the international mathematics education community.

The International Mathematical Olympiad (IMO) is a competition for high school students. China has taken part in the IMO 21 times since 1985 and has won the top ranking for countries 14 times, with a multitude of golds for individual students. The six students China has sent every year were selected from 20 to 30 students among approximately 130 students who took part in the annual China Mathematical Competition during the winter months. This volume comprises a collection of original problems with solutions that China used to train their Olympiad team in the years from 2006 to 2008. Mathematical Olympiad problems with solutions for the years 2002–2006 appear in an earlier volume, Mathematical Olympiad in China.

Integration has a long history: its roots can be traced as far back as the ancient Greeks. The first genuinely rigorous definition of an integral was that given by Riemann, and further (more general, and so more useful) definitions have since been given by Lebesgue, Denjoy, Perron, Kurzweil and Henstock, and this culminated in the work of McShane. This textbook provides an introduction to this theory, and it presents a unified yet elementary approach that is suitable for beginning graduate and final year undergraduate students.

This comprehensive book is a state-of-the-art review of research and practices of mathematics education in Singapore. It traces the fascinating journey from the original development of the Singapore mathematics curriculum in the 1950s to the present day, and reports on diverse findings about the Singapore experience that are not readily available in print. All of the authors are active mathematics educators or senior mathematics teachers in Singapore, thus adding authenticity and distinctiveness to the stories covered in this book. The issues they so earnestly explore in this book will undoubtedly be of interest to graduate students, mathematics educators, and the international mathematics education community.

The International Mathematical Olympiad (IMO) is a competition for high school students. China has taken part in the IMO 21 times since 1985 and has won the top ranking for countries 14 times, with a multitude of golds for individual students. The six students China has sent every year were selected from 20 to 30 students among approximately 130 students who took part in the annual China Mathematical Competition during the winter months. This volume comprises a collection of original problems with solutions that China used to train their Olympiad team in the years from 2006 to 2008. Mathematical Olympiad problems with solutions for the years 2002–2006 appear in an earlier volume, Mathematical Olympiad in China.