Mathematical Reflections: Two Special Years - Aliyev, Yagub (My University, 2015)
Inspired by appreciative and constructive feedback from our faithful readers, I present Mathematical Reflections: two special years, a compilation and revision of the 2014 and 2015 volumes from the online journal of the same name. Since its inception in January 2006, the journal has attracted readers and contributors from all over the world. It successfully brings together enthusiasts with di↵erent mathematical and cultural backgrounds for the common purpose of making mathematics even more elegant and exciting. The journal publishes six issues each year. This book is aimed at high school students, participants in math competitions, undergraduates, and anyone who has a passion for mathematics. Many of the problems, solutions, and articles were submitted by passionate readers, and they all require creativity, experience, and comprehensive mathematical knowledge. In publishing this volume, my e↵orts were especially geared towards correcting and improving on many of the solutions and articles so that audience can enjoy them even more. The articles herein focus on a variety of interesting topics outside of mainstream curriculum. Students can expand their mathematical horizons through material outside the scope of their regular classes. For instructors, the articles provide an intriguing opportunity to move away from a structured curriculum and guide students through to the invaluable moments of discovery. All of the featured problems are original. In order to make the material more accessible to the readers, this book as well as the journal is organized by the mathematical ability required to solve the problems. The junior section presents introductory problems (though they are not necessarily easy). The senior and Olympiad sections are for students preparing for national or international contests such as the United States of America Mathematical Olympiad (USAMO) or the International Mathematical Olympiad (IMO). Lastly, the undergraduate section o↵ers college students a unique opportunity to solve non-routine problems in areas such as linear algebra, calculus, and graph theory. This book could not have seen the light of day without the loyal readers and collaborators of the online journal. I would like to thank them all and express my gratitude for their continuous support. I sincerely hope that others will follow in their footsteps and continue to carry the baton so that the mission of the journal to o↵er the opportunity for mathematics enthusiasts to publish original and interesting work will be fulfilled in future years as well. I would also like to thank Maxim Ignatiuc and Sean Elliott for their help in putting together the material submitted by our contributors. Many thanks to Gabriel Dospinescu for his pertinent observations. And a special thank you to Richard Stong for the many improvements in the manuscript. If you are interested in reading the journal, please visit its website: http://awesomemath.org/mathematical-reflections/. Readers may submit articles, problems, and solutions to reflections@awesomemath.org. Proceeds from the sale of this book will be used to sustain the journal in future years. Enjoy the problems and articles!
Keywords: Mathematics -- Problems, exercises, etc; Mathematics -- Study and teaching (Secondary); Mathematical recreations; Mathematics competitions; Problem solving -- Study and teaching; Olympiads -- Mathematics