According to the great mathematician Paul Erdös, God maintains perfect mathematical proofs in The Book. This book presents the authors candidates for such "perfect proofs," those which contain brilliant ideas, clever connections, and wonderful observations, bringing new insight and surprising perspectives to problems from number theory, geometry, analysis, combinatorics, and graph theory. As a result, this book will be fun reading for anyone with an interest in mathematics.
This book explores the idea that mathematics educators and teachers are also problem solvers and learners, and as such they constantly experience mathematical and pedagogical disturbances. Accordingly, many original tasks and learning activities are results of personal mathematical and pedagogical disturbances of their designers, who then transpose these disturbances into learning opportunities for their students. This learning-transposition process is a cornerstone of mathematics teacher education as a lived, developing enterprise. Mathematical Encounters and Pedagogical Detours unfold the process and illustrate it by various examples. The book engages readers in original tasks, shares the results of task implementation and describes how these results inform the development of new tasks, which often intertwine mathematics and pedagogy. Most importantly, the book includes a dialogue between the authors based on the stories of their own learning, which triggers continuous exploration of learning opportunities for their students.
Norman Author Pens Innovative Math Book "Mathematical Encounters for the Inquisitive Mind" a new work by Paul Chika Emekwulu of Norman takes an original approach to math. Emekwulu, an award-winning author and motivational speaker, hopes his works has something for everyone. The work is not strictly in line with any traditional curriculum. Sample Chapters include: A Student ́s Logic Under Trial: Verifying a summation strategy for first n Fibonacci numbers From Murder Scene to Building and Transforming Word Problems into Simple Equations Using Your Intuition for Self-Empowerment Mathematics Behind Bars: My Experience with U.S. Immigration (Courtesy of The Norman Transcript)
A number of years ago, Harriet Sheridan, then Dean of Brown University, organized a series oflectures in which individual faculty members described how it came about that they entered their various fields. I was invited to participate in this series and found in the invitation an opportunity to recall events going back to my early teens. The lecture was well received and its reception encouraged me to work up an expanded version. My manuscript lay dormant all these years. In the meanwhile, sufficiently many other mathematical experiences and encounters accumulated to make this little book. My 1981 lecture is the basis of the first piece: "Napoleon's Theorem. " Although there is a connection between the first piece and the second, the four pieces here are essentially independent. The sec ond piece, "Carpenter and the Napoleon Ascription," has as its object a full description of a certain type of scholar-storyteller (of whom I have known and admired several). It is a pastiche, contain ing a salad bar selection blended together by my own imagination. This piece purports, as a secondary goal, to present a solution to a certain unsolved historical problem raised in the first piece. The third piece, "The Man Who Began His Lectures with 'Namely'," is a short reminiscence of Stefan Bergman, one of my teachers of graduate mathematics. Bergman, a remarkable person ality, was born in Poland and came to the United States in 1939.
Celestial Encounters traces the history of attempts to solve the problem of celestial mechanics first posited in Isaac Newton's Principia in 1686. More generally, the authors reflect on mathematical creativity and the roles that chance encounters, politics, and circumstance play in it. 23 halftones. 64 line illustrations.
This book has been written to fIll a substantial gap in the current literature in mathemat ical education. Throughout the world, school mathematical curricula have incorporated probability and statistics as new topics. There have been many research papers written on specifIc aspects of teaching, presenting novel and unusual approaches to introducing ideas in the classroom; however, there has been no book giving an overview. Here we have decided to focus on probability, making reference to inferential statistics where appropriate; we have deliberately avoided descriptive statistics as it is a separate area and would have made ideas less coherent and the book excessively long. A general lead has been taken from the fIrst book in this series written by the man who, probably more than everyone else, has established mathematical education as an aca demic discipline. However, in his exposition of didactical phenomenology, Freudenthal does not analyze probability. Thus, in this book, we show how probability is able to organize the world of chance and idealized chance phenomena based on its development and applications. In preparing these chapters we and our co-authors have reflected on our own acquisition of probabilistic ideas, analyzed textbooks, and observed and reflect ed upon the learning processes involved when children and adults struggle to acquire the relevant concepts.
A sweeping cultural history of one of the most influential mathematical books ever written Euclid's Elements of Geometry is one of the fountainheads of mathematics—and of culture. Written around 300 BCE, it has traveled widely across the centuries, generating countless new ideas and inspiring such figures as Isaac Newton, Bertrand Russell, Abraham Lincoln, and Albert Einstein. Encounters with Euclid tells the story of this incomparable mathematical masterpiece, taking readers from its origins in the ancient world to its continuing influence today. In this lively and informative book, Benjamin Wardhaugh explains how Euclid’s text journeyed from antiquity to the Renaissance, introducing some of the many readers, copyists, and editors who left their mark on the Elements before handing it on. He shows how some read the book as a work of philosophy, while others viewed it as a practical guide to life. He examines the many different contexts in which Euclid's book and his geometry were put to use, from the Neoplatonic school at Athens and the artisans' studios of medieval Baghdad to the Jesuit mission in China and the workshops of Restoration London. Wardhaugh shows how the Elements inspired ideas in theology, art, and music, and how the book has acquired new relevance to the strange geometries of dark matter and curved space. Encounters with Euclid traces the life and afterlives of one of the most remarkable works of mathematics ever written, revealing its lasting role in the timeless search for order and reason in an unruly world.
Did you know that it's easier to add and subtract from left to right, rather than the other way round? And that you can be taught to square a three-digit number in seconds? In Think Like A Maths Genius, two mathematicians offer tips and tricks for doing tricky maths the easy way. With their help, you can learn how to perform lightning calculations in your head, discover methods of incredible memorisation and other feats of mental agility. Learn maths secrets for the real world, from adding up your shopping and calculating a restaurant tip, to figuring out gambling odds (or how much you've won) and how to solve sudoku faster.
This volume is dedicated to Paul Erdos, who has profoundly influenced mathematics in this century, with over 1200 papers on number theory, complex analysis, probability theory, geometry, interpretation theory, algebra set theory and combinatorics. One of Erdos' hallmarks is the host of stimulating problems and conjectures, to many of which he has attached monetary prices, in accordance with their notoriety. A feature of this volume is a collection of some fifty outstanding unsolved problems, together with their "values."
