"Beyond Primes" delves into the fascinating world of number theory beyond the realm of prime numbers. From exploring topics like composite numbers, perfect numbers, and cryptographically significant numbers, to investigating unsolved problems and conjectures in number theory, this book offers readers a captivating journey into the depths of mathematical exploration. With clear explanations and intriguing examples, "Beyond Primes" is an essential read for anyone interested in the beauty and complexity of number theory, offering insights into the mysteries that lie beyond the realm of primes.
"Exploring Numbers Beyond Primes" is a comprehensive and accessible introduction to the fascinating world of number theory, designed specifically for absolute beginners. This book takes readers on a captivating journey through the mysteries of prime numbers and Diophantine equations, offering clear explanations and engaging examples along the way. From the historical origins of number theory to modern approaches and future directions, each chapter provides a step-by-step exploration of key concepts, supported by vivid descriptions and relatable analogies. Whether you're a curious novice or an aspiring mathematician, "Exploring Numbers Beyond Primes" invites you to discover the beauty and wonder of numbers, inspiring a lifelong passion for mathematical inquiry.
Eli Maor examines the role of infinity in mathematics and geometry and its cultural impact on the arts and sciences. He evokes the profound intellectual impact the infinite has exercised on the human mind, from the "horror infiniti" of the Greeks to the works of M.C. Escher; from the ornamental designs of the Moslems, to the sage Giordano Bruno, whose belief in an infinite universe led to his death at the hands of the Inquisition. But above all, the book describes the mathematician's fascination with infinity, a fascination mingled with puzzlement. "Maor explores the idea of infinity in mathematics and in art and argues that this is the point of contact between the two, best exemplified by the work of the Dutch artist M.C. Escher, six of whose works are shown here in beautiful color plates."--Los Angeles Times "[Eli Maor's] enthusiasm for the topic carries the reader through a rich panorama." Choice "Fascinating and enjoyable.... places the ideas of infinity in a cultural context and shows how they have been espoused and molded by mathematics."-Science.
Whenever the topic of mathematics is mentioned, people tend to indicate their weakness in the subject as a result of not having enjoyed its instruction during their school experience. Many students unfortunately do not have very positive experiences when learning mathematics, which can result from teachers who have a tendency 'to teach to the test'. This is truly unfortunate for several reasons. First, basic algebra and geometry, which are taken by almost all students, are not difficult subjects, and all students should be able to master them with the proper motivational instruction. Second, we live in a technical age, and being comfortable with basic mathematics can certainly help you deal with life's daily challenges. Other, less tangible reasons, are the pleasure one can experience from understanding the many intricacies of mathematics and its relation to the real world, experiencing the satisfaction of solving a mathematical problem, and discovering the intrinsic beauty and historical development of many mathematical expressions and relationships. These are some of the experiences that this book is designed to deliver to the reader.The book offers 101 mathematical gems, some of which may require a modicum of high school mathematics and others, just a desire to carefully apply oneself to the ideas. Many folks have spent years encountering mathematical terms, symbols, relationships and other esoteric expressions. Their origins and their meanings may never have been revealed, such as the symbols +, -, =, π. ꝏ, √, ∑, and many others. This book provides a delightful insight into the origin of mathematical symbols and popular theorems such as the Pythagorean Theorem and the Fibonacci Sequence, common mathematical mistakes and curiosities, intriguing number relationships, and some of the different mathematical procedures in various countries. The book uses a historical and cultural approach to the topics, which enhances the subject matter and greatly adds to its appeal. The mathematical material can, therefore, be more fully appreciated and understood by anyone who has a curiosity and interest in mathematics, especially if in their past experience they were expected to simply accept ideas and concepts without a clear understanding of their origins and meaning. It is hoped that this will cast a new and positive picture of mathematics and provide a more favorable impression of this most important subject and be a different experience than what many may have previously encountered. It is also our wish that some of the fascination and beauty of mathematics shines through in these presentations.
From the author of the national bestseller Innumeracy, a delightful exploration and explanation of mathematical concepts from algebra to zero in easily accessible alphabetical entries. "Paulos . . . does for mathematics what The Joy of Sex did for the boudoir. . . ."--Washington Post Book World. First time in paperback.
This volume presents a series of studies that expand laws, invariants, and principles of psychophysics beyond its classical domain of sensation. This book's goal is to demonstrate the extent of the domain of psychophysics, ranging from sensory processes, through sensory memory and short-term memory issues, to the interaction between sensation and action. The dynamics and timing of human performance are a further important issue within this extended framework of psychophysics: Given the similarity of the various cortical areas in terms of their neuroanatomical structure, it is an important question whether this similarity is paralleled by a similarity of processes. These issues are addressed by the contributions in the present volume using state-of-the-art research methods in behavioral research, psychophysiology, and mathematical modeling. The book is divided into four sections. Part I presents contributions concerning the classical domain of psychophysical judgment. The next two parts are concerned with elementary and higher-order processes and the concluding section deals with psychophysical models. The sections are introduced by guest editorials contributed by independent authors. These editorials present the authors' personals view on the respective section, providing an integrated account of the various contributions or highlighting their focus of interest among them. While also voicing their own and sometimes different point of view, they contribute to the process of discussion that makes science so exciting. This volume should be of great interest to advanced students in neuroscience, cognitive science, psychology, neuropsychology, and related areas who seek to evaluate the range and power of psychological work today. Established scientists in those fields will also appreciate the variety of issues addressed within the same methodological framework and their multiple interconnections and stimulating "cross-talk."
Mathematics is a subject taught from kindergarten through to high school, and yet it is the one subject that most adults are almost proud to admit to not having been very good at, and, therefore, tend to avoid it where they can. However, one of the key factors in mathematics is its ability to enable us to solve everyday problems. When we consider 'the worst-case scenario' of the situation, it is analogous to solving a mathematical problem by considering extremes. Or, we might consider the best path to take from point A to point B, where geometric relationships can be helpful. This book is intended to demonstrate a variety of neglected aspects of mathematics, in order to demonstrate the power and beauty of the field of mathematics beyond where most people, students, and teachers believe is possible.The chapters of the book explore a multitude of topics: unusual arithmetic calculations and shortcuts, entertaining and instructional problem-solving strategies, unusual applications of algebra, and how geometry allows us to better appreciate physical relationships. Only a basic mathematical knowledge is needed to understand these topics and problems; however, the book also demonstrates that, armed with even this level of understanding, our mathematical skills far exceed what we learned at school! The final chapter is the most challenging, and explores a curious problem-solving technique.
Beyond Nature-Nurture: Essays in Honor of Elizabeth Bates is a very special tribute to the University of California at San Diego psycholinguist, developmental psychologist, and cognitive scientist Elizabeth Ann Bates, who died on December 14, 2003 from pancreatic cancer. Liz was a force of nature; she was also a nurturing force, as is evidenced by this collaborative collection of chapters written by many of her closest colleagues and former students. The book covers a brilliant career of wide-ranging interdisciplinary interests, such as the brain bases of language in children and adults; language and cognitive development in normal and neurologically impaired populations of children; real-time language processing in monolinguals and bilinguals; and crosslinguistic comparisons of language development, language use, and language loss. In this volume the contributors provide up-to-date reviews of these and other areas of research in an attempt to continue in the directions in which she has pointed us. The genius of Bates is founded on a deep dedication to science, supported by an enduring sense of humor. The volume is introduced by the editors' collection of "Bates's aphorisms," the wisdom of which guide much of the field today: "[T]he human capacity for language could be both innate and species-specific, and yet involve no mechanisms that evolved specifically and uniquely for language itself. Language could be viewed as a new machine constructed entirely out of old parts." (Bates & MacWhinney, 1989) The volume also contains a list of her many important publications, as well as some personal reflections of some of the contributors, noting ways in which she made a difference in their lives. Beyond Nature-Nurture: Essays in Honor of Elizabeth Bates appeals to international scholars in the fields of developmental psycholinguistics, cognitive science, crosslinguistic research, and both child and adult language disorders. It is a state-of-the-art overview of many areas of cognitive science, and can be used in a graduate-level classroom in courses designed as seminars in any of these topics.
Few financial crises, historically speaking, have attracted such attention as the Mississippi and South Sea Bubbles of 1719–20. The twin bubbles had major economic and political implications, sending shock waves through the whole of Europe; they astonished contemporaries, and, to a large extent, they still resonate today. This volume offers new readings of these events, drawing on fresh research and new evidence that challenge traditional interpretations. The chapters engage, in particular, with: the geographical frame of the 1719-20 bubbles their social, cultural, economic and political impact the ways in which contemporaries understood speculation the contributions and impact of a diverse array of participants popular and print memorialization of the events Overall, the volume helps to rewrite the history of the 1719–20 bubbles and to recontextualize their place within eighteenth-century history.
