A Navy ship fights to survive an inexplicable event in this action-packed Bermuda Triangle thriller . . . Every year, all across the planet, people simply vanish, never to be seen again. Some areas of the world are well known for this phenomenon—like the area that would become known as the Bermuda Triangle after the famed Flight 19 incident off the Florida coast in 1945. Now, in the present day, an unexplainable event has occurred in the same area—an event that cannot be ignored by the military. The Navy ship Eclipse and its crew are sent to investigate, but after several days come up empty. Then, two days before the planned return to port, the event reoccurs, and the Eclipse is caught up in something it cannot escape. The ship and its crew suddenly find themselves completely isolated, all communication lost, surrounded by a terribly hostile environment where each day is a struggle to survive—in this intense, fast-paced novel of self-reliance, mystery, and discovery.

Simple geometric shapes and symbols combine to make the universal, powerful and sacred model Karen French calls the Gateway to the Heavens. In this book, French explains the meaning and purpose of these shapes, how they mould our reality and perception of it, and how they have a direct bearing on what you are and why you are here. These shapes and symbols contain messages that have been consistently represented in religion, philosophy, mythology, mysticism, the arts and sciences. Their messages are built into our genetic make-up and we recognise them instinctively. The book is divided up into three parts. Part 1 covers the properties of the basic geometric shapes and numbers. Part 2 describes how these in turn form layers of construction, creating principals that are fundamental to the purpose of the universe. The spiral sustains reality, the cross highlighting the central point of existence and the Heart where we weigh up our choices. Part 3 describes how we can use these principles to create positive change in our lives by helping us to expand our awareness of reality.

Challenge: Can you find all the integers a, b, c satisfying 2a2+3b2=5c2? Looks simple, and there are in fact a number of easy solutions. But most of them turn out to be anything but obvious! There are infinitely many possibilities, and as any computer will tell you, each of a, b, c will usually be large. So the challenge remains … Find all integers a a, b, c satisfying 2a2+3b2=5c2 A major advance in number theory means this book can give an easy answer to this and countless similar questions. The idea behind the approach is transforming a degree-two equation in integer variables a, b, c into a plane curve defined by a polynomial. Working with the curve makes obtaining solutions far easier, and the geometric solutions then get translated back into integers. This method morphs hard problems into routine ones and typically requires no more than high school math. (The complete solution to 2a2+3b2=5c2 is included in the book.) In addition to equations of degree two, the book addresses degree-three equations—a branch of number theory that is today something of a cottage industry, and these problems translate into “elliptic curves”. This important part of the book includes many pictures along with the exposition, making the material meaningful and easy to grasp. This book will fit nicely into an introductory course on number theory. In addition, the many solved examples, illustrations, and exercises make self-studying the book an option for students, thus becoming a natural candidate for a capstone course.

Gateway to Complex Analysis is complex analysis for the beginners. Its aim is to introduce the knowledge of complex analysis, a powerful tool, to those who have no prior knowledge of this subject. The present book starts with the history and the applications of the complex analysis and reaching to classical Nevanlinna theory which occupies the central place in complex analysis and ending with the application of Nevanlinna theory in Difference operators. The concepts are presented in an informal and conceptual style rather than in conventional definition or proof format. The author invites suggestions which could be considered for the improvement of the subsequent editions of this work. Complex analysis is an extremely useful and beautiful part of mathematics and forms the basis of many techniques employed in many branches of mathematics and physics. We have provided the notions of derivatives and integrals, familiar from calculus, to the case of complex functions of a complex variable.

Since the time of the Greek philosopher Zeno (fifth century BCE), our faculty of analytic understanding has failed to comprehend motion through the ages. The reason is the paradox or contradiction associated with motion. One fundamental contradiction is the conflict between the finite body and the infinite divisibility of the unit distance ab. Indeed, how is it possible to move from a to b if we must first pass through an infinite series of sub-distances in one instant? How can we traverse an unlimited series—a series without limit—yet reach its limit? Because the heart of the problem is the conflict between the finite and the infinite, its solution depends on reconciling this contradiction and transforming this reconciliation into the founding principle of motion. Having accomplished these two things, this work investigates the sweeping consequences they have regarding the geometric form of the physical universe, the Aristotelian ontology of the physical body, the nature of our finite brain, the finite analytic paradigm of empirical science and the meaning of our technological acceleration. This book will appeal to a wide range of readers with interests in the logical mechanics of the physical universe, the hidden powers of our finite brain, and the utility of robots in the future. Although some of the presentation requires the understanding of elementary mathematical equations, the argument is conducted at the deepest level: that of principles. This approach enables readers to follow the book’s reasoning without technical training on the subject.

Nebula and Hugo award-winning author David Brin continues his bestselling Uplift series in this second novel of a bold new trilogy. Imaginative, inventive, and filled with Brin's trademark mix of adventure, passion, and wit, Infinity's Shore carries us further than ever before into the heart of the most beloved and extraordinary science fiction sagas ever written. For the fugitive settlers of Jijo, it is truly the beginning of the end. As starships fill the skies, the threat of genocide hangs over the planet that once peacefully sheltered six bands of sapient beings. Now the human settlers of Jijo and their alien neighbors must make heroic--and terrifying--choices. A scientist must rally believers for a cause he never shared. And four youngsters find that what started as a simple adventure--imitating exploits in Earthling books by Verne and Twain--leads them to the dark abyss of mystery. Meanwhile, the Streaker, with her fugitive dolphin crew, arrives at last on Jijo in a desperate search for refuge. Yet what the crew finds instead is a secret hidden since the galaxies first spawned intelligence--a secret that could mean salvation for the planet and its inhabitants...or their ultimate annihilation.

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.

A Gateway to Higher Mathematics integrates the process of teaching students how to do proofs into the framework of displaying the development of the real number system. The text eases the students into learning how to construct proofs, while preparing students how to cope with the type of proofs encountered in the higher-level courses of abstract algebra, analysis, and number theory. After using this text, the students will not only know how to read and construct proofs, they will understand much about the basic building blocks of mathematics. The text is designed so that the professor can choose the topics to be emphasized, while leaving the remainder as a reference for the students.

Mrs.S.N.Santhalakshmi, Assistant Professor & Head of The Department, Department of Computer Applications, Nandha Arts & Science College, Erode, Tamil Nadu, India. Dr.Goutam Panigrahi, Assistant Professor, Department of Mathematics, National Institute of Technology, Durgapur, West Bengal, India. Dr. Saibal Majumder, Assistant Professor, Department of Computer Science and Engineering(Data Science), Dr. B.C. Roy Engineering College, Durgapur, West Bengal, India. Dr. Chandan Bandyopadhyay, Associate Professor & Head of the Department, Department of Computer Science and Engineering(Data Science), Dr. B.C. Roy Engineering College, Durgapur, West Bengal, India.