Digital Roots

As media environments and communication practices evolve over time, so do theoretical concepts. This book analyzes some of the most well-known and fiercely discussed concepts of the digital age from a historical perspective, showing how many of them have pre-digital roots and how they have changed and still are constantly changing in the digital era. Written by leading authors in media and communication studies, the chapters historicize 16 concepts that have become central in the digital media literature, focusing on three main areas. The first part, Technologies and Connections, historicises concepts like network, media convergence, multimedia, interactivity and artificial intelligence. The second one is related to Agency and Politics and explores global governance, datafication, fake news, echo chambers, digital media activism. The last one, Users and Practices, is finally devoted to telepresence, digital loneliness, amateurism, user generated content, fandom and authenticity. The book aims to shed light on how concepts emerge and are co-shaped, circulated, used and reappropriated in different contexts. It argues for the need for a conceptual media and communication history that will reveal new developments without concealing continuities and it demonstrates how the analogue/digital dichotomy is often a misleading one.

What is it that brings all these different things together? The subatomic particles and the Vedic square. The hydrogen atom and the golden section. Fibonacci numbers, consciousness, and alchemy. Nikola Tesla, music, and the ether. Electromagnetism, gravity, and the fourth dimension. The procession of the equinox, the Mayan dooms day, the Hindu Brahma cycle, and Atlantis. It is Numbers, or more precisely; their Digital Root. In this book the author examines the amazing world of numbers, particularly those which have intrigued and fascinated ancient and modern mathematicians alike. However, he does it from a very novel point of view; by implementing the digital root operation, in which the individual digits of any of these numbers are summed up until a single digit is left over. The author will show that when applying this simple operation to magical numbers, and to many other groups of numbers, an amazing world of hidden interconnections; repetition cycles; numerical symmetries; and geometrical patterns emerge. Especially when the geometrical (the circle) and the numerical aspects of the digital root world are combined together. It is in this circular/numerical world where numbers, individually and collectively, exist in their most basic, yet perfect and symmetrical states, and where the basic nine numbers are differentiated into three groups of amazing properties, which will be shown to underlie the essence of the whole universe; from the atom and its forces to the solar system and its geometry. This book will take us on a numerical and spiritual journey: starting from prime and figurate numbers; to Fibonacci sequence and the golden section; to alchemy and the Mayan calendar; to the atoms and its forces, along with the ether and the fourth dimension. In addition, the author will show how these new revelations of the digital root world are corroborating the numerological and mystical qualities that have been attributed to numbers by philosophers and mystics throughout the ages. This book will paint a so holistic and meaningful image of the world that will forever change our perception, not only towards numbers, but towards the whole universe as well.

This second edition updates the well-regarded 2001 publication with new short sections on topics like Catalan numbers and their relationship to Pascal's triangle and Mersenne numbers, Pollard rho factorization method, Hoggatt-Hensell identity. Koshy has added a new chapter on continued fractions. The unique features of the first edition like news of recent discoveries, biographical sketches of mathematicians, and applications--like the use of congruence in scheduling of a round-robin tournament--are being refreshed with current information. More challenging exercises are included both in the textbook and in the instructor's manual. Elementary Number Theory with Applications 2e is ideally suited for undergraduate students and is especially appropriate for prospective and in-service math teachers at the high school and middle school levels. * Loaded with pedagogical features including fully worked examples, graded exercises, chapter summaries, and computer exercises * Covers crucial applications of theory like computer security, ISBNs, ZIP codes, and UPC bar codes * Biographical sketches lay out the history of mathematics, emphasizing its roots in India and the Middle East

Presents mathematical shortcut and "how to develop a calculator in your head."

Tips for simplifying tricky operations Get the skills you need to solve problems and equations and be ready for algebra class Whether you're a student preparing to take algebra or a parent who wants to brush up on basic math, this fun, friendly guide has the tools you need to get in gear. From positive, negative, and whole numbers to fractions, decimals, and percents, you'll build necessary skills to tackle more advanced topics, such as imaginary numbers, variables, and algebraic equations. * Understand fractions, decimals, and percents * Unravel algebra word problems * Grasp prime numbers, factors, and multiples * Work with graphs and measures * Solve single and multiple variable equations

"This book is the second in series, in which it has been described that by using the formulas given by Vedic Mathematics, we can easily do our calculations orally in the shortest possible time. Along with this, you will also be able to know the introduction of ancient Indian mathematicians and their contribution to mathematics. This book has been written in very simple language. To make the formulas easily understandable,42 videos and practice questions have also been included in this book. The contest of the book is useful for all the students, teachers, and job aspirants participating in various competitive exams, certificate courses as it helps in quick calculations and it is also beneficial for diploma course in Vedic Mathematics."

This book brings the techniques from Vedic Mathematics and Trachtenberg System together. We have not attempted to do a comparative study of these techniques and make a judgment on which one is better. Instead we have simply, presented the techniques in a sequence that makes most sense. There are inherent strengths in these two approaches. While looking at all the speed improvement techniques, we have ensured that we focus on techniques for defect prevention and error minimization as well. Speed coupled with improved accuracy must be our paramount focus during any problem solving process. This book attempts to elucidate several key techniques, examples and practice problem sets.