The Square Root of Negative One


Book Description

The writer of this book is an American citizen, was in the military overseas, and was imprisoned in a foreign system. A new language had to be learned all the way around; the writer had to learn more than one language of the host. There were conversations with various liberation groups from all over Europe, including England, the isles, and even Spain, just to name a few. The Baader-Meinhof Gang, the Red Army Faction, the Second June MovementIran had chased these liberators to Germany, and the community was full of political prisoners, and the police state was very active. Even people from the African continent escaped NATO-supplied reactionaries who were equipped with Western weaponry, especially from Angola and South Africa, to name a few. So much of the conversations revolved around capitalism, communism, socialism, different dictatorships, and apartheid and religious zealots who hated everyone but themselves, but really, if you hate anyone, you hate yourself. So finding the square root of negative one is like finding the solution to all these problems that many people have. In an ordinary way, there is no solution, and all answers given seemed to be false. Yet because of I, there is truth to be told. So this math problem translates into social relations in all countries and in many prisons.




An Imaginary Tale


Book Description

Today complex numbers have such widespread practical use--from electrical engineering to aeronautics--that few people would expect the story behind their derivation to be filled with adventure and enigma. In An Imaginary Tale, Paul Nahin tells the 2000-year-old history of one of mathematics' most elusive numbers, the square root of minus one, also known as i. He recreates the baffling mathematical problems that conjured it up, and the colorful characters who tried to solve them. In 1878, when two brothers stole a mathematical papyrus from the ancient Egyptian burial site in the Valley of Kings, they led scholars to the earliest known occurrence of the square root of a negative number. The papyrus offered a specific numerical example of how to calculate the volume of a truncated square pyramid, which implied the need for i. In the first century, the mathematician-engineer Heron of Alexandria encountered I in a separate project, but fudged the arithmetic; medieval mathematicians stumbled upon the concept while grappling with the meaning of negative numbers, but dismissed their square roots as nonsense. By the time of Descartes, a theoretical use for these elusive square roots--now called "imaginary numbers"--was suspected, but efforts to solve them led to intense, bitter debates. The notorious i finally won acceptance and was put to use in complex analysis and theoretical physics in Napoleonic times. Addressing readers with both a general and scholarly interest in mathematics, Nahin weaves into this narrative entertaining historical facts and mathematical discussions, including the application of complex numbers and functions to important problems, such as Kepler's laws of planetary motion and ac electrical circuits. This book can be read as an engaging history, almost a biography, of one of the most evasive and pervasive "numbers" in all of mathematics. Some images inside the book are unavailable due to digital copyright restrictions.




Statistical Regression and Classification


Book Description

Statistical Regression and Classification: From Linear Models to Machine Learning takes an innovative look at the traditional statistical regression course, presenting a contemporary treatment in line with today's applications and users. The text takes a modern look at regression: * A thorough treatment of classical linear and generalized linear models, supplemented with introductory material on machine learning methods. * Since classification is the focus of many contemporary applications, the book covers this topic in detail, especially the multiclass case. * In view of the voluminous nature of many modern datasets, there is a chapter on Big Data. * Has special Mathematical and Computational Complements sections at ends of chapters, and exercises are partitioned into Data, Math and Complements problems. * Instructors can tailor coverage for specific audiences such as majors in Statistics, Computer Science, or Economics. * More than 75 examples using real data. The book treats classical regression methods in an innovative, contemporary manner. Though some statistical learning methods are introduced, the primary methodology used is linear and generalized linear parametric models, covering both the Description and Prediction goals of regression methods. The author is just as interested in Description applications of regression, such as measuring the gender wage gap in Silicon Valley, as in forecasting tomorrow's demand for bike rentals. An entire chapter is devoted to measuring such effects, including discussion of Simpson's Paradox, multiple inference, and causation issues. Similarly, there is an entire chapter of parametric model fit, making use of both residual analysis and assessment via nonparametric analysis. Norman Matloff is a professor of computer science at the University of California, Davis, and was a founder of the Statistics Department at that institution. His current research focus is on recommender systems, and applications of regression methods to small area estimation and bias reduction in observational studies. He is on the editorial boards of the Journal of Statistical Computation and the R Journal. An award-winning teacher, he is the author of The Art of R Programming and Parallel Computation in Data Science: With Examples in R, C++ and CUDA.




Intermediate Algebra 2e


Book Description




The Story Of Numbers


Book Description

'… this could make an ideal end-of-year prize for a high-school student who is fascinated by all aspects of number. The subsections provide ideas and opportunities for mathematical exploration. This book might also be deemed a suitable resource for first-year undergraduates in that, via independent study, it would allow such students to broaden their knowledge of various number-theoretic ideas. I would recommend it for the purposes given above.'The Mathematical GazetteThis book is more than a mathematics textbook. It discusses various kinds of numbers and curious interconnections between them. Without getting into hardcore and difficult mathematical technicalities, the book lucidly introduces all kinds of numbers that mathematicians have created. Interesting anecdotes involving great mathematicians and their marvelous creations are included. The reader will get a glimpse of the thought process behind the invention of new mathematics. Starting from natural numbers, the book discusses integers, real numbers, imaginary and complex numbers and some special numbers like quaternions, dual numbers and p-adic numbers.Real numbers include rational, irrational and transcendental numbers. Iterations on real numbers are shown to throw up some unexpected behavior, which has given rise to the new science of 'Chaos'. Special numbers like e, pi, golden ratio, Euler's constant, Gauss's constant, amongst others, are discussed in great detail.The origin of imaginary numbers and the use of complex numbers constitute the next topic. It is shown why modern mathematics cannot even be imagined without imaginary numbers. Iterations on complex numbers are shown to generate a new mathematical object called 'Fractal', which is ubiquitous in nature. Finally, some very special numbers, not mentioned in the usual textbooks, and their applications, are introduced at an elementary level.The level of mathematics discussed in this book is easily accessible to young adults interested in mathematics, high school students, and adults having some interest in basic mathematics. The book concentrates more on the story than on rigorous mathematics.




System Dynamics


Book Description

This unique textbook takes the student from the initial steps in modeling a dynamic system through development of the mathematical models needed for feedback control. The generously-illustrated, student-friendly text focuses on fundamental theoretical development rather than the application of commercial software. Practical details of machine design are included to motivate the non-mathematically inclined student.




A Quest for Truth and Wisdom


Book Description

Truth to some may be what is seen in the natural universe. Truth to some may be what is expressed by some individual who seems to be successful or charismatic. Truth to some may be what the Bible says. Truth to some may span a complex variety of issues, and to others, to be quite simple. Websters Dictionary says to attain wisdom a person must have good sense, good judgment, insight, and knowledge. Does that limit the number of persons who can have wisdom? This search for truth and wisdom comes from the perspectives of Western culture, scientific approach, logic, reason, and monotheistic philosophies. Monotheism encompasses Christianity, Islam, Judaism, and some other lesser-known belief systems. This subject might be treated differently from the perspectives of Eastern cultures, emotion, mysticism, or more spiritual concepts and polytheistic religious philosophies. The latter perspectives are not discussed here. This work addresses some aspects of the concepts of truth. Questions are asked and answers are suggested. Original Greek scripture is referenced rather than any translation or interpretation that could have been influenced by a particular theological philosophy, organized church, church tradition, or seminary. I propose a third concept to add to Evolution and Creation, or Intelligent designthe Eternal or Forever concepteverything has simply always been and always will be. No beginning and no end. I discuss aspects of the nature of man. I discuss intelligence, intellectualism, and education. I discuss global intelligence and terrorism in the world of today. I discuss dualisms in American culture. I discuss science and our limited view in space and time. I discuss difficult or significant passages in the Bible, with emphasis on the original Greek.




Business Secrets from the Bible


Book Description

Find success in finance, friendships, , and spirituality with the advice of a well-known expert It's safe to say that nearly everyone is seeking a happier, more successful life. So then why do so few attain it? Business Secrets from the Bible proposes a new way to view and approach success—one based upon key concepts from the Bible that are actually surprisingly simple. Written especially for those seeking success in the realms of money, relationships, and spirituality, this book encourages readers to realize their common mistakes, come to terms with them, and turn those mistakes into future triumphs. Filled with concrete advice for improved finances, spirituality, and connection, this resource takes a practical approach and aims to change not just the minds, but the actions of readers with a self-evident and persuasive pathway. Drawing on his wisdom and knowledge of the Bible, the author reveals the clear link between making money and spirituality, and urges readers to focus on self-discipline, integrity, and character strength in order to achieve personal prosperity. Special emphasis is given to establishing positive attitudes toward making money and adopting effective Biblically-based strategies. Demonstrates how earnings and profits are God's reward for forming relationships with others and serving them Stresses the importance of service, sharing, change, leadership, and creating boundaries and structures Encourages readers to focus on other people's desires and teaches why and how to make connections with many people Suggests ways for readers to transform themselves and continue toward success even in the face of fear and uncertainty Attaining wealth and well-being is no longer a mystery. Let this book identify and correct the errors that are keeping you from fulfillment and happiness.




Complex Analysis


Book Description

Complex Analysis is an introductory textbook designed for absolute beginners, offering a clear and straightforward exploration of complex numbers and functions. The book presents fundamental concepts in a step-by-step manner, making complex analysis accessible to those with little or no prior mathematical knowledge. Through practical examples and intuitive explanations, readers will discover the beauty of complex functions, the significance of Cauchy's integral formula, and the application of power series. Ideal for students and curious learners alike, this book serves as a solid foundation for further studies in mathematics.




Einstein and Human Consciousness


Book Description

Which is more important: the practical or the sublime? Are you a Doer or a Dreamer? Brad Buettner has over twenty-four years of experience utilizing his physics degree in a wide array of engineering and management assignments. With this background he examines early twentieth-century physics and human relationships observed during his professional tenure to illustrate how Einstein’s theory of relativity pertains to our perception of time and how it explains divisions in our outlook. By applying the theory of relativity to human consciousness, Buettner discovers the motivation for personal inclination toward either the practical or the abstract. Buettner defines total reality as containing more than the reality our senses perceive. When discussing alternate forms of reality, however, he insists on measurable and observable conclusions, eliminating references to mysticism, magic, or mystery. He outlines an engaging search for the unlikely possibility of interaction with the reality that existed before the Big Bang. Einstein and Human Consciousness: Eternity is an Instant provides stunning revelations concerning human reality. Does your world extend beyond that perceived by the physical senses? If so, why? Buettner offers the answers to these questions by explaining an aspect of reality that was previously elusive.