It is a bridge from the computational courses (such as calculus or differential equations) that students typically encounter in their first year of college to a more abstract outlook. It lays a foundation for more theoretical courses such as topology, analysis and abstract algebra. Although it may be more meaningful to the student who has had some calculus, there is really no prerequisite other than a measure of mathematical maturity. Topics include sets, logic, counting, methods of conditional and non-conditional proof, disproof, induction, relations, functions and infinite cardinality.

    In an era of the military space race, Erich von Däniken boldly proclaimed that Earth had been visited by more advanced beings early in our history. But prescientific man had no concept of space ships, so he called their vehicles “chariots,” and those driving the chariots became “gods.” Over the next five decades, von Däniken’s more than 40 books built an ever-stronger case for Earth being visited by extraterrestrial visitors. And Chariots became an international best seller, with 30 million copies sold in more than two dozen languages. Also during that time, the case for ET visitations millennia ago was being reexamined by contemporary UFO researchers, who found evidence of modern visitations. And von Däniken expanded his perspective to encompass the present. Now, he presents his long-awaited sequel to Chariots of the Gods, proclaiming that the gods never left us with all-new material to show that ancient aliens are still with us. The Gods Never Left Us contends that recent advancements in biotechnology, astrophysics, engineering, and artificial intelligence not only give us a fresh perspective on his ancient astronaut theory but actually validates it. We are—as a race—embarking on the exact same trajectory of our own interplanetary colonization, just as von Däniken suggested Earth itself was colonized. ETs are definitely at work today. And that affects all of us. Why do they do what they do? What could an extraterrestrial species possibly gain from observing us in the same way we look at ants? What have these strangers wanted for the past thousands of years? Can’t they leave us alone? And what makes it so difficult for us to acknowledge the existence of these extraterrestrials? That is what this book deals with. "Erich's newest book is a fascination journey from the ancient past into the present with a plethora of scientific evidence and documented research. As always, he ads his own "to the point" take on it all. Readers may also like that his newest work moves in a slightly different direction from his past books. A thoroughly enlightening and enjoyable Read." —Bruce Cunningham, Director, Ancient Mysteries International LLC & Publisher of Advanced Archaeology Review magazine

    

    Linear Equations; Vector Spaces; Linear Transformations; Polynomials; Determinants; Elementary canonical Forms; Rational and Jordan Forms; Inner Product Spaces; Operators on Inner Product Spaces; Bilinear Forms For all readers interested in linear algebra.

    

    The book is also ideal for university and third-level physics or engineering courses on solar photovoltaics, with exercises to check students' understanding and reinforce learning. It is the perfect companion to the Massive Open Online Course (MOOC) on Solar Energy (DelftX, ET.3034TU) presented by co-author Arno Smets. The course is available in English on the nonprofit open source edX.org platform, and in Arabic on edraak.org. Over 100,000 students have already registered for these MOOCs.

    As you identify your tribe and divinely align in time with God's calendar, you will discover how to find your position in God's Kingdom, how to war effectively for your inheritance, and then walk in His blessings.A Time to Advance: Understanding the Significance of the Hebrew Tribes and Months will help you understand how God is developing His whole conquering army for today. You will also understand how each part moves together, and the redemptive quality of God's covenant plan for Israel. This will help ground you on how we are grafted into a movement in days ahead.As you learn how to think like God thinks and study the Hebrew tribes and months, you will receive prophetic understanding of how the Lord orders your steps throughout the year. You will also see your place in God's next Triumphant Reserve that is rising in the Earth today!

    The objective here is to explain science in a simple, attractive and fun form that is open to all.The first axiom of this approach was set out as follows: “We believe in the magic of science. We hope to show you that sci-ence is not a secret art, accessible only to a dedicated few. It involves learning about nature and society, and aspects of our existence which affect us all, and which we should all therefore have the chance to understand. We shall interpret science for those who might not speak its language fluently, but want to understand its meaning. We don’t teach, we just tell stories about the beginnings of science, the natural phenomena and the underlying principles through which they occur, and the lives of the people who discovered them.”The aim of the writings collected in this series is to present some key scientific events, ideas and personalities in the form of short stories that are easy and fun to read. Scientific and philo-sophical concepts are explained in a way that anyone may under-stand. Each story may be read separately, but at the same time they all band together to form a wide-ranging introduction to the history of science and areas of contemporary scientific research, as well as some of the recurring problems science has encountered in history and the philosophical dilemmas it raises today.Review“If I were the only survivor on a remote island and all I had with me were this book, a Swiss army knife and a bottle, I would throw the bottle into the sea with the note: ‘Don’t worry, I have everything I need.’”— Ciril Horjak, alias Dr. Horowitz, a comic artist“The writing is understandable, but never simplistic. Instructive, but never patronizing. Straightforward, but never trivial. In-depth, but never too intense.”— Ali Žerdin, editor at Delo, the main Slovenian newspaper“Does science think? Heidegger once answered this question with a decisive No. The writings on modern science skillfully penned by Sašo Dolenc, these small stories about big stories, quickly convince us that the contrary is true. Not only does science think in hundreds of unexpected ways, its intellectual challenges and insights are an inexhaustible source of inspiration and entertainment. The clarity of thought and the lucidity of its style make this book accessible to anyone … in the finest tradition of popularizing science, its achievements, dilemmas and predicaments.”— Mladen Dolar, philosopher and author of A Voice and Nothing More“Sašo Dolenc is undoubtedly one of our most successful authors in the field of popular science, possessing the ability to explain complex scientific achievements to a broader audience in a clear and captivating way while remaining precise and scientific. His collection of articles is of particular importance because it encompasses all areas of modern science in an unassuming, almost light-hearted manner.”— Boštjan Žekš, physicist and former president of the Slovenian Academy of Sciences and Arts

    They'll also find the related analytic geometry much easier. The clear review of algebra and geometry in this edition will make calculus easier for students who wish to strengthen their knowledge in these areas. Updated to meet the emphasis in current courses, this new edition of a popular guide--more than 104,000 copies were bought of the prior edition--includes problems and examples using graphing calculators..

    

    So it's not surprising that we persist in thinking that we're in with a chance, whether we're playing the lottery or working out the likelihood of extra-terrestrial life. In Chance, a (not entirely) random selection of the New Scientist's sharpest minds provide fascinating insights into luck, randomness, risk and probability. From the secrets of coincidence to placing the perfect bet, the science of random number generation to the surprisingly haphazard decisions of criminal juries, it explores these and many other tantalising questions.Following on from the bestselling Nothing and Question Everything, this book will open your eyes to the weird and wonderful world of chance - and help you see when some things, in fact, aren't random at all.

    Twenty-two years later, he did. April 1945 – Berlin. The world had been at war for more than five-and-a-half years – approximately seventy million people were dead across the globe. The epicentre of the twelve-year-old Third Reich was now surrounded, enveloped by bitter Soviet forces hardened by Nazi barbarity in the east over the last four years. As the buildings were blasted into rubble, pounded by Russian guns and bombs, before their troops and tanks, Hitler was hunkered down in his last headquarters – the dark and damp bunker under the Reich Chancellery. As the Third Reich began to crumble as fast as the city’s buildings, what was the state of mind of the tyrant? Only his closest and fanatical allies saw the collapse, none more so than Hitler’s servants, Otto Gunsche and Heinz Linge – two individuals which witnessed the final act of their regime. An act tinged over the last ten days in late April with selfish betrayal, increasingly forlorn hope, pleas, desperation and eventually suicide. As the Soviets closed in with impending vigour, in the concrete tomb below ground and under the thunderous booms of the petrifying battle for Berlin, the mind of the dictator disintegrated into drugs, delusion and a determination to die. Not by the enemy bullet but one of his own. This is the story of the people who held a unique place in world history – the ones who were there when the nightmare of Nazism and the horrors which accompanied it was finally banished as a dark chapter in the story of the human race.

    It provides a simple, thorough survey of elementary topics, starting with set theory and advancing to metric and topological spaces, connectedness, and compactness. 1975 edition.

    In the four main sections of the book, Stein tells the stories of the mathematical thinkers who discerned some of the most fundamental aspects of our universe. From their successes and failures, delusions, and even duels, the trajectories of their innovations—and their impact on society—are traced in this fascinating narrative. Quantum mechanics, space-time, chaos theory and the workings of complex systems, and the impossibility of a "perfect" democracy are all here. Stein's book is both mind-bending and practical, as he explains the best way for a salesman to plan a trip, examines why any thought you could have is imbedded in the number π , and—perhaps most importantly—answers one of the modern world's toughest questions: why the garage can never get your car repaired on time.Friendly, entertaining, and fun, How Math Explains the World is the first book by one of California's most popular math teachers, a veteran of both "math for poets" and Princeton's Institute for Advanced Studies. And it's perfect for any reader wanting to know how math makes both science and the world tick.

    In the paper, Wigner observed that the mathematical structure of a physical theory often points the way to further advances in that theory and even to empirical predictions.