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.

    Would you believe that these five pieces can be reassembled in such a fashion so as to create two apples equal in shape and size to the original? Would you believe that you could make something as large as the sun by breaking a pea into a finite number of pieces and putting it back together again? Neither did Leonard Wapner, author of The Pea and the Sun, when he was first introduced to the Banach-Tarski paradox, which asserts exactly such a notion. Written in an engaging style, The Pea and the Sun catalogues the people, events, and mathematics that contributed to the discovery of Banach and Tarski's magical paradox. Wapner makes one of the most interesting problems of advanced mathematics accessible to the non-mathematician.

    But what if free will doesn't exist? What if our lives are largely predetermined, hardwired in our brains - and our choices over what we eat, who we fall in love with, even what we believe are not real choices at all? Neuroscience is challenging everything we think we know about ourselves, revealing how we make decisions and form our own reality, unaware of the role of our unconscious minds. Did you know, for example, that:* You can carry anxieties and phobias across generations of your family?* Your genes and pleasure and reward receptors in your brain will determine how much you eat?* We can sniff out ideal partners with genes that give our offspring the best chance of survival?Leading neuroscientist Hannah Critchlow draws vividly from everyday life and other experts in their field to show the extraordinary potential, as well as dangers, which come with being able to predict our likely futures - and looking at how we can alter what's in store for us. Lucid, illuminating, awe-inspiring The Science of Fate revolutionises our understanding of who we are - and empowers us to help shape a better future for ourselves and the wider world.

    This is such a book. Max Born is a Nobel Laureate (1955) and one of the world's great physicists: in this book he analyzes and interprets the theory of Einsteinian relativity. The result is undoubtedly the most lucid and insightful of all the books that have been written to explain the revolutionary theory that marked the end of the classical and the beginning of the modern era of physics.The author follows a quasi-historical method of presentation. The book begins with a review of the classical physics, covering such topics as origins of space and time measurements, geometric axioms, Ptolemaic and Copernican astronomy, concepts of equilibrium and force, laws of motion, inertia, mass, momentum and energy, Newtonian world system (absolute space and absolute time, gravitation, celestial mechanics, centrifugal forces, and absolute space), laws of optics (the corpuscular and undulatory theories, speed of light, wave theory, Doppler effect, convection of light by matter), electrodynamics (including magnetic induction, electromagnetic theory of light, electromagnetic ether, electromagnetic laws of moving bodies, electromagnetic mass, and the contraction hypothesis). Born then takes up his exposition of Einstein's special and general theories of relativity, discussing the concept of simultaneity, kinematics, Einstein's mechanics and dynamics, relativity of arbitrary motions, the principle of equivalence, the geometry of curved surfaces, and the space-time continuum, among other topics. Born then points out some predictions of the theory of relativity and its implications for cosmology, and indicates what is being sought in the unified field theory.This account steers a middle course between vague popularizations and complex scientific presentations. This is a careful discussion of principles stated in thoroughly acceptable scientific form, yet in a manner that makes it possible for the reader who has no scientific training to understand it. Only high school algebra has been used in explaining the nature of classical physics and relativity, and simple experiments and diagrams are used to illustrate each step. The layman and the beginning student in physics will find this an immensely valuable and usable introduction to relativity. This Dover 1962 edition was greatly revised and enlarged by Dr. Born.

    The colonists were fighting for rights they felt they deserved, not only as British citizens, but as human beings. The belief that rights to life, liberty, and the pursuit of happiness were God given and not dependent upon any government or ruler gave the revolutionaries the courage to fight against overwhelming odds and eventually win their freedom. Inside you will read about... ✓ A Series of Oppressions ✓ Death and Taxes ✓ Out of Many, One ✓ War in Earnest ✓ Voices of Liberty ✓ Independence And more! The new government they created for the United States of America would be unlike anything seen before in world history, and their fight has continued to change the world to this day.

    An exploration of technology used by ancient civilizations and the support it provides for certain biblical interpretations.

    Written by two of the field's true pioneers, Spacetime Physics can extend and enhance coverage of specialty relativity in the classroom. This thoroughly up-to-date, highly accessible overview covers microgravity, collider accelerators, satellite probes, neutron detectors, radioastronomy, and pulsars.  The chapter on general relativity with new material on gravity waves, black holes, and cosmology.

    Presenting to the world his remarkable observations using the recently invented telescope--the craters of the moon, the satellites of Jupiter--Galileo dramatically challenged our idea of the perfection of the heavens and the centrality of the Earth in the universe. Indeed, the appearance of the little book is regarded as one of the great moments in the history of science. Planned to coincide with the 400th anniversary of the publication of the Starry Messenger, this is a major new biography of Galileo, a fresh and much more rounded view of the great scientist than found in earlier works. Unlike previous biographers, Heilbron shows us that Galileo was far more than a mathematician: he was deeply knowledgeable in the arts, an expert on the epic poet Ariosto, a fine lutenist. More important, Heilbron notes that years of reading the poets and experimenting with literary forms were not mere sidebars--they enabled Galileo to write clearly and plausibly about the most implausible things. Indeed, Galileo changed the world not simply because he revolutionized astronomy, but because he conveyed his discoveries so clearly and crisply that they could not be avoided or denied. If ever a discoverer was perfectly prepared to make and exploit his discovery, it was the dexterous humanist Galileo aiming his first telescope at the sky. In Galileo, John Heilbron captures not only the great scientist, but also the creative, artistic younger man who would ultimately become the champion of Copernicus, the bête-noire of the Jesuits, and the best-known of all martyrs to academic freedom.

    The material of this book is indispensable for anyone who wishes to understand the real spiritual roots of Western civilization.

    If it takes a book to get it across, I hope this book will do it. It ought to.”—Thomas Schelling, Distinguished University Professor, School of Public Policy, University of Maryland, and 2005 Nobel Prize Laureate in Economics “With humor, insight, piercing logic and a nod to history, Ziliak and McCloskey show how economists—and other scientists—suffer from a mass delusion about statistical analysis. The quest for statistical significance that pervades science today is a deeply flawed substitute for thoughtful analysis. . . . Yet few participants in the scientific bureaucracy have been willing to admit what Ziliak and McCloskey make clear: the emperor has no clothes.”—Kenneth Rothman, Professor of Epidemiology, Boston University School of Health The Cult of Statistical Significance shows, field by field, how “statistical significance,” a technique that dominates many sciences, has been a huge mistake. The authors find that researchers in a broad spectrum of fields, from agronomy to zoology, employ “testing” that doesn’t test and “estimating” that doesn’t estimate. The facts will startle the outside reader: how could a group of brilliant scientists wander so far from scientific magnitudes? This study will encourage scientists who want to know how to get the statistical sciences back on track and fulfill their quantitative promise. The book shows for the first time how wide the disaster is, and how bad for science, and it traces the problem to its historical, sociological, and philosophical roots. Stephen T. Ziliak is the author or editor of many articles and two books. He currently lives in Chicago, where he is Professor of Economics at Roosevelt University. Deirdre N. McCloskey, Distinguished Professor of Economics, History, English, and Communication at the University of Illinois at Chicago, is the author of twenty books and three hundred scholarly articles. She has held Guggenheim and National Humanities Fellowships. She is best known for How to Be Human* Though an Economist (University of Michigan Press, 2000) and her most recent book, The Bourgeois Virtues: Ethics for an Age of Commerce (2006).

    Focused on groups, rings and fields, this text gives students a firm foundation for more specialized work by emphasizing an understanding of the nature of algebraic structures. KEY TOPICS: Sets and Relations; GROUPS AND SUBGROUPS; Introduction and Examples; Binary Operations; Isomorphic Binary Structures; Groups; Subgroups; Cyclic Groups; Generators and Cayley Digraphs; PERMUTATIONS, COSETS, AND DIRECT PRODUCTS; Groups of Permutations; Orbits, Cycles, and the Alternating Groups; Cosets and the Theorem of Lagrange; Direct Products and Finitely Generated Abelian Groups; Plane Isometries; HOMOMORPHISMS AND FACTOR GROUPS; Homomorphisms; Factor Groups; Factor-Group Computations and Simple Groups; Group Action on a Set; Applications of G-Sets to Counting; RINGS AND FIELDS; Rings and Fields; Integral Domains; Fermat's and Euler's Theorems; The Field of Quotients of an Integral Domain; Rings of Polynomials; Factorization of Polynomials over a Field; Noncommutative Examples; Ordered Rings and Fields; IDEALS AND FACTOR RINGS; Homomorphisms and Factor Rings; Prime and Maximal Ideas; Gr�bner Bases for Ideals; EXTENSION FIELDS; Introduction to Extension Fields; Vector Spaces; Algebraic Extensions; Geometric Constructions; Finite Fields; ADVANCED GROUP THEORY; Isomorphism Theorems; Series of Groups; Sylow Theorems; Applications of the Sylow Theory; Free Abelian Groups; Free Groups; Group Presentations; GROUPS IN TOPOLOGY; Simplicial Complexes and Homology Groups; Computations of Homology Groups; More Homology Computations and Applications; Homological Algebra; Factorization; Unique Factorization Domains; Euclidean Domains; Gaussian Integers and Multiplicative Norms; AUTOMORPHISMS AND GALOIS THEORY; Automorphisms of Fields; The Isomorphism Extension Theorem; Splitting Fields; Separable Extensions; Totally Inseparable Extensions; Galois Theory; Illustrations of Galois Theory; Cyclotomic Extensions; Insolvability of the Quintic; Matrix Algebra MARKET: For all readers interested in abstract algebra.

    It can urge the reader to explore new methodologies to have maximum fun with numbers, and opt for a higher course in mathematics. The book was specifically designed to help the student community, and develop a strong affinity towards problem solving.the book offers many complicated, and interesting challenges for the user, keeping them engaged throughout. A large number of solved problems are also included in challenge and thrill of pre-college mathematics, to give readers an insight into the subject. The book can be an eye-opener for school students of class 7 and above. The materials given in the book are powerful enough to help them develop a strong interest for the subject. The concepts are explained in a simple and comprehensive manner, providing them with a good understanding of mathematical fundamentals.what makes the book distinct is its detailed sections on geometry, that can improve the reasoning skills of students. There are also detailed accounts on algebra and trigonometry, enhancing the competitive ability of the users. The topics such as combinatorics, number theory, and probability are also explained in detail, in the book. Each chapter was designed with the intention of motivating students to appreciate the excitement that mathematical problems can provide. Published in 2003 by new age international publishers, the book is available in paperback. Key features: the book includes a collection of more than 300 solved numerical problems, compiled from various national, as well as international mathematical olympiads.it is widely recommended by students and teachers, alike as an essential preparatory book for those writing competitive examinations.

    Based on a true story where the author incurs many failures in life but believes that failure comes to those who deserve something bigger. He continuously fails in many entrepreneurial ventures but his attitude towards great sayings keeps him going. Despite not having the best of qualifications, he defies the rule and the common notion that only qualified make it large. Common beliefs of the masses have been challenged at every point.The mention of the business ventures he undertakes while in college and the problems solved by his early philosophical knowledge. Despite being discouraged by the non-entrepreneurial environment, he dares to rise against the wind. He has done something worth writing and written something worth reading! "Awesome book. Very well written. I recommend this book to every teenager as it would surely transform their lives and it will help them to create opportunities for themselves. We need young entrepreneurs in India."- Verified Purchase on Amazon.in"Amazing book.. i have no words in praise of this book..everyone should read this.. must read for everyone..i assure you, this will change your life.." Verified Purchase on Amazon.inAbout The AuthorK Sraff is an entrepreneur. He has undertaken various profit, non-profit ventures, most of which have been mentioned in the book. He has highlighted on a philosophy that "When you help others, the universe conspires to help you...!" which also sets the core theme of the book. How an iPhone Made Me the Youngest Billionaairee has sold thousands of copies in India and abroad. Widely appreciated with over 200+ ratings in Goodreads, 100+ reviews on Amazon. The book speaks not just about dreams, change, but urges the readers to implement what they conceive!

    Penrose, a cat with a knack for math, takes children on an adventurous tour of mathematical concepts from fractals to infinity.

    I’m Tim. I’m a single cell in society’s body. U.S. society, to be specific.So let me explain why we’re here.As a writer and a generally thinky person, I’ve spent a lot of my life thinking about the society I live in, and societies in general. I’ve always imagined society as a kind of giant human—a living organism like each of us, only much bigger.When you’re a single cell in the body of a giant, it’s hard to understand what the giant’s doing, or why it is the way it is, because you can’t really zoom out and look at the whole thing all at once. But we do our best.The thing is, when I’ve recently tried to imagine what society might look like, I haven’t really been picturing this:Giant stick figure: "I am grown up."Based on what I see around me, in person and online, it seems like my society is actually more like this:Giant stick figure throwing a giant tantrum because their chocolate ice cream fell on the ground.Individual humans grow older as they age—but it kind of seems like the giant human I live in has been getting more childish each year that goes by.So I decided to write a blog post about this. But then something else happened.When I told people I was planning to write a post about society, and the way people are acting, and the way the media is acting, and the way the government is acting, and the way everyone else is acting, people kept saying the same thing to me.Don’t do it. Don’t touch it. Write about something else. Anything else. It’s just not worth it.They were right. With so many non-controversial topics to write about, why take on something so loaded and risk alienating a ton of readers? I listened to people’s warnings, and I thought about moving on to something else, but then I was like, “Wait what? I live inside a giant and the giant is having a six-year-old meltdown in the grocery store candy section and that’s a not-okay thing for me to talk about?”It hit me that what I really needed to write about was that—about why it’s perilous to write about society."