The new edition provides invitations - not requirements - to use technology, as well as new conceptual problems, and new projects that focus on writing and working in teams.

    A long-buried personal sadness is enfolding her—and her career is stalled—when she stumbles upon an unusual group of immigrants living in rural California. She follows them on their annual return to the remote Azorean islands in the Atlantic Ocean, where bulls run down village streets, volcanoes are active, and the people celebrate festas to ease their saudade, a longing so deep that the Portuguese word for it can’t be fully translated.Years later, California is in a terrible drought, the wildfires seem to never end, and Diana finds herself still dreaming of those islands and the chuva—a rain so soft you don’t notice when it begins or ends.With her troublesome Labrador retriever, Murphy, in tow, Diana returns to the islands of her dreams only to discover that there are still things she longs for—and one of them may be a most unexpected love.

    Linear algebra is tightly integrated into the text.

    He discovered the Conway groups in mathematical symmetry, and invented the aptly named surreal numbers, as well as the cult classic Game of Life--more than a cool fad, Life demonstrates how simplicity generates complexity and the game provides an analogy for all mathematics and the entire universe. Moving to Princeton in 1987, as a mathemagician he deployed cards, ropes, dice, coat hangers, and even the odd Slinky as props to extend his winning imagination and share his mathy obsessions with signature contagion. He is a jet-setting ambassador-at-large for the beauties of all things mathematical.Genius At Play is an intimate investigation into the mind of an endearing genius, laying bare Conway's personal and professional idiosyncrasies. The intimacy comes courtesy of the man himself. He generously granted Roberts full access, though not without the occasional grudge and grumble: "Oh hell," he'd say. "You're not going to put that in the book. Are you?!?

    From manhole covers to bubbles to subway maps, each page gives you a glimpse of the world through renowned mathematicians' eyes and reveals how their theorems and equations can be applied to nearly everything you encounter. Covering dozens of your favorite math topics, you'll find fascinating answers to questions like:How are the waiting times for buses determined?Why is Romanesco Broccoli so mesmerizing?How do you divide a cake evenly?Should you run or walk to avoid rain showers?Filled with compelling mathematical explanations, Math Geek sheds light on the incredible world of numbers hidden deep within your day-to-day life.

    During his life he created numerous works of art and kept voluminous notebooks that detailed his artistic and intellectual pursuits.The collection of writings and art in this magnificent book are drawn from his notebooks. The book organizes his wide range of interests into subjects such as human figures, light and shade, perspective and visual perception, anatomy, botany and landscape, geography, the physical sciences and astronomy, architecture, sculpture, and inventions. Nearly every piece of writing throughout the book is keyed to the piece of artwork it describes.The writing and art is selected by art historian H. Anna Suh, who provides fascinating commentary and insight into the material, making Leonardo's Notebooks an exquisite single-volume compendium celebrating his enduring genius.

    

    Take a journey through the fascinating story of fractions, numbers, patterns, and shapes in order to better understand the complex world we live in.Continuing the "Big Ideas" series' trademark combination of authoritative, clear text and bold graphics to chart the development of maths through history, the book explores and explains some of the most complex and fascinating mathematical subjects. Delve into everything from the mathematical ideas and inventions of the ancient world such as the first number systems, magic squares, and the Chinese abacus, through to the developments in mathematics during medieval and Renaissance Europe, to the rise of group theory and cryptography more recently.This diverse and inclusive account of mathematics will have something for everybody: for those interested in the maths behind world economies, secret spies, modern technology and plenty more, taking readers around the world from Babylon to Bletchley Park. Tracing maths through the Scientific Revolution to its 21st-century use in computers, the internet, and AI, The Maths Book uses an innovative visual approach to make the subject accessible to everyone, casual readers and students alike.

    His illuminating explanation is addressed to the person who wants to understand the place of mathematics in modern civilization but who has been intimidated by its supposed difficulty. Mathematics is the language of size, shape, and order—a language Hogben shows one can both master and enjoy.

    Just about everyone has at least heard of Albert Einstein's formulation of 1905, which came into the world as something of an afterthought. But far fewer can explain his insightful linkage of energy to mass. David Bodanis offers an easily grasped gloss on the equation. Mass, he writes, "is simply the ultimate type of condensed or concentrated energy," whereas energy "is what billows out as an alternate form of mass under the right circumstances." Just what those circumstances are occupies much of Bodanis's book, which pays homage to Einstein and, just as important, to predecessors such as Maxwell, Faraday, and Lavoisier, who are not as well known as Einstein today. Balancing writerly energy and scholarly weight, Bodanis offers a primer in modern physics and cosmology, explaining that the universe today is an expression of mass that will, in some vastly distant future, one day slide back to the energy side of the equation, replacing the "dominion of matter" with "a great stillness"--a vision that is at once lovely and profoundly frightening. Without sliding into easy psychobiography, Bodanis explores other circumstances as well; namely, Einstein's background and character, which combined with a sterling intelligence to afford him an idiosyncratic view of the way things work--a view that would change the world. --Gregory McNamee

    Subsequent sections deal with integrating factors; dilution and accretion problems; linearization of first order systems; Laplace Transforms; Newton's Interpolation Formulas, more.

    Described as the 'shorthand of mathematics', the Trachtenberg system only requires the ability to count from one to eleven. Using a series of simplified keys it allows anyone to master calculations, giving greater speed, ease in handling numbers and increased accuracy.Jakow Trachtenberg believed that everyone is born with phenomenal abilities to calculate. He devised a set of rules that allows every child to make multiplication, division, addition, subtraction and square-root calculations with unerring accuracy and at remarkable speed. It is the perfect way to gain confidence with numbers.

    Amazingly, the story unveiled in it is true.In the world of math, the Poincaré Conjecture was a holy grail. Decade after decade the theorem that informs how we understand the shape of the universe defied every effort to prove it. Now, after more than a century, an eccentric Russian recluse has found the solution to one of the seven greatest math problems of our time, earning the right to claim the first one-million-dollar Millennium math prize.George Szpiro begins his masterfully told story in 1904 when Frenchman Henri Poincaré formulated a conjecture about a seemingly simple problem. Imagine an ant crawling around on a large surface. How would it know whether the surface is a flat plane, a round sphere, or a bagel- shaped object? The ant would need to lift off into space to observe the object. How could you prove the shape was spherical without actually seeing it? Simply, this is what Poincaré sought to solve.In fact, Poincaré thought he had solved it back at the turn of the twentieth century, but soon realized his mistake. After four more years' work, he gave up. Across the generations from China to Texas, great minds stalked the solution in the wilds of higher dimensions. Among them was Grigory Perelman, a mysterious Russian who seems to have stepped out of a Dostoyevsky novel. Living in near poverty with his mother, he has refused all prizes and academic appointments, and rarely talks to anyone, including fellow mathematicians. It seemed he had lost the race in 2002, when the conjecture was widely but, again, falsely reported as solved. A year later, Perelman dropped three papers onto the Internet that not only proved the Poincaré Conjecture but enlightened the universe of higher dimensions, solving an array of even more mind-bending math with implications that will take an age to unravel. After years of review, his proof has just won him a Fields Medal--the 'Nobel of math'--awarded only once every four years. With no interest in fame, he refused to attend the ceremony, did not accept the medal, and stayed home to watch television.Perelman is a St. Petersburg hero, devoted to an ascetic life of the mind. The story of the enigma in the shape of space that he cracked is part history, part math, and a fascinating tale of the most abstract kind of creativity.

    The clarity and eloquence of the presentation make it popular with teachers and students alike. The text aims to expand the reader's view of the field and to present standard material in a novel way. All of the most important topics in the field are covered with a fresh perspective, including iterative methods for systems of equations and eigenvalue problems and the underlying principles of conditioning and stability. Presentation is in the form of 40 lectures, which each focus on one or two central ideas. The unity between topics is emphasized throughout, with no risk of getting lost in details and technicalities. The book breaks with tradition by beginning with the QR factorization - an important and fresh idea for students, and the thread that connects most of the algorithms of numerical linear algebra.

    An analysis of the claims of science shows that this discipline is just as much about faith and belief (vs. fact) as is Christian doctrine. Quantum mechanics has rendered atheism obsolete and has provided us with insights concerning the possible nature and origin of the Biblical God. Einstein's Special Theory of Relativity has virtually proved that we all live forever in some kind of timeless state. Quantum observation, a consequence of quantum physics, has provided us with strong evidence that the true God is He of the Bible. Augustine of Hippo said that he probably would never have been converted were it not for Plato. Other theses entertained in this volume are that mind is primary in our world, which is the thought of God; that God emanates from The Truth, synonymous with goodness and all that is good for cognitive individuals; that faith is much more than blind belief in Him; and that the history of the Jews provides us with powerful evidence that they are the chosen people of the true God. Christianity is unique among religions in terms of reason, logic, and common sense. Here is an example of the writing to be found in my book: "Quantum observation is heavily involved with the concept of form and substance, something that greatly interested Plato. In our world, we can discern two aspects of a material object: substance, the "stuff" of which it is composed, and form, which is its shape. These two characteristics are always connected on the human level of size; according to our physical senses, any separation of them is ridiculous. On the bizarre quantum level, however, elemental entities can exist as form alone or as substance alone. When these are in the state of form, they are waves, and, when they assume the mode of substance, they exist as discrete packets--ultimately, of energy. These are distinct bodies of substance that we call quanta. I am privileged to have received an endorsement of my work from Charles Taliaferro, Chair, Department of Philosophy, St. Olaf College; Editor-in-Chief, Open Theology. It reads as follows: "Because medical doctors or physicians have made vital contributions to philosophy, from Maimonides, Avicenna, and John Locke in the history of philosophy to Raymond Tallis today, it should not surprise us to see Dr. James Frederick Ivey's superb contribution to our philosophical reflection on the bearing of current physics on Biblical faith. Perhaps it takes a person well trained in the application of science in medicine to see the ways in which the application of science, especially modern physics, quantum mechanics, and relativity have important applications in our thinking about God, the Bible, and Judeo-Christianity. The terrain is not unexplored by philosophers, theologians, and popular writers, but it is rare to see the kind of engaging clarity, breadth, and conscientious, mature reflection to be found in Ivey's book." I have a second professorial endorsement that reads thus: "In his book, The Physics and Philosophy of the Bible, Dr. James Ivey, although a physician, has done his homework in both the physical sciences and philosophy. He argues that modern physics, relativity and quantum mechanics, strongly infer the existence of God. He concludes that the historical man, Jesus of Nazareth, was not a lunatic or a liar, but truly God. He submits that Biblical Christianity has all the truth in it and is radically different from all other faiths. His book is a must read for those who have problems with science versus theology." David A. Kaufmann, Ph.D., Past Secretary, Creation Research Society and Professor of Applied Physiology (Retired), University of Florida, Gainesville, FL.