Intuition and computational abilities are stressed. Original material on DE and multiple integrals has been expanded.

    It provides a transition from elementary calculus to advanced courses in real and complex function theory and introduces the reader to some of the abstract thinking that pervades modern analysis.

    The novel approach taken here banishes determinants to the end of the book and focuses on the central goal of linear algebra: understanding the structure of linear operators on vector spaces. The author has taken unusual care to motivate concepts and to simplify proofs. For example, the book presents - without having defined determinants - a clean proof that every linear operator on a finite-dimensional complex vector space (or an odd-dimensional real vector space) has an eigenvalue. A variety of interesting exercises in each chapter helps students understand and manipulate the objects of linear algebra. This second edition includes a new section on orthogonal projections and minimization problems. The sections on self-adjoint operators, normal operators, and the spectral theorem have been rewritten. New examples and new exercises have been added, several proofs have been simplified, and hundreds of minor improvements have been made throughout the text.

    The book includes full discussions of many problems of current interest which are not treated in any extant book, and all these matters are considered with perception and understanding."—S. Chandrasekhar "A tour de force: lucid, straightforward, mathematically rigorous, exacting in the analysis of the theory in its physical aspect."—L. P. Hughston, Times Higher Education Supplement"Truly excellent. . . . A sophisticated text of manageable size that will probably be read by every student of relativity, astrophysics, and field theory for years to come."—James W. York, Physics Today

    These sections together make an appropriate one-term advanced/graduate level course (mathematical prerequisites: vector analysis and simple partial-differential equations). The book is printed to make it easy for readers to identify these sections.• The remaining Track 2 material provides a wealth of advanced topics instructors can draw from to flesh out a two-term course, with Track 1 sections serving as prerequisites.

    This book can be cut, drawn in, folded into shapes and will even take you to the fourth dimension. So join stand-up mathematician Matt Parker on a journey through narcissistic numbers, optimal dating algorithms, at least two different kinds of infinity and more.

    This work includes differential forms and the elegant forms of Maxwell's equations, and a chapter on probability and statistics. It also illustrates and proves mathematical relations.

    It now has 600,000 to a million page hits daily. Every now and then, Munroe would get emails asking him to arbitrate a science debate. 'My friend and I were arguing about what would happen if a bullet got struck by lightning, and we agreed that you should resolve it . . . ' He liked these questions so much that he started up What If. If your cells suddenly lost the power to divide, how long would you survive? How dangerous is it, really, to be in a swimming pool in a thunderstorm? If we hooked turbines to people exercising in gyms, how much power could we produce? What if everyone only had one soulmate?When (if ever) did the sun go down on the British empire? How fast can you hit a speed bump while driving and live?What would happen if the moon went away?In pursuit of answers, Munroe runs computer simulations, pores over stacks of declassified military research memos, solves differential equations, and consults with nuclear reactor operators. His responses are masterpieces of clarity and hilarity, studded with memorable cartoons and infographics. They often predict the complete annihilation of humankind, or at least a really big explosion. Far more than a book for geeks, WHAT IF: Serious Scientific Answers to Absurd Hypothetical Questions explains the laws of science in operation in a way that every intelligent reader will enjoy and feel much the smarter for having read.

     Euclid in living color   Nearly a century before Mondrian made geometrical red, yellow, and blue lines famous, 19th century mathematician Oliver Byrne employed the color scheme for the figures and diagrams in his most unusual 1847 edition of Euclid's Elements. The author makes it clear in his subtitle that this is a didactic measure intended to distinguish his edition from all others: “The Elements of Euclid in which coloured diagrams and symbols are used instead of letters for the greater ease of learners.” As Surveyor of Her Majesty’s Settlements in the Falkland Islands, Byrne had already published mathematical and engineering works previous to 1847, but never anything like his edition on Euclid. This remarkable example of Victorian printing has been described as one of the oddest and most beautiful books of the 19th century. Each proposition is set in Caslon italic, with a four-line initial, while the rest of the page is a unique riot of red, yellow, and blue. On some pages, letters and numbers only are printed in color, sprinkled over the pages like tiny wild flowers and demanding the most meticulous alignment of the different color plates for printing. Elsewhere, solid squares, triangles, and circles are printed in bright colors, expressing a verve not seen again on the pages of a book until the era of Dufy, Matisse, and Derain.

    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.

    Aimed at undergraduate students in mathematics, physics, and engineering, the book's intuitive explanations, lack ofadvanced prerequisites, and consciously user-friendly prose style will help students to master the subject more readily than was previously possible. The key to this is the book's use of new geometric arguments in place of the standard calculational ones. These geometric arguments are communicatedwith the aid of hundreds of diagrams of a standard seldom encountered in mathematical works. A new approach to a classical topic, this work will be of interest to students in mathematics, physics, and engineering, as well as to professionals in these fields.

    Unique in basing relativity on the Principle of Equivalence of Gravitation and Inertia over Riemannian geometry, this book explores relativity experiments and observational cosmology to provide a sound foundation upon which analyses can be made. Covering special and general relativity, tensor analysis, gravitation, curvature, and more, this book provides an engaging, insightful introduction to the forces that shape the universe.

    This book covers relevant geometric principles and how to represent objects algebraically so they can be computed and applied. Recent major developments in the theory and practice of scene reconstruction are described in detail in a unified framework. Richard Hartley and Andrew Zisserman provide comprehensive background material and explain how to apply the methods and implement the algorithms. First Edition HB (2000): 0-521-62304-9

    Using a "physics first" approach to the subject, renowned relativist James B. Hartle provides a fluent and accessible introduction that uses a minimum of new mathematics and is illustrated with a wealth of exciting applications. KEY TOPICS: The emphasis is on the exciting phenomena of gravitational physics and the growing connection between theory and observation. The Global Positioning System, black holes, X-ray sources, pulsars, quasars, gravitational waves, the Big Bang, and the large scale structure of the universe are used to illustrate the widespread role of how general relativity describes a wealth of everyday and exotic phenomena. MARKET: For anyone interested in physics or general relativity.

    There are classical logic puzzles, lateral thinking puzzles, “who am I?” riddles, mathematical brain teasers, word ladders, ditloids, and a large selection of illustrated pen and paper, coins, cups, and toothpicks puzzles (please view the preview of this book for a full listing). This is the first time a collection of such breadth has been compiled and formatted especially for Kindle devices. The puzzles have been carefully organized into 25 chapters, and each question is hyperlinked to its solution, to provide utmost ease of navigation. Alongside the world’s most famous riddles, are some lesser known gems, and some brand new puzzles, in print here for the first time. Our aim was to create a definitive compendium of riddles and puzzles to bring enjoyment to people of all ages. We hope you will enjoy unraveling them as much as we enjoyed creating and editing them. Here are a handful of sample riddles: Outside the Box Riddles: You need to divide a round birthday cake into eight pieces, so each of your guests will have something to eat. How can you do this by making only three straight cuts with a knife, and without moving any of the pieces? The king’s two bodyguards developed an ingenious method for assuring the king’s safety. With the king standing between them, they would face in opposite directions; one looking to the west and the other to the east, but at the same time, and without the use of any reflective surfaces, they would both be able to observe the king clearly. How was this possible? Pure Logic Riddles: There are two glasses. One contains water, and the other contains an equal quantity of wine. A teaspoon of water is removed and mixed into the glass of wine. A teaspoon of the wine-water mixture is then removed and mixed into the glass of water. Which of the mixtures is now purer? The sorcerer’s tower was enchanted in such a way that it was able to build itself. Bricks, slates, tiles, and panes of glass, all flew to it of their own accord and danced into position. The tower doubled in size every day until after 100 days it reached a height that provided fine views over the entire realm. How many days did the tower take to reach half its full height? Lateral Thinking Puzzles: Five men are going to church. It starts to rain, and four of the men begin to run. When they arrive at the church, the four men who ran are soaking wet, whereas the fifth man, who didn’t run, is completely dry. How is this possible? Think Twice Riddles: If you are running a race, and you overtake the person in second place, what place do you move into? Word Riddles: SOS is read the same forwards, backwards, and even upside-down. What four-letter word also shares these properties? Number Puzzlers: How many letters are there in the answer to this question? You have an opportunity to buy a hen. In fact, you have been offered a choice between two quite remarkable animals. One of the hens produces six dozen dozen eggs per month, and the other produces a half dozen dozen. Admittedly, both seem impressive. Does it matter which hen you choose? Traditional Poetic Riddles: Five creatures cross a field of snow; But leave a single track behind Whose loops and bows are soon, I know, Unravelled by the mind. Coins, Cups, and Toothpicks Illustrated Riddles: A coin is dropped into an empty bottle and a cork is then inserted in the neck of the bottle. How is it possible to remove the coin without taking out the cork, or breaking the bottle?