Each chapter, or unit, is divided into easily comprehended small "bites" that enable learners to master the material step-by-step, rather than being overwhelmed by masses of information covered too quickly. The book provides extremely detailed explanations of procedures and techniques, and was written in the conviction that anyone can thoroughly master its content. A four-part organization covers sentential logic, monadic predicate logic, relational predicate logic, and extra credit units that glimpse into alternative methods of logic and more advanced topics. For individuals interested in the formal study of logic.

    Abstract ideas, for the most part, arise via conceptual metaphor-metaphorical ideas projecting from the way we function in the everyday physical world. Where Mathematics Comes From argues that conceptual metaphor plays a central role in mathematical ideas within the cognitive unconscious-from arithmetic and algebra to sets and logic to infinity in all of its forms.

    Shilov, Professor of Mathematics at the Moscow State University, covers determinants, linear spaces, systems of linear equations, linear functions of a vector argument, coordinate transformations, the canonical form of the matrix of a linear operator, bilinear and quadratic forms, Euclidean spaces, unitary spaces, quadratic forms in Euclidean and unitary spaces, finite-dimensional algebras and their representations, with an appendix on categories of finite-dimensional spaces.The author begins with elementary material and goes easily into the advanced areas, covering all the standard topics of an advanced undergraduate or beginning graduate course. The material is presented in a consistently clear style. Problems are included, with a full section of hints and answers in the back.Keeping in mind the unity of algebra, geometry and analysis in his approach, and writing practically for the student who needs to learn techniques, Professor Shilov has produced one of the best expositions on the subject. Because it contains an abundance of problems and examples, the book will be useful for self-study as well as for the classroom.

    We wouldn’t have unraveled DNA or discovered Neptune or figured out how to put 5,000 songs in your pocket. Though many of us were scared away from this essential, engrossing subject in high school and college, Steven Strogatz’s brilliantly creative, down‑to‑earth history shows that calculus is not about complexity; it’s about simplicity. It harnesses an unreal number—infinity—to tackle real‑world problems, breaking them down into easier ones and then reassembling the answers into solutions that feel miraculous. Infinite Powers recounts how calculus tantalized and thrilled its inventors, starting with its first glimmers in ancient Greece and bringing us right up to the discovery of gravitational waves (a phenomenon predicted by calculus). Strogatz reveals how this form of math rose to the challenges of each age: how to determine the area of a circle with only sand and a stick; how to explain why Mars goes “backwards” sometimes; how to make electricity with magnets; how to ensure your rocket doesn’t miss the moon; how to turn the tide in the fight against AIDS. As Strogatz proves, calculus is truly the language of the universe. By unveiling the principles of that language, Infinite Powers makes us marvel at the world anew.

    Prepare for exams and succeed in your mathematics course with this comprehensive solutions manual! Featuring worked out-solutions to the problems in CALCULUS: THE CLASSIC EDITION, 5th Edition, this manual shows you how to approach and solve problems using the same step-by-step explanations found in your textbook examples.

    Python is easy to learn, and it's perfect for exploring topics like statistics, geometry, probability, and calculus. You’ll learn to write programs to find derivatives, solve equations graphically, manipulate algebraic expressions, even examine projectile motion.Rather than crank through tedious calculations by hand, you'll learn how to use Python functions and modules to handle the number crunching while you focus on the principles behind the math. Exercises throughout teach fundamental programming concepts, like using functions, handling user input, and reading and manipulating data. As you learn to think computationally, you'll discover new ways to explore and think about math, and gain valuable programming skills that you can use to continue your study of math and computer science.If you’re interested in math but have yet to dip into programming, you’ll find that Python makes it easy to go deeper into the subject—let Python handle the tedious work while you spend more time on the math.

    In Burn Math Class, Jason Wilkes takes the traditional approach to how we learn math -- with its unwelcoming textbooks, unexplained rules, and authoritarian assertions-and sets it on fire. Focusing on how mathematics is created rather than on mathematical facts, Wilkes teaches the subject in a way that requires no memorization and no prior knowledge beyond addition and multiplication. From these simple foundations, Burn Math Class shows how mathematics can be (re)invented from scratch without preexisting textbooks and courses. We can discover math on our own through experimentation and failure, without appealing to any outside authority. When math is created free from arcane notations and pretentious jargon that hide the simplicity of mathematical concepts, it can be understood organically -- and it becomes fun! Following this unconventional approach, Burn Math Class leads the reader from the basics of elementary arithmetic to various "advanced" topics, such as time-dilation in special relativity, Taylor series, and calculus in infinite-dimensional spaces. Along the way, Wilkes argues that orthodox mathematics education has been teaching the subject backward: calculus belongs before many of its so-called prerequisites, and those prerequisites cannot be fully understood without calculus. Like the smartest, craziest teacher you've ever had, Wilkes guides you on an adventure in mathematical creation that will radically change the way you think about math. Revealing the beauty and simplicity of this timeless subject, Burn Math Class turns everything that seems difficult about mathematics upside down and sideways until you understand just how easy math can be.

    Addressing readers with both a general and scholarly interest in mathematics, Nahin weaves into this narrative entertaining historical facts, mathematical discussions, and the application of complex numbers and functions to important problems.

    Lacking the ability to measure their longitude, sailors throughout the great ages of exploration had been literally lost at sea as soon as they lost sight of land. Thousands of lives, and the increasing fortunes of nations, hung on a resolution.The scientific establishment of Europe—from Galileo to Sir Issac Newton—had mapped the heavens in both hemispheres in its certain pursuit of a celestial answer. In stark contrast, one man, John Harrison, dared to imagine a mechanical solution—a clock that would keep precise time at sea, something no clock had ever been able to do on land. Longitude is a dramatic human story of an epic scientific quest and Harrison's forty-year obsession with building his perfect timekeeper, known today as the chronometer. Full of heroism and chicanery, it is also a fascinating brief history of astronomy, navigation, and clock-making, and opens a new window on our world.On its 10th anniversary, a gift edition of this classic book, with a forward by one of history's greatest explorers, and eight pages of color illustrations.

    Even when dealing with standard material, Stillwell manages to dramatize it and to make it worth rethinking. In short, his book is a splendid addition to the genre of works that build royal roads to mathematical culture for the many." (Mathematical Intelligencer)This second edition includes new chapters on Chinese and Indian number theory, on hypercomplex numbers, and on algebraic number theory. Many more exercises have been added, as well as commentary to the exercises explaining how they relate to the preceding section, and how they foreshadow later topics.

    He solidified his standing as the nation's foremost political forecaster with his near perfect prediction of the 2012 election. Silver is the founder and editor in chief of FiveThirtyEight.com. Drawing on his own groundbreaking work, Silver examines the world of prediction, investigating how we can distinguish a true signal from a universe of noisy data. Most predictions fail, often at great cost to society, because most of us have a poor understanding of probability and uncertainty. Both experts and laypeople mistake more confident predictions for more accurate ones. But overconfidence is often the reason for failure. If our appreciation of uncertainty improves, our predictions can get better too. This is the "prediction paradox": The more humility we have about our ability to make predictions, the more successful we can be in planning for the future.In keeping with his own aim to seek truth from data, Silver visits the most successful forecasters in a range of areas, from hurricanes to baseball, from the poker table to the stock market, from Capitol Hill to the NBA. He explains and evaluates how these forecasters think and what bonds they share. What lies behind their success? Are they good-or just lucky? What patterns have they unraveled? And are their forecasts really right? He explores unanticipated commonalities and exposes unexpected juxtapositions. And sometimes, it is not so much how good a prediction is in an absolute sense that matters but how good it is relative to the competition. In other cases, prediction is still a very rudimentary-and dangerous-science.Silver observes that the most accurate forecasters tend to have a superior command of probability, and they tend to be both humble and hardworking. They distinguish the predictable from the unpredictable, and they notice a thousand little details that lead them closer to the truth. Because of their appreciation of probability, they can distinguish the signal from the noise.

    Includes such gems as:? There are 42 eyes in a deck of cards, and 42 dots on a pair of dice ? In order to fill in a map so that neighboring regions never get the same color, one never needs more than four colors ? Hells Angels use the number 81 in their insignia because the initials H and A are the eighth and first numbers in the alphabet respectively

    Birth of a Theorem is Villani’s own account of the years leading up to the award. It invites readers inside the mind of a great mathematician as he wrestles with the most important work of his career.But you don’t have to understand nonlinear Landau damping to love Birth of a Theorem. It doesn’t simplify or overexplain; rather, it invites readers into collaboration. Villani’s diaries, emails, and musings enmesh you in the process of discovery. You join him in unproductive lulls and late-night breakthroughs. You’re privy to the dining-hall conversations at the world’s greatest research institutions. Villani shares his favorite songs, his love of manga, and the imaginative stories he tells his children. In mathematics, as in any creative work, it is the thinker’s whole life that propels discovery—and with Birth of a Theorem, Cédric Villani welcomes you into his.

    Including a selection of exercises, adjusted for this edition, at the end of each chapter, it offers a new and simpler treatment of the representability of recursive functions, a traditional stumbling block for students on the way to the Godel incompleteness theorems.

    This volume contains two of his most important works: The Epitome of Copernican Astronomy (books 4 and 5 of which are translated here) is a textbook of Copernican science, remarkable for the prominence given to physical astronomy and for the extension to the Jovian system of the laws recently discovered to regulate the motions of the Planets. Harmonies of the World (book 5 of which is translated here) expounds an elaborate system of celestial harmonies depending on the varying velocities of the planets.