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.

    Crease tells the stories behind ten of the greatest equations in human history. Was Nobel laureate Richard Feynman really joking when he called Maxwell's electromagnetic equations the most significant event of the nineteenth century? How did Newton's law of gravitation influence young revolutionaries? Why has Euler's formula been called "God's equation," and why did a mysterious ecoterrorist make it his calling card? What role do betrayal, insanity, and suicide play in the second law of thermodynamics?The Great Equations tells the stories of how these equations were discovered, revealing the personal struggles of their ingenious originators. From "1 + 1 = 2" to Heisenberg's uncertainty principle, Crease locates these equations in the panoramic sweep of Western history, showing how they are as integral to their time and place of creation as are great works of art.

    You may find it for free on the web. Purchase of the Kindle edition includes wireless delivery.

    xn + yn = zn, where n represents 3, 4, 5, ...no solution"I have discovered a truly marvelous demonstration of this proposition which this margin is too narrow to contain."With these words, the seventeenth-century French mathematician Pierre de Fermat threw down the gauntlet to future generations.  What came to be known as Fermat's Last Theorem looked simple; proving it, however, became the Holy Grail of mathematics, baffling its finest minds for more than 350 years.  In Fermat's Enigma--based on the author's award-winning documentary film, which aired on PBS's "Nova"--Simon Singh tells the astonishingly entertaining story of the pursuit of that grail, and the lives that were devoted to, sacrificed for, and saved by it.  Here is a mesmerizing tale of heartbreak and mastery that will forever change your feelings about mathematics.

    Having just completed his masterpiece, The General Theory of Relativity—which provided a brand-new theory of gravity and promised a new perspective on the cosmos as a whole—he set out at once to share his excitement with as wide a public as possible in this popular and accessible book.Here published for the first time as a Penguin Classic, this edition of Relativity features a new introduction by bestselling science author Nigel Calder.

    The book begins with the basic concepts of logic and set theory, to familiarize students with the language of mathematics and how it is interpreted. These concepts are used as the basis for a step-by-step breakdown of the most important techniques used in constructing proofs. To help students construct their own proofs, this new edition contains over 200 new exercises, selected solutions, and an introduction to Proof Designer software. No background beyond standard high school mathematics is assumed. Previous Edition Hb (1994) 0-521-44116-1 Previous Edition Pb (1994) 0-521-44663-5

    It makes a lovely gift from parent to child and a perfect learning companion to help all school children. It is a treasure trove of easy methods to take important information from the back of the mind to the tip of children's tongues.

    From unicorns, salamanders, satyrs, giants, elves and trolls, to dragons, nymphs, mermaids, werewolves and griffins — take an enchanting journey through the history, folklore, and mythology of these beasts from virtually every culture in the world. With stories and amazing facts on even the most obscure mythological creature, this is a cornucopia of magic and folklore.

    Focusing on the power of combining movement with intuition, Tara walks readers through the importance of moving with ease and creating space in their lives. Strala isn’t about strict poses; it’s about your body and your abilities. By moving how it feels good to move, readers will not only get a great workout but also release stress, free up space in their minds, and open themselves up to creativity. Tara lays out simple, step-by-step information on everything from how to use the breath in movement, to how to create ease, to how to set up a home practice. More than ten routines—each illustrated with clear, instructional photos—offer both easy and more difficult tracks, appealing to beginners and seasoned yogis alike, and aim to help readers dissolve stress, get better sleep, gain energy, or even wind down after a tough day. Tara also offers up both a 7-day jumpstart and a 30-day program to help readers bring yoga—and its varied benefits—easily into their lives.“My goal is to help you feel connected and gain strength, calm, clarity, and ease from the inside out. Get ready to feel amazing, and enjoy the ride!” —Tara

    Spartan Warrior Workout takes you from merely being in shape to having the strength and endurance to withstand the ultimate test.Whether you're a veteran in the weight room or a new recruit, Spartan Warrior Workout will challenge you like nothing you have ever tried before:• Arms and shoulders are sculpted with kettlebell cleans and presses • Abs are toned with windmills and planks • Back and butt are strengthened with kettlebell swings and pull-ups • Chest is chiseled with bench presses and push-ups • Legs and glutes are shaped with jumping lunges and squatsMore than just exercises, the book's guidelines on active rest, pre-hab and nutrition will help keep your body healthy and fueled as you push yourself to the limit and reach higher levels of fitness.

    Gödel received public recognition of his work in 1951 when he was awarded the first Albert Einstein Award for achievement in the natural sciences--perhaps the highest award of its kind in the United States. The award committee described his work in mathematical logic as "one of the greatest contributions to the sciences in recent times."However, few mathematicians of the time were equipped to understand the young scholar's complex proof. Ernest Nagel and James Newman provide a readable and accessible explanation to both scholars and non-specialists of the main ideas and broad implications of Gödel's discovery. It offers every educated person with a taste for logic and philosophy the chance to understand a previously difficult and inaccessible subject.New York University Press is proud to publish this special edition of one of its bestselling books. With a new introduction by Douglas R. Hofstadter, this book will appeal students, scholars, and professionals in the fields of mathematics, computer science, logic and philosophy, and science.

    What will it take to turn this opportunity into reality in every classroom, school, and district? Continuing its tradition of mathematics education leadership, NCTM has defined and described the principles and actions, including specific teaching practices, that are essential for a high-quality mathematics education for all students. Principles to Actions: Ensuring Mathematical Success for All offers guidance to teachers, specialists, coaches, administrators, policymakers, and parents: Builds on the Principles articulated in Principles and Standards for School Mathematics to present six updated Guiding Principles for School MathematicsSupports the first Guiding Principle, Teaching and Learning, with eight essential, research-based Mathematics Teaching PracticesDetails the five remaining Principles--the Essential Elements that support Teaching and Learning as embodied in the Mathematics Teaching PracticesIdentifies obstacles and unproductive and productive beliefs that all stakeholders must recognize, as well as the teacher and student actions that characterize effective teaching and learning aligned with the Mathematics Teaching PracticesWith Principles to Actions, NCTM takes the next step in shaping the development of high-quality standards throughout the United States, Canada, and worldwide.

    This book reveals how anyone can begin to visualize the enigmatic 'imaginary numbers' that first baffled mathematicians in the 16th century.

    It covers areas such as fundamentals, logic, counting, relations and digraphs, trees, topics in graph theory, languages and finite-state machines, and groups and coding.

    This set couples a book containing the six easiest chapters from Richard P. Feynman's landmark work, Lectures on Physics—specifically designed for the general, non-scientist reader—with the actual recordings of the late, great physicist delivering the lectures on which the chapters are based. Nobel Laureate Feynman gave these lectures just once, to a group of Caltech undergraduates in 1961 and 1962, and these newly released recordings allow you to experience one of the Twentieth Century's greatest minds—as if you were right there in the classroom.