Now that you're making the shift to online teaching, it's time to answer your biggest questions about remote, digitally based instruction:How do I build and nurture relationships with students and their at-home adults from afar? How do I adapt my best teaching to an online setting? How do I keep a focus on students and their needs when they aren't in front of me? Jennifer Serravallo's Connecting with Students Online gives you concise, doable answers based on her own experiences and those of the teachers, administrators, and coaches she has communicated with during the pandemic. Focusing on the vital importance of the teacher-student connection, Jen guides you to:effectively prioritize what matters most during remote, online instruction schedule your day and your students' to maximize teaching and learning (and avoid burnout) streamline curricular units and roll them out digitally record highly engaging short lessons that students will enjoy and learn from confer, working with small groups, and drive learning through independent practice partner with the adults in a student's home to support your work with their child. Featuring simplified, commonsense suggestions, 55 step-by-step teaching strategies, and video examples of Jen conferring and working with small groups, Connecting with Students Online helps new teachers, teachers new to technology, or anyone who wants to better understand the essence of effective online instruction. Along the way Jen addresses crucial topics including assessment and progress monitoring, student engagement and accountability, using anchor charts and visuals, getting books into students' hands, teaching subject-area content, and avoiding teacher burnout.During this pandemic crisis turn to one of education's most trusted teaching voices to help you restart or maintain students' progress. Jennifer Serravallo's Connecting with Students Online is of-the-moment, grounded in important research, informed by experience, and designed to get you teaching well-and confidently-as quickly as possible. Jen will be donating a portion of the proceeds from Connecting with Students Online to organizations that help children directly impacted by COVID-19.

    It offers a comprehensive and accessible treatment of the theory of algorithms and complexity—the elegant body of concepts and methods developed by computer scientists over the past 30 years for studying the performance and limitations of computer algorithms. The book is self-contained in that it develops all necessary mathematical prerequisites from such diverse fields such as computability, logic, number theory and probability.

    By presenting actual experiences and analyzing them as they are described, the author conveys the developmental thought processes employed and shows a style of thinking that leads to successful results is something that can be learned. Along with spectacular successes, the author also conveys how failures contributed to shaping the thought processes. Provides the reader with a style of thinking that will enhance a person's ability to function as a problem-solver of complex technical issues. Consists of a collection of stories about the author's participation in significant discoveries, relating how those discoveries came about and, most importantly, provides analysis about the thought processes and reasoning that took place as the author and his associates progressed through engineering problems.

    

    No, hang on, let's make this interesting. Between zero and infinity. Even if you stick to the whole numbers, there are a lot to choose from - an infinite number in fact. Throw in decimal fractions and infinity suddenly gets an awful lot bigger (is that even possible?) And then there are the negative numbers, the imaginary numbers, the irrational numbers like pi which never end. It literally never ends.The world of numbers is indeed strange and beautiful. Among its inhabitants are some really notable characters - pi, e, the "imaginary" number i and the famous golden ratio to name just a few. Prime numbers occupy a special status. Zero is very odd indeed: is it a number, or isn't it?How Numbers Work takes a tour of this mind-blowing but beautiful realm of numbers and the mathematical rules that connect them. Not only that, but take a crash course on the biggest unsolved problems that keep mathematicians up at night, find out about the strange and unexpected ways mathematics influences our everyday lives, and discover the incredible connection between numbers and reality itself. ABOUT THE SERIESNew Scientist Instant Expert books are definitive and accessible entry points to the most important subjects in science; subjects that challenge, attract debate, invite controversy and engage the most enquiring minds. Designed for curious readers who want to know how things work and why, the Instant Expert series explores the topics that really matter and their impact on individuals, society, and the planet, translating the scientific complexities around us into language that's open to everyone, and putting new ideas and discoveries into perspective and context.

    In Tammet's world, numbers are beautiful and mathematics illuminates our lives and minds. Using anecdotes, everyday examples, and ruminations on history, literature, and more, Tammet allows us to share his unique insights and delight in the way numbers, fractions, and equations underpin all our lives. Inspired by the complexity of snowflakes, Anne Boleyn's eleven fingers, or his many siblings, Tammet explores questions such as why time seems to speed up as we age, whether there is such a thing as an average person, and how we can make sense of those we love. Thinking In Numbers will change the way you think about math and fire your imagination to see the world with fresh eyes.

    Sonic weapons of this sort include the "psychoacoustic correction" aimed at Panama strongman Manuel Noriega by the U.S. Army and at the Branch Davidians in Waco by the FBI, sonic booms (or "sound bombs") over the Gaza Strip, and high-frequency rat repellants used against teenagers in malls. At the same time, artists and musicians generate intense frequencies in the search for new aesthetic experiences and new ways of mobilizing bodies in rhythm. In Sonic Warfare, Steve Goodman explores these uses of acoustic force and how they affect populations.Traversing philosophy, science, fiction, aesthetics, and popular culture, he maps a (dis)continuum of vibrational force, encompassing police and military research into acoustic means of crowd control, the corporate deployment of sonic branding, and the intense sonic encounters of sound art and music culture.Goodman concludes with speculations on the not yet heard--the concept of unsound, which relates to both the peripheries of auditory perception and the unactualized nexus of rhythms and frequencies within audible bandwidths.

    All things are possible, only one thing actually happens; everything else is in the realm of probability. The twin disciplines of probability and statistics underpin every modern science and sketch the shape of all purposeful group activity- politics, economics, medicine, law, sports-giving humans a handle on the essential uncertainty of their existence. Yet while we are all aware of the hard facts, most of us still refuse to take account of probability-preferring to drive, not fly; buying into market blips; smoking cigarettes; denying we will ever age. There are some people, though-gamblers, risk buyers, forensic experts, doctors, strategists- who find probability's mass of incomplete uncertainties delightful and revelatory. "Chances Are" is their story. Combining philosophical and historical background with portraits of the men and women who command the forces of probability, this engaging, wide-ranging, and clearly written volume will be welcomed not only by the proven audiences for popular books like "E=MC2" and "The Golden Ratio" but by anyone interested in the workings of fate.

    Today, unfortunately, the traditional place of mathematics in education is in grave danger. The teaching and learning of mathematics has degenerated into the realm of rote memorization, the outcome of which leads to satisfactory formal ability but does not lead to real understanding or to greater intellectual independence. This new edition of Richard Courant's and Herbert Robbins's classic work seeks to address this problem. Its goal is to put the meaning back into mathematics.Written for beginners and scholars, for students and teachers, for philosophers and engineers, What is Mathematics? Second Edition is a sparkling collection of mathematical gems that offers an entertaining and accessible portrait of the mathematical world. Covering everything from natural numbers and the number system to geometrical constructions and projective geometry, from topology and calculus to matters of principle and the Continuum Hypothesis, this fascinating survey allows readers to delve into mathematics as an organic whole rather than an empty drill in problem solving. With chapters largely independent of one another and sections that lead upward from basic to more advanced discussions, readers can easily pick and choose areas of particular interest without impairing their understanding of subsequent parts.Brought up to date with a new chapter by Ian Stewart, What is Mathematics? Second Edition offers new insights into recent mathematical developments and describes proofs of the Four-Color Theorem and Fermat's Last Theorem, problems that were still open when Courant and Robbins wrote this masterpiece, but ones that have since been solved.Formal mathematics is like spelling and grammar - a matter of the correct application of local rules. Meaningful mathematics is like journalism - it tells an interesting story. But unlike some journalism, the story has to be true. The best mathematics is like literature - it brings a story to life before your eyes and involves you in it, intellectually and emotionally. What is Mathematics is like a fine piece of literature - it opens a window onto the world of mathematics for anyone interested to view.

    At the time we were hoping that our approach of writing a book which would be both accessible without mathematical sophistication and portray these exiting new fields in an authentic manner would find an audience. Now we know it did. We know from many reviews and personal letters that the book is used in a wide range of ways: researchers use it to acquaint themselves, teachers use it in college and university courses, students use it for background reading, and there is also a substantial audience of lay people who just want to know what chaos and fractals are about. Every book that is somewhat technical in nature is likely to have a number of misprints and errors in its first edition. Some of these were caught and brought to our attention by our readers. One of them, Hermann Flaschka, deserves to be thanked in particular for his suggestions and improvements. This second edition has several changes. We have taken out the two appendices from the firstedition. At the time of the first edition Yuval Fishers contribution, which we published as an appendix was probably the first complete expository account on fractal image compression. Meanwhile, Yuvals book Fractal Image Compression: Theory and Application appeared and is now the publication to refer to.

    In a series of penetrating essays, Chomsky cuts through the confusion and prejudice that has infected the study of language and mind, bringing new solutions to traditional philosophical puzzles and fresh perspectives on issues of general interest, ranging from the mind-body problem to the unification of science. Using a range of imaginative and deceptively simple linguistic analyses, Chomsky defends the view that knowledge of language is internal to the human mind. He argues that a proper study of language must deal with this mental construct. According to Chomsky, therefore, human language is a biological object and should be analyzed using the methodology of the sciences. His examples and analyses come together in this book to give a unique and compelling perspective on language and the mind.

    Admittedly real life wasn’t like that. But only, they argued, because we didn’t have enough data to be certain.Then the cracks began to appear. It proved impossible to predict exactly how three planets orbiting each other would move. Meteorologists discovered that the weather was truly chaotic – so dependent on small variations that it could never be predicted for more than a few days out. And the final nail in the coffin was quantum theory, showing that everything in the universe has probability at its heart.That gives human beings a problem. We understand the world through patterns. Randomness and probability will always be alien to us. But it’s time to plunge into this fascinating, shadowy world, because randomness crops up everywhere. Probability and statistics are the only way to get a grip on nature’s workings. They may even seal the fate of free will and predict how the universe will end.Forget Newton’s clockwork universe. Welcome to Dice World.

    Generous support from a number of foundations provided the means for assembling and maintaining an experienced staff to co-operate with members of the Institute's Physics Department in the examination, improvement, and development of physics curriculum materials for students planning careers in the sciences. After careful analysis of objectives and the problems involved, preliminary versions of textbooks were prepared, tested through classroom use at M.I.T. and other institutions, re-evaluated, rewritten, and tried again. Only then were the final manuscripts undertaken.

    That they exist, Simon Singh reveals, underscores the brilliance of the shows' writers, many of whom have advanced degrees in mathematics in addition to their unparalleled sense of humor. While recounting memorable episodes such as “Bart the Genius” and “Homer3,” Singh weaves in mathematical stories that explore everything from p to Mersenne primes, Euler's equation to the unsolved riddle of P v. NP; from perfect numbers to narcissistic numbers, infinity to even bigger infinities, and much more. Along the way, Singh meets members of The Simpsons' brilliant writing team-among them David X. Cohen, Al Jean, Jeff Westbrook, and Mike Reiss-whose love of arcane mathematics becomes clear as they reveal the stories behind the episodes. With wit and clarity, displaying a true fan's zeal, and replete with images from the shows, photographs of the writers, and diagrams and proofs, The Simpsons and Their Mathematical Secrets offers an entirely new insight into the most successful show in television history.

    The science of complexity studies how single elements, such as a species or a stock, spontaneously organize into complicated structures like ecosystems and economies; stars become galaxies, and snowflakes avalanches almost as if these systems were obeying a hidden yearning for order. Drawing from diverse fields, scientific luminaries such as Nobel Laureates Murray Gell-Mann and Kenneth Arrow are studying complexity at a think tank called The Santa Fe Institute. The revolutionary new discoveries researchers have made there could change the face of every science from biology to cosmology to economics. M. Mitchell Waldrop's groundbreaking bestseller takes readers into the hearts and minds of these scientists to tell the story behind this scientific revolution as it unfolds.