Two merry mathematicians explore the geometry of gift-wrapping, board game theory, and much more in this hilarious holiday treat. How do you apply game theory to select who should be on your Christmas shopping list? What equations should you use to decorate the Christmas tree? Will calculations show Santa is getting steadily thinner—shimmying up and down chimneys for a whole night—or fatter—as he munches on cookies and milk in billions of houses across the world? In The Indisputable Existence of Santa Claus, distinguished mathematicians Hannah Fry and Thomas Oléron Evans demonstrate, with eminently readable clarity, how applied mathematics are so thoroughly interwoven throughout our everyday lives by explaining mathematical concepts through one very merry motif: Christmas. In their quest to provide mathematical proof for the existence of Santa, the authors take readers on a festive journey through a traditional holiday season, wherein every activity, from wrapping presents to playing board games to cooking the perfect turkey, is painstakingly and hilariously analyzed. Because who hasn’t always wondered how to set up a mathematically perfect Secret Santa? Lighthearted and diverting with Christmasy diagrams, sketches and graphs, equations, Markov chains, and matrices, The Indisputable Existence of Santa Claus brightens up the bleak midwinter with a stockingful of mathematical marvels.

The successful 30-Second series tackles numbers, with experts on maths and data demystifying the essential numerical topics. We know that we use numbers pretty often, some of us confidently, others reluctantly. But are we aware of just how essential they are to almost every decision we make? Counting and measuring when we’re shopping, travelling, studying or playing are just the beginning; the applications of numbers are endless, from assessing variables and analysing data to the calculations and predictions of advanced artificial intelligence. 30-Second Numbers exploresnumber categories,the science of measuring, how guesstimates work, and the visualisation of numbers, taking you behind the digits into the world of statistics, probability, risk and ratios. Sections include: Fundamental Numbers - A guide to the different kinds of basic numbers, from rational to prime, complex to continuous. Statistical Variations and Tests - Samples, populations and random variables are all explored in this section on all things stats! Probability and Risk - Learn about prediction and hypothesis testing, as well as absolute and relative risk. Visualising numbers - From numerical bias to logarithms and algorithms, this section shows us all the different ways we can visualise numbers. Using Numbers - Big data, artificial intelligence and machine learning are all covered in this section, about how these concepts are applied in the real world. Numbers are our way of imposing order on the world, and each of the 50 topics here uses just 300 words and one picture to give you a sense of control, helping you to understand trends in statistical data, how algorithms are used and the methods involved in machine learning. In addition, each section contains a profile of a famous mathematician whose work has greatly contributed to how we understand numbers today, from Fibonacci to Pierre de Fermat. With this book, numbers need never be daunting again. The 30 Second series is a handy collection of quick guides which explain the key aspects of core subjects, from numbers to literature to art to Ancient China to biology, and lots more! These titles use only 300 words to explore each section within a topic, making them quick and digestible for those looking to learn a lot, fast!

In Rutherford and Fry’s comprehensive guidebook, they tell the complete story of the universe and absolutely everything in it – skipping over some of the boring parts. This is a celebration of the weirdness of the cosmos, the strangeness of humans and the fact that amid all the mess, we can somehow make sense of life. Our brains have evolved to tell us all sorts of things that feel intuitively right but just aren’t true: the world looks flat, the stars seem fixed in the heavenly firmament, a day is 24 hours... This book is crammed full of tales of how stuff really works. With the power of science, Rutherford and Fry show us how to bypass our monkey-brains, taking us on a journey from the origin of time and space, via planets, galaxies, evolution, the dinosaurs, all the way into our minds, and wrestling with some truly head-scratching questions that only science can answer: What is time, and where does it come from? Why are animals the size and shape they are? What is a thought? How horoscopes work (Spoiler: they don’t, but you think they do) Does my dog love me? Why nothing is truly round Do you need your eyes to see?

The complete story of the universe and absolutely everything in it (minus the boring parts). Despite our clever linguistic abilities, humans are spectacularly ill-equipped to comprehend what’s happening in the universe. Our senses and intuition routinely mislead us. The Complete Guide to Absolutely Everything (Abridged) tells the story of how we came to suppress our monkey minds and perceive the true nature of reality. Written with wit and humor, this brief book tells the story of science—tales of fumbles and missteps, errors and egos, hard work, accidents, and some really bad decisions—all of which have created the sum total of human knowledge. Geneticist Adam Rutherford and mathematician Hannah Fry guide readers through time and space, through our bodies and brains, showing how emotions shape our view of reality, how our minds tell us lies, and why a mostly bald and curious ape decided to begin poking at the fabric of the universe. Rutherford and Fry shine as science sleuths, wrestling with some truly head-scratching questions: Where did time come from? Do we have free will? Does my dog love me? Hilarious sidebars present memorable scientific oddities: for example, hypnotized snails, human-sized ants, and the average time it takes most animals to evacuate their bladders. (A surprisingly consistent twenty-one seconds, if you must know.) Both rigorous and playful, The Complete Guide to Absolutely Everything (Abridged) is a celebration of the weirdness of the cosmos, the strangeness of humans, and the joys and follies of scientific discovery.

During his years working as an instructional coach for a national network of schools, Geoff Krall had the chance to witness several inspirational moments when math class comes alive for middle or high school students--when it is challenging but also fun, creative, and interactive. In Necessary Conditions: Teaching Secondary Math with Academic Safety, Quality Tasks, and Effective Facilitation, Krall documents the essential ingredients that produce these sorts of moments on a regular basis and for all students. They are Academic Safety, Quality Tasks, and Effective Facilitation. Academic Safety: Krall implements equitable classroom experiences that help fight stigmas associated with race and gender in schools. This allows students to feel socially and emotionally secure while nurturing their identities as mathematicians and increasing engagement during classroom discussions Quality Tasks: Teachers can adapt or create dynamic, student-centered lessons that break down math into small, manageable sections, removing the frustrations felt by students who aren't considered math people Effective Facilitation: This book shows how to incorporate teaching moves and math routines designed for engagement, persistence, and interactivity. Teachers can allow students to explore safely while maintaining consistent classroom expectations My work as a math instructional coach for a network of schools has afforded me the unique opportunity to visit exceptional teachers across the country, documenting their tasks, teaching moves, and academically safe learning environments. You'll experience dispatches from these effective classrooms in which we'll observe how teachers attend to all three elements that make up the ecosystem. -- Geoff Krall from his book, Necessary Conditions