検索キーワード： 数学

Nearly a hundred years after its publication, Kurt Gödel's famous proof that every mathematical system must contain propositions that are true - yet never provable - continues to unsettle mathematics, philosophy, and computer science. Yet unlike Einstein, with whom he formed a warm and abiding friendship, Gödel has long escaped all but the most casual scrutiny of his life. 

 Math Without Numbers is a vivid and wholly original guide to the three main branches of abstract math - topology, analysis and algebra - which turn out to be surprisingly easy to grasp. Milo Beckman upends the conventional approach to mathematics, inviting you to think creatively about shape and dimension, the infinite and infinitesimal, symmetries, proofs and how these concepts all fit together. How many shapes are there? Is anything bigger than infinity? And can mathematics even be described as 'true'?

At its simplest, Bayes’s theorem describes the probability of an event, based on prior knowledge of conditions that might be related to the event. But in Everything Is Predictable, Tom Chivers lays out how it affects every aspect of our lives. He explains why highly accurate screening tests can lead to false positives and how a failure to account for it in court has put innocent people in jail. A cornerstone of rational thought, many argue that Bayes’s theorem is a description of almost everything.

Statistics has played a leading role in our scientific understanding of the world for centuries, yet we are all familiar with the way statistical claims can be sensationalised, particularly in the media. In the age of big data, as data science becomes established as a discipline, a basic grasp of statistical literacy is more important than ever. In The Art of Statistics, David Spiegelhalter guides the listener through the essential principles we need in order to derive knowledge from data.

If you move at high speed, time slows down, space squashes up, and you get heavier. Travel fast enough and you could weigh as much as a jumbo jet, be flattened thinner than a CD without feeling a thing - and live forever! As for the angles of a triangle, they do not always have to add up to 180 degrees. And then, of course, there are black holes. These are but a few of the extraordinary consequences of Einstein's theory of relativity. 

Every day, most of us will read or watch something in the news that is based on statistics in some way. Sometimes it'll be obvious—'X people develop cancer every year'—and sometimes less obvious—'How smartphones destroyed a generation'. Statistics are an immensely powerful tool for understanding the world, but in the wrong hands they can be dangerous. Introducing you to the common mistakes that journalists make and the tricks they sometimes deploy, How to Read Numbers is a vital guide that will help you understand when and how to trust the numbers in the news.

Boolean algebra, also called Boolean logic, is at the heart of the electronic circuitry in everything we use - from our computers and cars, to our kitchen gadgets and home appliances. How did a system of mathematics established in the Victorian era become the basis for such incredible technological achievements a century later?

So many people dream of becoming their own boss or succeeding in their chosen profession, and with the resources available today, more entrepreneurs and professionals are achieving great success! However, success should be defined for the long term. As opportunities start to grow, so does the competition. Getting your business up and running or starting on your career path is one thing, but having a sustainable business or career is another. Many people make the mistake of making plans, but having no follow-through. This is where analytics comes in.

Bayes' rule appears to be a straightforward, one-line theorem: by updating our initial beliefs with objective new information, we get a new and improved belief. To its adherents, it is an elegant statement about learning from experience. To its opponents, it is subjectivity run amok. Sharon Bertsch McGrayne here explores this controversial theorem and the human obsessions surrounding it.

Many people take math in high school and promptly forget much of it. But math plays a part in all of our lives all of the time, whether we know it or not. In The Joy of x, Steven Strogatz expands on his hit New York Times series to explain the big ideas of math gently and clearly, with wit, and insight.

These stories from Quanta Magazine map the routes of mathematical exploration, showing listeners how cutting-edge research is done, while illuminating the productive tension between conjecture and proof, theory and intuition. Listeners of The Prime Number Conspiracy are headed on "breathtaking intellectual journeys to the bleeding edge of discovery strapped to the narrative rocket of humanity's never-ending pursuit of knowledge," says Quanta editor-in-chief Thomas Lin. 

Math intervention, writing intervention, neurobiology, and cognitive-based learning - Jonily Zupancic and Cheri Dotterer are sharing how to incorporate them into your classroom. Jonily is a secondary math teacher and instructional coach for math K-12. Cheri is an occupational therapist specializing in neurology-based treatment across the lifespan and a Strategy-based Interventionist. Jonily secretly calls Cheri her Lesson Plan Whisperer because Cheri is always in her head, reminding her of the foundations of development before academics begin. They met in 2018 and have been talking ever since....

Number theory is the branch of mathematics that is primarily concerned with the counting numbers. Of particular importance are the prime numbers, the "building blocks" of our number system. The subject is an old one, dating back over two millennia to the ancient Greeks, and for many years has been studied for its intrinsic beauty and elegance, not least because several of its challenges are so easy to state that everyone can understand them, and yet no one has ever been able to resolve them. But number theory has also recently become of great practical importance.

Raising students' math achievement doesn't mean ripping up your planning book and starting over. In Accessible Mathematics Steven Leinwand shows how small shifts in the good teaching you already do can make a big difference in student learning. Steve focuses on the crucial issue of classroom instruction. He scours the research and visits highly effective classrooms for practical examples of small adjustments to your teaching that lead to deeper student learning in math. Some of his 10 classroom-tested teaching shifts may surprise you and others will validate your thinking. 

Causal Inference provides a brief and nontechnical introduction to randomized experiments, propensity scores, natural experiments, instrumental variables, sensitivity analysis, and quasi-experimental devices. Ideas are illustrated with examples from medicine, epidemiology, economics and business, the social sciences, and public policy.

As Nobel Prize-winning economist Ronald Coase once cynically observed, "If you torture data long enough, it will confess." Lying with statistics is a time-honored con. In Standard Deviations, economics professor Gary Smith walks us through the various tricks and traps that people use to back up their own crackpot theories. Sometimes, the unscrupulous deliberately try to mislead us. Other times, the well-intentioned are blissfully unaware of the mischief they are committing.

Probing the life and work of Kurt Gödel, Incompleteness indelibly portrays the tortured genius whose vision rocked the stability of mathematical reasoning—and brought him to the edge of madness.

Statistically Speaking is the Office for National Statistics' podcast, offering in-depth interviews on the latest hot topics in the world of data, taking a peek behind the scenes of the UK’s largest independent producer of official statistics and exploring the stories behind the numbers.

Keep it casual with the Casual Inference podcast. Your hosts Lucy D’Agostino McGowan and Ellie Murray talk all things epidemiology, statistics, data science, causal inference, and public health. In partnership with the American Journal of Epidemiology.

Sparked by observing teachers struggle to implement rich mathematics tasks to engage students in deep thinking, Peter Liljedahl has translated his 15 years of research into this practical guide on how to move toward a thinking classroom. Building Thinking Classrooms in Mathematics, Grades K-12 helps teachers implement 14 optimal practices for thinking that create an ideal setting for deep mathematics learning to occur.